Cathy Yenca gives Graphing Stories a go and the going gets tough (and interesting) when she runs into Christopher Danielson’s step-function:
The last video we tried today was Ponies in Frame. I heard the most awesome muttering as soon as the video began. “Oh! I get it. This one’s discrete.” [..] It wasn’t all lollipops and rainbows. A comment laced with negativity that resonated with Lauren and me was an outburst that “graphing used to be so easy, and this just made it hard.” How would you take a comment like that? What does that comment say about the student’s true level of understanding?
Jonathan Newman has his students analyze parametric motion by creating stop-motion videos.
Nicora Placa reminds us that the one of the best ways to assess a student’s understanding of direct proportions is to give her an indirect proportion and see if she treats it directly.
At a workshop last week, the following task caused a bit of confusion. “If a small gear has 8 teeth and the big gear has 12 teeth and the small gear turns 96 times, how many times will the big gear turn?” Several participants were convinced it was 144.
They came up with the following pre-simplified expressions for the nth step:
2n(n+1) + 3
1 + (n2 +n2) + (n+1) + (n+1)
2[n(n+1)] + 3
2n(n+1) + 3
3 + [(n+1)n] + [(n+1)n]
3+2(n+1) + 2[(n+1)(n-1)]
2n2 + 2n + 3
For each of these, I had the student put the expression on the board. I then had different students explain the thinking of the student who came up with the expression and relate it to the pictured pattern. I saw a real improvement here from when I had them do this activity the first time last week. I had many more students volunteer to explain the thinking of their cohorts and much less hesitation to work out what the terms in the expressions represented.