Mathematical Processes

Problem Solving
- Achievement Objectives
- Suggested Learning Experiences

Developing Logic and Reasoning
- Achievement Objectives
- Suggested Learning Experiences

Communicating Mathematical Ideas
- Achievement Objectives
- Suggested Learning Experiences

The mathematics curriculum intended by this statement will provide opportunities for students to:

develop flexibility and creativity in applying mathematical ideas and techniques to unfamiliar problems arising in everyday life, and develop the ability to reflect critically on the methods they have chosen;

become effective participants in problem-solving teams, learning to express ideas, and to listen and respond to the ideas of others;

develop the skills of presentation and critical appraisal of a mathematical argument or calculation, use mathematics to explore and conjecture, and learn from mistakes as well as successes;

develop the characteristics of logical and systematic thinking, and apply these in mathematical and other contexts, including other subjects of the curriculum;

become confident and competent users of information technology in mathematical contexts;

develop the skills and confidence to use their own language, and the language of mathematics, to express mathematical ideas;

develop the knowledge and skills to interpret written presentations of mathematics.

Problem Solving
Developing Logic and Reasoning
Communicating Mathematical Ideas

The mathematical processes skills – problem solving, reasoning, and communicating mathematical ideas – are learned and assessed within the context of the more specific knowledge and skills of number, measurement, geometry, algebra, and statistics.

Problem solving

Achievement objectives

Within a range of meaningful contents, students should be able to:	L1	L2	L3	L4	L5	L6	L7	L8

pose questions for mathematical exploration;

effectively plan mathematical exploration;

devise and use problem-solving strategies to explore situations mathematically;

find, and use with justification, a mathematical model as a problem-solving strategy;

devise and use with justification a mathematical model as a problem-solving strategy;

use equipment appropriately when exploring mathematical ideas.

Suggested Learning Experiences

Students should be:	L1	L2	L3	L4	L5	L6	L7	L8
posing questions and setting goals for mathematical exploration

- exploring their own interests

- brainstorming possible questions for investigation

- predicting the outcomes of mathematical enquiry

- reflecting on their own work

- critically evaluating their work;

developing effective planning skills by identifying component tasks, and devising negotiating, and following sets of instructions;

choosing and using equipment and resources (including equipment and resources (including calculators, computer, and everyday objects) appropriately;

devising, using, and modifying problem-solving strategies:

- seeking solutions through trial and error, "acting it out", trying alternatives, and looking for patterns

- making lists and tables

- trying simpler cases

- being systematic , using symmetry, working backwards, marking models, and using interpolation

- trying different approaches, eliminating possibilities, and writing equations

- using and justifying mathematical models

- examining extreme cases and using extrapolation;

- drawing on skills and knowledge from a range of different content areas

Developing logic and reasoning

Achievement objectives

Within a range of meaningful contexts, students should be able to:	L1	L2	L3	L4	L5	L6	L7	L8

classify objects;

classify objects, numbers, and ideas;

interpret information and results in context;

make conjectures in a mathematical context;

generalise mathematical ideas and conjectures;

prove or refute mathematical conjectures;

critically follow a chain of reasoning;

use words and symbols to describe and continue patterns;

use words and symbols to describe and generalise patterns.

Suggested learning experiences

describing and continuing picture patterns

Students should be:	L1	L2	L3	L4	L5	L6	L7	L8

classifying and interpreting:

- categorising and sorting objects and pictures

- organising and interpreting data, using diagrams, graphs, and models

- organising and interpreting tables

- interpreting symbols;

recognising and working with patterns in a variety of forms and contexts:

- describing and continuing picture patterns

- describing and continuing word and number patterns

- describing a rule for continuing a pattern

- generalising from patterns;

developing arguments and thinking flexibly:

- making simple deductions

- making simple conjectures

- recognising logical arguments

- proving and refuting

- following a chain of reasoning

- finding logic flaws in arguments

- demonstrating methods of mathematical proof, including proof by contradiction and counter example

- proving by induction.

Communicating mathematical ideas

Achievement objectives

Within a range of meaningful contexts, students should be able to:	L1	L2	L3	L4	L5	L6	L7	L8

use their own language, and mathematical language and diagrams, to explain mathematical ideas;

devise and follow a set of instructions to carry out a mathematical activity;

record and talk about the results of mathematical exploration;

record, in an organised way, and talk about the results of mathematical exploration;

record information in ways that are helpful for drawing conclusions and making generalisations;

report the results of mathematical explorations concisely and coherently.

Suggested learning experiences

Students should be:	L1	L2	L3	L4	L5	L6	L7	L8

recording in words, pictures, and concrete materials:

- presenting diagrams (charts and graphs)

- using symbols appropriately

- displaying data in tables;

presenting mathematical ideas and results to others:

- explaining results in words and pictures

- reporting in words and diagrams

- making written and oral reports

- reporting in formal mathematical language;

explaining, discussing, and presenting arguments:

- making clear statements

- making logical and concise statements and deductions;

working co-operatively as part of a group by listening attentively, generating ideas, and participating in reflective discussion.

Assessment and Evaluation

Format

Senior courses

Mathematical Processes