Home > Common Core > Turtle Multiplication and Conceptual Understanding

## Turtle Multiplication and Conceptual Understanding

Math teachers love algorithms.  I think one of the reasons I love math so much is that there are rules to follow.  I know that says a lot about my personality.  When I was in the classroom, my students would say, “Just show me how to do it.”  I also heard, “I can follow the steps and get the right answer, but I have no idea what I am doing.”  Unfortunately, I could relate to these students.  Much of my math career as a student was like this.  It was only when I began to teach it that I truly understood the whys and hows of math.  I think this is one thing Common Core will fix for students.  They may hate it and resist it at the beginning, but they will retain it.

When I was in the classroom, I was guilty of reducing mathematics to an algorithm.  I taught cute tricks like “Outers over Inners” to simplify complex fractions.   I think all teachers are guilty of this at some point.  I came across this video in an elementary classroom that testified to this:

http://www.teachertube.com/viewVideo.php?video_id=77588

The teacher was teaching students how to multiply a two digit number by a two digit number.  I had heard from several teachers how great this “new” method was for students.  It is so cute!  I had to bite my tongue.  If you watch the video, my questions are “Why does the turtle drop an egg?” and “Why do we draw a collar on the turtle?”  I need students to understand this.  What happens if I have a three digit times a two digit?  Does turtle multiplication still work?  I need conceptual understanding that transcends to problems of varying types.

Here is how I would love to see multiplication by two digit numbers taught:

http://www.teachertube.com/viewVideo.php?video_id=154703

What are your thoughts?  Are we hurting students by teaching cute algorithms in isolation?  Is procedure really what matters?  What other “tricks” do we teach that hinder conceptual understanding?

Categories: Common Core
1. November 16, 2013 at 4:04 pm

Yes! Yes to all of this. I’m working on a project doing exactly what you described. Please check out NixTheTricks.com and leave some comments. This month I am trying to typeset what we have so far. I’ll figure out how to get that on to the website soon but the PDFs are on my blog for now.

• November 16, 2013 at 4:39 pm

I love your site! Thank you for sharing. I’m so excited that you have started this effort. I will definitely spend some time on your site. Thank you for visiting my blog.

2. November 17, 2013 at 2:21 am

You’re a better person than me. I would have bit their tongues, not mine. Because the turtle thing is truly terrible.

But, yeah, I’ve been guilty of this. My two bits on cute mnemonics: http://reflectionsinthewhy.wordpress.com/2012/01/23/bacon-and-eggsponents/