Learning, Math

Failure is a Prerequisite…And 2 Math Gems

Have I mentioned I love Gaping Void?  Good.

Here is one of their latest posts:



The cartoon was accompanied by the text: “it’s something we tell our children every day”.  

Do we?

Sometimes I wonder.

My kids use Khan Academy for math.  At the moment we are working on fractions (fourth graders) and we have just started to move into unchartered waters for some students.  They are unsure.  They don’t know what they are doing.  They are scared to fail.  I can see it in their hesitation, their avoidance of tasks that are deemed “too hard”.  So, what to do?

Today, I decided to show them the coaches report that I generated for the links we are working on at the moment.  It looks like this:

Khan Academy


For those of you who are unfamiliar, red means “struggling”, grey is “not yet started”, the pale blue means “practiced”, slightly darker blue means “level one”, darker still means “level two”, and the darkest blue is “mastered”. When I pulled this graph up, there were a few gasps around the room.  Struggling!  Red! Oh no! I got everyone’s attention on the board and said, “There are some people I am very concerned about according to this graph.  Do you know who they are?”

Of course, “the red people” was the chorus around the room. When I asked why, the response was that those people were not doing good, that they didn’t know, that they were failing.

No, I told them.  They are not the people I am concerned about. I am concerned about the grey people – the ones who are yet to try.  If you are in the red or in the blue, I know how to help you, how to move you on from where you are at. If you won’t try or haven’t tried, how can I know how to help you?  You might fail, yes.  But you might succeed too.  And I know that if you do move to the red, you won’t be there for long because “failure is the prerequisite for learning”.

I promised you “2 math gems” = and here they are:


Gem #1

If you are at all like me, you have written a test for students that requires them to show their work. Well, last weekend, I read this article that invites students to choose whether or not they show their working.  The ideas behind this option are sound and really made me question why I ask this of my students and wonder what the consequence is on thinking in my students.  The author, David Ginsburg, goes on to suggest mixing up the usual “show your thinking” question with a different take on the format: He suggests giving students a completed equation and asking them to explain why it is or is not correct.  This naturally means they have to explain their thinking.


Gem #2

Via one of my favorite blogs, Engage their Minds, I was introduced to the math version of Would You Rather…? It is awesome – and just happened to have a fraction problem up today which suited us perfectly.

Would You Rather....?

A quick run-through of the site shows me that some decent math skills are required but there is also the element of personal choice BUT you must explain your choice MATHEMATICALLY (not just based on personal preference).  It is really cool – check it out. I can see kids making these for each other too.  And if you have younger kids, Terri from ETM, has created some Would You Rather questions for Valentines Day with a slightly lower level of math skills needed.  Check it out!


5 thoughts on “Failure is a Prerequisite…And 2 Math Gems”

    1. You inspire me with your commitment to sharing your passion. Really. I am in awe. And only a tiny bit jealous 🙂 I love all that you share and read everything – even when I don’t have time to comment. Thanks so much for being so generous with your art!

  1. Hey, Sonya. Thanks for introducing me to Gaping Void; love those. Your ‘show your work’ problems remind me of my introduction to programming problems: we have similar types of problems and the scenarios and suggestions you’ve given are very applicable to my classes.

    We also do another variation on this that might work in your class: a ‘fix this’ problem. This is a bit lower skill level than your example. I give the students a complete piece of code and tell them the intended inputs and outputs. Then I tell them it is ‘broken’ and have them explain how to fix it. For a mid-level student, this is the step beneath ‘is it correct or not’ and they can just focus on how to make it correct.

    Thanks for enriching my teaching, and my life.

    1. This sounds good. I like the removal of one of the parameters. Makes the focus easier for some, for sure. We should catch up soon! Saddle up a camel and head over anytime! 🙂

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