M1Maths

Modules - Maths Skills

Mental Arithmetic       Problem Solving       Investigating

Modelling       Algorithms       Communicating

It might be argued that, for many students, skills like mental arithmetic and problem solving will be more important to them in life than being able to do things like solve quadratic equations, use trigonometry and find the mid-point of a line segment. Thus it is hoped that significant time will be devoted to skills development. Often, curricula and programs are so tightly packed with content knowledge that the teaching of skills tends to be squeezed out. However, in the longer run, having the skills can allow students to develop the content knowledge more quickly. Not only this, the learning will be more soundly based and thus better retained. This idea is elaborated here.

Devoting a quarter to a third of learning time to the skills is probably appropriate. To this end, a lot of material is provided in the modules on Mental Arithmetic, Problem Solving, Investigating and Communicating.

Investigating is a skill ignored in many programs, but it can be helpful in convincing students that mathematics is something that they can develop themselves in response to a need rather than something handed down from on high in immutable and unquestionable form and without which no progress can be made.

Unlike with the knowledge modules, each skill is presented as a single module divided into sections for the different levels.

Module:   Skills:   Mental Arithmetic

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• know the addition and multiplication facts to 9+9 and 9x9 and the corresponding subtraction and division facts

• develop, choose and use a flexible range of methods for performing arithmetic calculations mentally and on paper

• have a sense of the size of numbers; be able to estimate the result of a calculation before performing it and check the reasonableness of an answer after calculating it

Module:   Skills:   Problem Solving

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• attack problems by understanding them, trying anything, and working from both ends

  show persistence in solving problems

  use the problem solving strategies: operation, guess and check, picture, list, pattern, equation

  solve Fermi problems

  present solutions appropriately

Module:   Skills:   Investigating

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• investigate using the approach: data, pattern, show, extend

Module:   Skills:   Modelling

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• understand the process of mathematical modelling

• produce a mathematical model of a real-life situation, making and documenting reasonable assumptions and values for variables

• process the maths to produce applicable results

• apply the mathematical results to the real-life situation to generate useful information

• assess the validity and reliability of the information generated

Module:   Skills:   Algorithms

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Module:   Skills:   Communicating

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• communicate mathematical ideas effectively and in conventional style

• prove mathematical statements

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