The Multiplication Sundae and the Bad Taste of Incentives

Earlier this week I received an email asking for incentive ideas for a school wide fact fluency focus:

Hi Graham,
I need some insight about math facts and incentive programs. I follow your site and have read Not Your Mom’s Flashcards:Conceptual Understanding of Multiplication and watched From Memory to Memorization: There is a Difference. I know facts are about being efficient, accurate and flexible. With that said our school would like to start an incentive program to encourage students to learn their facts. Ex. In the hallway, picture of student and medals earned and a quarterly bingo math party with snacks and prizes. I am all about balance but… I want to make sure we do what is right for all students. My principal would like an incentive program for facts and I want to lead us in the right direction.

If you search the Internet, there are tons of incentives for fact fluency and the Multiplication Sundae is a big seller.  But the problem I have with the sundae is that some kids never even earn the bowl, let alone the ice cream. And the cherry? It doesn’t stand a chance!

In the same week, I was reminded why incentives for fact fluency crush my soul.  I was at my daughter’s award ceremony, she’s a 3rd grade student. During the presentation they awarded all students that had mastered their multiplication facts with an award. There were a handful of students from her class that earned this award. As a dad, I was proud because my daughter received the award but I know she learned her facts the right way.  But what absolutely crushed me is the other 17 students in her class that didn’t receive the award and how they now believe they’re not good at math.  So I’ll ask the question…Is the award worth it?

I really appreciate the email and all the work we do as teachers to motivate our students but now I can’t escape 2 questions:

  1. Is there an incentive idea/program that addresses equity? An idea where EVERY student can be successful?
  2. What role (if any) should incentives play in our schools?

I like to think if we can’t address question #1 with “yes” then question #2 is answered for us…incentives don’t belong.


About gfletchy

K-8 math consumer trying to listen and learn each day. Stay thirsty my friends!
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10 Responses to The Multiplication Sundae and the Bad Taste of Incentives

  1. I too have a third grader and she has done well with the fact fluency focus in her classroom. What breaks my heart is that I’ve watched my daughter go from someone who is flexible in thinking about quantity to someone who is rigid in her thinking and now holds the belief that that there is a specific way to “do math.” She now has latched onto the idea that doing math is about being fast and knowing the answers. This is not the message I’m trying to promote in my district.

    I recently blogged about my own experience as a child with this sort of emphasis and how it lead to dead ends by middle school. I think knowing facts from memory is important, but it’s not what math is all about. Programs like this not only promote inequity, they also promote the wrong messages about math to kids who do well w/in such programs. It’s a loss for everyone.

  2. Steven says:


    We see the ramifications teachers confusing fluency with memorization in middle school. Middle schools students (and elementary as well) who are not given the opportunity to develop a conceptual understanding of multiplication before they are asked to memorize their facts really have their mathematical thinking stifled before it even begins. The resulting lag in numeracy development continues throughout for the students. Teachers who say “it just makes harder math easier” when the kids “know” their facts miss the underlying point of the importance of the need to develop a student’s own strategies to understand any problem. If we can somehow continue to swing the pendulum towards conceptual understanding first and foremost I think the “harder math” gets easier and easier, even without the facts being memorized.

    Thanks for all of your work and dedication to math and reasoning:)

    • Steven, thank you so much for writing this! I hear it all the time – students need to know basic facts so they can do the harder math. Then, we apply flimsy practice that leads students to dead-ending in their math journey.

  3. stamp36 says:

    I agree with you Graham they are not equitable and push the idea further that some people are math people. I could not memorize my math facts and no one showed me strategies. My daughter like yours is now learning them the right way. I feel if we create engagement, spark curiosity and create growth mindsets it will create intrinsic incentive. Have you heard for George Couuros? May have spelt his last name wrong. Lol. He is a speaker that came to our board and is on Twitter all the time talked about creating the intrinsic need to want to learn and be successful. He was totally against reward systems in schools and what he said made a lot of sense. If you haven’t heard of him follow him on Twitter. I think both of your questions are extremely valid. My heart goes out to those kids in your daughters class who never got an reward. I was one of those students!! I luckily had hockey to boost my confidence and esteem or I probably would have been totally crushed by my schooling experience. Hopefully that school looks at other options.

  4. xiousgeonz says:

    It should be possible to have “incentives” or rewards which honor progress and send a message that if you didn’t get the award, it’s because you haven’t gotten to *that* *particular* *point* in the scavenger hunt (as opposed to a straight line) … yet.
    If I had influence on one of the 17, that’s what I’d be espousing.
    It’s not an exact match to your situation, but I find especially frustrating when people say “I know you’re right about this and this and this… but I’m going to do things this way anyway. Aren’t I a good listener???” They genuinely think they are (but hey, they are *so* much wiser than anybody else, right???).

  5. deschatjes says:

    when my daughter was in Grade 2 or 3 and was confronted with the times tables, she sat down with a little notebook and then wrote out all the tables, 2 to 12. Then a little while later she came to me and said “look mum, there’s a pattern in all of them except for the 7 times tables” and showed me how the last digit had a repeating pattern. At that point I knew she would be ok and never obsessed about her learning the “maths facts” of times tables. She’s now in G8 and going on to do ad maths in iGCSE next year. She tells me she’s still one of the slowest in her class on the maths facts but that she’s a good problem solver. And I’m happy with that too. I also like that she has some meta-cognitive skills and can analyse where she is in her learning.

    • gfletchy says:

      Love the fact that your daughter recognize the importance of problem solving and not memorization. Kudos to her…and her mom:-)
      Thanks for sharing your story deschatjes and reminding us all of what’s important.

  6. Pingback: Math Coach Update: Year 3 - darcmathcoach

  7. Ink says:

    You rock! I noticed that you have the suggested order for teaching multiplication linked in two different places. One has the nines following ones and the other has threes following ones. I can see where the strategies for 9 might be easier using knowledge of multiples of 10 and should be before threes. Which order are you recommending? 2, 5, 0, 1, 3 or 2, 5, 0, 1, 9

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