Association of Teachers of Mathematics in Maine
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Week Eight: Chapter 5B Determining the Direction of the discussion: Selecting, sequencing and connecting students’ responses

04 Mar 2014 7:10 AM | Anonymous member (Administrator)

Write a brief reflection about your learning from the discussion you held to show connections among different solutions and mathematical ideas.


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Have you ever asked students in your classes to volunteer solutions to the task that they were assigned?  What are the best and worst experiences you have had when you have used this strategy for sharing?  How do you see “selecting” as leading to a more consistent outcome?

Comments

  • 04 Mar 2014 2:35 PM | Deleted user
    One night a week I teach a college course to build the background of pre-service teachers in geometry. One of the questions this week was on measurement. I involved solving a measurement problem which included ratios.
    A length of stick was 35 paperclips long and every 5 paperclips measured the same amount as 2 rods. Students were asked to solve it many ways. The first person drew pictures and talked about groups of paperclips. Although there was an answer now on the board, 4 more people got up to explain how they would solve the problem, each with an increasingly more complicated type of approach until they were using some simple algebra. At that time I thought how closely this matched the suggestions in this book. I felt that each person added a new level of understanding. By the time the last person had explained they had managed to link the problem to proportions and algebra in general. This was a great way to share understand and matched the guidelines of the book.
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    • 05 Mar 2014 9:20 AM | Deleted user
      Yeah for you to also teach a college course. Hopefully, with your guidance we will have some great math teachers!! It is great when these experiences happen, and sometimes we just can't plan it!!!

      Donna
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  • 11 Mar 2014 2:36 PM | Deleted user
    For about 8 years, I taught the Investigations Math Program to students in grades 3 & 4. In the beginning, students volunteered to share their work during the discussion aspect, and I would call on no more than three students who raised their hand. It became just that, sharing. It was difficult to connect the ideas from one example to the next. The discussion had no meaning and I struggled to get students to connect ideas because the “selection” process was so random. So it became one student sharing, asking for questions or comments, and then the next and last one. It was just like a student sharing his weekend activities. Comments were “I like how you drew that picture,” with no in-depth discussion or true understanding of the concept we were working on.
    Over time, I learned that I needed to be more proactive with this process, but also wanted to make sure all students in my classroom had an opportunity to share their thinking- not just those who had the “best” representation. I began to choose students from the most concrete level to more abstract level of understanding, with the idea of students becoming more “efficient” as they solved problems. This method allowed students at the more concrete level see various representations and listen to the ideas of other students with a more abstract way of solving the problem. Students definitely listen to each other more than the teacher, and students then were more willing to try someone else’s idea. My students became risk takers, knowing that that they also had another method in their “tool box” if they got stuck on a problem.
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    • 20 Mar 2014 11:59 AM | Deleted user
      Donna, I appreciate the discussion of sequencing student solutions to highlight efficiency. Often what happens is students begin to discuss the idea of efficiency. They don't all pick up and use more efficient strategies, but some do. I know second grade teachers often comment about students that insist on drawing every flower mentioned in the problem.
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  • 20 Mar 2014 12:09 PM | Deleted user
    In order to have a discussion with a sequence of responses that builds mathematical ideas, teachers need to anticipate likely responses. This is a key component that doesn't always happen. Monitoring student work and planning for the roll-out of the ideas depends on the prior anticipation.

    I often have students volunteer. When we do mental math exercises, there is usually no record of strategies used. I can sometimes get to students who solve quickly and ask about their strategies, but often the sharing is "blind." With a whiteboard, several solutions can be posted and compared. Occasionally, students offer incorrect solutions, but often, they change their minds and feel good about revising answers. Tough experiences include students who get correct answers using incorrect strategies--strategies that might work only for the given numbers. It can be difficult to come up with counter examples on the spot. Such incorrect strategies yielding correct solutions can't always be anticipated.

    Selecting responses can avoid those unknowns, and it's useful when student work is recorded.
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    • 30 Mar 2014 8:07 PM | Anonymous member (Administrator)
      I agree with you Jim about needing to anticipate responses when planning a lesson and keeping track of who to have share. It was interesting to read about the tough experience. Being able to help a student understand that their strategy worked but not for the right math reasons can be tough. Sometimes other students can help with this, it really depends on the student who shared and his/her mathematical disposition.
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  • 30 Mar 2014 7:45 PM | Anonymous member (Administrator)
    Deciding who should share, what they should share, and the order in which people should share is what I'm doing while students are working. Selecting, as described by Smith and Stein, is a crucial part of my job as the classroom teacher. There are times when some students want to share and I have to plan the order of sharing so that the mathematics unfolds in a way that I think will be helpful to the whole class. When I first starting paying attention to this I didn't always plan well and sometimes the first person to share didn't really leave much for anyone else to share. I learned to plan the sharing process while students were working. I've also learned to touch base with students during their explore time. I sometimes see something that I'd like a student or a group to share and want to make sure the they are comfortable sharing, so I talk to them about what I'd like them to share and why I think it would be important for the whole class to hear from them. This usually works. If a student/or group is hesitant I ask if it's okay if I share their work with the hope that they will be encouraged to share next time. One of the sentences that really says it all is: "...through selecting, sequencing, and connecting that teachers guarantee that key ideas are made public so that all students have the opportunity to make sense of mathematics. (p 59)
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