It is possible that I have a slight bias, but I think math is the most important subject in school. Sadly, with today’s math teachers and curriculum, most kids will go through school unaware of the power and beauty of math.
As a math tutor of children from grade 3 to high school, I am always thinking of ways to approach concepts so that kids can “get it.” It’s not convincing to say,”this is what we do to get the right answer.” There is nothing compelling about that and it wouldn’t convince me to listen. Success is when the reaction is “cool.” Or for a complex concept, “I’m good at this!”
For the older set, grades 6 and up, I have started to use the word “efficiency.” To explain most of the processes in math, I show that we could do things the long way – but that mathematicians have come up with shortcuts or efficient ways to do things so that we can make it easier to understand and write.
8/16 is the same as 1/2 but we simplify so that it easier to understand.
5 x 6 is the same as 5 + 5 + 5 + 5 + 5 + 5 but the former is easier to write.
73 is the same as 7 x 7 x 7 but using exponents is clearer and is easier to write.
Explaining how we get to the shortcuts:
Why is it important to see what is behind the short cut? We want the child to get the process and not just memorize the shortcut.
When children learn multiplication, I show using cutouts of grid paper what each multiplication question looks like (7 x 5 is 5 rows of 7). They can count the squares to verify the answer. I teach them about squaring: a number times itself can be written as a square: 6 x 6 = 62 They see that 6 x 6 is a square – hence the name.
I explain dimensions when I talk about perimeter, area and volume. Perimeter (2 x (l + w)) is a length measurement so it is 1 dimension (cm); Area (l x w) is surface area (cm x cm = cm2) so it is 2 dimensions; and Volume is length x width x height so it is 3 dimensions (cm x cm x cm = cm3).
When explaining the exponent rules, I show how to do it the long way to derive the rule:
10 x 100 = 1000
101 x 102 = 103
So the rule is: you add up the exponents when multiplying (2 + 1 = 3). The converse applies to division of numbers with exponents.
Why do we care if our kids “get” math? My take on math is that it is the best subject for teaching our kids how to solve complex problems, apply information and rules that they know, and develop accuracy and efficiency in their problem solving. It is the most important way that we can teach our kids how to think creatively within constraints. Looking ahead to life after school, these are great tools to bring to any career.
Test for you: can you show why any number to the power of 0 is 1?
No googling the answer…