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  • Amy Johnson

    December 5, 2021 at 8:33 pm

    I have evolved from being able to compute proportions to seeing how the computations work and how these ideas of ratio thinking and rate reasoning build a conceptional understanding of proportionality. I would love to go back to high school algebra with this understanding. I think I would have not felt like I got lucky when I did well on a test. I never understood why students would tell me they guessed and just got lucky that it was right. I think this statement is that they haven’t had enough experiences to realize that they were using ideas that make sense without confidence but they are really on the way to truly understanding.

    I think another a-ha that I have about these concepts is that they build from such early math experiences and it isn’t about being told a fact and memorizing it. I never really considered that these ideas build from counting up to multiplication. My own fraction sense and the idea of multiplying by a reciprocal is so much stronger just because I had experience with the concept concretely and with models. I now have models that I can use with my students.