Transcript Learning from misconceptions in mathematics

Secondary Strategy
Learning from misconceptions
in mathematics
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)
Secondary Stratgey