I have been having wonderful conversations on Twitter recently with Kassia (@kassiaowedekind), Simon (Simon_Gregg), Mike (@MikeFlynn55), Elham (@ekazemi) around the topic of students making claims, more specifically differentiating between claims and conjectures. I have to admit, I have really just formed my own idea of how I differentiate between the two, so it was nice to hear others’ perspectives around this. I consider a conjecture a noticing they think to be true, more on a case by case basis. A claim, to me, becomes more generalized and then followed with a proof. (I have also had great convo with Malke (@mathinyourfeet) around these proofs w/geometry).
The conversation last night started with Kassia…(Look Kassia, I finally learned to embed tweets:)
@MathMinds Do you differentiate between claim and conjecture in your class? If so, how?
— Kassia Wedekind (@kassiaowedekind) May 3, 2015
Mike gave us a nice perspective of claims based on his work with Virginia Bastable….
My students have now started to say, “I have a claim to make” when they notice something happening over and over again. In those moments, I don’t really think about “what” they are calling it because I am just so excited to hear them talking about the patterns and regularities they are seeing. But is what they are saying a conjecture or claim? Does it make it to the claim wall to be revisited and proven? This year being my first work in really having students think about making “claims” beyond just noticings, I have made a “Claim Wall.” Students see things happening in certain cases and I ask them if they can write a statement for “any time we…” to see if they can make it more general. I like Simon’s idea to expand on my wall…
We all agreed that the proof piece is the difficult piece of going from being a conjecture or unproven claim to a substantiated, generalized claim. I find my students prove over and over again that it “works here and here and here…” but have trouble with the why. It is hard to do, even as adults putting it into words is difficult.
What I love most about these conversations is the fact that the next day it continues, but this time with the kids. Simon tweets this morning about a claim that two of his students made while folding paper…
— Simon Gregg (@Simon_Gregg) May 4, 2015
Which coincidentally would help my students tremendously to think about when proving their claim from Friday’s number talk…
— Kristin Gray (@MathMinds) May 4, 2015
The coolest part about this claim was that it stemmed from a multiplication of fraction number talk, yet they proof show division. I loved that. Also loved the explanation that accompanied their statement. I did ask them if this was true for taking half of any fraction because they seemed to be just dealing in unit fractions at this point. So is this a conjecture or a claim? I am not sure. How generalized would make it a claim? Could it be “When taking any unit fraction of another fraction…”
Would love any thoughts, conjectures or claims on this…:)
To be continued…