Association of Teachers of Mathematics in Maine
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Week 12: Discussion Question (Option 1)

09 Feb 2018 7:20 AM | Anonymous member (Administrator)

Do your students think they have to be right in order to talk? Do you? What can you do to welcome partially formed thinking? (p 314)

Comments

  • 09 Feb 2018 8:07 AM | Anonymous member
    I can tell that a majority of my students think they have to be right in order to talk. I do have a handful of students that don't think this way, but this tends to occur in very small classes and the students all trust each other. I don't think that students need to think that they're answers are correct in orders to share in my class but they have to think about the math. I am currently trying to encourage them to think about what is happening in the problem before shouting out the answer. I try to ask a few leading questions whenever I can to try and get some responses which partially formed thinking.
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    • 11 Feb 2018 8:05 PM | Deleted user
      In my classroom I feel that students think they need to have the right answer before participating in a discussion. Like you I am working on getting more to participate by asking questions as well.
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  • 09 Feb 2018 11:21 AM | Anonymous member
    I think a lot of my students think they have to be right in order to talk - but I do have some that will give me their best reasoning. I try to encourage the thinking by actually saying "I like your thinking" or "I like where you are going with this - tell me more" or even "who wants to volunteer what they are thinking?" "Is there another way to look at this?" Or, sometimes I go around the room to see what everyones thinking is.
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    • 19 Feb 2018 5:46 PM | Anonymous member
      I like "Who wants to volunteer what they are thinking?" :)
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  • 09 Feb 2018 1:17 PM | Anonymous member
    I am very pleased that most students no longer feel the need to be "right" in order to talk. Unfortunately, there are still a couple who do, and even that is too many. Upon reflection, it dawned on me that if I met one on one with these students, explained what I was observing, talked with them about it, etc…they may well embrace the goal of stating their thinking even when they are not sure they are right. The two students I am thinking of also have language retrieval issue so I will need to be more deliberate in "giving" them language to use to express themselves. I don't think I have done this enough, but there is still time!
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  • 09 Feb 2018 4:26 PM | Anonymous member
    My students know they don’t have to be right and I don’t think they need to as well but they need to be able to think about the answers they are giving. I go through spells where my students don’t trust what they are thinking and randomly blurt out answers. Being the first to say something is not the goal, it is to make a conjecture based on what they know or think. I have 4 small groups in a special ed setting and we tend to do many ‘think alouds’. This process requires everyone to share a piece of what they know. Many times one student will remember one piece and then we build on it from there. We learn from each other and together. The ultimate goal is to increase our independence when solving problems so we can be successful on our own.
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    • 09 Feb 2018 6:23 PM | Anonymous member
      My students know that they have the right to talk and they generally do. They are very good at listening to each other and providing positive feedback. The only issue I do have, is some students lack the confidence to talk. They will talk if called on, but they don't generally volunteer what they have do say. I do find in a partnership or small group, they do speak more. I welcome partially formed thinking by modeling it myself. I will frequently say aloud what I am thinking as I figure out a problem. Then as a class I will ask them to do the same. They are much more likely to try after they have seen me struggle through mistakes and pursue until I find the answer.
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    • 16 Mar 2018 9:24 PM | Anonymous member
      Love your comments!
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  • 11 Feb 2018 12:15 PM | Anonymous member
    Overall, I feel that my students have shifted away from thinking they have to be right to talk. I have tried very hard this year to talked to my students and provide them with activities where they learned that it isn't about getting the right answer it is about the process. One way I have got my students to become more free about talking about math is through the SnowBall Activity. I have each child complete the same word problem. Then they crumple up their work and throw it into the center of the table. Each child picks up someone else's paper and the children have the opportunity to examine someone else's work. This activity allows the children to examine and talk about math. I try to have them talk about what they noticed is the same about the way they solved the problem and the person's paper they are looking at. Then they talk about what is different. By regularly doing this activity my students' openly talk about math without the fear of needing to be right. We don't write names on our paper so this helps all children to participate without fear of judgement.

    When I was growing up I did fear talking about how I had solved a problem because I didn't want to be wrong. I didn't look at math as the process of solving a problem I thought about it as getting the right answer. Now that I am teaching students I have really tried to find ways for children to talk about math without the fear of having to get the right answer.

    Another way that I have tried to get my student's talking about math is through partner work. A couple of weeks ago, my students were working on composing shapes from pattern blocks. As the shapes they were composing became more invovled they needed more pattern blocks, but we were limited in the amount of triangles we had. A few of my students decided to work together to compose shapes so they would have enough pattern blocks. I observed these students talking together. They were communicating with each other and it wasn't just one student doing all the work. It was great to see how open the students were with eachother and they were not afraid to try new ways to complete the task.

    I feel that the current shift in math instruction has helped students to become less fearful of talking about how they solve problems and they are seeing that it is more about the process of how they got their answer then just getting the problem right.
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    • 11 Feb 2018 12:31 PM | Anonymous member
      Nice job Amanda!!! You rock!
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    • 19 Feb 2018 5:49 PM | Anonymous member
      I can immediately see how well the snowball activity works to get students talking and proving without being conscious that it is their work. Much stress is alleviated. :)
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  • 11 Feb 2018 12:44 PM | Anonymous member
    We have many discussions about how our classroom is the place where we can make mistakes and count on each other to be there as support. We have talked about the growth mindset and that mistakes happen while we are learning. I do believe most of of my students feel comfortable taking risks in math and talking without having to be right. I do still have a few who are hesitant to participate voluntarily in math discussions unless they know they are right, but will talk if called on and encouraged to share. The interesting thing is that they have valuable thinking to add to the discussion regardless of being right or not. I will continue to work on helping those few students build up their confidence and belief in themselves as mathematicians and help them to realize their contributions, right or wrong, are important.

    I myself, like to be right. I am comfortable in my classroom working with the kids and making mistakes. They are great teaching points. However, in groups with peers, I do not like the feeling of not knowing if I am right or wrong. I do not enjoy activities that force that vulnerability. When working with peer, I get stressed and the feeling of being stupid floods my body when I am not sure of something in math. I am not sure if that will ever go away completely, but I'm working on it.
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  • 11 Feb 2018 8:08 PM | Deleted user
    I believe that the majority of my students feel they need to be right in order to participate in math discussions. I do not believe this to be the case and try to encourage all my students to participate in math discussions. To encourage partially formed thinking one thing I can do as the teacher is ask more questions to prompt thinking about strategies. I can also use more partner work during the math block where students can share their thinking before coming to the entire group.
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  • 11 Feb 2018 10:17 PM | Anonymous member
    This is the biggest obstacle to group work in my math class. Kids just don't want to throw out an idea or thought about a problem i large or small groups. They fear being wrong. Being wrong is an imperfection they don't want to share in public. I encourage kids to share ideas in class discussions, praise kids that are sharing right and wrong answers, and discuss the importance of being wrong and growing from their misconceptions. But it goes back to the earlier weeks of this book talk. The confident continue to throw out misinformation and learn from their mistakes while those who lack confidence hold back, just think they are wrong and struggle to grow.
    Some of the best class discussions can come from a comment that is "wrong". Misconceptions are great springboards to discovery.
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  • 12 Feb 2018 7:13 AM | Deleted user
    At the beginning of the year most of the students felt they needed the right answer to talk. Now, most of the students know it is beneficial for them to speak up because whatever they have to say, right or wrong, is going to help us get to the correct answer. I encourage them to use what they know and venture into unknown territory when presented with new concepts.
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  • 15 Feb 2018 10:36 AM | Anonymous member
    We work really hard in our class to create a culture of risk takers. I would say the majority of students participate even when they know they might revise their thinking. We celebrate ideas and thinking, not correct answers.

    However, I do know that I have 2 students who are extremely hesitant to verbalize their thinking. I continue to support and encourage them.
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  • 15 Feb 2018 11:18 PM | Deleted user
    Hi,
    In some classes at the high school in recent years, it is very difficult to overcome some of the social group barriers that have been set in stone among students. Daring to speak by “whispering or lip-synching” their potential answer to a question is common, if I ask the whole class for input.

    For the past week or so, I have had students working in groups of three. In this small group setting students are more willing to communicate (right or wrong). Unfortunately, even in this situation there are “impatient students” that have the answer and are not willing or unable to give their peers a chance to “think” about the prompt at hand. Sometimes I have them write down possible solutions on white boards or Stickie-Notes. This allows other students time to ponder a bit longer, but means “wait-time” for students that are done.

    To encourage partially informed thinking, a question or prompt must be complex - at an analytical level that it stumps most or all students for a reasonable time period. Some of the PSAT or SAT practice questions that are not multiple-choice can come in handy. If I cut and paste several of these on a paper, the students that might come up with the answer to one of them will still have others to work on if their group peers want / need to spend more time on one question.

    These type of questions are also great ways to promote discussion about “connections” to more basic skills that will need to be combined in some way to solve a problem. Getting students to think about “what skills do I need to solve the problem” and which of those skills do I feel confident about”. I also think that discussing strategies used to solve promotes partially formed thinking.

    I observed (again) recently that “reducing fractions” is a skill that is very easy for some students, but a real struggle for others. When using proportions in the Similarity Unit, I try to give students multiple strategies for proving that fractions are equivalent, so those that aren’t confident about reducing can still work through the problem. (Note: a mini-lesson for reducing is in order, with some peer-to-peer teaching).

    Pam
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  • 16 Feb 2018 11:37 AM | Anonymous member
    One of the reasons students are placed in my small alternative math class is to build confidence. At the start of the year, we spend a couple of weeks focusing on "Growth Mindset". I find that over time my students really come to believe and feel relief and a certain excitement in the fact that the brain grows when we are struggling with trying to figure something out even if or especially if we make mistakes along the way. For the most part, after the first month or so of the year, my students are fine with thinking aloud and sharing their thoughts as they as working through a problem or strategy. They really like hearing what other students are thinking. I share my thinking as I work through problems and students join in the process with their own strategies and ideas, and it is a great way to pick up on "misthinking".
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  • 17 Feb 2018 3:43 PM | Deleted user
    The answer to this question is a double "NO" from me! Kindergarten is an important time to shape thoughts of the young minds of all answers are welcome no matter right or wrong. When I ask for answers to a problem presented to my class, the kids raise their hands with no hesitation. I welcome all answers and we work through the misconceptions making all answers successful in the end. Even misconceptions turn into a learning experience for kiddos as bringing their thinking to a new level is what we are stiving for in the end. I am thankful that my students face any math challenge with confidence and never feel that trying equals wrong.
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  • 17 Feb 2018 11:49 PM | Anonymous member
    I don't believe that my students think they have to be right in order to talk. I've tried hard to create a classroom culture where student thinking is valued - right, wrong, partially formed. I have found that being particularly enthusiastic ("Oh, I was hoping someone would ask/bring that up!") and taking that path in the discussion makes a difference in whether or not that student (and others) will take a risk.
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  • 18 Feb 2018 12:56 PM | Anonymous member
    I would say that most of my students feel they need to be right in order to talk. We are working on this by sharing ideas, thinking, and strategies - not just the answers. I loved the ideas and classroom examples in this chapter. In reading through them, I am excited to incorporate such activities, groupings, and discussions in my classroom. It's very impressive to see how students have learned the process of collaboration, are willing to take risks, and accept feedback so well. It's reassuring to see that it's possible!
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  • 18 Feb 2018 6:33 PM | Anonymous member
    It is a process having the children feel comfortable talking about their math strategies and answers. They have been getting use to talking in pairs and working on problems together. Since partners will do the sharing in front of the rest of the class, pressure is taken off the individuals. We explore different strategies and discuss what can be learned from mistakes. Actually, many times I thank children for sharing their incorrect answers since it allows us to learn from them. The children are enjoying getting out of the workbooks and exploring math in different ways. I see them enjoying the activities, the partnerships, and the discussions.
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  • 19 Feb 2018 5:44 PM | Anonymous member
    At the pre-k level, my students don't believe they have to be right to talk. They want to offer and have lots to offer. They want to be heard. It is fun to participate. For lining up, students receive a number and must go find that number on the floor and stand on it. Some figure out early on that if one lines up to receive a number first, then that person will usually be last in line when we leave the room for a special because the number is usually 20. (I always forget to mix up the numbers.) Some figure out that if it is their turn to be the leader, they save number 2 for their friend. They share what they learn with their friends. They are naturally helpful when I collect the numbers and they need to say the number they have. They love to help their friends count and tell the number to say. When the little girl last week, complained that she always gets last, I asked her why that is. She thought. We talked about her being first in line to get a number. I noticed the next day, she was last (number 20) again, but didn't complain. The day after, she wasn't last. Time to experiment is needed for what is important to the students. At very early ages, we need to encourage, not discourage speaking.

    Pre-k students not hesitating to speak is very different from many middle school students who want to hide and not be noticed. If we start early on with these methods of learning, I think it will be much easier for middle school students to feel better about themselves and willing to try to participate and feel worthy for contributing.
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  • 19 Feb 2018 9:57 PM | Anonymous member
    I DO.....think most kids are timid to raise their hands, for fear that the answer is wrong. They do not want to be embarrassed if the answer is not correct. I try very hard, even if their answer is incorrect, to try to rephrase it again to another student, but first showing acceptance of that students answer, even if it is a positive affirmation that they used awesome strategies to come to that answer. Then I may say does someone else have a different answer? I think even if their answer is incorrect, as long as we are accepting of their answers, they are more willing to make the effort of giving an answer without fear of embarrassment, or feelings of failure.
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  • 21 Feb 2018 12:18 PM | Anonymous member
    I have welcomed partially formed thinking by encouraging my students to share what they think they know about a problem vs the solution. Maybe they have an entry point or they notice something that others may not have noticed. I try to celebrate students ideas and thoughts and focus less on the solution. Sharing each journey to the solution is when I learn the most about my students.
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  • 25 Feb 2018 12:08 PM | Anonymous member
    I think the confidence of answering in discussion is dependent on the classroom climate, but also with the students own experiences. I encourage students to contribute and thank them for getting the conversation started! When students attempt to answer, but struggle, I have them "call on a friend" to help add on. Even if a first response gives a right answer I like to ask what others think and ask for "thumb feedback". Students like that and feel they can contribute at their comfort level.
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  • 27 Feb 2018 4:34 AM | Deleted user
    It was difficult this week for me to decide which prompt to answer. I think the two ideas of using white boards and not having to be right to talk go hand in hand. I have a small group of 4th graders who see me once a week for math problem solving. They sit around two large tables pushed together, each with a white board in hand. We begin our "club" time by reading a problem aloud. Often there's some new vocabulary words in the problem (integer, prime, distinct, etc.) that need to be explained. Then the students take out their white boards, talk with elbow partners, think, revise, and make sense of the problem. Sometimes they'll even come up to the wall whiteboard to work. Do they feel they need to be right? I know they're all working towards a correct answer - that's their ultimate goal, but as they're working, they often make and learn from errors. I do try to highlight some of the lessons we learn along the way. But still - due to time constraints (once again), I think I don't spend enough time honoring all thinking. My focus tends to me on alternate strategies that work - and then comparing/discussing which strategies are more efficient than others. I'm going encourage more vertical whiteboard work, and also listen for and encourage more risk-taking.
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  • 04 Mar 2018 12:21 PM | Anonymous member
    I have some students think they have to be right or want to be right if they speak. Then I have some that will blurt out whatever comes to mind without any thought or filter.

    I tend to feel that I have to be right as well. The students tend to think that I know all the answers. LOL. I do let them know that when I don't know the answer when I don't. I think out loud and try to work it out in front of them. Let them see the thinking process. If it is taking too long, I tell them that I don't really know and will have to get back to them, or sometimes they see me ask another teacher. They have also seen other teachers come in during class and ask questions of me.

    I do ask a lot of questions like, what do you think? They are opening up more. I am always encouraging and appreciative of their thoughts and wrong answer.
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  • 16 Mar 2018 9:34 PM | Anonymous member
    Some still do, unfortunately, likely due to a variety of reasons: past experience with put downs by classmates or teachers. My co-teacher and I work hard to set up a safe classroom for respectful conversations. We give students time to process and reflect and encourage them to wonder! Our students helped us create our classroom protocols for maintaining an optimal learning environment. We have discussed and presented growth mindset information meant to share with students (Jo Boaler and Carol Dweck resources, etc...).

    We encourage participation from all and emphasize that think-alouds are welcomed forms of participation as students work through their thinking. It's awesome and more and more students are feeling comfortable as the semesters go along. We teach 90 min. classes for 1/2 the school year. As teachers we also allow ourselves think aloud and work through problems as well, especially when we adapt to students' comments and questions.
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  • 27 Mar 2018 8:16 PM | Anonymous member
    My students start out talking when they know they are right. I try to push conversations by asking others to show or say how they did something different. Then we ask, "Did it work?" or "Did you figure out something when you did that?" I also have tried using sentence stems to help everyone try speaking up about working through our math. One student might use the "I agree with.......", and someone else might use the "I don't agree because......". I think more practice with sentence stems would really help my students learn to talk about math. They think it is just numbers, and they don't want to talk because they think it is more work. I would like to see them realize how talking helps them to clarify their thinking and learning.
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