What Should Children Know? (And How To Teach These Topics)

Core Knowledge in the Content Areas

Problem Solving Skills
Being able to solve problems is fundamental to all other components of mathematics. Children learn the concept that a question can have more than one answer and a problem can have more than one solution by participating in problem solving activities. To solve problems, a child must be able to explore a problem, a situation, or a subject; think through the problem, situation, or subject; and use logical reasoning. These abilities are needed to not only solve routine/everyday problems, but also novel/unusual ones.
Using problem solving skills not only helps children think mathematically, but also promotes their language development and their social skills when they work together. Children are naturally curious about how to solve everyday problems.
Adults can take advantage of this inherent curiosity by discussing everyday challenges, asking children to propose ways to solve them, and asking them to explain how they arrived at their solutions. Adults can also invite children to propose problems and ask questions about them. This helps them learn to analyze different types of problems and realize that many problems have multiple possible solutions.

Common Steps That Prepare Children to Learn Math
The process of solving problems often involves the following steps: understanding the problem; coming up with a plan to solve the problem; putting that plan into action; and, finally, observing the outcome and reflecting on whether the solution was effective, and whether the answer arrived at makes sense. Solving problems not only involves learning this series of steps, but also requires children to develop the qualities needed to solve problems. Children who are able to solve problems have a number of characteristics. For example, children who are effective problem solvers are able to focus their attention on the problem and its individual component parts. They can formulate hypotheses about the problem/situation, and then test them for veracity. They are willing to take risks within reason. They are persistent if they do not solve a problem right away, and do not give up if their first attempt at solving a problem is unsuccessful. They maintain flexibility, and experiment with alternate methods. They also demonstrate self-regulation

Using Problem Solving Skills in Daily Life
Young children continually explore their environments to unravel mysteries about how things work. For example, preschoolers use math concepts to understand that they have three toys, to comprehend that three fingers equals three toys, or to understand that two cookies plus one more equals three cookies. To do abstract mathematics in the future, young children will need two major skills that are also used to solve problems: being able to visualize a scenario, and being able to apply common sense thinking. Thinking and planning to achieve goals within the constraints of the properties of the surrounding environment is a natural behavior for young children. They will persist in their efforts to get an older sibling to stop another activity to play with them, to repair broken toys with tape or chewing gum, to manipulate a puzzle or plastic building blocks to get one uncooperative piece to fit, etc.
The great 20th century mathematician and teacher George Polya stated that problem solving is 'the most characteristically human activity.' He pointed out that problem solving is a skill learned by doing, and that developing this skill requires a great deal of practice.

Games/Activities That Encourage the Use of Problem Solving Skills
One method that has been found to enhance children's reasoning skills is using adult-child conversations to play mental mathematics games. For example, once children are able to count beyond five, adults can give them basic oral story problems to solve (e.g., 'If you have two plums and I give you two more, how many will you have?'). Using children's favorite foods in story problems, which takes advantage of their ready ability to envision these foods, is a good place to start. Thereafter, adults can add story problems involving pets, toys, cars, shopping, and other familiar objects/animals/activities. Experts advise adults not to restrict the types of problems presented to a child based solely on the child's grade level. Children can work with any situation if they can form mental imagery. Adults can sometimes insert harder tasks (e.g., problems involving larger numbers, problems involving division with remainders, or problems with negative number answers). Even toddlers can solve problems such as how to divide three cookies between two people. The division may not be fair, but it will likely be efficient. Adults should use the Socratic method, asking guiding questions to allow children to arrive at a solution to a problem themselves, rather than telling them a 'right' answer.

Beneficial Practices of Playing Mental Math Games
Adults can use children's favorite foods and toys to pose story problems to children that involve addition and subtraction. For example, they can ask them questions like 'If I give you [this many] more, how many will you have?' or 'If we take away [this many], how many are left?' It is better to ask children questions than to give them answers. It is important to use turn taking. In this method, the adult poses a story problem to the child, and then the child gets to pose one to the adult. Adults must try to solve the problem, even if the child makes up numbers like 'bazillion' or 'eleventy.' Games should be fun, not strictly factual like math tests. Adults can introduce age-appropriate story topics as children grow older. At the end of early childhood/around school age, children can handle the abstract algebraic concept of variables/unknown numbers (which some experts call 'mystery numbers') and use this concept in games. Adults can pose riddles where 'x' or 'n' is the unknown number, and children must use an operation (e.g., x + 4 = 7) to solve the riddle.

Reasoning Skills

Communicating with Children to Promote Mathematical Reasoning Skills
Adults reciprocally talk to and listen to children during communication that is focused on using mathematical skills like problem solving, reasoning, making connections, etc. To promote young children's understanding, adults can express mathematical concepts using pictures, words, diagrams, and symbols. Encouraging children to talk with their peers and adults helps them clarify their own thoughts and think about what they are doing.
Communicating with children about mathematical thinking problems also develops their vocabularies and promotes early literacy and reading skills. Adults should listen to what children want to say, and should have conversations with them. Communicating about math can also be accomplished through reading children's books that incorporate numbers and/or repetition or rhyme. In addition to talking, adults can communicate math concepts to children by drawing pictures or diagrams and using concrete objects (e.g., blocks, crayons, pieces of paper, fingers, etc.) to represent numbers and/or solve problems.
Children also share their learning of math concepts through words, charts, drawings, tallies, etc. Even toddlers hold up fingers to tell others how old they are.

Using Reasoning Skills to Understand and Apply Early Mathematical and Scientific Concepts
A major component of problem solving is reasoning. Children reason when they think through questions and find usable answers. They use reasoning skills to make sense of mathematical and scientific subject matter.
Children use several abilities during the reasoning process. For example, they use logic to classify objects or concepts into groups. They follow logical sequences to arrive at conclusions that make sense. They use their analytical abilities to explain their own thought processes. They apply what they have learned about relationships and patterns to help them find solutions to problems. They also use reasoning to justify their mental processes and problem solutions. To support children's reasoning, adults can ask children questions, give them time to think about their answers, and listen to their answers. This simple tactic helps children learn how to reason. Adults can also ask children why something is as it is—letting them think for themselves rather than looking for a particular answer—and listen to the ideas they produce.

Role of Representation Skills in Children's Learning
Young children develop an understanding of symbolic representation—the idea that objects, written letters, words, and other symbols are used to represent other objects or concepts—at an early age. This is evident in their make-believe/pretend play, and in their ability to learn written language and connect it to spoken language. As children develop early math skills, representing their ideas and information they acquire helps them organize, document, and share these ideas and facts with others. Children may count on their fingers; create tallies using check marks/tick marks and/or words; draw pictures or maps; and, as they grow older, make graphs. Teachers must help children apply mathematical process skills as they use learning center materials. For example, when a child enjoys sorting rocks by color, the teacher can state that the child is classifying them, bridging informal math activities with math vocabulary. Asking the child how s/he is categorizing the rocks emphasizes math vocabulary. Asking the child after s/he finishes what other ways s/he could classify the rocks encourages problem solving.

Making Connections and Helping Children Transition from Intuitive to Formal Math Thinking
Children informally learn intuitive mathematical thinking through their everyday life experiences. They naturally apply mathematical concepts and reasoning to solve problems they face in their environment. However, one frequent problem among children when they begin formal education is that they can come to see academic mathematics as a collection of procedures and rules, instead of viewing it as a means of finding solutions to everyday, real-life problems. This view will interfere with children's ability to apply the formal mathematics they learn to their lives in a practical and useful way. Teachers can help prevent this outcome by establishing the connection between children's natural intuitive math and formal mathematics. They can do this by teaching math through the use of manipulative materials familiar to children. They can use mathematics vocabulary words when describing children's activities, which enables children to develop an awareness of the natural mathematical operations they use in their daily lives. When a teacher introduces a new mathematical concept to children, s/he can give illustrative examples that draw upon the children's actual life experiences.

Relationship of Mathematics to Everyday Life and Other Academic Subjects
We use math throughout our lives during everyday activities.
There are countless examples and combinations of various mathematical concepts in the real world. Additionally, math concepts inform other academic content areas, including music, art, and the sciences. Therefore, it is important for children not to view math as an isolated set of procedures and skills. Children comprehend math more easily when they can make connections, which involve applying common mathematical rules to multiple, varied functions, processes, and real-life activities. For example, adults can ask children to consider problems they encounter daily and solve them. When a parent asks a child to help put away groceries, the child practices sorting categories of foods and packages, and experiments with comparative package sizes and shapes. Parents need not be concerned with what specific mathematical processes are involved, but should simply look for examples of math in everyday life and expose children to these examples on a regular basis. For example, pouring liquid into containers of various sizes and speculating which one will hold the most is an easy, fun activity that incorporates a number of skills and concepts, including estimation, measurement, spatial sense, and conservation of liquid volume.

Patterns and Relationships
Patterns are generally defined as things that recur or are repeated regularly. Patterns can be found in images, sounds, numbers, events, actions, movements, etc. Relationships are generally defined as connections or associations between things that are identified and/or described using logic or reasoning. Being aware of patterns and relationships among aspects of the environment helps us comprehend the fundamental structure of these aspects.
This awareness enables us to predict what will occur next in a series of events, even before it actually happens. This gives us more confidence in our environment and in our ability to interact with it. We find patterns and relationships in such areas of life as art, music, and clothing. Math-specific activities like counting numbers and working with geometrical shapes, lines, arcs, and curves also involve patterns and relationships. When children understand patterns and relationships, they can understand repetition; rhythm; categorization; and how to order things from smallest to biggest, from shortest to longest, etc.
Adults can help young children develop their understanding of patterns and relationships in life by looking at pictures and designs with them, encouraging and guiding them to identify patterns within drawings, paintings, and abstract designs such as prints on fabrics and other decorative designs. When children participate in movement activities, including dancing to music, running, skipping, hopping, playing simple musical instruments, etc., adults can help them identify patterns in their own and others' movements.
Adults can encourage young children to participate in hands-on activities, such as stringing wood, plastic beads, or penne and other hollow dry pasta tubes onto pieces of string to make necklaces with simple patterns (e.g., blue-yellow-blue-yellow). As children grow older, adults can encourage them to create more complicated patterns. They can alternate a larger number of colors, and they can vary the numbers of each color in more complex ways (e.g., three blue, two yellow, one red, etc.).

Contribution of Number Sense and Number Operations to Math Comprehension
Counting is one of the earliest numeracy skills that young children develop. Even before they have learned the names of all the numbers, young children learn to count to three, then to five, etc.  However, number sense involves a great deal more than just counting. Number sense includes understanding the various applications of numbers. For instance, we use numbers as tools for conveying and manipulating information, as tools for describing quantities, and as tools for characterizing relationships between or among things. Children who have developed number sense are able to count with accuracy and competence. Given a specific number, they can count upwards from that number. They can also count backwards. They are able to break down a number and then reassemble it. They are able to recognize relationships between or among different numbers. When children can count, are familiar with numbers, and have good number sense, they can also add and subtract numbers. Being familiar with numbers and being able to count easily helps young children understand all other areas of mathematics.

Activities to Help Develop Number Sense and Numeracy Skills

As children complete their daily activities, it is beneficial for adults to count real things with children and encourage them to count as well. This helps children understand numbers by using their own experiences with objects in the environment, and gives them practice counting and using numbers. To help children understand that we use numbers to describe quantities and relationships, adults can ask children to sort objects by size, shape, or color similarity. They can also ask children to sort objects according to their differences (e.g., which object is bigger/smaller). Adults can also discuss with children how numbers are used to find street addresses and apartment numbers, and to keep score during games. To help children count upwards and downwards with efficiency and accuracy, adults can point out that counting allows us to determine how many items are in a group. Adults should point to each object as they count it. They can count on their fingers and encourage young children to do the same.  Adults should also help children count without repeating or skipping any numbers.

Spatial Sense and Geometry
Spatial sense is an individual's awareness of one's own body in space and in relation to the objects and other people around the individual.
Spatial sense allows young children to navigate environmental spaces without colliding with objects and other people; to see and hear adequately, and to be aware of whether others can see and hear them; and to develop and observe a socially and culturally appropriate sense of their own and others' personal space. Geometry is the area of mathematics involving space, sizes, shapes, positions, movements, and directions. Geometry gives descriptions and classifications of our physical environment. By observing commonplace objects and spaces in their physical world, young children can learn about solid objects and substances, shapes, and angles. Adults can help young children learn geometry by identifying various shapes, angles, and three-dimensional figures for them; asking them to name these shapes, angles, and figures when they encounter them in the future; and asking them to describe different shapes, draw them in the air with their fingers, trace drawings of the shapes with their fingers, and then draw the shapes themselves.

Activities to Help Develop Spatial Sense and Geometry
Because it involves many physical properties like shape, line, and angle, as well as abstract concepts, young children learn geometry most effectively via hands-on activities. Learning experiences that allow them to touch and manipulate concrete objects, such as boxes, containers, puzzles, blocks, and shape sorters, usually work best. Everyday activities can also help children learn geometry concepts. For example, adults can cut children's sandwiches into various geometrical shapes and let children fit them together and/or rearrange them into new patterns. Children become better able to follow directions and navigate through space when they develop geometric knowledge and spatial sense. Adults can provide activities that promote the development of geometric knowledge and spatial sense. For example, they can let children get into and out of big appliance boxes; climb over furniture; and go into, on top of, out of, under, around, over, and through different objects and structures to allow children to experience the relationship between their bodies and space and solids. As they mature, children can play games in which they search for 'hidden' shapes. Such shapes may be irregular, may lack flat bases, or may be turned in various directions.

Measurement
Measurement is the process of determining how long, wide, and tall something is physically and how much it weighs by using measuring units such as inches, feet, yards, square feet, ounces, and pounds. Measurement is also used to quantify time using units like seconds, minutes, hours, days, weeks, months, years, centuries, millennia, etc. Measurement is not just a formal means of quantifying size, area, and time. It is also an important method for young children to seek and identify relationships between and among things they encounter outside of school in everyday life. When young children practice measuring things, they are able to understand not only the sizes of objects and beings, but also their comparative sizes (i.e. how large or small something is compared to another object used as a reference). Furthermore, they are able to figure out how big or little something is on their own.
While it is obviously important for children to eventually learn standardized measurement units like inches, feet, yards, etc., adults can facilitate early development of measurement skills by letting children choose their own measurement units. For example, they might use their favorite toy to describe a playmate or sibling as 'three teddy bears tall'; or they might describe a room as 'seven toy cars long.' Similarly, when children are too young to know formal time measurements like minutes and hours, adults can support children's ability to quantify time using favorite TV shows. For example, four-year-olds can often relate to the idea of one episode of a show
(whether it is 30 minutes or 60 minutes long) as a time measurement. Adults can apply this with statements like, 'Daddy will be home in one episode.' Numerous everyday activities, including grocery shopping, cooking, sewing, gardening, woodworking, and many others, involve measurement. Adults can ask children to help with these tasks, and then discuss measuring with children as they participate.

Measurement of Time
Younger children typically do not have an understanding of the abstract concept of time. However, adults can still help children understand that time elapses, and that we count/measure this process. For example, adults can ask younger children simple questions, such as 'Who can stand on one foot longer?' This comparison strategy helps children figure out which of two or more actions/activities takes a longer/the longest period of time. Even when children do not yet understand what 'five minutes' means, adults should still make such references (e.g., 'You can play for five minutes longer, and then we must leave.'). Repeating such references will eventually help children understand that time passes. Adults can time various everyday activities/events and tell children how long they took. They can also count the second hand's ticks on a watch/clock (e.g., 'one second…two seconds…three seconds…'). This familiarizes children with counting, and with using counting to track the passage of time. Until children are old enough to understand abstractions like today/yesterday/tomorrow, adults can use concrete references like 'after lunch' or 'before bedtime.'

Fractions
Fractions are parts or pieces of a whole. While adults understand this and do not remember ever not understanding it, very young children think differently in this regard. As Piaget showed, children in the preoperational stage of cognitive development cannot perform logical or mathematical mental operations. They focus on one property of an object rather than all of its properties, a practice he called centration. Hence, if you cut an apple into pieces, very young children see that there are more pieces than there were before, and they believe that several apple pieces are more than one apple. They cannot yet comprehend the logical sequence of dividing an apple into fractions. To comprehend fractions, children must know what a whole unit consists of, how many pieces the unit is divided into, and whether the pieces are of equal size. Adults can help children understand fractions through informal sharing activities, such as slicing up a pizza or a pan of brownies, and/or equally dividing household/preschool chores and play materials.

Estimation
Estimation is making an educated or informed guess about a measurement when no actual measurement is available. As adults, we often make estimates about the sizes of objects when we do not know their exact measurements, about the amounts of substances we have not actually measured, and about the numbers of small objects in large collections when we have not actually counted the objects. However, young children are in the process of learning the concepts of sizes and numbers. Children must comprehend concepts of comparison and relativity (e.g., larger, smaller, more, less, etc.) before they will be able to make accurate estimates. When children start to develop the ability to estimate amounts or sizes, this process helps them learn related math vocabulary words, such as 'about' or 'around,' and 'more than' and 'less than' [something else]. Through estimating, they also learn how to make appropriate predictions and arrive at realistic answers. It is important for young children to learn how to make estimates, to recognize when it is appropriate to apply the estimation method, and to recognize when their estimates are reasonable.

Activities to Help Develop Estimation
To accustom young children to the idea of estimating, adults should regularly use words related to estimation in their conversations with children
(e.g., 'around,' 'about,' 'approximately,' 'near,' 'more than [some other amount or number],' 'less than [some other amount or number],' 'between [two numbers or amounts],' etc.). During everyday activities like shopping or eating, adults can ask children to estimate amounts of foods, numbers of items, or lengths of time. Later, adults can help children compare the actual outcome with their original estimate. This process helps children learn to make realistic/reasonable estimates. Activities promoting estimation skills can be very simple. Adults can ask children, for example, to guess which of their friends is tallest, and then test the accuracy of the guess using real measurements. When children grow older, adults can write down estimates and real measurements, and can then repeat the exercise described above or present a similar one. With repetition, children will eventually begin making more accurate estimates. The goal is not for children to come up with exact measurements, but ones that are close to actual amounts/numbers. Giving children opportunities to practice improves their estimating skills.

Probabilities and Statistics
In general, when people work with statistics, they present them in graphs or charts to organize them, interpret them, and make it easier to see relationships among individual statistics. Graphs are a visual alternative that depict mathematical information and show relationships among individual statistics, especially changes over time. Graphs also allow for the comparison of different groups. Probabilities indicate the likelihood that something will happen. Adults use probabilities to predict things, such as people's risks of developing or dying from various diseases or medical conditions; the chances of accidents; children's risks of experiencing academic difficulties, dropping out, or developing emotional and behavioral disorders; and the chances that a certain area will receive rain or snow. Scientists use probabilities to predict the likelihood of various behaviors or outcomes they are studying. They use statistics to show the numbers and proportions of responses or results obtained in research studies. Calendars are one type of chart. Adults can help children use them to organize daily and weekly activities, and to understand how we organize information.

Charts and Graphs
According to experts, almost every daily activity can be charted in some way. For example, adults can help children peel the little stickers off of plums, bananas, etc. and stick them to a piece of paper/poster board divided into columns. After a week, they can count each column to determine how many pieces of each kind of fruit they ate. Similarly, adults can show children how to use removable stickers or color forms to document the number of times they performed any daily activity. For example, children could place a color form near the telephone every time it rings and/or every time somebody picks it up to make a call. They could also place a color form near the front door every time somebody comes in, goes out, and/or rings the doorbell/knocks. This enables children to count the number of times given events occur by recording them. Some children are better able to understand math by viewing and making graphs. This is because creating graphs involves representing quantities visually instead of just listing numbers.

Counting
Counting is considered a math skill milestone for young children. Typical four-year-olds enjoy counting aloud. Experts identify three levels of counting. The first is counting from 1 to 12, which requires memorization. The second level is counting from 13 to 19, which requires not only memorization, but also an understanding of the more unusual rules for 'teen' numbers. The third level is counting from 20 on. This process is very consistent, and the numbers are ordered according to regular rules. Experts in math education believe that at this level of counting, children are discovering a regular mathematical pattern for the first time, which is base ten (i.e. 20, 30, 40, 50, etc. are 2 tens, 3 tens, 4 tens, 5 tens, etc., and after the base a number between 1 and 9 is added). Researchers and educators in early childhood mathematics programs recommend encouraging children as young as four years old to learn to count up to 100. They find that doing this helps young children learn about and explore patterns in depth.

Perceiving and Identifying Shapes
The three levels of perceiving shapes that children typically move through sequentially are seeing, naming, and analyzing. Very young children recognize simple shapes like circles, squares, and triangles. As their cognitive and language skills develop, they learn the names for these shapes, and use these names to identify single shapes. The third level is analyzing each shape to understand its properties. Whereas identifying shapes visually is intuitive and based on association, analyzing their properties is more abstract, since a shape can have a number of different appearances. For example, three-year-olds can differentiate a triangle from other shapes.
However, if you show them a very tall, skinny/short, wide/lopsided/crooked triangle, they will have trouble identifying it as a triangle. At the analysis level, children realize that a triangle has three sides, which are not necessarily equal in length. An activity that young children enjoy is closing their eyes, reaching into a bag of assorted shapes, finding a triangle by touch, and explaining why it is a triangle. This involves both the second and third levels of naming and analysis.

Integrating Math into Everyday Activities and Using Early Childhood Math Curricula
Integrating math into the context of everyday activities has been the philosophy of early childhood math education until recently. For example, when teachers have children line up, they ask them who is first, second, third, etc. to practice counting. When children play with blocks, teachers ask them to identify their shapes and whether one block is larger/smaller than another. During snack times, teachers help children learn
1:1 correspondence by having them place one snack on each plate. These activities are quite valuable. However, some educators maintain that they are insufficient when used on their own, because in larger classes it is not always possible to take advantage of 'teachable moments' with every child. Therefore, this educational approach cannot be applied systematically. These educators recommend that in addition to integration strategies, EC teachers should use a curriculum. The HighScope curriculum, the Creative Curriculum, and Big Math for Little Kids are just a few examples.  Many teachers combine several curricula, selecting parts of different programs. Using a curriculum allows teachers to use a more planned approach to integrate math into all activities.

Clinical Interview

Background, Method, and Advantages
Clinical interviews have long been used by individual and family therapists, as well as by researchers. Piaget used them along with observations and case histories to understand young children's thinking as he formulated his cognitive developmental theory. Interviewers ask structured/semi-structured/open-ended questions and listen to the responses, often recording them for accuracy. This method gives the interviewer a way to find out what the respondent is thinking and feeling inside, which cannot be determined by observing outward behaviors alone. In educational settings, a teacher might ask a child questions like, 'How did you do this?' 'What is happening now?' 'Can you tell me more about this?' 'Why are you doing this?'
'What are you thinking about now?' etc. Flexible questioning helps uncover the child's thought process, which is what is leading him/her to engage in specific behaviors. Just observing the behaviors alone does not allow the child to express his/her knowledge. While fully interviewing each child in a classroom is not practical, teachers can adapt this method by asking clinical interview-type questions as part of their instruction.

Using Questioning
Teachers can gain a lot of information and insight about how children are learning math concepts by observing their behaviors. For children to actually express their knowledge and thinking processes, however, teachers must ask them questions. For example, when a teacher introduces new shapes to young children, s/he can ask them the shapes' names, how they differ from one another, and why they think the shapes differ. Teachers can then use children's various responses to elicit further responses from them. This technique requires children to use language in significant ways during math activities.
Therefore, these activities not only teach math skills, but also promote literacy development. Asking clinical interview-type questions promotes children's development of math communication skills, one of the essential components of math education. Additionally, being able to put one's knowledge and thoughts into words is a skill that is very important in all areas of education, not just math education. Using clinical interview-type questions helps children learn to use language to explain their thinking, share ideas, and express themselves, promoting and strengthening children's awareness of the functions of mathematical language.

Characteristics of Young Children's Thinking and Learning That Inform EC Math Curricula
Young children think in concrete ways and cannot understand abstract concepts, so effective EC math curricula typically use many concrete objects that children can see, feel, and manipulate to help them understand math concepts. Young children also naturally learn through exploring their environments, so good EC math curricula have many exploration and discovery activities that allow and encourage hands-on learning. In everyday life, young children start to observe relationships as they explore their surroundings.
They match like objects, sort unlike objects, categorize objects, and arrange objects in simple patterns based on shared or contrasting properties. They start to understand words and phrases like 'a little,' 'a lot,' 'more,' 'less,' and 'the same [as…].' Preschoolers use available materials such as sticks, pieces of string, their feet, their hands, their fingers, etc. as tools to measure objects. They also use rulers, measuring cups, and other conventional tools. They use their measurements to develop descriptions, sequences, and arrangements, and to compare various objects.

Activities That Help Children Develop Spatial Awareness
When preschool children build structures with blocks and put together pieces of puzzles during play, they are not only having fun, but are also developing spatial awareness. The relationships of objects to each other and within space are important concepts for children to learn, and serve as a foundation for the principles of geometry and physics that children will learn later. When they are moving around, preschoolers begin to notice how other people and objects are positioned in space, and how their own bodies move through space in relationship to objects and other people. This type of spatial awareness supports children's developing gross motor skills, coordination, and social skills. Young children can and should learn a number of math concepts and skills, such as the ones recommended by preschool math curricula like the High Scope program's 'Numbers Plus' preschool mathematics curriculum. These concepts and skills include number symbols and names, counting, shapes, spatial awareness, relationships of parts to the whole, measurement, units, patterns, and analyzing data.

Rational Numbers and Irrational Numbers
In mathematics, rational numbers are numbers that can be written as ratios or fractions. In other words, a rational number can be expressed as a fraction that has a whole number as the numerator (the number on top) and the denominator (the number on the bottom). Therefore, all whole numbers are automatically rational numbers, because all whole numbers can be written as fractions with a denominator of 1 (e.g., 5 = 5/1, 68 = 68/1, 237 = 237/1, etc.). Even very large, unwieldy fractions (e.g., 9,731,245/42,754,021) are rational numbers, because they can be written as fractions. Irrational numbers can be written as decimal numbers, but not as fractions, because the numbers to the right of the decimal point that are less than 1 continue indefinitely without repeating.  For example, the value of pi (π) begins as 3.141592…, and continues without end. The square root of 2 (√2) = 1.414213….
There are an infinite number of irrational numbers between 0 and 1. However, irrational numbers are not used as commonly in everyday life as rational numbers.

Cardinal, Ordinal, Nominal, and Real Numbers
Cardinal numbers are numbers that indicate quantity. For example, when we say 'seven buttons' or 'three kittens,' we are using cardinal numbers. Ordinal numbers are numbers that indicate the order of items within a group or a set. For example, when we say 'first, second, third, fourth, fifth, etc.,' we are using ordinal numbers. Nominal numbers are numbers that name things. For example, we use area code numbers along with telephone numbers to identify geographical calling areas, and we use zip code numbers to identify geographical mailing areas. Nominal numbers, therefore, identify categories or serve as labels for things. However, they are not related to the actual mathematical values of numbers, and do not indicate numerical quantities or operations. Real numbers include all rational and irrational numbers. Rational numbers can always be written as fractions that have both numerators and denominators that are whole numbers. Irrational numbers cannot, as they contain non-repeating decimal digits. Real numbers may or may not be cardinal numbers.

Activities and Games That Make Learning Fun

Button Board 
By gluing buttons of various sizes and colors to a piece of cardboard, teachers can initiate a number of activities that help preschoolers learn math concepts while having fun. Preschoolers are commonly learning shapes and how to draw them. Teachers can give children lengths of string/twine/yarn or long shoelaces and show them how to wrap them around different buttons to form shapes like rectangles, triangles, and squares. To practice counting and 1:1 correspondence, teachers can ask children to wrap their string around a given number of buttons. Preschoolers need to learn the concept that spoken number words like 'five' can equate to a group of five concrete objects (such as buttons), and this activity promotes that learning. The button board is also useful for giving preschool children practice with sorting or classifying objects into groups based on a common characteristic. For example, the teacher can ask children to wrap their pieces of string around all the big buttons, all the little buttons, only the red buttons, only the blue buttons, etc.

Beanbags and Hopscotch
Teachers can encourage preschool children's counting and number development by creating a grid on the floor with the numbers 1 to 10 using masking tape, construction paper, and markers. Teachers could also draw the grid outdoors by drawing on pavement with chalk. The teacher arranges the numbers in ascending order within the grid of 10 squares/rectangles. S/he asks the children if they can name these numbers. The teacher provides beanbags.
Each child gets a chance to throw a beanbag into any one of the numbered squares. Children can see how far they can throw and/or practice their aim.
Each child names the number inside the square/rectangle where his/her beanbag lands. The children then play a version of hopscotch by hopping from numbered square to square, collecting their beanbags, and then hopping back. If desired, the teacher can write the number each child's beanbag lands on onto a
'scoreboard' graph. Children will observe his/her writing the same numbers found on the floor/ground onto a 'scoreboard.' Teachers can review learning after the game to assess whether children can count using number words, name selected numbers, and throw accurately with consistency.

Reusing Sectioned Plastic Trays
A teacher can wash and reuse the compartmentalized plastic trays from the grocery store that are used for vegetable and fruit to create a preschool counting activity. The teacher supplies beads, pennies, erasers, or other small objects, as well as about a dozen sticky notes. S/he writes a number on each note. For older preschoolers, the teacher can write the numeral and the word (e.g., '7' and 'seven'). For younger children, the teacher can write the numeric symbol ('7,' for example) plus seven dots or other marks as a clue to that number symbol. The teacher puts one numbered note in each compartment and the supply of small objects in the central dip compartment.
Then, s/he guides each child to transfer the correct number of each small object to the correct compartment. The child should count aloud while transferring each small object, and should repeat this process until all compartments with a numbered sticky note have the correct number of objects.
Children can then repeat the process to practice and perfect their counting, or the teacher can place notes with different numbers in the tray's compartments.

Fishing for Numbers
Teachers can help preschoolers practice identifying numbers and counting by creating a fun 'fishing for numbers' game. Teachers cut 10 fish shapes that are about 6 inches long from pieces of construction paper that are different colors. Teachers then write a single number between 1 and 10 on each 'fish.' Near each fish 'mouth,' the teacher punches a hole and inserts a paper clip through it. The teacher makes 'fishing rods' by tying strings to dowels and gluing a magnet to each string. After spreading out the fish so the children can easily see the numbers, the teacher assigns each child a number and they 'fish' for it, picking up the fish by bringing the magnet close to the paper clip. The children then 'reel in' their catches. This gives children practice correctly identifying number names. The game can be adapted for more advanced math concepts as well. For example, the teacher can cut out fish shapes of various sizes and have children 'fish' for larger/smaller fish. The activity can also be adapted to promote literacy development. The teacher can write letters instead of numbers on the fish to give students practice with alphabet recognition, or s/he can write a Dolch word/sight word on each fish to give students practice recognizing and identifying important vocabulary words.

Collages
Fundamental math skills that prepare preschoolers for kindergarten include shape recognition. To introduce children to an activity they will view as fun rather than as work, teachers can show children how to make a collage of a familiar figure. This will also give children the opportunity to experiment with an artistic process. For example, they can create a Santa Claus or an Easter Bunny as a holiday art project. They can make collages of other imaginary/real people for various events/seasons/topics. 
Teachers cut out paper templates, including circles for heads, triangles for hats, squares for bodies, and narrow rectangular strips for limbs. First, they help children name each shape. They have each child trace the template shapes onto paper and cut them out with child-safe scissors. The teacher then instructs children to arrange their cutout shapes on a piece of cardboard/construction paper. Once they are in the correct positions, the children glue the shapes in place. Teachers can subsequently teach additional shapes (octagons, ovals, etc.), challenging children to make new, different collages.

Grab Bag
Young children learn to name numbers in a way that is similar to how they learn to recite alphabet letters. However, learning to associate number symbols with concrete objects in the real world environment is a major advance in their cognitive development. The concept of 1:1 correspondence entails matching number symbols to the quantities they represent, an essential early math skill. Teachers can support the development of this math skill with a simple 'grab bag' game youngsters enjoy. The teacher writes a number from 1 to 10 on each of ten cards, folding each card in half and putting them into a paper lunch bag. The teacher provides each child with a handful of pennies/play coins/buttons/little blocks to use as counting tokens. Each child takes a turn closing his/her eyes and pulling a card out of the bag. The child reads the number on the card, counts out the corresponding number of pennies/tokens, and puts them with the card. As children learn, teachers can place additional and/or different numbers (e.g., 11 to 20) in the grab bag. To promote the development of early literacy skills, teachers can also include the name of the number on each card.

Pattern Resist Art
A significant mark of progress in early math skills development is the ability to not only identify various shapes, but also to draw them. Once young children develop this ability, they typically want to practice it all the time. Teachers can encourage this by helping children make pattern resist paintings. The teacher tapes white paper to children's tables/trays, gives them crayons, and invites them to fill the paper with drawings of different shapes of various sizes and colors. Teachers can introduce young children to new shapes (e.g., ovals, stars, crescent moons, etc.) by drawing them on separate pieces of paper for children to look at and copy. Then, the teacher replaces the crayons with water, watercolor paints, and brushes; shows the children how to dip brushes into paint and water to dilute the colors; and allows them to paint over their crayoned shapes, covering all the white paper with color. The children see the shapes show through the paint, creating the pattern resist. Dipping brushes and diluting various colors also develop children's color recognition skills and their hand-eye coordination.

Ice Cube Necklaces
In hot weather, making ice cube necklaces is a fun activity that helps young children cool off while learning to sequence objects. The activity also helps children develop their manual motor skills and learn about liquid and solid states of matter. Regular ice cube trays are fine; those with 'fun-shaped' compartments are even better. The teacher cuts plastic drinking straws so that they will fit into each ice cube compartment. The children participate, watching and/or helping pour water into trays and adding various food colorings/fruit juices. The teacher places one straw clipping into each compartment. While putting the trays into the freezer, the teacher tells children that 32° Fahrenheit/0° Celsius is the temperature at which water freezes. Children practice making scientific observations by noting how long the water takes to freeze. They empty the cubes into a big bowl. The children put on bathing suits or other clothing that can get wet, and the class goes outdoors. The teacher provides strings that are knotted at one end, and calls out a color pattern (e.g., one blue cube, then a yellow cube, etc.). Children follow the teacher's instructions to create color-patterned necklaces they can tie, wear, and watch melt.

Red Rover
Red Rover is a good game for groups of children who are attending parties or playing outdoors at parks/playgrounds. Two teams take turns calling and roving. The child called runs to the other team and tries to fit into its line. If successful, s/he gets to call another player to bring back to his/her home team. If not, s/he joins the opposite team. The game continues until one team has no more members. Teachers can adapt this game to teach shape recognition by cutting out various shapes from construction paper of different colors and pinning a shape to each child's shirt. In large groups, more than one child can have the same shape or color. Instead of children's names, the teacher instructs players to use shapes and colors when calling (e.g., 'Red Rover, Red Rover, blue circles come over!'). This supports the development of shape and color recognition skills. Teachers can vary action verbs (e.g., '….hop over/jump over/skip over') to support vocabulary development and comprehensive skills. When children perform such movements, they are also practicing and developing gross motor skills.

Counting on Fingers
A common practice among preschool children is counting on their fingers. Young children learn concretely before they develop abstract thought, so they must have concrete objects to work with to understand abstract mathematical concepts. They use their fingers to count because fingers are concrete. A simple activity that allows children to continue finger counting while removing additional visual support is 'blind finger counting.' Using eyesight to count objects we can see is relatively easy. However, when children cannot see objects, they must learn to count mentally instead. This allows them to take another step in their progress from concrete to abstract thinking. To count mentally without visual reinforcement takes practice. Teachers can tape a shoebox lid to the box and cut a small hole in it. Children can fit a hand through the hole, but cannot see inside. Children close their eyes; the teacher drops several small objects into the box; and each child reaches in, counting the objects using only touch. Varying objects and quantities maintains the fun of this activity.

Sorting and Categorization
One of the major learning accomplishments of young children is being able to identify similarities and differences among objects.
Developing this ability enables children to sort like objects into groups, and to place objects into categories based on their differences. When preschoolers compare and contrast objects, they demonstrate an important early step in the development of critical thinking, analytical, and problem solving skills. For an easy, entertaining guessing game, adults can select assorted household items familiar to children and put them into a bag/pillowcase. They then give children various clues (e.g., 'I stir lemonade with this…,' 'It's made of wood,'
'We keep it in the kitchen drawer…,' etc.) and ask them to guess which items are in the bag. It is important to give young children one to two minutes to consider each clue before they make a guess. Adults repeat clues when children guess incorrectly. If children guess correctly, they are allowed to look inside the bag. Youngsters greatly enjoy seeing that the object they guessed is actually inside the bag. Adults can gradually make the game more challenging by beginning with very common objects, and then eventually progressing to more unusual ones.

Baking Cookies
Young children are typically curious about adult activities like baking. They usually want to know more about the process, and often ask many questions. They also love to be included and to participate, frequently offering/asking to help. Letting them help builds their self-esteem and self-efficacy (i.e. their confidence in their competence to accomplish a task).
Adults can allow children to help while also providing instruction and practice with shape recognition, measurement, sorting, and categorization.  The adult prepares a favorite cookie recipe. Some children can help measure ingredients, which helps develop the math skill of measurement. With the dough rolled out, children use cookie cutters of various shapes. Recognizing, naming, and selecting the shapes promote the development of shape recognition skills.
Adults 'shuffle'/mix the baked cookie shapes and have children separate cookies with like shapes into groups, which promotes sorting skills. Having children identify similar/different shapes, sizes, and colors promotes categorization skills. Arranging cookie shapes into patterns for children to identify promotes pattern recognition skills, which are necessary to the development of math skills and many other skills. Giving each child a cookie to eat afterward is naturally reinforcing.

Creative Crafts
Prerequisite abilities that young children need in order to develop early math skills include the ability to identify, copy, expand, and create patterns; as well as the ability to count. Adults can promote the development of these skills by giving children a craft project and introducing them to an interactive game they can play using their crafts. First, the children paint six ping pong balls red on one side to make red-and-white balls.
Then, the children paint six ping pong balls blue on one side to make blue-and-white balls. Once the paint dries, the adult puts several balls into an egg carton so that one color is face up. The adult starts making a simple pattern (e.g., two white, then two red, then two blue), and asks each child to continue the pattern. Then, the adult allows each child to create his or her own original color patterns. Once a child masters creating patterns using solid colors, he or she can then use both the white and colored sides of the balls to create more complex patterns. Children can design an infinite number of patterns, which are often quite artistic.

Shape Matching Games
In one type of shape matching game, EC teachers help children make a game board out of construction paper that is shaped like a tree. Teachers first help the children cut a treetop and leaf shapes from green paper. They discuss children's preferences for tall/short and thick/thin trunks, giving them practice using descriptive vocabulary words, particularly ones related to size. This step builds both general and math concept vocabulary. Children cut trunks from brown paper and paste/glue them on the treetops. While out of the children's sight, the teacher cuts 5 to 10 (or more) pairs of shapes per child/tree from different colors of construction paper.
Pairs should not match exactly (e.g., a blue square can be paired with a red square). The teacher glues one of each pair of shapes to each child's tree while the child is not looking. The teacher then gives each child the rest of the shapes, and invites children to see how quickly they can match each shape to its 'partner' on the tree. The teacher can provide 'warmer/cooler' distance clues, and should provide reinforcement each time a child correctly matches a pair of shapes. Teachers can make this activity more challenging by using more shapes and/or getting students to match shapes that are different sizes (e.g., children can be asked to match smaller diamonds to larger diamonds).

Homemade Beanbag Game
Young children enjoy tossing objects and practicing their aim. Adults can make a beanbag game that helps children learn numbers and identify sets, while also allowing them to construct their own game rules.
First, the adult should cover five big, equally-sized coffee (or similar) cans with paper that is adhesive on one side. The adult should then use markers to write a number from 1 to 5 and draw the corresponding number of dots on each can. The next step is to fill 15 tube socks with beans and knot/tie/sew them shut. The following numerals and the corresponding number of dots should be written on each homemade beanbag using markers: the number 1 on five beanbags, the number 2 on four beanbags, the number 3 on three beanbags, the number 4 on two beanbags, and the number 5 on one beanbag. Next, the adult should attach the cans to the floor with tape or Velcro. Then, the adult should mark a line on the floor that children must stand behind, and should direct children ONLY to toss the beanbags into the cans. Children will devise various games/rules.
First, they may simply toss the beanbags into the cans; then, some may try to toss beanbags into a can that has the same number as the one marked on the beanbag. Eventually, some may throw three beanbags into the '3' can. They may/may not keep score. Allowing children to determine the details and rules gives them an opportunity to develop their imagination and decision making skills, and to create their own games while learning number and set identification.

Guessing Game
Adults can adapt the format of '20 Questions,' 'I Spy,' and other similar guessing games to focus on numbers and help children learn number concepts. For example, adults could say, 'I'm thinking of a number from 1 to 10….' and then give children 10 guesses. Adults give children cues as they guess, such as 'higher' and 'lower,' to help them narrow down the number of possible correct answers. As children improve, adults can increase the number range (e.g., from 0 to 50) or use larger numbers (e.g., from 20 to 40). As children's skills and self-confidence develop, adults can reverse roles, having children think of numbers and give clues while adults guess. Young children enjoy the fun of guessing, getting closer using clues, deducing correct answers, and fooling adults with their own clues. Concurrently, they learn to describe numbers, compare them, and sequence them. Adults can make the game more difficult by limiting the number of guesses allowed and/or setting time limits. They can make it easier by providing a written number line for children to reference. This game requires no materials (or just a basic number line), is a great way to pass time, and entertains children while helping to develop numeracy skills.

Arts and Crafts
According to the U.S. Department of Agriculture, preschoolers need three ½-cup servings of fruit and three ½-cup servings of vegetables daily. However, many young children are picky/resistant. Adults can motivate them to eat produce with a 'food rainbow' project. Adults show children a picture of a rainbow, and discuss its colors and their sequence (teaching some earth science, optics, and color theory!). A fun art project is allowing students to color their own rainbows, which improves fine motor skills. Then, adults can have children cut out pictures from grocery circulars and name each food. The adult can help children find one healthy fruit/vegetable for each color, gluing each food to its corresponding stripe on the rainbow. Adults can then help children pull apart cotton balls and glue them to their rainbow pictures to represent clouds. Children can then post their food rainbows on refrigerators as artwork and as healthy eating reminders. At the bottom, children can draw and color one box (bottom-up) for each food they eat (e.g., blue = blueberries, orange = carrots, red = apples, etc.) to create a bar graph. Children should try to 'eat' the entire rainbow every week. This activity gives children the opportunity to produce colorful art, eat better, track and document their diets, and develop graphing skills.

Treasure Hunt
A treasure hunt is an ideal outdoor activity for young children, and can also be adapted for indoor fun. The treasure can be anything
(e.g., a small toy/play money/chocolate 'coins'/rocks spray painted gold or silver, etc.). The adult should put the treasure in a paper bag marked with a large X. The adult should hide it somewhere where it is not visible, but will not be overly difficult for children to find. Then, the adult should make a treasure map, using few words and many pictures, sketching landmark objects in the area (trees, houses, etc. if the activity will be done outdoors, and furniture, walls, etc. if the activity will be done indoors). The adult should ensure the map is developmentally appropriate for young children, and that they will be able to read it independently. Adults with time and motivation can make the map look authentic by soaking it in tea/coffee, drying it in a 200° oven, or even charring its edges. Adults should include a dotted line on the map that reinforces the simple directions and indicates the path to the treasure, which is indicated on the map by a large X. Children have fun, use their imaginations, make connections between symbols and images to corresponding real-world physical objects, and begin learning to read maps.

Pasta Necklace
Stringing beads/noodles is an activity that helps young children develop hand-eye coordination, which they will need for writing and other everyday activities that require fine motor coordination. Noodles are typically the perfect size for young children's hands. They are inexpensive, usually costing less than comparably-sized beads. Moreover, pasta is non-toxic, an advantage when working with little persons who put things in their mouths.
Hollow, tubular noodles like penne, ziti, wagon wheels, etc. are ideal. Fishing line/craft beading string/other stiff string is best; soft, limp string/yarn is harder for young children to manipulate. Using multicolored vegetable pasta removes the need to use markers or dye to add color. If using white pasta, children can color the noodles with markers, but adults should keep in mind that the ink can bleed onto skin/clothes even when it is dry. Adults should cut pieces of string that are long enough to allow children to easily slip the necklaces on and off after they are tied. Adults should also use a knot to secure a noodle to one end of the string. By providing more than one noodle shape, adults can invite children to string the noodles to create patterns, which develops pattern recognition and pattern creation abilities. These abilities also inform repetition, rhythm, categorization, and sequencing skills, which are important in math, music, art, literature, clothing design, etc.

Number Dash
A game for young children that some educators call 'Number Dash' (Miller, ed. Charner, 2009) builds foundational math concepts and skills, while providing physical activity. It can involve small or large groups (the referenced authors say 'the more the merrier'). Help children write large numbers on a paved area with sidewalk chalk. Make sure numbers are spread far enough apart so children will not collide while running. There should be one of each number for each child (e.g., six '1s,' '2s,' '3s,' etc. if there are six children). Use chalk colors that contrast with the pavement color to ensure the numbers will be highly visible. Tell children to run ('dash') to whichever number you call out and stand on it until you call another number. Call out numbers randomly. Encourage children who have located the number to help their classmates/playmates. This game develops gross motor skills, number writing skills, and number recognition skills. It also provides experience with playing organized games, following rules, following directions, and cooperating with and helping others. This game can also be played with letters, colors, and/or shapes.

Introducing Standard Measurement Using a Ruler
A teacher is introducing standard measures to her class as part of a unit on measurement, one of the early math skills. She shows the children a ruler, explaining that it is one foot long, and that we can use it to measure inches and parts of inches. She demonstrates placing the ruler on paper to measure a given length, explaining that the ruler can also be used as a straight edge for drawing lines. One child asks, 'How come you started with zero? Why don't you start with one like when we count?' The teacher responds, 'That's a very good question! Zero means none/nothing. When we count, we start with one because we already have at least one of something. When you were born, you were not one year old; your age began at zero. After a year, on your first birthday, you were one year old. We also begin measuring distances at zero/none/nothing. The first piece/unit of measurement is one, not two. The distance from zero to one is equal to one. To get to one inch, for example, we need to start at zero.'

Learning About Geometric Shapes and Their Properties
A teacher has been working with students to help them develop their shape identification skills. They can recognize shapes by sight, and have also learned the defining properties of different shapes (number of sides, etc.). The teacher shows the class a figure. She asks how many rectangles they can find in the figure.
One student answers, 'There is one rectangle,' which is incorrect because a square is a rectangle; this figure has four rectangles that are squares.
Moreover, the entire figure is itself a rectangle. Another student therefore says, 'There are five rectangles.' This response is also incorrect. Two adjacent squares also form a rectangle; this means there are three additional rectangles. Three adjacent squares also form a rectangle; this means there are two additional rectangles. Thus, the figure has a total of 10 rectangles.
Solving this puzzle requires the use of many skills, including analyzing visual information, synthesizing visual information, recognizing patterns, recognizing shapes, and identifying the properties of shapes.

Collecting, Organizing, and Displaying Data Using Sticky Notes and a Teacher-Made Chart
A preschool teacher is teaching her group of ten children about basic data collection, data arrangement, and data display. She shows children yellow, blue, and green sticky notes, and has each child select his/her favorite color. Five children choose yellow notes, three select blue, and two choose green. By choosing one of three colors, each child has participated in data collection. The teacher draws lines to divide a sheet of paper into three columns, and labels each column with one of the colors. She helps the children place their chosen sticky notes in the correct columns. By arranging the colored sticky notes into columns, the teacher and children have organized the data they gathered. Once all notes are in their proper color columns, the completed chart is an example of how collected, organized data can be displayed.

Yellow sticky note - Blue sticky note - Green sticky note
BLUE - YELLOW - GREEN

Selecting One of Three Colors of Sticky Notes, Organizing Them by Color, and Displaying Them
The teacher had ten children each choose one of three colors of sticky notes, an example of basic data collection. She used a chart with three columns to organize the children's choices as follows:
Yellow sticky note - Blue sticky note - Green sticky note
BLUE - YELLOW - GREEN
The chart displays the collected and organized data. The teacher asks the children which color was chosen the most. Seeing five yellow notes, they answer, 'yellow.' She asks which color was chosen the least, and they say, 'green.' She asks them to use numbers to arrange the color choices from most popular to least popular. They arrive at, 'five yellow, three blue, and two green.' Together, the teacher and the children point to and count ten children. She tells them five equals half of ten, and asks which color half of the children chose. Together, they figure out it was yellow. These are examples of analyzing and interpreting data.

Science Concepts Young Children Learn During Everyday Activities
Science entails asking questions, conducting investigations, collecting data, and seeking answers to the questions asked by analyzing the data collected. Natural events that can be examined over time and student-centered inquiry through hands-on activities that require the application of problem solving skills are most appropriate for helping young children learn basic science. In their everyday lives, young children develop concepts of 1:1 correspondence through activities like fitting pegs into matching holes or distributing one item to each child in a class. They also develop counting concepts by counting enough items for each child in the group or counting pennies in a piggy bank. They develop classification concepts when they sort objects into separate piles according to their shapes or some other type of category (e.g., toy cars vs. toy trucks). When children transfer water, sand, rice, or other substances from one container to another, they develop measurement concepts. As they progress, children will apply these early concepts to more abstract scientific ideas during grade school.

Science Concepts Infants and Toddlers Learn in Normal Developmental Processes
Infants use their senses to explore the environment, and are motivated by innate curiosity. As they develop mobility, children gain more freedom, allowing them to make independent discoveries and think for themselves. Children learn size concepts by comparing the sizes of objects/persons in the environment to their own size, and by observing that some objects are too large to hold, while others are small enough to hold. They learn about weight when trying to lift various objects. They learn about shape when they see that some objects roll away, while others do not. Babies learn temporal sequences when they wake up wet and hungry, cry, and have parents change and feed them. They also learn this concept by playing, getting tired, and going to sleep. As soon as they look and move around, infants learn about space, including large/small spaces. Eventually, they develop spatial sense through experiences like being put in a playpen/crib in the middle of a large room. Toddlers naturally sort objects into groups according to their sizes/shapes/colors/uses. They experiment with transferring water/sand among containers of various sizes. They learn part-to-whole relationships by building block structures and then dismantling them.

Naturalistic, Informal, and Structured Learning Experiences
Children actively construct their knowledge of the environment through exploring it. Young children's learning experiences can be naturalistic (i.e. spontaneously initiated by the child during everyday activities). During naturalistic learning, the child controls his/her choices and actions. Informal learning experiences also allow the child to choose his or her actions and activities, but they include adult intervention at some point during the child's engagement in naturalistic pursuits. In structured learning experiences, the adult chooses the activities and supplies some direction as to how the child should perform the associated actions. One consideration related to EC learning that teachers should keep in mind is that within any class or group of children, there are individual differences in learning styles. Additionally, children from different cultural groups have varying learning styles and approaches. EC teachers can introduce science content in developmentally appropriate ways by keeping these variations in mind.

Naturalistic Learning Experiences
Motivated by novelty and curiosity, young children spontaneously initiate naturalistic experiences during their everyday activities. Infants and toddlers in Piaget's sensorimotor stage learn by exploring the environment through their senses, so adults should provide them with many objects and substances they can see, hear, touch, smell, and taste.
Through manipulating and observing concrete objects/substances, preschoolers in Piaget's preoperational stage begin learning concepts that will enable them to perform mental operations later on. Adults should observe children's actions and progress, and should give positive reinforcement in the form of looks, facial expressions, gestures, and/or words encouraging and praising the child's actions. Young children need adult feedback to learn when they are performing the appropriate actions. For example, a toddler/preschooler selects a tool from the toolbox, saying, 'This is big!' and the mother responds, 'Yes!' A four-year-old sorting toys of various colors into separate containers is another example of a naturalistic experience. A five-year-old who observes while painting that mixing two colors yields a third color is yet another example.

Informal Learning Experience
Informal learning experiences involve two main components.
First, the child spontaneously initiates naturalistic learning experiences during everyday activities to explore and learn about the environment. Second, the adult takes advantage of opportunities during naturalistic experiences to insert informal learning experiences. Adults do not plan these in advance, but take advantage of opportunities that occur naturally. One way this happens is when a child is on the right track to solve a problem, but needs some encouragement or a hint from the adult. Another way is when the adult spots a 'teachable moment' during the child's naturalistic activity, and uses it to reinforce a basic concept. For example, a three-year-old might hold up three fingers, declaring, 'I'm six years old.' The parent says, 'Let's count fingers: one, two, three. You're three years old.' Or, a teacher asks a child who has a box of treats if s/he has enough for the whole class, and the child answers, 'I don't know.' The teacher then responds, 'Let's count them together,' and helps the child count.

Structured Learning Experiences
Naturalistic learning experiences are spontaneously initiated and controlled by children. Informal learning experiences involve unplanned interventions by adults during children's naturalistic experiences, which is when adults offer suitable correction/assistance/support. Structured learning experiences differ in that the adult pre-plans and initiates the activity/lesson, and provides the child with some direction. For example, a teacher who observes a four-year-old's need to practice counting can give the child a pile of toys, and then ask him/her how many there are. To develop size concepts, a teacher can give a small group of children several toys of different sizes, and then ask the children to inspect them and talk about their characteristics. The teacher holds up one toy, instructing children to find one that is bigger/smaller. If a child needs to learn shape concepts, the teacher might introduce a game involving shapes, giving the child instructions on how to play the game. Or, a first grade teacher, recognizing the importance of the concept of classification to the ability to organize scientific information, might ask students to bring in bones to classify during a unit on skeletons.

Kindergarten Activity for Collecting and Organizing Data
Preschoolers and kindergarteners continue their earlier practices of exploration to learn new things, and they apply fundamental science concepts to collect and organize data in order to answer questions. To collect data, children must have observation, counting, recording, and organization skills.  One activity kindergarteners and teachers enjoy is growing bean sprouts. For example, the teacher can show children two methods: one using glass jars and paper towels saturated with water, the other using cups of dirt. The children add water daily as needed, observe developments, and report to the teacher, who records their observations on a chart. The teacher gives each child a chart that they add information to each day. The children count how many days their beans took to sprout in the glass jars and in the cups of dirt. They then compare their own results for the two methods, and they compare their results to those of their classmates. The children apply concepts of counting, numbers, time, 1:1 correspondence, and comparison of numbers. They also witness the planting and growing process.

Science Process Skills
Science process skills include observation (using the senses to identify properties of objects/situations), classification (grouping objects/situations according to their common properties), measurement (quantifying physical properties), communication (using observations, classifications, and measurements to report experimental results to others), inference (finding patterns and meaning in experiment results), and prediction (using experimental experience to formulate new hypotheses). Inferences and predictions must be differentiated from objective observations. Classification, measurement, and comparison are basic math concepts which, when applied to science problems, are called process skills. The other science process skills named, as well as defining and controlling variables, are equally necessary to solve both science and math problems. For example, using ramps can help young children learn basic physics concepts. Teachers ask children what would happen if two balls were rolled down a ramp at the same time, if two balls were rolled down a ramp of a different height/length, if two ramps of different heights/lengths were used, etc. In this activity, children apply the scientific concepts of observation, communication, inference, and prediction, as well as the concepts of height, length, counting, speed, distance, and comparison.

Scientific Method
Children are born curious, and naturally engage in problem solving to learn. Problem solving and inquiry are natural child behaviors. EC teachers can use these behaviors to promote children's scientific inquiry. Scientific inquiry employs the scientific method. The first step in the method is to ask a question, which is another natural child behavior. Just as adult scientists formulate research questions, the first step of the scientific method for children is asking questions they want to answer. Next, to address a question, both adults and children must form a hypothesis (i.e. an educated guess about what the answer will be). The hypothesis informs and directs the next steps: designing and conducting an experiment to test whether the hypothesis is true or false. With teacher instruction/help, children experiment. For example, they might drop objects of different weights from a height to see when each lands, as Galileo did.
Teachers help record outcomes. The next steps are deciding whether the results prove/disprove the hypothesis and reporting the results and conclusions to others.

Physical Science and Matter
Physical science is the study/science of the physical universe surrounding us. Everything in the universe consists of matter (i.e. anything that has mass and takes up space) or energy (i.e. anything that does not have mass or occupy space, but affects matter and space). Three states of matter are solid, liquid, and gas. Solids preserve their shape even when they are not in a container. Solids have specific, three-dimensional/crystalline atomic structures and specific melting points. Liquids have no independent shape outside of containers, but have specific volumes. Liquid molecules are less cohesive than solid molecules, but more cohesive than gas molecules. Liquids have flow, viscosity (flow resistance), and buoyancy. Liquids can undergo diffusion, osmosis, evaporation, condensation, solution, freezing, and heat conduction and convection. Liquids and gases are both fluids, and share some of the same properties. Gases have no shape, expanding and spreading indefinitely outside of containers. Gases can become liquid/solid through cooling/compression/both. Liquids/solids can become gaseous through heating. Vapor is the gaseous form of a substance that is solid/liquid at lower temperatures. For example, when water is heated it becomes steam, a vapor.

Liquids
Of the three states of matter—solid, liquid, and gas—liquids have properties that fall somewhere in between those of solids and gases. The molecules of solids are the most cohesive (i.e. they have the greatest mutual attraction). Gas molecules are the least cohesive, and liquid molecules are in between. Liquids have no definite shape, while solids do. Liquids have a definite volume, whereas gases do not. The cohesion of liquid molecules draws them together, and the molecules below the surface pull surface molecules down, creating surface tension. This property can be observed in containers of water.
Liquid molecules are also attracted to other substance's molecules (i.e. adhesion). Surface tension and adhesion combined cause liquids to rise in narrow containers, a property known as capillarity. Liquids are buoyant (i.e. they exert upward force so objects which have more buoyancy than weight float in liquids, while objects which have more weight than buoyancy sink in liquids). Liquids can be made solid by freezing, and can be made gaseous by heating/evaporation. Liquids can diffuse, which means they can mix with other molecules. Liquid diffusion across semi-permeable membranes is known as osmosis.

Solids
Solids are one of the three forms of matter. The other two are liquids and gases. Solids maintain their shape when they are not inside of containers, whereas liquids and gases acquire the shapes of containers holding them. Containers also prevent liquids and gases from dispersing. Of the three forms of matter, solids have the most cohesive molecules. Solid molecules are most attracted to each other, and solid molecules are held together most strongly. Solid atoms are organized into defined, three-dimensional, lattice-shaped patterns (i.e. they are crystalline in structure). Solids also have specific temperatures at which they melt. Some substances that seem solid, such as plastic, gel, tar, and glass, are actually not true solids. They are amorphous solids because their atoms do not have a crystalline structure, but are amorphous (i.e. the positions of their atoms have no long-range organization). They also have a range of melting temperatures rather than specific melting points.

Gases
Gas, liquid, and solid are the three states of matter. Gases have the least cohesive (i.e. mutually attracted) molecules of the three states of matter, while solids have the most cohesive molecules. Gases do not maintain a defined shape, while solids do. If not contained within a receptacle, gases spread and expand indefinitely. Gases can be elementary or compound. An elementary gas is composed of only one kind of chemical element. At normal temperatures and pressures, 12 elementary gases are known: argon*, chlorine, fluorine, helium*, hydrogen, krypton*, neon*, nitrogen, oxygen, ozone, radon*, and xenon*. Compound gases have molecules containing atoms of more than one kind of chemical element. Carbon monoxide (which contains one carbon and one oxygen atom) and ammonia (which contains nitrogen and hydrogen atoms) are common compound gases. Heating gas molecules/atoms charges them electrically, making them ions. Plasma combines positive gas ions and electrons. Some gases are colorless and odorless, while others are not. Some burn with oxygen, while others do not. *Noble/inert gases have single atoms that do not normally form compounds with other elements.

Light

Reflection and Scattering
When a beam of light hits a smooth surface like a mirror, it bounces back off that surface. This rebounding is reflection. In physics, the law of reflection states that 'the angle of incidence equals the angle of reflection.' This means that when light is reflected, it always bounces off the surface at the same angle at which it hit that surface. When a beam of light hits a rough rather than a smooth surface, though, it is reflected back at many different angles, not just the angle at which it struck the surface. This reflection at multiple and various angles is scattering. Many objects we commonly use every day have rough surfaces. For example, paper may look smooth to the naked eye, but actually has a rough surface. This property can be observed by viewing paper through a microscope. Because light waves striking paper are reflected in every direction by its rough surface, scattering enables us to read words printed on paper from any viewing angle.

Absorption
When light strikes a medium, the light wave's frequency is equal or close to the frequency at which the electrons in the medium's atoms can vibrate. These electrons receive the light's energy, making them vibrate.
When a medium's atoms hang on tightly to their electrons, the electrons transmit their vibrations to the nucleus of each atom. This makes the atoms move faster and collide with the medium's other atoms. The energy the atoms got from the vibrations is then released as heat. This process is known as absorption of light. Materials that absorb light, such as wood and metal, are opaque. Some materials absorb certain light frequencies but transmit others.
For example, glass transmits visible light (and therefore appears transparent to the naked eye), but absorbs ultraviolet frequencies. The sky looks blue because the atmosphere absorbs all colors in the spectrum except blue, which it reflects. Only blue wavelengths/frequencies bounce back to our eyes. This is an example of subtractive color, which we see in paints/dyes and all colored objects/materials. Pigments absorb some frequencies and reflect others.

Refraction
When light moves from one transparent medium to another (e.g., between water and air/vice versa), the light's speed changes, bending the light wave. It bends either away from or toward the normal line, an imaginary straight line running at right angles to the medium's surface. We easily observe this bending when looking at a straw in a glass of water. The straw appears to break/bend at the waterline. The angle of refraction is the amount that the light wave bends. It is determined by how much the medium slows down the light's speed, which is the medium's refraction index. For example, diamonds are much denser and harder than water, and thus have a higher refraction index. They slow down and trap light more than water does. Consequently, diamonds sparkle more than water. Lenses, such as those in eyeglasses and telescopes, rely on the principle of refraction. Curved lenses disperse or concentrate light waves, refracting light as it both enters and exits, thus changing the light's direction. This is how lenses correct (eyeglasses) and enhance (telescopes) our vision.

Magnetism
Magnetism is the property some objects/substances have of attracting other materials. The form of magnetism most familiar to us is certain materials attracting iron. Magnets also attract steel, cobalt, and other materials. Generators supplying power include magnets, as do all electric motors. Loudspeakers and telephones contain magnets. Tape recorders use magnets. The tape they play is magnetized. Magnets are used in compasses to determine the location of north and various corresponding directions. In fact, the planet Earth is itself a giant magnet (which is why compasses point north).
Hence, like the Earth, all magnets have two poles: a north/north-seeking pole and a south/south-seeking pole. Opposite poles attract, and like poles repel each other. Magnets do not need to touch to attract/repel each other. A magnet's effective area/range is its magnetic field. All materials have some response to magnetic fields. Magnets make nearby magnetic materials into magnets, a process known as magnetic induction. Materials that line up parallel to magnetic force field lines are paramagnetic, while materials that line up perpendicular to magnetic force field lines are diamagnetic.

Modern Theory of Magnetism and What Scientists Do/Do Not Know
Scientists have known about the effects of magnetism for hundreds of years. However, they do not know exactly what magnetism is, or what causes it. French physicist Pierre Weiss proposed a theory of magnetism in the early 20^th century that is widely accepted. This theory posits that every magnetic material has groups of molecules—domains—that function as magnets. Until a material is magnetized, its domains have a random arrangement, so one domain's magnetism is cancelled out by another's. When the material comes into a magnetic field—the range/area wherein a magnet is effective—its domains align themselves parallel to the magnetic field's lines of force. As a result, all of their north-seeking/north poles point in the same direction. Removing the magnetic field causes like poles to repel one another as they normally do. In easily magnetized materials, domains revert to random order. In materials that are harder to magnetize, domains lack sufficient force to disassemble, leaving the material magnetized.
Later versions of Weiss's theory attribute domain magnetism to spinning electrons.

Insulation, Conduction, and the Flow of Electricity
The smallest units of all matter are atoms. The nuclei of atoms are orbited by negatively charged electrons. Some materials have electrons that are strongly bound to their atoms. These include air, glass, wood, cotton, plastic, and ceramic. Since their atoms rarely release electrons, these materials have little or no ability to conduct electricity, and are known as electrical insulators. Insulators resist/block conduction. Metals and other conductive materials have free electrons that can detach from the atoms and move around. Without the tight binding of insulators, materials with loose electrons enable electric current to flow easily through them. Such materials are called electrical conductors. The movements of their electrons transmit electrical energy. Electricity requires something to make it flow (i.e. a generator). A generator creates a steady flow of electrons by moving a magnet close to a wire, creating a magnetic field to propel electrons. Electricity also requires a conductor (i.e. a medium through which it can move from one place to another).

Movement of Electrical Currents by a Generator
Magnetism and electricity are related, and they interact with each other. Generators work by using magnets near conductive wires to produce moving streams of electrons. The agent of movement can range from a hand crank, to a steam engine, to the nuclear fission process. However, all agents of movements operate according to the same principle. A simple analogy is that a generator magnetically pushes electrical current the way a pump pushes water. Just as water pumps apply specific amounts of pressure to specific numbers of water molecules, generator magnets apply specific amounts of 'pressure' to specific numbers of electrons. The number of moving electrons in an electrical circuit equals the current, or amperage. The unit of measurement for amperage is the ampere, or amp. The amount of force moving the electrons is the voltage. Its unit of measurement is the volt. One amp equals 6.24 x 10¹⁸ electrons passing through a wire each second. For example, a generator could produce 1 amp using 6 volts when rotating 1,000 times per minute. Today's power stations rely on generators.

Positions and Motions of Objects and Newton's Laws of Physics
Moving physical objects changes their positions. According to Newton's first law of motion, an object at rest tends to stay at rest and an object in motion tends to stay in motion, unless/until an opposing force changes the object's state of rest/motion. For example, an object at rest could be a small rock sitting on the ground. If you kick the rock into the air, it moves through the air. The rock will continue to move, but when a force like gravity acts on it, it falls/stops moving. The resulting motion from kicking the rock illustrates Newton's third law of motion: for every action there is an equal and opposite reaction. The acceleration or increase in velocity (a) of an object depends on its mass (m) and the amount of force (F) that is applied to the object. Newton's second law of motion states that F = ma (force equals mass times acceleration). Thus, moving objects maintain their speeds unless some force(s) cause acceleration or slowing/stopping, as frictional forces do.

Heat
Heat is transmitted through conduction, radiation, and convection. Heat is transmitted in solids through conduction. When two objects at different temperatures touch each other, the hotter object's molecules are moving faster. They collide with the colder object's molecules, which are moving slower. As a result of the collision, the molecules that are moving more rapidly supply energy to the molecules that are moving more slowly. This speeds up the movement of the (previously) slower moving molecules, which heats up the colder object. This process of transferring heat through contact is called thermal conductivity. An example of thermal conductivity is the heat sink. Heat sinks are used in many devices. Today, they are commonly used in computers. A heat sink transfers the heat building up in the computer processor, moving it away before it can damage the processor. Computers contain fans, which blow air across their heat sinks and expel the heated air out of the computers.

Acoustical Principles and the Human Hearing Process
When any physical object moves back and forth rapidly, this is known as vibration. The movements that occur during vibration disturb the surrounding medium, which may be solid, liquid, or gaseous. The most common sound conducting medium in our environment is gaseous: our atmosphere (i.e. the air). A. object's vibratory movements represent a form of energy. As this acoustic energy moves through the air, it takes the form of waves, sound waves specifically. The outer ear receives and amplifies the sound and transmits it to the middle ear, where tiny bones vibrate in response to the sound energy and transmit it to the inner ear. The inner ear converts the acoustic energy into electrical energy. The electrical impulses are then carried by nerves to the brain. Structures in the brain associated with hearing receive these electrical signals and interpret them (i.e. make sense of them) as sounds. The ears' reception of sound waves is auditory sensation, and the brain's interpretation of them is auditory perception.

Solar System

Solar System's Location and Components
The universe is composed of an unknown (possibly infinite) number of galaxies or star systems, such as the Spiral Nebula, the Crab Nebula, and the Milky Way. Our sun, Sol, is one of billions of stars in the Milky Way.
The solar system's planets are held in position at varying distances (according to their size and mass) from the Sun by its gravitational force. These planets orbit or revolve around the Sun. From the closest to the Sun to the farthest away, the solar system's planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Pluto was historically included as the ninth planet, but was demoted to a 'dwarf planet' by the International Astronomical
Union in 2006. Due to angular momentum, planets rotate on their axes, which are imaginary central lines between their north and south poles. One complete Earth rotation equals what we perceive as one 24-hour day. As the Earth turns, different portions face the Sun. These receive daylight, while the portions turned away from the Sun are in darkness. One complete revolution of the Earth around the Sun represents one calendar year.

Pluto
Since more powerful observatories have enabled greater detection and measurement of celestial objects, the International Astronomical
Union has defined three criteria for defining a planet. First, it must orbit the Sun. Pluto meets this criterion. Second, it must have enough gravitational force to shape itself into a sphere. Pluto also meets this criterion. Third, a planet must have 'cleared the neighborhood' in its orbit. This expression refers to the fact that as planets form, they become the strongest gravitational bodies within their orbits. Therefore, when close to smaller bodies, planets either consume these smaller bodies or repel them because of their greater gravity, clearing their orbital area/'neighborhood.' To do this, a planet's mass must sufficiently exceed the mass of other bodies in its orbit.
Pluto does not meet this criterion, having only 0.07 times the mass of other objects within its orbit. Thus, astronomers reclassified Pluto as a 'dwarf planet' in 2006 based on its lesser mass and the many other objects in its orbit with comparable masses and sizes.

Earth
Earth is roughly spherical in shape. Its North and South Poles at the top and bottom are farthest away from and least exposed to the Sun, so they are always coldest. This accounts for the existence of the polar ice caps. The Equator, an imaginary line running around Earth at its middle exactly halfway between the North and South Poles, is at 0° latitude. Sunrises and sunsets at the Equator are the world's fastest. Days and nights are of virtually equal length at the Equator, and there is less seasonal variation than in other parts of the world. The equatorial climate is a tropical rainforest. Locations close to the North Pole, like Norway, are at such high latitudes that their nights are not dark in summertime, hence the expression
'Land of the Midnight Sun." They also have very little light in wintertime. As Earth revolves around the Sun over the course of a year, the distance and angle of various locations relative to the Sun change, so different areas receive varying amounts of heat and light. This is what accounts for the changing seasons.

Rocks Found on the Earth's Surface

Sedimentary Rocks
Earth's rock types are sedimentary, igneous, and metamorphic. These categories are based on the respective processes that form each type of rock. Igneous rocks are formed from volcanoes. Metamorphic rocks are formed when igneous and sedimentary rocks deep inside the Earth's crust are subjected to intense heat and/or pressure. Sedimentary rocks are formed on
Earth's surface, and characteristically accumulate in layers. Erosion and other natural processes deposit these layers. Some sedimentary rocks are held together by electrical attraction. Others are cemented together by chemicals and minerals that existed during their formation. Still others are not held together at all, but are loose and crumbly. There are three subcategories of sedimentary rock. Clastic sedimentary rocks are made of little rock bits—clasts—that are compacted and cemented together. Chemical sedimentary rocks are frequently formed through repeated flooding and subsequent evaporation. The evaporation of water leaves a layer of minerals that were dissolved in the water. Limestone and deposits of salt and gypsum are examples.
Organic sedimentary rocks are formed from organic matter, such as the calcium left behind from animal bones and shells.

Metamorphic Rocks
Sedimentary rocks are formed on the Earth's surface by layers of eroded material from mountains that were deposited by water, minerals like lime, salt and gypsum deposited by evaporated floodwater, and organic material like calcium from animal bones and shells. Igneous rocks are formed from liquid volcanic rock—either magma underground or lava on the surface—that cools and hardens. Metamorphic rocks are formed from sedimentary and igneous rocks. This happens when sedimentary and/or igneous rocks are deep inside the Earth's crust, where they are subjected to great pressure or heat. The process of metamorphism does not melt these rocks into liquid, which would happen inside a volcano. Rather, the pressure and/or heat change the rocks' molecular structure. Metamorphic rocks are thus more compact and denser than the sedimentary or igneous rocks from which they were formed. They also contain new minerals produced either by the reconfiguration of existing minerals' structures or by chemical reactions with liquids infiltrating the rock. Two examples of metamorphic rocks are marble and gneiss.

Igneous Rocks
Igneous or volcanic rocks are formed from the magma emitted when a volcano erupts. Magma under the Earth's surface is subject to heat and pressure, keeping it in liquid form. During a volcanic eruption, some magma reaches the surface, emerging as lava. Lava cools rapidly in the outside air, becoming a solid with small crystals. Some magma does not reach Earth's surface, but is trapped underground within pockets in other rocks. Magma cools more slowly underground than lava does on the surface. This slower cooling forms rocks with larger crystals and coarser grains. The chemical composition and individual cooling temperatures of magma produce different kinds of igneous rocks. Lava that cools rapidly on the Earth's surface can become obsidian, a smooth, shiny black glass without crystals. It can also become another type of extrusive rock, such as andesite, basalt, pumice, rhyolite, scoria, or tuff (formed from volcanic ash and cinders). Magma that cools slowly in underground pockets can become granite, which has a coarse texture and large, visible mineral grains. It can also become another type of intrusive rock, such as diorite, gabbro, pegmatite, or peridotite.

Erosion
Erosion is a natural process whereby Earth's landforms are broken down through weathering. Rain, wind, etc. wear away solid matter. Over time, rain reduces mountains to hills. Rocks break off from mountains, and in turn disintegrate into sand. Weathering and the resulting erosion always occur in downhill directions. Rain washes rocks off mountains and down streams.
Rains, rivers, and streams wash soils away, and ocean waves break down adjacent cliffs. Rocks, dirt, and sand change their form and location through erosion.
They do not simply vanish. These transformations and movements are called mass wasting, which occurs chemically (as when rock is dissolved by chemicals in water) or mechanically (as when rock is broken into pieces). Because materials travel as a result of mass wasting, erosion can both break down some areas and build up others. For example, a river runs through and erodes a mountain, carrying the resulting sediment downstream. This sediment gradually builds up, creating wetlands at the river's mouth. A good example of this process is
Louisiana's swamps, which were created by sediment transported by the Mississippi River.

Living Organisms
All living organisms have fundamental needs that must be met. For example, plants that grow on land need light, air, water, and nutrients in amounts that vary according to the individual plant. Undersea plants may need less/no light. They need gases present in the water, but not in the air above the water. Like land plants, they require nutrients. Like plants, animals (including humans) need air, water, and nutrients. They do not depend on light for photosynthesis like most plants, but some animals require more light than others, while others need less than others or none at all. Organisms cannot survive in environments that do not meet their basic needs. However, many organisms have evolved to adapt to various environments. For example, cacti are desert plants that thrive with only tiny amounts of water, and camels are desert animals that can also go for long periods of time with little water.
Penguins and polar bears have adapted to very cold climates. Internal cues
(e.g., hunger) and external cues (e.g., environmental change) motivate and shape the behaviors of individual organisms.

Types of Animal Life Cycles
Most animals, including mammals, birds, fish, reptiles, and spiders, have simple life cycles. They are born live or hatch from eggs, and then grow to adulthood. Animals with simple life cycles include humans.
Amphibians like frogs and newts have an additional stage involving a metamorphosis, or transformation. After birth, they breathe through gills and live underwater during youth (e.g., tadpoles). By adulthood, they breathe through lungs and move to land. Butterflies are examples of animals (insects) that undergo complete metamorphosis, meaning they change their overall form.
After hatching from an embryo/egg, the juvenile form, or larva, resembles a worm and completes the majority of feeding required. In the next stage, the pupa does not feed, and is typically camouflaged in what is called an inactive stage. Mosquito pupae are called tumblers. The butterfly pupa is called a chrysalis, and is protected by a cocoon. In the final stage, the adult (imago) grows wings (typically) and breeds. Some insects like dragonflies, cockroaches, and grasshoppers undergo an incomplete metamorphosis. There are egg, larva, and adult stages, but no pupa stage.

Ecology
Ecology is defined as the study of interactions between organisms and their environments. Abiotic factors are the parts of any ecosystem that are not alive, but which affect that ecosystem's living members. Abiotic factors also determine the locations of particular ecosystems that have certain characteristics. Abiotic factors include the sunlight; the atmosphere, including oxygen, hydrogen, and nitrogen; the water; the soil; the temperatures within a system; and the nutrient cycles of chemical elements and compounds that pass among living organisms and their physical environments. Biotic factors are the living organisms within any ecosystem, which include not only humans and animals, but also plants, microorganisms, etc. The definition of biotic factors also includes the interactions that occur between and among various organisms within an ecosystem. Sunlight determines plant growth and, hence, biome locations.
Sunlight, in turn, is affected by water depth. Ocean depths where sunlight penetrates, called photic zones, are where the majority of the photosynthesis on Earth occurs.

Organism Reproduction
A few examples of the many ways in which organisms reproduce include binary fission, whereby the cells of prokaryotic bacteria reproduce; budding, which is how yeast cells reproduce; and asexual reproduction. The latter occurs in plants when they are grafted, when cuttings are taken from them and then rooted, or when they put out runners. Plants also reproduce sexually, as do humans and most other animals. Animals, including humans, produce gametes (i.e. sperm or eggs) in their gonads through the process of meiosis. Gametes are haploid, containing half the number of chromosomes found in the body's cells. During fertilization, the gametes combine to form a zygote, which is diploid. It has the full number of chromosomes (half from each gamete), which are arranged in a genetically unique combination. Zygotes undergo mitosis, reproducing their gene combination with identical DNA sequences in all new cells, which then migrate and differentiate into organizations of specialized organs and tissues. These specialized organs in biologically mature organisms, alerted by signals such as hormonal cues, undergo meiosis to create new haploid gametes, beginning the cycle again.

Plant Reproduction
Most plants can reproduce asexually. For example, cuttings can be rooted in water and planted. Some plants put out runners that root new growths. Many plants can be grafted to produce new ones. Plants also reproduce sexually. Plants' sexual life cycles are more complex than animals', since plants alternate between haploid form (i.e. having a single set of chromosomes) and diploid form (i.e. having two sets of chromosome) during their life cycles.
Plants produce haploid cells called gametes* (equivalent to sperm and egg in animals) that combine during fertilization, producing zygotes (diploid cells with chromosomes from both gametes). Cells reproduce exact copies through mitosis (asexual reproduction), becoming differentiated/specialized to form organs. Mature diploid plants called sporophytes—the plant form we usually see—produce spores. In sporophytes' specialized organs, cells undergo meiosis.
This is part of the process of sexual reproduction, during which cells with half the normal number of chromosomes are produced before fertilization occurs.
The spores produced by the sporophyte generation undergo mitosis, growing into a haploid plant of the gametophyte generation that produces gametes*. The cycle then repeats.

Ecological Relationships
Organisms interact, both with other organisms and their environments. Relationships wherein two differing organisms regularly interact so that one or both of them benefit are known as ecological relationships. In mutualistic relationships, both organisms benefit. For example, bacteria live in termites' digestive systems. Termites eat wood. However, they cannot digest the cellulose (the main part of plant cell walls) in wood. The bacteria in termites' guts break down the cellulose for them, releasing the wood's nutrients. Reciprocally, the termites as hosts give the bacteria a home and food. In commensalistic relationships, one organism benefits and the other one is unaffected. One example is barnacles attaching to whales. Barnacles, which are filter feeders, benefit from the whales' swimming, which creates currents in the water that bring the barnacles food. The whales are not disturbed by the barnacles. In parasitic relationships, the parasite benefits, but the host suffers. For example, tapeworms inside animals' digestive tracts get nutrients.
The hosts lose the nutrients stolen by the worms, and can sustain tissue damage because of the presence of the tapeworms.

Levels of Self-Awareness
Even newborns demonstrate differentiation of body through rooting and orienting responses, which are triggered by touching the cheek. (1)
Differentiation: At this level, children recognize correspondence between their movements and those in the mirror, and differentiate their mirror images from other individuals. They differentiate the self. (2) Situation: A. this level, beyond matching the surface properties of what they feel and what they see in the mirror, and beyond differentiating the self, children realize that their reflection is unique to their self. They also realize that their body/self and other things are situated in space. (3) Identification: A. this level, beyond differentiating and situating the self, children now identify their reflection as 'me.' When psychologists place a dot/sticky note on a child's face before s/he looks in a mirror, the child reaches toward his or her own face to touch/remove it, demonstrating self-recognition and an emerging self-concept. (4) Permanence: At this level, children identify a permanent self across time and space, recognizing themselves in photos and home movies regardless of year/age/clothing/location/setting, etc. (5) Self-consciousness/'meta' self-awareness: At this level, children recognize their self from others' perceptions/perspectives as well as their own. They experience pride, shame, and other 'self-conscious' feelings.

Progression of Self-Awareness Between Birth and Two Years of Age
From birth, infants differentiate their bodies from the environment, and differentiate internal from external stimuli (i.e. self-touch/stimulation vs. non-self/others' touch/stimulation). From two months old, babies show a sense of their body's position relative to other things in their environment.  They systematically imitate others' facial expressions and movements. They also explore and consider the environment's responses to their own actions. Additionally, they smile and socially interact face-to-face with others, showing a new sense of shared experiences. By four months, infants systematically reach for and touch objects they see, showing hand-eye coordination. From four to six months, they regulate their reaching based on their sitting/posture and balance. By six months, babies can differentiate video of themselves from that of other, identically dressed babies. Babies between the ages of four and seven months can differentiate live video of themselves from that of experimenters imitating the same behaviors. By two years, children develop an understanding of symbolic representation, and know that mirror images and pictures of themselves stand for themselves. They also start to develop language skills and develop the ability to engage in pretend play.

Factors Contributing to the Development of Interpersonal Relationships
(1) The first basic factor that contributes to the development of interpersonal relationships in early childhood is child-adult relationships. These are the earliest interpersonal interactions, and start to develop at birth. When children's needs are consistently met by adults, children learn to trust adults. In his famous theory of development, Erikson called the first stage of psychosocial development and the central conflict of infancy basic trust vs. mistrust. (2) The second factor is autonomy, which refers to making decisions and doing things for oneself. Toddlers develop autonomy.
Erikson called his second stage of psychosocial development and the central conflict of toddlerhood autonomy vs. shame and self-doubt. Children who are consistently given developmentally appropriate autonomy are more likely to respect others' autonomy, a key feature of interpersonal development. (3) The third basic factor is pretend play, which emerges as children's understanding of symbolic representation develops and they begin to use things to stand for other things. Pretending to be grown-ups engaging in adult activities helps children learn about adult skills and roles. Interacting with peers in make-believe scenarios prepares children for real-life adult interactions.
Constructive ECE approaches do not involve punishing children who have not developed sufficient interpersonal relationship awareness. Instead, they encourage adults to teach children socially acceptable behaviors and reward positive interpersonal interactions.

Interactions and Relationships with Peers 
By the time they are a year old, most babies have begun to interact with their peers, particularly when it comes to activities involving concrete objects. The development of walking and talking abilities in normally developing toddlers by the time they are two years old enables them to coordinate their behavior when playing with peers. They can imitate one another's behaviors, and can alternate roles during play, as they understand symbolic representation and can create make-believe scenarios. Pretend play increases from the ages of three to five years, as do prosocial behaviors, which include helping and caring for others. At the same time, egocentrism and aggressive behaviors decrease, as children are more able to consider others' viewpoints and feelings. Emergent social interaction skills such as these form the foundation for children's early peer relationships. When children demonstrate preferences for certain peers and choose to play and otherwise interact with them over others, this is the beginning of what will develop into preschool friendships, which are based mostly upon mutual play activities and exchanges of concrete things. Children tend to form daycare friendships with members of their own sex only over time.

Current Views on Conflict Resolution
ECE experts find that while many elementary and secondary schools have implemented conflict resolution programs, children should start learning how to resolve conflicts at younger ages. For example, experts associated with the successful HighScope EC curriculum have designed an approach to conflict resolution for children from 18 months to six years old.
The steps in EC conflict resolution are similar to those used to resolve adult conflicts in education, law, labor relations, and diplomacy. Such problem solving steps have also been found to be effective in daycares, Head Start programs, preschools, nursery schools, and kindergartens. While the steps are the same regardless of the age of the children, they are applied differently according to children's developmental levels. Adults supply much of the language to describe problems and solutions for toddlers; preschoolers can often do this themselves. After experiencing the conflict resolution process, elementary school students can frequently function as mediators for classmates. Even very young children with limited language skills should be encouraged to agree and participate through nodding, pointing, and answering yes/no questions. Conflict mediation and resolution skills help children develop lifelong problem solving and social skills.

Conflict Resolution Approach Designed for Children Between the Ages of 18 Months and 6 Years
The steps used to mediate EC conflicts resemble the steps used in adult mediation. For example, EC experts at the HighScope Educational
Research Foundation designed a conflict resolution approach for children aged
18 months to 6 years that consists of these six steps: (1) Calmly approach the children who are in conflict and stop any harmful behaviors. (2) Acknowledge what the children are feeling. (3) Collect information about the conflict. (4) Restate what the problem is. (5) Ask children to suggest possible solutions, and help them choose one together. (6) Follow up by providing support as needed. Experts find that children as young as 18 months demonstrate emergent problem solving skills. They observed young children's abilities to immediately and honestly express emotions. They noted that with adult support, children can frequently generate simple and creative problem solutions. While school conflict resolution is typically aimed at preventing violence, teaching conflict resolution skills can also help children develop the social skills needed to grow into independent, productive members of society.

Parenting Styles Identified by Psychologists
Psychologists (Baumrind, 1967; Maccoby & Martin, 1983) have identified four parenting styles:  (1) Authoritarian These parents are strict, punitive, demanding, and unresponsive. They do not explain reasons for their rules to children. Their children are obedient and proficient at completing academic/technical tasks, but they are less competent socially and less happy. They also have lower self-esteem. (2) Authoritative: This is the ideal parenting style. These parents are responsive, nurturing, and forgiving. They are assertive without being restrictive or intrusive. They set rules, but explain them. They are democratic, address children's questions and input, and use supportive rather than punitive discipline. Their children tend to be competent, successful, and happy. (3) Permissive: These parents are indulgent, lenient, nontraditional, and undemanding. They are nurturing, responsive, and communicative with children, but do not expect their children to show much maturity and/or self-control. They avoid confrontation and seldom use discipline, often acting more like friends than parents. Their children's self-regulation skills are deficient and they are not as happy as many of their peers. They tend to have difficulty with authority and perform poorly in school. (4) Uninvolved These parents are undemanding, unresponsive, and uncommunicative. They meet their children's basic needs, but are relatively detached from their children's lives. In extreme cases, these parents may neglect/reject children. Their children have low self-esteem and lack self-control.

Family Systems Theory

Characteristics of Families Affecting the Early Development of Children
Family systems theory studies the behavior of the family unit rather than the behavior of individual family members. Family behavior includes the interactions among family members and how the family unit responds to stress. Some family characteristics have been identified as particularly pertinent to ECE (Christian/NAEYC, 2006). They are boundaries, roles, rules, hierarchy, climate, and equilibrium. Hierarchy is a family's balance of power, control, and decision making. Culture, religion, age, gender, and economic status influence the family hierarchy, which shifts whenever changes occur in the family's composition. Climate refers to a family's emotional quality, and includes the physical and emotional environments in which families raise children. These environments reflect a family's belief about families and children. Family climate determines whether a child feels safe/loved/supported or frightened/rejected/unhappy in his/her family. Equilibrium refers to the family's balance and consistency. It is disrupted by stress and change, and is maintained or protected by family traditions, customs, and rituals.

Family Influences on Early Childhood Development
Family systems theory examines not individual behavior but family behavior, including communication, interaction, connection/separation, loyalty/autonomy, and responses to stress within the context of the family unit.
Family system components particularly influential in early childhood development include the following: (1) Boundaries This refers to limits, separateness, and togetherness (i.e. what/whom the family includes/excludes).
'Disengaged' families value independence over belonging, and are open to new input. 'Enmeshed' families value togetherness over autonomy, and have more closed/restrictive boundaries. (2) Roles Each family member has a role (e.g., helper, clown, peacemaker, victim, rescuer, etc.). Family members also tend to assume these roles in social, school, and work contexts. (3) Rules: Family interaction rules have long-term influences (e.g., parents who view life as predictable are likely to plan ahead, while those who view life as less controllable may not prevent/avoid problems, but rather address them as they occur). Family rules can be unspoken. Also, the rules of family cultures and school cultures can conflict. The other three of the six prominent influences on EC are hierarchy, climate, and equilibrium.

Human Socialization and Major Socializing Agencies
Socialization is the process by which individuals learn their society's norms, values, beliefs, and attitudes; and what behaviors society expects of them relative to those parameters. This learning is imparted by agencies of socialization. The family, peer groups, and leaders of opinion are considered primary socializing agencies. The family is probably the most important because it has the most significant influence on individual development. Families influence the self-concept, feelings, attitudes, and behaviors of each individual member. As children grow, they encounter peer groups throughout life, which also establish norms and values to which individual group members conform. Schools, workplaces, religions, and mass media are considered secondary socializing agencies. Schools dictate additional academic and behavioral norms, values, beliefs, and behaviors. Workplaces have their own cultures that continue, modify, and/or add to the values and behaviors expected of their members. Religions also regulate members' behavior through beliefs, values, goals, and norms that reflect moral principles within a society. Mass media communicate societal conventions (e.g., fashion/style), which enables individuals to learn and adopt new behaviors and/or lifestyles.

Influence of Institutions on the Development of Individual Identity, Relationships, Beliefs, and Behaviors
Family is the first and most important socializing agent.
Infants learn behavioral patterns from mothers. Their primary socialization is enabled through such early behaviors as nursing, smiling, and toddling. Babies soon interact with other family members. All the infant's physiological and psychological needs are met within the family. Babies learn their sleeping, eating, and toileting habits within the family environment. Babies' personalities also develop based on their early experiences, especially the amounts and types of parental love and affection they receive. School is also a critical socializing agent. Children extend family relationships to society when they go to school. Cognitive and social school experiences develop children's knowledge, skills, beliefs, interests, attitudes, and customs, and help determine the roles children will play when they become adults. In addition to family relationships, receiving reinforcements at school and observing and imitating teachers influence personality development. Peer groups that are based on friendships, shared ideas, and common interests in music, sports, etc. teach children/teens about conforming to rules and being rejected for not complying with these rules. Mass media like TV profoundly influence children, both negatively and positively.

Culture
While no single definition of culture is universally embraced, one from the cultural anthropology perspective is '…a system of shared beliefs, values, customs, behaviors and artifacts that members of society use to cope with their worlds and with one another, and that are transmitted from generation to generation through learning.' (Bates and Fratkin, 2002) Cultural groups are based on a wide range of factors, including geographic location, occupation, religion, sexual orientation, income, etc.
Individuals may follow the beliefs and values of more than one culture concurrently. For instance, recent immigrants often espouse values and beliefs from both their original and adopted countries. Traditionally, social systems like education and healthcare have approached cultural diversity by focusing on race/ethnicity and common beliefs about various racial/ethnic group customs.
These are frequently generalizations (e.g., lumping Mexican, Cuban, and Puerto
Rican cultures together and describing them as 'Latino' culture). This type of practice can lead to oversimplified stereotypes, and therefore to unrealistic behavioral expectations. Service professionals need more detailed knowledge of cultural complexities and subtleties to effectively engage and interact with families.

Collectivism and Individualism
Certain world cultures are oriented more toward collectivism, while others are oriented more toward individualism. Native
American, Latin American, Asian, and African cultures are more often collectivistic, focusing on interdependence, social interactions, relationships, and connections among individuals. North American, Canadian, European, and Australian cultures are more commonly individualistic, focusing on independence, uniqueness, self-determination, and self-actualization (realizing one's full potential). Individualism favors competition and distinguishing oneself as an individual, while collectivism favors cooperation that promotes and contributes to the harmony and well-being of the group. Individualist cultures value teaching young children object manipulation and scientific thinking, while collectivist cultures value social and relational behaviors.
For example, adults in collectivist cultures may interpret a child's first steps as walking toward the adult, while adults in individualist cultures interpret them as developing motor skills and autonomy. These interpretations signify what each culture values most, forming the child's cultural orientation early in life. The planning and design of educational and other programs should be informed by a knowledge of these and other cultural differences.

Cultural Competence

Culturally Competent Professionals
A culturally competent professional demonstrates the ability to enable '…mutually rewarding interactions and meaningful relationships in the delivery of effective services for children and family whose cultural heritage differs from his or her own.' (Shonkoff, National Research Council and Institute of Medicine, 2000) Providing interpreters and/or translators does not on its own constitute cultural competence. Hiring racially diverse educational staff in schools is also not enough. Culturally competent educators demonstrate highly developed self-awareness of their own cultural values and beliefs. They must also have and/or develop communication skills that allow them to elicit information from students and families regarding their own cultural beliefs.
Further, they must be able to understand how diverse cultural views may affect a child's education, as well as how parents/families receive, comprehend, interpret, and respond to educators' communications. Therefore, educators must develop communication skills to meet educational goals.

Aspects of Cultural Competence
It is important for educational professionals to acquire and demonstrate cultural competence at the individual level to effectively interact with individual children and their families. Moreover, cultural competence is also important at the program level, the school level, and the system level.
According to the National Center for Cultural Competence (NCCC), system level cultural competence is a continuing process that includes '…valuing diversity, conducting self-assessments (including organizational assessments), managing the dynamics of differences, acquiring and institutionalizing cultural knowledge, and adapting to the diversity and cultural contexts of the individuals and communities served.' (Goode, 2001) Individual educational interactions are informed by a knowledge of cultural diversity and of the importance of such diversity in educational settings, an ability to adapt to the population's cultural needs, and a willingness to engage in ongoing self-reflection. This same set of knowledge and skills is also applied at the system level. Family engagement is important in EC care and education. This includes understanding the developmental needs of families as well as their children, especially when families and/or children speak different languages.

Acculturation Versus Assimilation
Acculturation describes the process whereby people adapt or change their cultural traditions, values, and beliefs as a result of coming into contact with and being influenced by other cultures over time. Some cultures adopt certain characteristics from other cultures they are exposed to, and two or more separate cultures may sometimes virtually fuse. However, assimilation, wherein various ethnic groups unite to form a new culture, is different from acculturation. One dominant culture may assimilate others. A historical example is the Roman Empire, which forced many members of ancient
Greek, Hebrew, and other cultures to abandon their own cultures and adopt Roman law, military allegiance, traditions, language, religion, practices, and customs (including dress). The extent of a diverse cultural group's acculturation influences how it interacts with social systems like education and healthcare. Groups that are strongly motivated to maintain their cultural identity may interact less with mainstream systems that significantly conflict with or vary from their own cultural beliefs.

Measuring the Acculturation of Immigrants and Diverse Cultural Groups in America
Social scientists currently use indices such as people's country of birth, how long they have lived in America, their knowledge of the English language, and their level of English language use to study acculturation. However, these factors are measured not because they are the core elements of acculturation, but because they are easier to validly and reliably measure than the underlying cultural beliefs, attitudes, and behaviors they reflect, which are harder to quantify. The interactions between American educators and culturally diverse families can be problematic on both sides.
Educators have difficulty interacting, communicating, and collaborating with families that come from a variety of other countries, speak various other languages, and differ in their degree of acculturation to American culture. On the other hand, immigrant and culturally diverse families encounter a foreign language, different cultural customs and practices, and an unfamiliar educational system with different methods of assessment, placement, curriculum planning and design, instruction, and evaluation—not to mention different special education laws and procedures. Thus, the acculturation challenges related to interactions between American educators and culturally diverse families are bilateral.

Cultural Differences in Parents' Goals for Raising Their Children
Depending on their cultural group, parents have varying goals for their children, and use different practices to achieve those goals.
For example, research on four different cultural groups in Hawaii found the following differences related to what parents visualized when they pictured their children as successful adults: Native Hawaiians most wanted their children to have social connections, be happy in their social networks, and demonstrate self-reliance as adults. Caucasian American parents most valued self-reliance, happiness, spontaneity, and creativity as developmental outcomes for their children. Filipino American parents most valued the development of traits related to obedience, citizenship, respect for authority, and good conduct and manners in their children. Japanese American parents placed priority on their children's achievement, as well as their ability to live well-organized lives, stay in contact with family, and master the demands of life. Such distinct, significant differences imply that these parent groups would vary in how they would respond to young children's assertive behaviors, in their disciplinary styles (e.g., permissive, authoritative, authoritarian), and in the emphasis they would place on activities focusing on physical and cognitive skill mastery vs. social competence and connection.

Educational Services Accessed by Different Cultures
Parents in America have been found to show distinct preferences for the kinds of care and educational services they access for their children. For example, Caucasian parents in America are more likely to turn to preschool centers for help with their young children's care and instruction. This preference is influenced not only by custom, but also by scientific evidence that center-based preschool experience improves children's skills and prepares them for school. Hispanic parents in America are more likely to use home-based and/or family-based care settings. This preference probably reflects the more collectivist Hispanic perspective, which places more importance on social relationships than on structured learning in early childhood. Educators can take a culturally competent approach to such cultural diversity by looking for ways in which young children's school readiness skills can be promoted in family and home-based child care settings.

Different Views on Care, Education, and the Nature of Their Cognitive Abilities
Depending on their native culture, parents vary in terms of the early experiences they select for their young children. For example, Latino parents tend to prefer family-based/home-based care. White parents tend to prefer center-based daycare and education designed to promote school readiness.
Another cultural difference is parental beliefs about children's learning capacities. For example, research in California found that the majority of Latino parents believed their children's learning capacity is set at birth; only a small minority of white parents held this belief. Parents subscribing to a transactional child development model view the complex interaction between child and environment as creating a dynamic developmental process. These parents are more likely to value the stimulation of early childhood development, seek/implement activities that will provide such stimulation, and access early intervention services for children with developmental delays/difficulties. Parents subscribing to a view of fixed, innate cognitive capacity are less likely to believe their children's cognitive abilities can be influenced by educational experiences, and may not see the benefits of or seek out early learning stimulation and intervention.

Cultural and Other Influences and How Much Parents in America Read to Their Children
Researchers analyzing national early childhood surveys have identified significant variations in how often white, Asian, and Hispanic parents read to their young children. This variation is not solely due to varying cultural values. Additional factors include parents' financial limitations; time limitations; familiarity and comfort with accessing libraries and other government resources, websites, etc.; and literacy levels in both
English and their native languages. Educators must realize that trying to encourage or even teach parents to read to their children earlier and/or more often is unlikely to be successful if parents do not place value or priority on the benefits of being read to, or do not view the outcomes of reading aloud to children as benefits. Reading to children is known to promote school readiness and academic success. Educators should also understand that some children, despite not being read to in early childhood, become successful adults.
Additionally, some cultures, including African Americans, emphasize oral learning traditions more than written ones, developing different skills, such as the basic understanding of story flow.

Factors Affecting Parents Who Are Immigrants to America
Parents educated in other countries may not know a great deal about the American educational system, and may not be aware of the educational demands made on their children, even in early childhood. Educators need to work with these parents to find common ground by identifying shared goals for children. While culturally diverse parents may disagree with some educators' goals, they can collaborate with educators to promote those on which they do agree. Immigrant parents may also be unaware of additional services available in America for children with developmental and/or learning problems.
Educators can help parents by providing this information. Another consideration is that some other cultures have more paternalistic educational systems.
Parents from such cultures, rather than vocally advocating for their children who need services, tend to wait for teachers/specialists to voice concerns before communicating any problems they have observed. Thus, they could miss out on the chance to obtain helpful services. Even worse, educators could misconstrue their behavior as a lack of interest in children's progress, or as resistance to confronting problems.

Developmental Milestones Varying by Culture
Research has found that different cultures have different age expectations for many early childhood developmental milestones. For example, Filipinos expect children to eat using utensils at 32.4 months. Anglo families expect children to do this at 17.7 months, and Puerto Ricans expect children to reach this milestone at 26.5 months. Filipino cultures expect children to sleep all night by 32.4 months; Puerto Rican and Anglo cultures expect this at 14.5 and 14.4 months, respectively. Similarly, while Anglos expect children to sleep by themselves at around 13.8 months and Puerto Ricans at around 14.6 months, Filipinos do not expect this until 38.8 months.
Filipinos expect children to eat solid food by 6.7 months; Anglos by 8.2 months; and Puerto Ricans by 10.1 months. In Anglo families, an 18-month-old not drinking from a cup could indicate developmental delay if parents introduced the cup when s/he was one year old and regularly continued encouraging cup use. But, Filipino parents of an 18-month-old have likely not even introduced the child to a cup yet, so the fact that the child is not using a cup would not be cause for concern from a development standpoint.
When EC researchers investigated the average expectations of different cultural groups of when children would reach various developmental milestones, some of the milestones they examined included: eating solid food, weaning from nursing, drinking from a cup, eating with the fingers, eating with utensils, sleeping alone, sleeping through the night, choosing one's own clothes, dressing oneself, and playing alone. They also looked at daytime and nighttime toilet training. Educators must become aware of different cultures' different socialization goals before assuming culturally diverse children have developmental delays. On the other hand, they must also avoid automatically attributing variations in milestone achievement to cultural child rearing differences when full developmental assessments might be indicated. Family expectations and values influence the complex process of developmental assessment. When families and assessors share common cultures, it is more likely that valid data will be collected and interpreted. When their cultures differ, however, it is more likely that the assessment information will be misinterpreted. Employing EC teachers/care providers who are familiar with the child, family, and assessment setting as mediators can make developmental assessments more culturally competent.

Essential Geographical Concepts
Ten concepts considered essential to the study of geography are: location, distance, achievability, pattern, morphology, agglomeration, utility value, interaction, area differentiation, and spatial interrelatedness.
(1) Location: This concept identifies 'where' a place is and examines the positive and negative properties of any place on the surface of the Earth.
Absolute location is based upon latitude and longitude. Relative location is based upon changing characteristics of a region, and is influenced by surrounding areas. For example, urban areas have higher land prices than rural ones. (2) Distance: This identifies 'how far' a place is, and is often described in terms of location. It is also related to the effort required to meet basic life needs. For example, the distance of raw materials from factories affects transportation costs and hence product prices. In another example, land costs less the farther it is from highways. (3) Achievability: The conditions on the Earth's surface dictate how accessible a geographic area is.
For example, villages on beaches are easier to reach. Villages surrounded by forests or swamps are harder to reach. As its economy, science, technology, and transportation develop, a region's level of dependency on other areas changes.
(4) Patterns: These are found in geographical forms and in how geographical phenomena spread, which affect dependency on those phenomena. For example, in fold regions (areas where the folding of rocks forms mountains), the rivers typically form trellis patterns. Patterns are also seen in human activity that is based on geography. For example, in mountainous regions, settlements predominantly form spreading patterns. (5) Morphology: This is the shape of our planet's surface resulting from inner and outer forces. For example, along the northern coast of Java, sugarcane plantations predominate on the lowlands. (6) Agglomeration: This is defined as collecting into a mass, and refers to a geographic concentration of people, activities, and/or settlements within areas that are most profitable and relatively narrow in size. (7) Utility value: This refers to the existence and relative usefulness of natural resources. For example, fishermen find more utility value in the ocean than farmers do, and naturalists perceive more utility value in forests than academics would. (8) Interaction: This is the reciprocal and interdependent relationship between two or more geographical areas, which can generate new geographical phenomena, configurations, and problems. For example, a rural village produces raw materials through activities like mining ores or growing and harvesting plant crops, while a city produces industrial goods. The village needs the city as a market for its raw materials, and may also need the city's industrial products. The city needs the village for its raw materials to use in industrial production. This interdependence causes interaction. (9) Area differentiation This informs the study of variations among regional geographical phenomena. For example, different plants are cultivated in highlands vs. lowlands due to their different altitudes and climates. Area differentiation also informs the study of regional variations in occupation (farming vs. fishing, etc.). (10) Spatial interrelatedness This shows the relationship between/among geographic and non-physical phenomena, like rural and urban areas. The example above of village-city interaction also applies here.

Geographical Maps

General Features and Purposes
Maps can be drawn to show natural or man-made features. For example, some maps depict mountains, elevations (altitudes), average rainfall, average temperatures, and other natural features of an area. Other maps are made to depict countries, states, cities, roads, empires, wars, and other man-made features. Some maps include both natural and man-made features (e.g., a map showing a certain country and its elevations). Different types of maps are described according to their purposes. For example, political maps are made to depict countries, areas within a country, and/or cities. Physical maps are drawn to display natural features of the terrain in an area, such as rivers, lakes, and mountains. Thematic maps are drawn to focus on a more specific theme or topic, such as the locations and names of battles during a war or the average amounts of rainfall a country, state, or region receives in a given year or month. Some maps are made for more than one purpose, and indicate more than one of the types of information described above.

Basic Tools Supplied on Maps
On maps depicting local, national, and world geography, cartographers supply tools for navigating these maps. For example, the compass rose indicates the directions of north, south, east, and west. By looking at the compass, people can identify the locational relationships of places (e.g., in South America, Chile is west of Argentina). The scale of miles indicates how distances on a map correspond to actual geographical distances, enabling us to estimate real distances. For example, the scale might show that one inch is equal to 500 miles. By placing a piece of paper on the map, we can mark it to measure the distance between two cities (e.g., Washington, DC, in the USA and Ottawa in Canada) on the map, and then line the paper up with the scale of miles to estimate an actual distance of approximately 650 miles between the two cities. Map keys/legends identify what a map's symbols and colors represent.

Grids
Maps show absolute geographic location (i.e. the precise 'address' of any place on the planet) using a grid of lines. The lines running from east to west are called parallels or latitudes, and they correspond to how many degrees away from the equator a place is located. The lines running from north to south are called meridians or longitudes, and they correspond to how many degrees away from the prime meridian a place is located. To determine the absolute location of a place, we find the spot on the map where its latitude and longitude intersect. This intersection is the place's absolute location.
For example, if we look at Mexico City on a map, we will find that its latitude is 19° north and its longitude is 99° west, which is expressed in cartography as 19° N, 99° W. Numbers of latitudes and longitudes like these are also referred to as coordinates.

Reading and Analyzing a Special Purpose Map
(1) First, read a map's title and look at the overall map.
This provides a general idea of what the map shows. For example, a map entitled 'Battles of the Punic Wars' would not be a good choice if someone was looking for the political boundaries of modern day Greece, Italy, and Spain. (2) Next, read the map's legend/key to see what symbols and colors the map uses, and what each represents. For example, some lines represent divisions between countries/states; some, roads; some, rivers; etc.  Different colors can indicate different countries/states, elevations, amounts of rainfall, population densities, etc. These are not uniform across all maps, so legends/keys are necessary references. (3) Use the legend/key to interpret what the map shows. For example, by looking at colors representing elevations, one can determine which area of a country has the highest/lowest altitude. (4) Draw conclusions about what the map displays. For example, if a country map mainly has one color that indicates a certain elevation range, it can be concluded that this is the country's most common elevation.

Graphs
Graphs display numerical information in pictorial forms, making it easier to view statistics quickly and draw conclusions about them. For example, it is easier to see patterns/trends like increases/decreases in quantities using visual graphs than columns of numbers. Line graphs, bar graphs, and pie charts are the most common types of graphs. Line graphs depict changes over time by plotting points for a quantity measured each day/week/month/year/decade/century etc. and connecting the points to make a line. For example, showing the population of a city/country each decade in a line graph reveals how the population has risen/fallen/both. Bar graphs compare quantities related to different times/places/people/things. Each quantity is depicted by a separate bar, and its height/length corresponds to a number. Bar graphs make it easy to see which amounts are largest/smallest within a group (e.g., which of several cities/countries has the largest population). Pie charts/circle graphs divide a circle/'pie' into segments/'slices' showing percentages/parts of a whole, which also facilitates making comparisons. For example, the city/country with the largest population is the largest segment on a pie chart or circle graph.

Importance of Chronological Thinking to Understanding History
To see cause-and-effect relationships in historical events and explore and understand relationships among those events, students must have a solid grasp of when things happened and in what time sequence (chronology).
Teachers can help students develop chronological thinking by using and assigning well-constructed/well-written narratives. These include histories written in the same style as stories, works of historical literature, and biographies. These hold students' attention, allowing them to focus on authors' depictions of temporal relationships among antecedents, actions, and consequences; of historical motivations and deeds of individuals and groups; and of the time structure of sequential occurrences. By middle school, students should have the skills needed to measure time mathematically (e.g., in years/decades/centuries/millennia), interpret data displayed in timelines, and calculate time in BCE and CE. High school students should be able to analyze patterns of historical duration (e.g., how long the U.S. Constitutional government has lasted) and patterns of historical succession (e.g., the development of expanding trade and communication systems, from Neolithic times through ancient empires and from early modern times to modern global interaction).

Educational Standards That Demonstrate Skills in Historical and Chronological Thinking
Students should be able to differentiate among past, present, and future. They should be able to identify the beginning, middle, and end/outcome of historical narratives/stories. They also should be able to construct their own historical narratives, including working forward and backward in time from some event to explain causes and temporal development of various events, issues, etc. Students should be able to calculate and measure calendar time, including days/dates, weeks, months, years, centuries, and millennia. They should be able to describe time periods using BCE/BC and CE/AD.
They should be skilled at comparing calendar systems (e.g., Roman, Gregorian, Julian, Hebrew, Muslim, Mayan, and others) and at relating the calendar years of major historical events. They should be able to look at timelines and interpret the information they contain, and make their own timelines using equidistant time intervals and recording events sequentially. Students should be able to explain change and continuity in history through reconstructing and applying patterns of historical duration and succession. They should be able to identify the structural principles that are the bases of alternative periodization models, and to compare these models.

Reasons/Purposes for Our Country's Laws and Teaching Citizenship
Young children must understand the purposes of rules/laws:
They identify acceptable/unacceptable citizen behaviors; make society and life predictable, secure, and orderly; designate responsibilities to citizens; and prevent persons in authority positions from abusing their roles by limiting their power. Understanding these functions of laws/rules enables children to realize that our government consists of individuals and groups authorized to create, implement, and enforce laws and manage legal disputes. Some creative EC teachers have used children's literature to illustrate these concepts. Children can relate personally to stories' characters, and story situations make the concepts real and concrete to children. Stories can be springboards for discussing rules and when they do/do not apply. One activity involves children in small groups making class rules (e.g., 'No talking' and 'Stay in your seat'), and then rewriting these to be more realistic (e.g., 'Talk softly in class; listen when others talk' and 'Sit down and get right to work'). Children consider issues of safety and fairness, and develop an understanding of judicial and legislative roles.