In my previous article, I mentioned that giving more Math homework to students who are weak may not really help them to improve.

I believe the solution is not about More Practice. It’s about HOW you practice.

What do I mean by this?

Many students, (not just teenagers, but us adults included) we do things without really thinking about them. Students tend to just do their Math work without critical thinking. The students whom we call “mathematically gifted” or “smarter than me” are so-called smarter because they know how to think critically and most of them do so unconsciously.

Take a look at the following example :

Solving Simultaneous Equation is probably the easiest topic in SPM Add Math. It’s just a direct question, find x and y by substitution.

Skills required to master this topic ?

1) Algebra skills (addition, minus, multiply and divide)
2) Fraction calculation skills
3) Negative numbers skills
4) Transfer of variable from Left Hand Side to Right Hand Side.

All these skills are learnt in Form 3.

So most students will just do this question without thinking. They don’t ask –

” What is the purpose in finding x and y?, what does it actually mean – find the value of x and y?, Does the value x and y that I find here actually represent something else? What is an equation actually?:
“where else / what other chapters will I need to do this – solving 2 equations?” “how else can I apply this type of question?”

Asking questions will prompt the brain into critical thinking, which is sadly something very lacking among students in Malaysia. As a result, we see many students who are weak in Application Questions because they don’t know how to “relate” the Math Concepts and apply accordingly.

Coming back to the example above –

Solving Simultaneous Equation, finding x and y is very very important as it is the Intersection Points of 2 lines on a graph.

 
If students were to ask the questions I put up earlier, they would know that

1) each equation represents 1 line on the graph.

2) The linear equation represents a staight line,

3) the non linear represents a curve.

4) The straight line will cut the curve at 2 points.

5) Therefore the values of x and y that you find will be in 2 pairs.

6) Each pair represent the coordinates of the 2 intersection points.

And – now here’s the ultimate reason why asking questions and thinking critically when doing Math work is so important.

Check out this question below.

Look at Question 8a)

Many students will stare at the question 8a) for a long time with a blank in their head.

Why?    because they are unable to relate  Form 4 Chap 4 Simultaneous Equation with this graph which is from Integration Chap 3 Form 5.

How do you find the value of k then?

Try it and let me know your answer :)

PS :- Check out Part 2 of this article here.