Association of Teachers of Mathematics in Maine

Chapter 6

23 Jul 2018 12:26 PM | Anonymous member (Administrator)

Figure 6.1 (p. 180) describes several types ways to promote transfer learning. What sort of mix of “hugging” and “bridging” opportunities do you give your students? Do you have a favorite task or routine that is effective for promoting transfer learning? How do you know it is effective?


How often do you have students using metacognitive strategies to assess their learning or facilitate their problem solving? What questions do you ask them to consider? How do you know those questions are effective at helping them to deepen their understanding of mathematical concepts?

Comments

  • 23 Jul 2018 6:54 PM | Anonymous member
    What sort of mix of “hugging” and “bridging” opportunities do you give your students? Do you have a favorite task or routine that is effective for promoting transfer learning? How do you know it is effective?

    I think I still do too much of the "hugging" and not enough of the "bridging." It is easy for me to make connections for the students and to ask them questions that are purposeful. Last year I implemented a new routine that had students working together in groups to solve more complicated tasks. We did this every 3 or 4 days, and the students loved it. They had to come up with their own strategies and explain why their answer did or did not make sense. The process we used took about 50 minutes of class time. I think it helped to transfer because they got better and better at problem solving as the year went on. Instead of complaining about not knowing what to do they looked forward to tasks.


    How often do you have students using metacognitive strategies to assess their learning or facilitate their problem solving? What questions do you ask them to consider? How do you know those questions are effective at helping them to deepen their understanding of mathematical concepts?

    As I mentioned above the problem solving routine asked them to reflect on their process. Students had their own think time to decide what were the important parts of the task. What did they plan to do with those important pieces of information? What about the problem made them choose a certain strategy. As the year went on their conversations deepened so that students were challenging each others thinking.

    This year I am trying out a new routine where the students will reflect on their learning every 5 classes. They will use a small group discussion protocol to see if they can form their own connections with procedures and concepts they have learned. I will ask them to reflect on similarities and differences with things we have been learning and see if they can generalize from tasks and problems we have been doing to other types of problems.
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  • 26 Jul 2018 11:01 AM | Anonymous member
    In order to reach a DOK 3 level for each performance indicator (standard), all learners are given 'hugging' opportunities to promote transfer learning. These activities usually ask learners to apply their skills and knowledge to solve various problems. Learners who extend their knowledge to the 4 level see more of the 'bridging' paths. These learners are usually asked to create their own problems to apply their knowledge in new situations.

    This year, learners are given journals in the beginning of the year where they need to make an entry everyday. In the beginning of class they will date their journal and write down what their goals are for the day. If they are starting a new learning target, they will write down the target along with the success criteria. At the end of class they will answer some reflective questions including whether or not their achieved their own personal goal that they set out to do.
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  • 26 Jul 2018 12:04 PM | Anonymous member
    When I was a classroom teacher, I taught all of the grade 6 math, and one class period of writing. I do feel that I did some "hugging," but I know that my ultimate goal in teaching was in the "bridging."
    I feel that I often tried to support transfer of knowledge within math topics (For example, I tried to show the connections between multiplication and division and ratios, or the connections between ratios and graphs, etc. ) My goal was to create independent problem solvers who could decide how to solve problems, and reason about their answers. All of the problem solving was connected to real world situations, and the goal was always to use knowledge they gained to connect to more difficult problems. I believe the areas I fell short most often in the classroom were in making cross content connections (though there were times I definitely worked with the literacy teacher to try to plan for this as much as I could), and in the creation of new and original content. I rarely had students who were academically ready for that level of thinking, and we tended to stay in the realm of solving problems, and justifying and explaining. Not that it NEVER occurred, but it was not the majority of the time.
    As a coach, I work with teachers to recognize the students who are ready for higher levels of thinking and we go to these types of tasks.

    In terms of metacognition, I did and continue to feel strongly in how I implement this and encourage and support others in implementing this. Much of the formative assessments that were implemented in my classroom involved some self-reflection. It may have been self questioning such as expecting them to ask themselves if an answer made sense or making sure that they knew what part of a problem they struggled with and what part they felt confident in prior to asking me for help. I often gave exit slips which required to not only show that they knew how to answer something they had learned, but to express how they felt about the learning for the day, and/or how actively they participated in the learning for the day. Students did self reflections on rubrics for group work for themselves and other members of the group as well.
    I love the question on page 188 (Fig. 6.3): "What advice would I have for another student who was about to start this same lesson?" I would love to try that out and see what students would say!
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