This year was the first time I’ve presented at the NCTM annual meeting. In one session, I talked about my work on helping students build justification with fractions. In the other, I presented with Megan Gundogdu about how we have been using lesson study to build capacity at a middle school in the Bronx. I really enjoyed sharing the work and I loved meeting some of you in person and learning more about what you are all working on.
I included the slides below from the justification talk for those who might want to take a closer look.
The main takeaway was that if we want to help students build justification, we need to explicitly create learning opportunities for students to:
- Reason about mathematics (using manipulatives, diagrams, contexts)
- Make connections between one’s activity with these tools and the solution
- Practice developing justifications
- Evaluate evidence used for justifications
- Revise justifications
I’d love to hear your feedback!
It would be a shame, as you say, if “justfy your answer” became as de rigeur as “and show your working”.
“Convince me that your answer is correct” might be a safer way of explaining “justification”.
There are kids who can “see” the answer” to lots of problems, and getting them to find a convincing argument may annoy them now, but should pay off in the longer term, as problems get trickier.
Any valid explanation should be ok. I am thinking of the builder, the 5 acres and the 1 and 5/6 acre building plot. To say “I say that there was 1/6 not built on, so 2 acres are accounted for, and there are another 3, so 3 and 1/6 is right” should be perfectly acceptable, without fraction bars, diagrams etc.
(on going back to the slides i see that you have said all this. I got carried away with the fraction stuff)
If I solve a quadratic equation with the formula can I justify my answer by showing that it satisfies the equation ?
I was puzzled by the “I need another beam like this one” problem. I had to read it three times before I figured out that the second calculation didn’t tell the store man how long the beam should be in Unit B units. I think feet and meters would have been more down to earth, with 3 and 1/3 feet in 1 meter.
I went to the Fraction bars site and downloaded it. —- Ouch!
Thank you for the amazing presentation at NCTM Annual Conference. I am still sharing (and processing!) all the amazing information I learned at the conference with colleagues and staff, and your presentation is one of the highlights I rave about. Thank you again, Nicola!