Mathematical competency according to PISA

PISA organizes mathematical competency into three classes:
1) reproduction, definitions, and computations;
2) connections and integration for problem solving;
3) mathematization, mathematical thinking, generalization, and insight.

1) Reproduction, definitions, and computations assesses students’ knowledge of
- facts
- representing, recognizing equivalents
- recalling mathematical objects and properties
- performing routine procedures
- applying standard algorithms
- developing technical skills

2) Connections and integration for problem solving assesses students’ abilities to
- make connections between the different strands and topics in mathematics
- integrate information in order to solve simple problems
- make connections among the different representations
- decode and interpret symbolic and formal language and understand its relation to natural language

3) Mathematization, mathematical thinking, generalization, and insight assesses students’ abilities to
- recognize and extract the mathematics embedded in the situation (to mathematize)
- use mathematics to solve the problem
- analyse, interpret, and develop their own models and strategies
- make mathematical arguments, including proofs and generalizations.

A grade - wise review of math questions

Question 1
For grade 9 students
- represent patterns and relationships in a variety of formats and use these representations to predict and justify unknown values
- construct and analyse tables and graphs to describe how changes in one quantity affect a related quantity
- explain the connections among different representations of patterns and relationships

For grade 10 students
- analyse graphs or charts of situations to derive specific information
- identify, generalize, and apply patterns
- construct and analyse graphs and tables relating two variables
- describe real-world relationships depicted by graphs, tables of values, and written descriptions

Question 2
For grade 9 students
- represent patterns and relationships in a variety of formats and use these representations to predict and justify unknown values
- construct and analyse tables and graphs to describe how changes in one quantity affect a related quantity
- 9C8 solve and create tasks involving linear equations and inequalities
Note: There is no outcome in grade 9 for solving a second-degree equation.

For grade 10 students
- model and express the relationships between arithmetic operations and operations on algebraic expressions and equations
- model real-world phenomena with linear, quadratic, exponential, and power equations and linear inequalities
- identify, generalize, and apply patterns
- construct and analyse graphs and tables relating two variables
- describe real-world relationships depicted by graphs, tables of values, and written descriptions
- solve problems using graphing technology
- solve quadratic equations by factoring
- explore and describe the dynamics of change depicted in tables and graphs

Question 3
For grade 9 students
- model, solve, and create problems involving real numbers
- determine the reasonableness of results in problem situations involving square roots, rational numbers, and numbers written in scientific notation
- select and use appropriate strategies in problem situations
- represent patterns and relationships in a variety of formats and use these representations to predict and justify unknown values
- construct and analyse tables and graphs to describe how changes in one quantity affect a related quantity
- explain the connections among different representations of patterns and relationships

For grade 10 students
- apply properties of numbers when operating upon expressions and equations
- model and express the relationships between arithmetic operations and operations on algebraic expressions and equations
- model real-world phenomena with linear, quadratic, exponential, and power equations and linear inequalities
- develop and apply strategies for solving problems
- interpret solutions to equations based on context
- evaluate and interpret non-linear equations using graphing technology