New(er) Math

The way we are learning to teach math today is very different from how I learned math in the 70’s.  It’s even quite different from what we called “New Math” when my children were in elementary school ten years ago and new inquiry-based mathematics curriculums were being introduced.  Parents (including me) who had learned math the “old way” were perplexed by the new methods and wanted to just show our children “how to do it” (i.e. via memorization and algorithms).   It wasn’t until I started substitute teaching in a class that used an inquiry-based curriculum that it began to make sense.  It still seemed difficult for some children though (including my younger daughter), as this particular curriculum left the investigation tasks very open-ended and mentioning the algorithms seemed almost taboo.   It was possible for a student to do the activity and not grasp the underlying concept.  It seemed that the pendulum had swung a little too far away from direct instruction.  

The newer math curricula that I am seeing in schools now (and I presume is being widely used across the country) are a nice blend between the two extremes of "old math" and "new math".  These curricula have something for a wider variety of learning styles – those who learn best from reading, seeing, hearing and/or doing – and combine direct instruction (mini lessons) with independent practice and investigation.  I like that the algorithms are no longer ignored, but instead are introduced as a “short cut” or "more efficient method" after the underlying concepts are understood.  This not only helps the students to remember how to use the algorithms, but also when to use them and why they work.  In addition, understanding the underlying concepts of algorithms helps students gain a sense of reasonableness when using them. 

By misskprimary on Flickr

This week I had a direct experience in which my old ways of thinking about math collided with the newer math methods I am learning.  Our math methods textbook asked us to solve 76 x 89 in our heads.  The old me would have started visualizing the algorithm in my head “6 x 9 = 54, write down 4 and carry the 5 . . . “ but the new, enlightened me first thought “the answer will be about halfway between 6300 and 7200 because I can round these numbers and see that 70 x 90 is 6300 and 80 x 90 is 7200.”  Next, I started breaking the problem up in a way that I never would have done before taking Math Methods classes this year.  I converted the 89 to a “friendly number” and multiplied 90 x 70 to get 6300 from which I could easily subtract one group of 70 to get 6230 and did the same with (90 x 6) – 6 to get 534 and could now easily add these two numbers to come up with my answer of 6764.  The funny thing is that I then quickly did the algorithm to "check" my work and the answers didn’t match.  Taking a second look I realized I had made an error with my old reliable algorithm!!  Good thing it’s not too late to teach this old dog some new tricks.