Friday, June 28, 2013
Sometimes a student whose confidence is quite fragile will present a solution method that is deeply flawed. What might teachers do to help the class see that discussing different solutions, right or wrong, helps move everyone towards understanding? How do you do this while being sensitive to the individual needs of students?
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Everyone benefits from hearing more than one student’s problem solving method, even when the solution is, or parts of the solution are incorrect. Teachers can collect solution methods from more than one student and refer to each solution method using a numbering system rather than labeling the solutions by the contributor’s name. Students can discuss the validity of each solution method, reject methods that do not make sense and begin to take ownership of their understanding. It is helpful if the teacher does not initially indicate if the solution is right or wrong, and has students work through the solutions with a partner or small group. Students can discover similarities and differences in their thought process and explain their thinking in their own words to their partner.
ReplyDeleteAgreed! Hearing and seeing another point of view is a part of the learning process. Even during the two days of class we had, I learned a couple of different ways of solving the problems that we were given just by hearing what others do. It's a great experience and opportunity to learn.
DeleteWhen using mathematic jargon leading a discussion as a student can be daunting. We as teachers want all the students to understand and be able to explain their mathematic method in a comfortable manner. In a case where the students solution method is flawed, the single best way to help the entire class see and discuss the answer, whether right or wrong, is to first not come right out and indicate that the student's answer is correct or incorrect. Let the particular student explain by either drawing their answer out visually for everyone to see. This could promote further whole class thinking and discussion. Another stragety could be to then ask classmates to help out, add on and discuss further on what they know on the problem. By collecting the other students methods, thoughts and solutions, this does not call out on the one student that may be sensitive or shy but instead they can discover the process together.
ReplyDeleteI think the Classroom Discussions book gives some good examples on how to use the students to find the correct solution, sometimes through flawed solutions. One of the examples was finding the coin combinations (pg. 103-105). In this case the students had to find all possible combinations of 35 cents. One student had found some of the combinations, but not all because he lacked a systematic strategy. Another student found all the combinations because she had a systematic strategy by ordering her combinations. By using the students correct example, in addition to another student explaining her process, he was able to then offer the correct explanation to the student that had missed coin combinations. This discussion allows ample explanation and reflection for those students that might not have reached the correct solution, or methodology was flawed.
ReplyDeleteI think the most important part of this situation comes from the work that has been done beforehand. Classroom climate is a huge factor in how comfortable students are to take risks in class and to share an answer without being 100% confident in the response. I also think that read-alouds and social curriculum are nice ways to build some of this climate into the classroom, without it being in direct response to a situation where a particular student has a flawed solution method. Then, when this situation comes along, it is easier for the teacher to address it.
ReplyDeleteI’m a big fan of the idea that no one is perfect, and that mistakes are how we learn. I also think the idea of thanking a student for their contribution is important, regardless of the veracity of the answer/method. Thanking a student for sharing their idea as the class works their way to various solution methods validates the contribution without validating the accuracy of the response, and still provides an opportunity for the student to feel a valued member of the classroom community. I would then want to plan follow-up instruction to make sure I could check in with that student to make sure that their understanding is coming along and that they are not stuck in the flawed solution method.
I agree that an important part of having productive discussions during which all students feel comfortable to share is the classroom climate. If the classroom is viewed as a comfortable, accepting place from the beginning, students will know that their thoughts are valued and that they will not be put down for being "wrong." All students need to understand that everyone is in the classroom to learn (I always include myself in that, too!) and that making mistakes is an important part of learning. That way, hopefully, students who have low confidence aren't crushed by one wrong answer.
DeleteIt is important to be very explicit about the benefits of discussing math topics and the different strategies that students are using. Participation in these discussions needs be looked at as an expected behavior within the classroom as opposed to a challenge or negative interaction. This can be achieved by creating a safe environment for kids to share in and role modeling giving and receiving feedback and assistance from others. If a student is hesitant, one strategy is to move on to another student and allow the hesitant student more think time before returning to them for discussion. I have used this and find that it works really well. I also give my students the opportunity to ask a peer for help when they are struggling to find the words or answer. The book suggests using the repeat strategy of having another student either repeat the question, answer, or information and then returning to the original student. I think this would work well and am interested in using it with my own students.
ReplyDeleteTo be sensitive to the student’s individual needs, I think it is important to review the expectations and benefits of class discussion with the student separately and determine why they are hesitant. Once this has been determined, you can slowly work with the student to improve their skills one step at a time.
I think your point about being very explicit about the benefit of math talk and that it is an expected behavior is very important. Too often, I think we don't explain to students why we do something a certain way or what the benefits are to a given approach. While I do not think we need to justify and explain all of our instructional methods and strategy to students, I think in this case it helps for students to know why they are doing it, that it is okay to be confused while trying to explain your thinking (it is hard to do, after all), and that the most important idea is to be willing to try and to keep trying. If we can be honest about what we are looking for from students and why, I feel that they will respond better when asked to do something new and potentially uncomfortable.
DeleteI think that being cognizant of the fragility of the confidence of your students is a vital part of being an effective teacher. As I mentioned during my post about productive versus non productive discussions, laying the groundwork to establishing a supportive classroom environment will pay off in the long run. As a teacher, you are the leader of your classroom and it is your responsibility to establish the precedence that mistakes and errors are an essential part of the learning process. One of the most effective teachers I have ever seen used an add-on activity where students could correct the work of others or respectfully disagree with another student’s reasoning as long as they were able to explain their reasoning by beginning with a statement that acknowledges the effort and/or correct aspects of the other students attempt at answering the question or problem. I was observing this class during the springtime when all of the classroom routines and expectations were clearly learned and strictly followed. Another way that a teacher could help his or her students realize the benefit of discussing correct as well as incorrect answers is by having students pair up and explain their answers to each other with the expectation that each partner would need to present the other students work and explain that student’s reasoning. By setting the expectation that each student would need to present and explain the other student’s reasoning may often lead to discussions between the two students in order to clarify misunderstandings and perceived errors before the they are asked to present to the group. As a teacher, you need to be in tune with the social dynamics of your classroom as well as the confidence and reactivity of your students. Be sure to assign partnerships that you believe will minimize the vulnerability of each student.
ReplyDeleteA student who struggles in math may have very low confidence and it is often difficult for that student to share his or her thoughts with the class. If such a student provides a solution that is flawed, it is tricky for the teacher to balance being sensitive to the student and needing to correct the student’s misconceptions. One strategy that is appealing to me is having students restate what others have shared. When one student is confused, the teacher can have the student ask another student to repeat the question, answer, or other piece of information. That way the student can attempt to clarify the misunderstanding on his or her own. The teacher can then immediately go back to the confused student to check for understanding. The teacher can also ask confused students to repeat and explain other students’ explanations or predict what came next in solving the problem.
ReplyDeleteMath is a subject that is hard for most students. I know I personally struggled with math throughout school. I lacked confidence and therefore would not participate because I feared the mocking of my fellow students. In order to an effective teacher it is important to make sure the classroom climate is supportive of all students and their ideas whether right or wrong. If the climate is understanding and open students should not feel like they are “stupid” or that their methods are “flawed”. If a student presents a method that is deeply flawed it is our job as a teacher to break apart that method and fill in the missing pieces. We need to balance the needs of all our students and customize our teaching to ensure that all our students are learning. Some students strive in small group learning because it is less intimidating, other students like large group discussions where the students explain the concepts to each other with us as the teacher facilitating the conversation. You as a teacher need to be able to adapt your teaching to each class of students you encounter.
ReplyDeleteAs part of your classroom culture you need to establish an environment of acceptance...this includes acceptance of all collective thoughts from all individuals. Establishing the practice of defending one's thinking will then just become part of your routine and it is understood that when you explain your thinking you might be wrong. Part of the routine that needs to be built is teaching kids how to disagree with someone in a civil way that does not belittle the other person's thinking. I teach them to use the starter phrase..."I disagree because..." or "I disagree and here is why...". That way the person who is being corrected is open to hear the disagreement vs. shutting down. In a case where a student's thinking is flawed if a fellow student does not lend different thinking to the situation then I will jump in and push the student to see the flaw or hole in their thinking. I try and lead the student to the "self-discovery" of the hole. If they can correct it themselves then their confidence will grow.
ReplyDeleteI agree that it is important for students to be able to disagree in a civil way and learn to accept feedback. This is a skill that will not only help them in school, but as they enter the work field and in day-to-day interactions with others. I also think you're idea about jumping in to help a student continue to hear the disagreement as opposed to shutting down is a good strategy, especially while students are still learning how to disagree constructively.
DeleteMike,
DeleteI completely agree with this post. It is important for students to be able to voice their disagreement in a civil thoughtful manner. It is our job to teach them how to do it. I like how you give them starter phrases. You are also teaching them that it is ok to disagree you just need to be able to support your thinking. This is a very important skill to have especially when you become an adult.
Everyone has shared some great ideas and strategies. Creating a classroom culture that encourages all students to participate really brings the group together as a community of learners; you can feel it as soon as you walk in the classroom. Although I want students to be competent in math, I try not to emphasize getting only the "correct" answer or praising only students who do. I tell students that I actually learn more about their thinking when they don't get the correct answer. By asking some follow up questions, most students are able to see what went wrong in their thinking. Also being able to talk about a problem with a partner before sharing with the class helps to work out a lot of misunderstandings.
ReplyDelete