Association of Teachers of Mathematics in Maine

Chapter 1 Response Choice 1

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  • 28 Nov 2018 10:49 AM
    Reply # 6936455 on 6930557

    As a high school math teacher, I teach Quadratic Functions to both an advanced and non-advanced Algebra 2 course. When I think about surface, deep, and transfer, I definitely know that there is more deep/transfer learning occurring at the advanced level. Those students have a ability to dive into the material and apply it in various contexts, while the non-advanced course focuses more on procedures. With this unit, I have incorporated ideas with geometry and calculating area using quadratic models, we have performed graph transformations to try and catch or deflect balls in different location using DESMOS, and we look into application involving gravity. We also end the unit with quadratic regression, which is basically fitting a curve to a set of data to make predictions.

    Moving forward, I would love to incorporate more deep learning into this unit, as quadratics are a baseline for a significant amount of higher STEM topics. At the non-advanced level, the applications vary from the advanced course, because those students are probably going to use what they learned for different purposes. I feel like there's definitely a deep element in both courses, but as with many math units it's more heavily weighted toward the surface level. I think a balance is crucial for math, especially when we face the "when am I going to need this?" question almost every day!

  • 28 Nov 2018 10:56 AM
    Reply # 6936492 on 6935164
    Anonymous wrote:

    When thinking about the Quadratics Unit I am about to start, I see the surface level learning that will need to happen as the foundation FOR the deeper learning that will happen once they understand what a quadratic equation is, and how each term contributes to the graph/real life situation represented. Once my students explore/understand these basic concepts we will be able to dig deeper into more problems that can be represented/solved using quadratics. 

    We begin each class with a challenge problem or two for the tables to discuss and formulate solutions to (The first day I put three parabolas on the board and ask for 2 similarities, 2 differences, and 1 question they want to ask). It is fun to see them put their heads together... even when earning the basics... and see them come up with various ways of looking at the situations and share their thoughts. The learning may be of basic facts that they need to build understanding of quadratics, but their discussions typically go deeper than I expect.  The way you phrase a question can often times lead them to not only scratch the surface, but also tap into their "what if..." gene causing them to create more questions than answers to the challenge problems. Love it when they make those statements that lead them where you wanted them to go!




    Michele, I would love to see some of the challenge problems you present for this unit! It feels often times as though the transformation into a realm where we can delve further into deep and transfer learning is going to have to be systemic. When my students are presented challenge questions, they often give up before any attempt to problem solve or have discussions.
  • 06 Dec 2018 10:19 AM
    Reply # 6948381 on 6930557

    I don't have much experience with the SOLO Model but it reminds me of the learning maps that I am incorporating into my Algebra II courses this semester.  When I break down the chapter, I think I am breaking it down into those different parts.  Students must first understand the basic vocabulary and big picture, then I begin to break it down into the deeper parts and then finish the unit with a more advanced application.  I've just finished up Rational Functions and we began by reviewing the basics of fractions, then moved into manipulating algebraic fractions, solving rational functions, and finished by exploring the graphs of rational functions.  I think there does need to be a balance in each unit, especially at the Algebra II level, and I strive to make that happen.

  • 07 Dec 2018 8:30 AM
    Reply # 6949613 on 6936492
    Anonymous wrote:
    Anonymous wrote:

    When thinking about the Quadratics Unit I am about to start, I see the surface level learning that will need to happen as the foundation FOR the deeper learning that will happen once they understand what a quadratic equation is, and how each term contributes to the graph/real life situation represented. Once my students explore/understand these basic concepts we will be able to dig deeper into more problems that can be represented/solved using quadratics. 

    We begin each class with a challenge problem or two for the tables to discuss and formulate solutions to (The first day I put three parabolas on the board and ask for 2 similarities, 2 differences, and 1 question they want to ask). It is fun to see them put their heads together... even when earning the basics... and see them come up with various ways of looking at the situations and share their thoughts. The learning may be of basic facts that they need to build understanding of quadratics, but their discussions typically go deeper than I expect.  The way you phrase a question can often times lead them to not only scratch the surface, but also tap into their "what if..." gene causing them to create more questions than answers to the challenge problems. Love it when they make those statements that lead them where you wanted them to go!




    Michele, I would love to see some of the challenge problems you present for this unit! It feels often times as though the transformation into a realm where we can delve further into deep and transfer learning is going to have to be systemic. When my students are presented challenge questions, they often give up before any attempt to problem solve or have discussions.
    Its kind of odd that the Challenge problems" I use are just "regular problems" that I ask out of the box questions about. The problems don't "scare them off" but the thinking goes deep. 

    An example would be to draw a quadratic on the board, then ask them to brainstorm everything and anything they know about the equation that could represent it. Give them 1 minute of think time with no talking to their peers (They can look through their notes to refresh their knowledge) then 5 minutes to talk to their tablemates.  They I whip around the room asking tables to share something...if other tables have that same thought they both have to erase it. We go until table has any "new" ideas to add. The table with the most number of unique thoughts (that are correct...you can ask them to clarify reasoning and tweak it as necessary) get a giant sticker. Any table with atleast 1 thing on their list that was unique gets a small sticker. They LOVED this activity! 

  • 08 Dec 2018 2:33 PM
    Reply # 6951315 on 6930557

    We started using Eureka this year and I have been impressed with how the topics that start out as surface learning are brought back into the learning in later lessons. This connection allows the students to bring what was previously surface learning to a deeper level. It's also just a great way to not let learning that was mastered back in September become obsolete through lack of use. 

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