“But I don’t think I understand, either from their article, Smith’s talk in Florida this summer, or your summary here, how you hold each student accountable for knowing every way to solve the problem. Can you help me out with that?”

I agree with Chris that accountability for making connections and tracing the logic of another student strategy is more the focus than being accountable for being able to use all of the strategies. Using re-engagement lessons has been a way that I have accomplished this in the past. The idea is that students will take a look at completed strategies from work they have previously engaged in with a group. The group analyzes the work and unpacks the logic so that each student can explain and justify the strategy.

I typically followed up such a session by having student discuss and debate the strategies for efficiency or breadth of application. Often I would challenge groups or individuals to apply one of the unfamiliar strategies to a novel problem.

Re-engagement lessons are a great way to respond to ‘worked problem’ camp that utilized that practice in a way that still quotes student work and remains student-centered.

]]>Your post got me thinking along the lines of another simple noncommutative example – subtraction. If f(x) = x – 3 (i.e. “input minus three) then I can see that the inverse function is clearly g(x) = x + 3 (i.e. “input plus three”). But if I start with f(x) = 3 – x (i.e. “three minus input”), I cannot concur that the inverse will follow the same pattern as before (i.e. “three plus input”). In fact, here I must think of the original function in a completely different way in order to arrive at an inverse through introspection (“f says ‘take the opposite of the input and add three’, so the inverse will need to say ‘subtract three and then take the opposite’. g(x) = -(x – 3)”

I guess, we don’t really have language for describing 2^x in a completely different way; thus the need for creating one to define the inverse with logarithms.

]]>Yes, we are all big fans of Zan at Desmos. She’s a great mind and a great spirit!

]]>Trying to figure out what kids are thinking (like in this post) is the most intriguing part of this job. I am excited to read about what you observe in the kindergarten classroom!

Tyler

P.S. Congrats on getting to work with the Desmos crew. I think they just hired a college friend of mine: Zan Armstrong. She is great!

]]>When I tried patterning like this with my preschool-2nd grade kids awhile back, they all agreed that patterns had to repeat exactly. ABABAB, or ABCABC, but not ABCBA or ABABBABBB. I would lay out a row of tiles, asking if I had a pattern. “No … no …” They seemed concerned or almost sorry for me when my patterns didn’t repeat — pitying my inability to make it work. And then they cheered when I got one “right.” :)

]]>Cheers and good luck my friend! ]]>