I’ve been marinating on NCTM for a good month now, and it has been interesting to go back and read my notes and see which sessions and key points have stuck with me. A small part of me was nervous to re-read the notes, fearing that I’d be see a list of ideas that seemed great at the time but that I’d abandoned after mere weeks. I was pleasantly surprised at the percentage of what I’d written that had already found its way into my practice as an educator. Here are some of those key takeaways from NCTM that have stayed with me for the past month:

  • Teaching tricks (e.g. cross-multiply, FOIL, keep-change-flip, etc.) is tempting. It feels good to have a student learn that day. But tricks are also dangerous. Students forget what the rule is, they generalize to dissimilar contexts, they don’t generalize to similar contexts (extending multiplying binomials to binomial by trinomials). Tricks are a poor foundation; can’t build much from them. (Nix the Tricks – Cardone)
  • Teachers’ role should be like a spotter in the weight room. They should be there to help support,but just helpful enough only to keep the weightlifter from dying. (Kaplinsky)
  • Don’t praise on a right answer until you hear the process. You have to value the process more than the solution. If you praise after the right answer, nothing after that gets heard. (Kaplinsky)
  • In problem-based learning, problems generate student need-to-knows, and math is what saves the day. (Krall)
  • You’d be surprised how eager people not in education are to help those in the service of education. When you want to do a real-world problem, bringing people in from the outside adds a lot of value to the problem. Consider cold e-mailing out of the blue. (Krall)
  • “Assessment is at its best when it is ongoing and most difficult to distinguish from the teaching that is occurring”  – Martin Kniep G. & Picone-Zocchia, J. (Krall)
  • With digital learning systems, be mindful of transactional (Student enters an answer, Computer or “teacher” spits something back) vs. interactional. We need more interactional, like Desmos activities. Teaching and learning is interactive, after all. Big concern about digital learning is going individual, which is not good for students. Students need real interactions. (Confrey)
  • “Your job is not to make them drink, it’s to make them thirsty” (can’t remember).
  • When a student says a correct answer, our job isn’t to nod. It’s to look for soft spots in their thinking. (Parker)
  • “All models are wrong. Some are useful” (Meyer)

Phil Daro, co-author of the Common Core, had two memorable sessions that had point after point that I wanted to write down. To paraphrase some of these key points that are still resonating with me one month later:

  • Lessons should be taught in thirds. 1st third is problem posing, developing the question and students working. 2nd third is student presentations of how they solved the problem (sequenced from most concrete to most abstract). Final third is teacher taking the reigns and illustrating grade-level thinking related to the problem. If any direct instruction, it comes in that final third, carefully scripted to reflect the essence of the mathematics of the lesson
  • Teaching is live. It’s interactive. Like a game of chess, where next moves are anticipated, but plans can change.
  • Do not sacrifice sense-making for coverage. Tricks and shortcuts may save time in the short-run, but this is not mathematics. On this, you can build nothing but misconceptions.
  • Don’t think in terms of “What standard am I teaching today?” This isn’t the way to look at mathematics. Teaching grade-level standards isn’t a real thing. Progressions extend over time. We’re always teaching multiple standards at once – looking back at some and peeking ahead at others. When mathematicians do math, they often prove things by tracing a topic back to basics (number lines, counting). This is considered deep mathematics, not remedial.
  • Successful video games provide low-threshold feedback (dings, vibrations). Every time the player does something, the game has to respond. The player has to be in control, and there needs to be evidence of it. In response to the question, “What motivates humans?” To quote Piaget: “The joy of being the cause.” Math class should reflect this.
    • Having difficulty when playing a video game doesn’t mean failure; it just means you haven’t succeeded yet. Video game designers: “Why would we tell any user that they failed our game? They’d never come back.”
  • In English class, the teacher gives the same essay prompt to the whole class, and the strong writers finish LAST. In math class, strong students finish first and want to move on to something new. We should find curricula that makes math class more like English class in that way.

I’m fascinated by what at NCTM stuck for me and what didn’t. I’m 100% sure that a different person could have attended the exact same sessions I did and come away with totally different memorable moments. What was meaningful to me had everything to do with my mental state of mind and the questions I’m pondering about my profession. With that in mind, I’ll post my full Google Doc of notes soon – maybe reading them will provide people with takeaways that didn’t initially jump out at me.

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