1. Secondary Strategy Learning from misconceptions in mathematics

2. 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

3. Secondary Stratgey Misconceptions from early experience 1You can’t divide smaller numbers by larger ones 2Division always makes numbers smaller 3The more digits a number has, the larger is its value 4Shapes with bigger areas have bigger perimeters 5Letters represent particular numbers 6‘Equals’ means ‘makes’

4. 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

5. 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.

6. Secondary Stratgey Areas of misconceptions Topic AFractions and decimals Topic BMultiplication and division Topic CArea and perimeter Topic DAlgebraic notation

7. 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)