Appendix: processes uncovered

(i) plan

• identify, describe and solve problems;
• inquire, explore, generate, design, measure and make;
• formulate a plan and identify sub-tasks;
• decide whether sufficient information is known;
• locate, gather and retrieve information;
• distinguish between important and irrelevant information.

(ii) strategies

• guess and check;
• make a list; draw a picture, table or graph;
• find a pattern, a relationship, and/or a rule;
• make a model;
• solve a simpler problem first;
• work backwards;
• eliminate possibilities;
• try extreme cases;
• write a number sentence;
• act out a problem;
• restate the problem;
• check for hidden assumptions;
• change the point of view;
• recognise appropriate procedures and justify them.

• use concrete materials;
• use Cartesian and other graphs to model change;
• use lines, networks, and tree diagrams to represent relationships and sequences;
• use flow diagrams to represent procedures;
• use formulae to model relationships;
• use diagrams and three dimensional models to model geometric situations; and
• apply the process of mathematical modelling to real world problems.

• restate the real problem as a mathematical problem;
• use estimation to check the solution;
• verify and interpret results with respect to the original question; and
• recognise that the best maths solution may not be the best real solution.

• sort and classify objects;
• describe objects and procedures unambiguously and give definitions; and
• organise information to support logic and reasoning.

• make and evaluate mathematical conjectures;
• infer, interpolate, and extrapolate;
• make and test hypotheses;
• make generalisations; and
• make appropriate and responsible decisions).

• draw logical conclusions;
• use models, facts, properties and relationships to provide reasons;
• justify answers and procedures;
• use patterns and relationships to analyse situations;
• develop confidence with spatial reasoning;
• develop confidence with graphical reasoning (interpretation of graphs);
• recognise the meanings of true, false and not proven; follow logical arguments;
• judge the validity of arguments;
• construct simple valid arguments;
• recognise and apply deductive reasoning;
• recognise and apply inductive reasoning;
• formulate counter examples;
• appreciate the pervasive use and power of reasoning as a part of mathematics.

• appreciate the axiomatic nature of mathematics; and
• construct proofs for mathematical assertions including indirect and inductive proofs.

• relate to others; and
• work cooperatively.

• understand what needs to be done in broad terms;
• reflect on and clarify thinking;
• relate everyday language to mathematical language, understand mathematical vocabulary;
• formulate definitions;
• express generalisations.

• follow instructions from the teacher;
• discuss difficulties;
• ask questions;
• present and explain results to others;
• discuss the implications and accuracy of conclusions;
• discuss other possible interpretations of conclusions.

• follow instructions from a text or a computer;
• debate possible courses of action with others;
• use reference material; and
• make a report.

• use graphs and diagrams to depict mathematical ideas visually;
• use symbols to represent ideas precisely;
• explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations;
• appreciate the economy, power, and elegance of mathematical notation.

• link concepts, procedures, and topics in mathematics;
• relate various representations of a concept or procedure to one another;
• recognise equivalent representations;
• see mathematics as an integrated whole.

• use mathematics in other school subjects

• use mathematics in everyday life, in work and leisure activities;
• relate results to one’s everyday experienced world.

• apply mathematics to familiar and unfamiliar situations;
• value the relationship between mathematics and history, culture and society.

• use measuring and drawing instruments.

• use simple, scientific, graphical, symbol manipulating calculators.

• use computers, and general applications such as word processing, databases, spreadsheets;
• use the Web as a resource for information;
• use specialist packages for handling and graphing data, for symbol manipulation and graphing, and for dynamic geometry.