The Importance Of Why.

 

As a teacher, I am always working on finding better ways of doing things and finding out "Why" I'm having students do certain things. So why do we look at the "Why" in math. 

Why is it important to discuss the why in math class as we teach algorithms, rules, and everything else.  Most students can tell you that to divide two fractions, you have to flip one and turn it into a multiplication but they can't tell you why?  

Years ago, I watched an Algebra teacher show students they needed to divide by a fraction and then multiply both sides by the reciprocal to make the denominator equal to one.  She used the proper mathematical language rather than flip and multiply.

There are at least three reasons for explaining the why to students and the best way to do it.  The first reason is that it helps deepen student understanding.  The why helps students better understand the concept. As long as students just learn the algorithms, or process, they don't have the opportunity to understand the concept.  One example is trying to explain why a negative times a negative equals a positive.  Personally, that is something I could never picture on number lines until I finally saw a wonderful explanation I can now use with my students.

Think of the negative times a negative in this context.  You pay rent or a mortgage of $1200 per month, every month.  So each month $1200 is taken out of your account thus it is -1200.  Over a year you've paid out $14,400or -$14,400.  The next year, your boss offers to pay 12 months of your rent instead so every month  is considered a negative because you aren't paying or -12 months to you and the boss is paying out -$1200 per month or -12 times -1200 or you now have $14,400 more in your budget this year.  That is the first explanation I've seen that I can use with the kids.  The why can be done with an example rather than a mathematical proof.  

Second, knowing the why can help students retain what they are learning.  When teachers rely on teaching algorithms only, students are more likely to forget the process or misremember the steps because they don't know why they are doing things. The why helps students remember.  Third, knowing why, helps increase student confidence in their ability to do math.  Many students recognize that knowing why helps connect all the dots that the algorithm doesn't. Furthermore, knowing the why explains why students do certain things in the process.

Often times, when we try to explain the why, we resort to the long mathematical explanations.  When we do that, we loose student attention.  It is better to allow students to try problems before providing the explanation of why it works.  Research indicates that even the best students can feel overwhelmed when they've gotten too much information before they've had enough time to practice a specific topic.  In other words, don't try to give them too much information, too soon, so delay until after students have had a chance to practice or they ask for the why.

So the next time, give students a chance to practice something before you provide either a visual representation or something short and precise such as the example I gave on multiplying a negative times a negative.  Let me know what you think.  Another day, I plan to discuss teaching students shortcuts and whether it is good or bad.  Let me know what you think, I'd love to hear.