**Common Primary Maths Misconceptions**

A. Language

1. Use the term 'sum' rather than 'calculation'.

We hear children say: 'I will do the sum 3-2'.

Sum is an addition calculation.

Difference is a subtraction calculation.

C. Shapes

1. Shape recognition

2. Angles

3. Parallel

lines?

4.

Line - Side

Common Primary Maths Misconceptions

3. Line - Side

A line has only one dimension: length. It continues forever in two directions (so it has infinite length), but it has no width at all.

A straight line connects two points via the shortest path, and then continues on in both directions.

A line segment is the portion of a line lying strictly between two points. It has a finite length and no width.

In a 2-D shape the lines are called sides.

B. Multiplication

‘multiplication makes bigger’

Is this statement always, sometimes or never true?

Doubling will make a number bigger.

Finding half of something will make it smaller.

Panorea Baka

Barnes Primary School

29/01/14

2. Numbers - Digits

Talking about numbers when referring to numbers and digits.

A digit is 'a number within a number'.

The teacher may discuss with the children sequences involving multiplying by smaller and smaller numbers to get the children thinking.

And then the teacher can provide activities in which the children have to use their understanding that multiplying does not always make bigger, such as the calculator activity.

Discussion activity:

12 x 4 = 48

12 x 2 = 24

12 x 1 = 12

12 x 1/2 = 6

12 x 1/4 = 3

9 x 9 = 81

9 x 3 = 27

9 x 1 = 9

9 x 1/3 = 3

9 x 1/9 = 1

6 x 8 is 6 lots of 8

Although this does the job, teaching the children that ‘x’ means ‘lots of’ is

not mathematically accurate

,

because this terminology suggests that the calculation needs to be carried out in a certain order.

However multiplication is

commutative

.

digits - letters

numbers - words

A digit is a mathematical symbol to represent a numeral in our base ten number system.

This emphasizes the understanding of

multiplication

as

repeated addition

.

Equivalent statements? Ask children to show that 2 statements mean the same thing.

e.g Show that 5x8 is the same as 8x5.

If the teachers have insufficient subject knowledge or if they possess the same misconceptions as their students, they will not be able to take the necessary actions to guide them into the reasonable understanding of Maths.

Misconceptions that the adults have and they pass them on to the students.

To help children recognise shapes draw them occasionally rotated, in different sizes, to force pupils look at the essential properties.

Avoid always drawing a square right angled or an isosceles triangle in the ‘usual’ position.

In maths there is not such thing as a diamond. It’s either a square or a rhombus.

Many students recognise as a triangle only the isosceles triangle because this is the prototype they are presented with since the early years.

A Y4 had 3 different triangles in front of him. He was asked which of these shapes is a triangle and he chose the isosceles prototype.

When he was asked why, he said: ''that’s the

simple

triangle because it’s the triangle that most people know''.

Many students believe that parallel lines also need to have equal lengths.

**Many students associate the length of an angle’s sides with the amount of the turn.**

Which angle is larger?

This misconception seems to be based on paying attention to the

length

of the

lines

rather than the amount of the

turn

.

Activities which emphasize the

physical

turning through an angle, with the lines used to show the starting direction, can help to avoid this misconception and will also be helpful at a larger stage when children are learning to use a protactor.

Which angle is larger?

This misconception seems to be based on paying attention to the

length

of the

lines

rather than the amount of the

turn

.

Activities which emphasize the

physical

turning through an angle, with the lines used to show the starting direction, can help to avoid this misconception and will also be helpful at a larger stage when children are learning to use a protactor.

Further thinking :

1. Can decimals or negative numbers be considered as odd or even?

2. The longer the number, the bigger it is.

3. Is 42.1 a 2 or a 3 digit number?

4. Any 2 digit number is bigger than 9.

Challenge:

How would you describe zero?

The multiplication of two whole numbers is equivalent to the addition of one of them with itself as many times as the value of the other one; for example, 3 multiplied by 5 (often said as "3 times 5") can be calculated by adding 5 copies of 3 together:

3 x 5 = 3 + 3 + 3 + 3 + 3 = 15

Here 3 and 5 are the "

factors

" and 15 is the "

product

".