Association of Teachers of Mathematics in Maine

Week 4: Call to Action (Option 2)

30 Nov 2017 8:17 AM | Anonymous member (Administrator)

Re-read Julie's approach to opening questions (page 63). Next time you start a discussion with your students, ask a thought-oriented question rather than an answer-focused one. What happened?

Comments

  • 01 Dec 2017 4:45 PM | Anonymous member
    This question is a great connection to the last about "students who won't try" .

    When a student who is confident through failure often does not have a problem answering this type of question because they know through failure that they have to go through a "thinking" process to solve a problem and they are willing to share their thinking and willing to listen to feedback.

    Students who are just gaining confidence in their math ability often revel in the opportunity to "explain" what they have just done to get their answer because they know they have accomplished something they could not do before.

    The remaining students who are answer oriented and reluctant to get things wrong are often a little snippy in the middle grades. They do not want to think about the solution other than right or wrong. Even if a student has the correct answer when a thought oriented question is asked, before the answer is given, the student will often think their answer is wrong. Sometimes they even change the answer because a thought oriented question is asked. Somehow a thought provoking question triggers a flight response for these students.
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  • 02 Dec 2017 12:30 PM | Anonymous member
    I have often used comments similar to these in my classroom as I want to encourage students - I often use "I like to hear your thinking" or "what else can we think of?" Students have to have trust in the teacher in order for them to want to participate. I am so excited - after many weeks of encouraging a student - a little slow with responses but usually ends up with the right answer - that math is not a race - actually has started raising her hand. Who hoo! This approach does work - and you get to see their thinking!
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  • 04 Dec 2017 7:11 AM | Anonymous member
    I try to start each lesson with an open ended question/problem. The class gets into small groups, discusses the question for about 5 minutes, then, individually, they solve their problem. Once they have completed this part they come back together to discuss their solutions and answers. It is fun to walk around and listen to their discussions. I am constantly reinforcing that it is OK to make mistakes. Mistakes almost always lead us to the correct solution and I thank students for sharing their mistakes.
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  • 05 Dec 2017 6:23 PM | Anonymous member
    In the past I have used a number of the day routine with my students where they come up with all the ways to make a particular number. This had seemed like an open questioning approach, but as I look back on how my students were completing this routine they seemed like the children were just going through the motions and looking to get the correct answer. They would not take risks and they didn't think deeper about how they had gotten their answer. As I looked at Julie's approach it got me thinking about helping my students to think deeper and learn from each other. Lately as a result of this book study I have begun have the students examine their answers. After our first day of the routine students were really struggling to come up with ways to make a particular number, but as a group we looked at some of the solutions and discussed how trying different ways as well as taking risk help us to understand numbers deeper. The students then went back to their papers and added more ways to make the particular number. I noticed all students no matter what their level were taking risks. We have been doing this routine for a couple of weeks now and students are coming up with ways that I had never even thought of. They are thinking about the process not just what the answer was. I find myself using the words with my students "I love that you know the answer, but I want to know how you got it." I want my students to understand that it is not all about the answer and be risk takers.
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  • 08 Dec 2017 5:38 PM | Anonymous member
    Grade 5 has been working on calculating the volume of rectangular prisms. Given one dimension, they were asked to find other possible dimensions for a given volume. They discovered that they could use factors to discover possible solutions.
    They were given a new problem. 12 cube shaped boxes that contain toys need to be placed in a display shaped like a rectangular prism. How many rectangular prisms with a different-size base can be made with the boxes? Students applied their factor strategy and decided that the answer was 4. They were able to explain how they arrived at their answer. I responded, “I understand your reasoning, but could there be more than 4 solutions? They checked their factors and were certain that they were correct. I asked, “Can you go back to the problem to be sure that we answered the question?” They pointed out different-size base and determined that their 4 solutions had different-size bases. “What other strategy can we use to solve the problem?” They chose to use unit cubes. Through building the cubes using their factors, they discovered that if they changed the orientation of the structures, they changed the area of the base. The discovered that there were 10 solutions.
    This worked pretty well. It wasn't at the beginning of an exercise, but after students had completed several problems for homework.
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  • 11 Dec 2017 11:14 AM | Deleted user
    In my classroom (with very small numbers of advanced math students), students often use multiple strategies, and then they share and talk about the strategies they used. However, too often we're also headed towards verifying the correct answers. Today, two 3rd graders took the math olympiad contest and both got the last problem wrong. This was the perfect opportunity for me to say, "Not a problem, this gives us the chance to explore your reasoning." They uncovered some solid understanding but also places where they had had misunderstandings. It was quite productive and not at all threatening to them to have made errors.
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  • 12 Dec 2017 5:20 PM | Anonymous member
    It was difficult for me to think about this approach with the group of 4 and 5 year old I have this year. I spend a great deal of time modeling my own thinking for them by talking my process through out loud. One of our first activities each morning is to have one student take attendance by counting the children in class. Usually I ask the counter of the day “How many are here? How do you know?” after they complete the job. I have begun to open up the discussion by asking if there is another way to figure out how many are here and was very surprised by the response. Students talked about all the coats being in cubbies so everyone is here, some noticed there were no empty mats for group. I will be curious to see what strategies they have when someone is absent.
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  • 15 Jan 2018 2:38 PM | Anonymous member
    I acted just as a scribe for what students shared, and wrote down everything, even when they contradicted each other. By putting down the stuff that clearly couldn't be right -- or at least, one of them had to be wrong, and the class didn't know which -- I saw more students trying to join the conversation. I think I normally try a different version of this, where I might repeat what they said but not write it down, but the visual of conflicting answers seemed to make a difference.
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