Chapter 5:
1. Under what circumstances or conditions do you think it makes sense to publicly share incorrect approaches with students? How would you do this so that students were not left thinking that incorrect approaches were valid?
2. Does who presents a solution to a task really matter as long as the desired solutions are made public? Why or why not?
1. If you see a common theme that occurs in a class you might want to bring it up. I would not bring up a student who did it incorrectly, but put a “hypothetical” student’s work up to show student some misinterpretations. If you can incorporate how their approach is slightly accurate would help show student that they are on the right track. If you can ask students which cases would this work, to deepen learning would help a majority of students. You need to create an environment this capable to take misconceptions. Once you have settled that, it makes it easier to allow those types of conversations.
ReplyDelete2. I think which student presents matters. If you select the same student time after time, other students will not feel like authors of the mathematics. If you want all students to take ownership of their learning you need make sure that you select enough students to show that everyone is capable of doing mathematics regardless of how deep their knowledge is.
1. I believe at the beginning of the year you have to be really honest with students that sometimes you may bring them forward to show an incorrect way of doing the problem. I think you have to make sure it isn't always the same student or one gender. We can't teach our kids that doing something incorrect is awful, but use it as a learning experience. However, I do think that when these misconceptions come up, we have to address them. This shows the students that there is a correct way to get to our learning goals. We have to get kids thinking that they don't have to always be perfect and they can never make mistakes.
ReplyDelete2. The selecting of who presents is very important. It is going to dictate how you get to your learning goals and how your discussion is going to flow. I do believe you can have different sequencing strategies, such as calling on the quiet child, or the method most commonly used, or moving from concrete to abstract. However, I don't think you can just ask anyone to come up and present. You really leave yourself open for your discussion to break down. Selecting and sequencing students also makes it so it isn't always that one student that gets to share or who is always volunteering answers. More students are sharing and building self esteem.
1) . I do think incorrect solutions are valid for students to see.. it teachers them common errors and error analysis skills. You have to have the write culture and explain to the students this is a teachable moment and we are going to learn from it. Class room culture and trust between teacher and student is very important when doing this. It is a big step for the student sharing their incorrect solution -- as we are so hung up with the valid answer and not the learning.
ReplyDelete2) You have to balance this... You need the solutions presented in a sequential method to meet the learning goal. Secondarily you need to make certain all students are helping with the presentations hopefully over the course of the class.
Jenelle Jarnagin
ReplyDelete1) When it is a common misconception that you are seeing in several groups, to help the know that it is not an unusual mistake and to be careful of it. It tells them that it is okay that they make a mistake. It also could be a correct strategy with a wrong values (like in Nick Bannister example where a group used .4 instead .04). Through questioning and prompting students would need to correct their mistakes with the help of their classmates. You have to be very careful and clear that it was an incorrect result and what the correct result is.
2) Order of presentation matters, it is what builds the discussion. If it becomes just a show and tell where it goes in any order then students will not see the connection between the strategies because it will be harder to draw those connections and bring them out in the discussion. Making the math visible is our overall goal so building from one strategy to another is going to be to help make understand the mathematical concepts that we are trying to teach.
1. I think that there are times when students might have an incorrect answer with a correct process. In this chapter we see that students answered 50 for the plan being better. In truth the plan will be better at 51 and the same at 50. This shows that the students understand the process but misread the question. I think having those students share and then having questions can help bring everyone to the same page. I also think that you have to keep in mind who you have in your room. You do not want a student to lose their confidence if you bring attention to their wrong answers.
ReplyDelete2. I absolutely think that who presents makes a difference. Students need to have a voice in class, but not all are going to raise their hands to participate. This is a great way to make sure that all students can share their ideas. I love the idea of keeping track with notes so that I do not call on the same students multiple times. I know this can be easy to do because many of the same students want to volunteer their work. It is nice to get as many people involved as we can.
Amanda Thorsen
There are times when it would be important to share incorrect approaches. An example would be when it might have been in the majority of discussions, even if it was just touched on. This way you can really help students to see why that particular approach wouldn’t work universally. Sometimes, asking them to use the approach with a slightly different problem is all you need to do.
ReplyDeleteI do think that students each need to take turns presenting solutions. First, it is a life skill to get up and talk in front of others. Second, being able to communicate effectively and to share your point so that others understand you is another life skill that can be used in all aspects of life. Finally, you want all students to gain confidence in their ability to communicate and reason mathematically.
1. I think it is important to share common errors in thinking. I feel we need to help students realize that we all make mistakes and instead of feeling bad and being frustrated we need to learn from them. That being said I think a teacher needs to be careful of how those common errors are presented. I think if you know your students you will know who is ok with having it shared and who would be totally embarrassed and would shut down. I think a teacher can find a way to present the mistake without putting any one student or group of students on the spot.
ReplyDelete2. Every student needs to feel like they have a voice in your classroom. Therefore it is important to keep track of who has or has not shared their group's strategy for a task. The ability to stand in front of your peers and explain something or defend how you did something is a life skill that a student needs to have the opportunity to practice in order to get better. A teacher again needs to know their students and can make decisions about how to let the quieter students share without overwhelming them in the situation and by doing so help them to grow in their confidence with this skill.
Great point about presenting being a life skill. The more opportunities we give students, the better they'll become!
Delete1) If there was a misconception that was very common in the room and was getting in the way of correct thinking for a large majority, I think that would be an appropriate instance to share an incorrect approach with students publicly. The key here would be to thoroughly explain why it is not correct or valid. I think this would be an important move, not just to show why it's incorrect in terms of an answer, but also showing students conceptually why it's wrong. This may help alleviate misconceptions in the future about similar ideas and concepts.
ReplyDelete2) Who presents matters, but sometimes it only matters to the person who presents. :) What I mean by that is in general, I would probably argue that who presents a solution doesn't necessarily matter, as long as the information becomes public, the math is understood, and students are learning in the direction of the goals. But on the other hand, it may be important to get someone into the role of sharing. As noted on page 64, "students' mathematical identities are affirmed by promoting their participation in classroom activities." For some students, getting up in front of the class to share a correct solution to a high-level task may be the turning point in their mathematical life. It may give them the jolt of confidence that they needed, along with a shot of motivation to stick with difficult problems in the future. In this case, it matters immensely.
Kate Wonders
ReplyDelete1. It would make sense to share incorrect answers with the class only if the classroom has a climate the is safe and students know it's ok to make mistakes. Students need to feel comfortable to fail and learn from their mistakes. It would also make sense to share incorrect answers if several students/groups made the same mistake or if the entire group could benefit from seeing the mistakes made.
2. I would be more beneficial for a student to present- rather than a teacher. It's important for students to see themselves and peers solving these difficult mathematical tasks. It should be different students ever time...and not always the "ELP" math student.
I think it comes down to setting the stage with students and having them understand that you can learn a lot from mistakes. Creating a safe culture of learning is key.
ReplyDeleteWith that being said and mutually understood, showing student work with mistakes can benefit everyone as long as the mistakes are analyzed, discussed and clearly understood. Revisiting these incorrect answers might be necessary if the mistakes persist.
I also think the teacher needs to understand their students on an individual basis to assure that no one feels "picked out" and embarrassed by the practice.
2. I think keeping shared strategies and solutions somewhat balanced among the students in your class is important. Calling on the same "safe answer students" could stifle participation in the activities by others. So being aware of "equity" in your classroom is important.
1. Under what circumstances or conditions do you think it makes sense to publicly share incorrect approaches with students? How would you do this so that students were not left thinking that incorrect approaches were valid?
ReplyDeleteIf it is an incorrect approach that you are observing is reoccurring, I think it is important to address this as a class and you wouldn't have to call out any students. As a class you could question them and guide them to figuring out what is wrong and fix that misconception. Building a culture of accepting mistakes and not being embarrassed by them may take time and adjusting but I think it is important that we get our students to embrace mistakes and learn from them. We also need to know our students and should not be calling out the same student all the time.
2. Does who presents a solution to a task really matter as long as the desired solutions are made public? Why or why not?
It does matter because if we are always calling on the same student then others may think their work doesn't matter. So their should always be a good balance and understanding that all students work is equally important (right or wrong).
Kelsey Burger
1. Under what circumstances or conditions do you think it makes sense to publicly share incorrect approaches with students? How would you do this so that students were not left thinking that incorrect approaches were valid? I believe I use incorrect approaches alot, but when I do I don’t use names and say, “Here’s what I’m seeing from a number of you. Let’s look at it.” Or something like that. TZhere is value in reviewing even wrong approaches.
ReplyDelete2. Does who presents a solution to a task really matter as long as the desired solutions are made public? Why or why not? No, but it is nice if you can find the less confident or less heralded students to present.
Jackie
ReplyDelete1. As far as to call up someone whom you know has the wrong answer just to give an example of a wrong answer-never. You can use a hypothetical situation, "As I was looking around, I saw a common mistake happening." Then you can go on and explain what the mistake was and see if they can come to the conclusion of WHY it was a mistake. I like what Brad said above that There is value in reviewing even wrong approaches, especially if it a common misperception.
2. I don't believe it does. If there is a good dialogue in the group, everyone should be on board with the explanation and should be able to tell it. I do think though, after you establish your routines and that its a safe area, I would call on volunteers for a while so people can see what is expected of them.
1. It makes sense to share incorrect solutions if there is a lot of confusion, if it is something that I am seeing in multiple groups, or if the background knowledge is missing or flawed. I would try to share them at the beginning of the discussion if possible so those students would know their thinking had an error and so they could be open and processing the other ideas along with the other groups. I don’t think it would be good to end with the misconception as a presentation since sometimes students only remember the last thing they hear, they might not have enough time to process why it is incorrect or they might not have time to get their questions answered. I would want to leave them with a correct approach at the end of the lesson.
ReplyDelete2. It is important for all students to present their thinking in class. This is something I need to work on. I now realize how important it is to give everyone a voice in class. It is important for students to get their ideas communicated, critiqued and validated by others. If I don’t have student present because they are shy, I am robbing them the chance to defend their ideas and answer questions. We know students learn more when they are given the chance to explain their thinking and without have a student participate in the presentation process in class I cannot guarantee that experience for all of my students.