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:


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:


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/

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