Association of Teachers of Mathematics in Maine

Prompt 1 - Option B

24 Oct 2014 6:00 AM | Anonymous member (Administrator)

Observe or record a mathematics lesson. Use the "Teacher and student actions" chart (p. 24) to evaluate how the lesson applies to the Mathematical Teaching Practice Implement tasks that promote reasoning and problem solving. What evidence do you see of the teacher and student actions listed in the chart? Where do you see missed opportunities for these teacher and student actions? Give specific examples of evidence of this Mathematics Teaching Practice and ways to enhance the practice in future lessons.

Comments

  • 09 Nov 2014 2:03 PM | Anonymous member
    To introduce Unit Analysis to my Pre-Algebra students I gave them this problem: if I were to pick up one of my students and throw him/her down the hall at 60 miles per hour, how far would the student travel in one second? The students were to use any strategy they wished to come up with an answer. After a few minutes of the students working with a partner, I recorded the answers on the board and the class discussed which answers seemed most reasonable and which arithmetic procedures seemed thorough. At this point, I did not comment on the correctness of any of the answers and didn't do so until the students had learned the unit analysis process with rates (several days later.)

    Only about half the students actually tried finding an answer to the problem even though I encouraged them to use calculators and answered questions of how many feet are in a mile. I need to find some methods that encourage all the students to persevere in tackling unfamiliar problems. All the students participated in the discussions about which answers seemed reasonable vs. unreasonable; however, the students who offered to share their strategies had difficulty in justifying why they chose specific processes.

    As a teacher I need to include more tasks like these in my daily teaching, and somehow find a way to encourage students to persevere while holding them accountable in their efforts.
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    • 13 Nov 2014 10:07 AM | Anonymous member
      Hi Julia,

      I love the question you posed! Really catches the attention of the students. Perhaps when you pose unfamiliar questions you can use a modified think-pair-share strategy to encourage students to persevere in problem solving. Have the students first think on their own, writing down what comes to mind (strategies they may use, what operations would be useful, what formulas they might need, etc.). Next have them pair up and share their thoughts, this allows them an opportunity to collaborate and start to attack the problem. After some time has passed, join up 2 pairs to make a group of four to share what they have completed thus far. Finally, have the groups of four work together to solve the problem and then share whole class!
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  • 09 Nov 2014 8:12 PM | Deleted user
    These subtraction stories in the reading reminded me of a recent conversation I had with a student. We were working on operations with polynomials. The activity was a floor plan of a house. The students had to find missing sides of rooms. One of my algebra 2 students had no problem finding area (multiplication), find the length of the house ( addition), but when she had to use subtraction there was no comprehension. I tried to explain a number of ways that she was given the length of the kitchen and part of the opposite length how would she find the remaining part. Finally, I had her draw out the room using colored markers, she was able to see the connection. An example of Math Practice: Model with Mathematics.

    I realize I didn't respond to the prompt, but the subtraction incident in an algebra 2 class has me shaking my head.
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  • 11 Nov 2014 9:43 PM | Anonymous member (Administrator)
    I like the multiple ways that are shown with subtractions. I believe this is true with most concepts in mathematics. There are multiple ways to represent the concepts and multiple ways to problem solve. This also provides opportunities for different levels of complexity too so we can reach the higher-level tasks.
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  • 14 Nov 2014 2:22 PM | Deleted user
    My math curriculum is largely exploration based. My biggest struggle is in supporting the students with out taking over student thinking. When my students are stuck I do ask questions to try to move them along, but after several attempts without any movement I find myself doing the thinking for them and talking my way through the problem. I feel my students have low perseverance and I need to find away to encourage greater perseverance.
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    • 30 Nov 2014 1:14 PM | Anonymous member (Administrator)
      I try to keep these questions in mind when I work with my students:
      Why do you think that ... ?
      How do you know that ... ?
      Can you tell me more about ... ?
      What if [this thing changed somehow] ?
      What do you think about ... ?
      The questions would be tailored to the situation. My students get frustrated with me sometimes, especially when I don't tell them the answers that they want to hear. And especially when all I do is pose more questions. But in doing so, I am helping them to develop perseverance. They know that I'm not going to give them "the answer." They have to work together, or on their own, to figure it out.
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  • 01 Dec 2014 9:00 PM | Deleted user
    I video taped a bit of two different math lessons. When I view the sessions, I can see how inattentive and distracted many students are, even in a small sized group such as I have. The inattention is very difficult to overcome. When I can plan an activity that gets everyone working at the same time with their own materials, they are definitely more engaged. I found that I was articulating our new learning for the lesson and relating it to methods learned prior to this one. Our program teaches multiple methods to solve problems so students may land on one they prefer, but they get an opportunity to try three different methods. We were learning about making ten while practicing two digit addition. We were learning a method called new groups below. I tried to get students to articulate how the method was different from one they already know (new groups above). It is difficult. They certainly need more practice in conversation around their understanding of math. The why of learning is interesting. They don't seem to mind the multiple method approach. They like telling about their preferences, and how one method is better for them. We practiced proof drawings as well to show how grouping ones made a new ten but they didn't really pick up on this aspect of the drawings. They missed the purpose of the proof!
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