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Chapter 5 – Option 1 (Reflection)

02/14/2020 9:21 PM | Karen Campe

Reflect on Shawn’s problem scenario and chart on pages 81-84 and how this encouraged thoroughness among the students.  Do your curriculum materials reduce the cognitive demand on students by over-scaffolding worksheets?  What ideas does Shawn’s approach give you for changing this?


  • 02/16/2020 8:39 PM | Luke
    Part 1: Adding an additional row on the chart is such a simple idea to get students to wrestle with themselves to find all solutions for a given situation. I like the interactions between Ryan, Johnny, and Nick in this situation. Kids in my honors class would sound just like this due to their internal competitive drive to conquer a problem until the end. They have the skills, speed, and inquisitive mind that fuels perseverance. However, only a handful of students in my standard classes would see it through to the end. These kids, along with my honors kids, would be asking clarifying and confirming questions along the way. However, they would be asking for different reasons. The honors kids will ask out of fear of being wrong (the need to be right) and my standard kids would ask out uncertainty (not seeing the big picture connections). I have to believe that over time providing this type of "open-ended" adjustment to a problem would foster some willingness to compete with one's self and with others. Many students may, however, lack the drive to look for the patterns, connections, and application of foundational skills to initiate and continue with the problem.
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    • 03/23/2020 10:13 PM | Karen Campe
      I also thought that the extra row in the chart was a brilliant move. This is easy to implement in many "lab recording" sheets & other worksheets that ask students to list several ways to do some math task.

      When I taught HS Geometry, we used dynamic geometry software to investigate quadrilaterals. Students were given a general list of things they could explore, and they were asked to find "some properties" of their type of shape. Like Luke, my students in Honors Geo wanted to know if they had "enough" properties (to get the grade they aspired to get). By refusing to answer them, I encouraged more exploration and deeper understanding.

      On the flip side, students in non honors classes tended to do less investigating, and wanted to know what the minimum number of properties was. I wouldn't say what the minimum was, and kept asking "can you find another?" to encourage more perseverance.
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  • 02/16/2020 9:01 PM | Luke
    Part 2: Our curriculum materials are from Curriculum Associates. Their Instruction book provides students with a problem or two that is worked out. Students have to answer questions as to why the math used in solving the problem works. This process assumes a lot of the student and their math skills. They have to follow a train of thought that is not theirs. At the extreme, they have to be experts in math in order to "see" why the math works. The second component of the program is its Practice and Problem-Solving book. The beginning of each lesson provides an example that is solved followed by questions related to the example. On the following page are individual problems that kids have to solve using the connections/skills from the Instruction book and example on the previous page. The word problems become more complex and require the students to not only apply the learned skills but to also transfer them to similar situations. I believe the cognitive demand is high as the complexity of the applications increase. The program assumes a lot in my opinion as the daily teaching requires additional background from the teacher. Since the materials I use are application based and open-ended, I find I have to do the opposite of Shawn and provide more of the skills for the students to attempt the problems.
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  • 02/24/2020 2:57 PM | Anonymous member (Administrator)
    I love the idea of having more rows then is needed. Students often want to know how many lines they need or how many words they need in writing. I think the open-endness of a chart like this has them really think about if what they have is enough or if there are more possibilities. I also wonder about whether just having the columns with no defined rows could do the same thing or be overwhelming in the thought process. For grades 3 - 5 we use Investigations. I was combing through some lessons and often they have tables or charts students fill in, often with just the columns defined and then open space, while other times there are columns and rows with some things labeled and somethings not. I will have to pay closer attention to this moving forward and help teachers make it more about extending student thinking then limiting or stopping it at a certain point.
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