Slide 1 :
Maths Misconceptions : Maths Misconceptions By: Khalid Abouzaid
Introduction : Introduction Everyone knows the feeling of struggling with a task that other people seem to breeze through. It might be programming the DVD player or even just reading maps.
Well, this is how some kids feel with maths, and their difficulties are often rooted in misunderstandings of concepts that we, as teachers, don't give a second thought to. How much could we help them make progress if we were more aware of these misconceptions, and were able to tackle them head-on? We all know, after all, that understanding our mistakes can be a powerful learning experience.
1.A number with three digits is always bigger than one with two : 1.A number with three digits is always bigger than one with two 325 > 25 right
12 < 111 right
4.6 < 3.24 wrong
why………………………………………………………..?
Slide 5 : Some children will swear blind that 3.24 is bigger than 4.6 because it's got more digits. Why? Because for the first few years of learning, they only came across whole numbers, where the ‘decimal point‘ does work. So remember to focus on the Place Value rather than the number of digits
2. When you multiply two numbers together, the answer is always bigger than both the original numbers : 2. When you multiply two numbers together, the answer is always bigger than both the original numbers 3 x 5 = 15 so 15 > 3and 15>5 right
15 x 11 = 165 so 165>15and165>11 right
½ x ¼ =1/8 so 1/8 > ½ and 1/8 > ¼ wrong
why………………………………………………………..?
Slide 7 : the product is always bigger than both the factors ,this rule works for whole numbers, but falls when one or both of the numbers is less than one. Remember that, instead of the word 'times' we can always substitute the word 'of.' So, 1/2 times 1/4 is the same as a half of a quarter. That immediately demolishes the expectation that the product is going to be bigger than both original numbers.
3. Which fraction is bigger: 1/4 or 1/8? : 3. Which fraction is bigger: 1/4 or 1/8?
Slide 9 : How many pupils will say 1/6 because they know that 6 is bigger than 3? This reveals a gap in knowledge about what the bottom number, the denominator, of a fraction does. It divides the top number, the numerator, of course. Remember Practical work, such as cutting pre-divided circles into thirds and sixths, and comparing the shapes, helps cement understanding of fractions.
Slide 10 : 1/8 1/4
4. Common regular shapes aren't recognised for what they are unless they're upright : 4. Common regular shapes aren't recognised for what they are unless they're upright
Slide 12 : Teachers can, inadvertently, feed this misconception if they always draw a square, right-angled or isosceles triangle in the 'usual' position. Why not draw them occasionally upside down, facing a different direction, or just tilted over, to force pupils to look at the essential properties? And, by the way, in maths, there's no such thing as a diamond! It's either a square or a rhombus.
Slide 13 :
5. The diagonal of a square is the same length as the side? : 5. The diagonal of a square is the same length as the side?
Slide 15 : Not true, but tempting for many young minds. So, how about challenging the class to investigate this by drawing and measuring. Once the top table have mastered this, why not ask them to estimate the dimensions of a square whose diagonal is exactly 5cm. Then draw it and see how close their guess was.
Slide 16 :
6. To multiply by 10, just add a zero : 6. To multiply by 10, just add a zero 12 x 10 = 70 but
23.7 x 10=237
, 0.35 x 10=3.5
,2/3 x 10=20/3= 6 2/3
Slide 18 : Not always! What about 23.7 x 10, 0.35 x 10, or 2/3 x 10? Try to spot, and unpick, the 'just add zero' rule wherever it rears its head, and use the concept of multiplication as repeating the addition
7. fraction: three red sweets and two blue : 7. fraction: three red sweets and two blue
Slide 20 : Have three red sweets and two blue. what fraction of the sweets is blue, how many kids will say 2/3 rather than 2/5? Why? Because they're comparing blue to red, not blue to all the sweets. Always stress that fraction is 'part to whole'.
8. Perimeter and area confuse many kids : 8. Perimeter and area confuse many kids
Slide 22 : A common mistake, when measuring the perimeter of a rectangle, is to count the squares surrounding the shape, in the same way as counting those inside for area. Now you can see why some would give the perimeter of a two-by-three rectangle as 14 units rather than 10.
Slide 23 : The perimeter :
number of squares surround the shape
The area:
Number of squares inside the shape Perimeter = 10 units Area = 6 squares
For more info : For more info www.standards.dfes.gov.uk/numeracy
www.teachernet.gov.uk/primarymaths
www.teachernet.gov.uk/maths
www.m-a.org.uk
www.atm.org.uk
www.mathsnet.net
www.curriculumonline.gov.uk