M1Maths

Maths Skills

Mental Arithmetic       Problem Solving       Investigating       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.

Skills: Mental Arithmetic

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

• 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

Skills: Problem Solving

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

• 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

Skills: Investigating

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

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

Skills: Communicating

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

• communicate mathematical ideas effectively and in conventional style
• prove mathematical statements

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