Unit 1: First Impressions

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    Kayla Marceniuk

    1. Math Tells Us Something About How it Should Be Taught
    2. The Brain is Plastic
    3. Working Memory is Limited
    4. Minds are Attuned to Change
    5. Minds Link Overlapping Events

    In what ways do the five Math Minds principles resonate with your current views about teaching and learning mathematics?
    Every individual creates unique connections the material that is taught. For example, some students may notice on their own that division and fractions are two sides of the same coin. Others may see fractions visually, and struggle to understand how it connects to division. Knowing that students create unique connections furthers ones understanding of why students work at different paces. Some students may struggle with core concepts, while still being able to understand certain complex concepts solely based on how they make connections between learned materials. (i.e. I understand algebra, but negative numbers are hard to wrap my head around).
    Always review previously needed concepts before introducing something new, introduce manipulatives, have students follow along with pen & paper.

    In what ways do they challenge your current views?
    I think the biggest challenge to my views so far is #1. I understand how we can see connections within Mathematics, how our brain adapts to new information, creating connections and altering our understandings to take in and apply new information. What I’m challenged by is how Mathematics tells us how to teach it. I can see that we start with a base concepts (numbers), expand on it (positive and negative), elaborate on applications (addition etc). What confuses me is knowing where math wants us to take it next. Do we choose for ourselves if we branch into, say, fractions, or is math trying to steer us towards a different concept and we don’t realize it? Thus, are we unintentionally missing key concepts or learning opportunities not only for ourselves but for our students?

    In what ways do they prompt you to think about things you may not have considered before?
    The biggest take away so far has been from the Long Division Lesson. The pacing, the information, the time given for self study, and then the realization that students require an involved approach. Sitting and listening won’t get them where they need to be (which should seem obvious). The lesson prompted me to think about how to create hands on lessons for mathematical concepts that seemed to have no immediate hands on option outside of following along with pen and paper (which for most people is not the most attention grabbing method). I thought about the use of manipulatives, the use of a concept board to show connections, and how to get students involved in teaching the concepts. It’s all still a work in progress though.

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