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  • Christine Pomatto

    June 11, 2022 at 6:35 pm

    I have been incorporating some curiosity path elements into my teaching for a few years after completing long-term professional development on task-based learning in 2019 and reading Peter Liljedahl’s book Building Thinking Classrooms last year. However, some of my lessons have remained direct instruction, in part because we are often taught that’s the best way to do it with special education students (I’m not sure that’s true).

    I chose one of my most teacher-led lessons to transform using the curiosity path. I’m not 100% sure I’m there, but it’s definitely better than it was before. I’m using the suggestion that the “spark” doesn’t have to be a real-world application: it can be math-based from the get-go.

    The lesson: converting fractions into decimals. I usually just teach them to turn the fraction bar into a division sign, and then we practice it.

    The lesson, reworked using the curiosity path:

    (Important background information: I teach 7th grade special education math. Many of my students have very low number sense. I hope to change that with lessons like this that help them think about the number line conceptually.)

    • Withholding information: I show an empty number line. Only the ends are marked, but not with numbers, just tick marks. I put down one 1/4 fraction tile starting at “0” (the first tick mark).
    • Anticipation: I think this will build some anticipation because students won’t have enough information to know what we’re going to do today. However, they might have some ideas about what information they might need. They might even be able to anticipate the question.
    • Notice & Wonder: I would expect the following types of comments: The tile is yellow. The tile says 1/4. The tile takes up about 1/4 of the length of the line (a stretch, but maybe someone will say it!). And the following types of questions: Why did you put that tile on the line? Are there supposed to be numbers on the line? What are the numbers? How many of those tiles could you fit on the line? And the question I hope they ask, in some way: What decimal number does the 1/4 reach to?
    • Estimate: Based on students’ questions during Notice & Wonder, I could begin to reveal some information. The first things I would reveal would be the 0 and the 1. I’d ask them to make estimates that are too low, too high, and their best guess. Then, I would reveal the 0.5. I’d ask them to revise their estimates. I think I would begin to get students guessing 0.2 and 0.3 at this point.

    From this point, I might consider “guiding” students to the right answer. But more than likely, I’ll leave their best guesses on the board or on chart paper for us to revisit later. I’d then repeat the process with several more fractions, starting with 3/4, but maybe building up some confidence with 2/5 or 4/5 first. I could keep track of all their “best guesses” on the board.

    I’m not sure how to wrap up this lesson. It would be easy to say “Okay now, let me tell you a trick: all you do is divide the numbers,” but I think I’d like them to try discovering it in some way. Does anyone have suggestions? The best I can come up with is to give them a calculator and an equivalent fraction–decimal pairing, asking them to figure out what they could type into their calculator to turn 1/4 into 0.25. I may also do some sort of matching activity where students have to match fractions (with pictures on the number line) to decimals. I could even do a separate notice and wonder there.

    I’d love any feedback you can give, since this lesson doesn’t have a clear conclusion. Thanks!