Secondary Strategy

Learning from misconceptions in mathematics

Secondary Stratgey

Objectives

• To clarify differences between pupils’ mistakes, misunderstandings and misconceptions

• To discuss common misconceptions and their impact on pupils’ performance at level 5+

• To explore and discuss teaching strategies to counter misconceptions

• To model departmental discussions on misconceptions

Secondary Stratgey

Misconceptions from early experience

1 You can’t divide smaller numbers by larger ones

2 Division always makes numbers smaller

3 The more digits a number has, the larger is its value

4 Shapes with bigger areas have bigger perimeters

5 Letters represent particular numbers

6 ‘Equals’ means ‘makes’

Secondary Stratgey

1. Calculate 0.6 ÷ 3 or 1 ÷ 10

2. Calculate 4 ÷ 1/2 or 3 ÷ 1/3

3. Order 3.5, 3.45, 4 and 3.3333 on a number line

4. Compare a square of side 4 cm and a rectangle 7 cm by 2 cm

Secondary Stratgey

5. Pupils who believe that letters stand for particular numbers are probably not sufficiently familiar with the concept of a variable to make sense of the algebraic use of letters. Using ‘think of a number’ problems, for example, will illustrate the variable nature of the unknown.

6. Pupils who read ‘equals’ as ‘makes’ probably do not understand the rules of an equation:that each side of the equals sign is in some sense equal to the other. This can lead to 3x + 2 = 3 x 5 = 15 + 2 = 17 in which the absence of equality needs to be pointed out.

Secondary Stratgey

Areas of misconceptions

Topic A Fractions and decimals

Topic B Multiplication and division

Topic C Area and perimeter

Topic D Algebraic notation

Secondary Stratgey

Activities to counter misconceptions

• Collecting together different but equivalent representations of a concept or process (e.g. activities in topics A and B)

• Testing the validity of generalisations by asking whether they are always, sometimes or never true (e.g. activities in topics C and D)