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Chapter 3 – Option 1 (Reflection)

01/31/2020 10:59 PM | Karen Campe

Write about obedience versus risk taking in mathematics. What came to mind when you read the passage on page 31?  What are you thinking now or what questions do you have?


  • 02/02/2020 9:32 PM | Luke
    When I first read the passage in the book and then again in this prompt, my knee jerk reaction is Yes, of course, students have to be obedient with the procedures of math. It is all about rules, steps, definitions and remembering... It's math. However, I find obedience versus risk-taking to be a constant struggle in myself, my teaching and my students. I think too that age (and ability) is a huge factor. In the primary grades, kids need time to explore, think, connect and build an initial understanding of math. However, as kids advance in their math career and build foundation skills they may, to a lesser degree, need less time to explore. I think kids need a solid skillset in order to access the math. However, having a deep understanding of the why and how is important in building the foundation of skills. Which do you teach first? Can you only teach one and not the other? In my current position, I feel that a majority of the kids lack the skillset (obedience?) to take risks. However, one could argue that a student may not have the skillset because s/he does not have a conceptual understanding because they did not "pursue the meaning" p. 31 before learning the routine. I find myself telling my students that they can all "do math" it is the student skills that get in the way. Most of the math I do involves basic facts of the four operations. It is sometimes hard to connect ideas and generate conjectures when the math operation stands in their way. Also, many kids carry their frustration from the year before and may feel defeated before they begin.
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    • 02/03/2020 11:45 AM | Patty Chenail
      I couldn't have formed a response any better than this. It is exactly what I too am grappling with. I am finding that as 8th graders/Algebra 1 students the majority are lacking the skillset to take risks. More than 50% of my population is diagnostically between grade 2 and 5 in what their brains are ready to learn. Despite this, I am working really hard and employing the techniques presented in this book! I'm focusing on the fact that math is all around us and trying to focus on what they can do.
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      • 02/04/2020 8:15 PM | Luke
        Sometimes the routine of skill practice and the ability to do something so trivial with success is far more beneficial than doing x, y, or z. Repetition of skill brings a calm to the room and a much-needed break from looking for an answer/connection that is based on understanding (having mastery of) a skill that is not mastered year after year.
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      • 02/07/2020 10:07 PM | Karen Campe
        I also feel that it is easier to take problem-solving risks once you have the basic skill-set.

        I've tried to combat this with problems like Shawn's triangle area problem in which more than one geometric skill could be used to solve. I would endeavor to share problems like these with multiple approaches.

        I've also become more flexible in my arithmetic strategies, which is a new challenge for me with my background in secondary math. There is a Twitter chat every Wednesday hosted by Pam Harris @pwharris called #MathStratChat (also on Facebook); Pam sets an arithmetic problem such as 4/5*10/3 or 72% of 250 or 36*76 or 39.01-9.95 and asks us to come up with clever, efficient, or unique solution strategies.

        Both of these categories would be fertile ground to help students build that skill-set so they can take risks on the next problem.
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  • 02/06/2020 3:44 PM | Jen Maxwell
    This chapter really resonated with me and the current goals I am working on with the teachers in my district. Earlier this year, I took Robert Kaplinsky's online Problem Solving workshop. He discussed the idea of intellectual autonomy. I have shared his shepherd problem with many of the teachers I work with. When given a word problem that didn't make any sense, students still plucked the numbers out of the problem and preformed some operation to arrive at an illogical answer. I started discussing this with the teachers and we realized that our kids are afraid to take risks. Since they were young, they have been told that math has a right answer and that they shouldn't question the teacher. We are trying to change that mentality and starting in kindergarten, we are encouraging our students to question each other AND the teacher. We are providing them with low floor high ceiling tasks and intervening only when necessary to promote their ability to take risks. Our students need to learn at a young age to question information presented to them and to ask clarifying questions when they do not understand. We have also experimented with inquiry based lessons that encourage students to discover the math on their own without being told the rule first.
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  • 02/07/2020 9:57 PM | Karen Campe
    Looking back on my years in high school and middle school classrooms, I fear that my teaching fell on the side of math as obedience to rules… learn these procedures to achieve success. I definitely didn’t model or encourage risk-taking to forge new directions.

    I am glad that I enabled some deep understanding by embracing the idea (page 32) that students can learn & take ownership of math that is new to them, despite the fact that other mathematicians have covered this ground already. One of my teaching approaches is to let students explore a mathematical situation, observe and reflect on a consequence, and build mathematical meaning for themselves (always followed-up by a class summary so that the important learnings are highlighted and interesting tangents are available for investigation).

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  • 02/25/2020 5:56 PM | Becky
    I feel very torn between the practicality of students needing to know basic facts and operations with automaticity in order to make mathematics simpler for them to manipulate when the concepts get more difficult and actually taking the time to let them discover why 2+8 is 10 and how 10-2 is 8. I struggle with having my young students memorize facts, I even made all the cute posters, file folders and contests to urge them along. Then I stopped and thought about why they just weren't getting it. I can not tell you how much time I spent covering base ten in so many different ways that next year giving plenty of time for discovery and risk taking and how big it paid off for me and my students. It is counter-intuitive for sure in math to move through bigger concepts without demanding obedience in learning basics because we as adults know it will make it easier BUT maybe that is simply not true. Maybe allowing kids to discover for themselves makes learning facts and other necessary ideas for more difficult math concepts actually easier. Now how do I do this? That is what I am struggling with now in my position as a behavioral resource room special educator who needs to help most students deal with math and who also has to teach a couple lower level students their individualized math. Grades 6-8 come with all kinds of attitude then add in my student's disabilities and it's a tricky place to be.
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