Chapter 4:
1. What do you see as the advantages of solving the task in which students will engage? Is this something you routinely do? Why or why not?
2. Why might you want to anticipate both correct and incorrect approaches to solving a task?
3. How might a monitoring chart such as the one shown in figure 4.5 be useful to you in your work?
1. I work math problems before my students work them. Some of the questions we are asking kids are HARD even for adults and manuals and answer keys are always wrong. I seem to see math as that 70's child, and it helps me see what needs to be done in the problem and if I am meeting the instructional goals. If I can't meet the instructional goals working the problem, how can I teach it. Sometimes I do problems with students as if I am a member of their group. I want them to see me doing the work and having struggles sometimes with a problem just like they do. My co-teacher and I try to always make the answer key ourselves and show our work, so students can see it and discuss it. Really knowing the problem also helps you with your questioning when a student is stuck and can't figure out what to do. Do I need to ask assessing questions or advancing questions. It will help with better discussions and who I am going to have show examples during those discussions.
ReplyDelete2.Showing kids misconceptions and errors is very important in my math class. I want kids to see where they are making mistakes instead of just saying,"You're wrong." As you are monitoring, you will want to watch for those mistakes, so you can steer kids in the right direction. I think this will stop some of the bad habits kids learn if we can get them stopped earlier in their thought and reasoning process. It also helps you plan your teaching. You may need to go back and teach things as a whole group or as an intervention for a small group.
3. The part of the monitoring chart I liked was the questions columns. I think as you become more comfortable with the 5 practices, you would not need the chart. You could just use a Post-It note. It really helps those of us that are just starting out.
Holly, I liked how you pointed out that we want students to see where they made their mistake so we can steer students in the right direction. We definitely don’t want students practicing the same error X times on their assignments!
Delete1. I see the opportunity to view the problem through their eyes. A lot of the problems that are in our textbook are pretty hard, even for the teachers. We try our best to attempt the problems we ask our students to do. I wish I did this sooner in my years of teaching. However, since reducing the amount of problems I have been better about solving the problems before I ask the students to do them. If I know what the question is asking, I can better assess my student’s knowledge.
ReplyDelete2. If I can anticipate the incorrect answers, this will allow me to find where the misconceptions came from. Then, I can rapidly help students fix those misconceptions. If I can anticipate the accurate answers, I can push students further. This allows me to not only assess where my students knowledge is, but stretch it further. This helps all students learn. It helps the students who need support and the students who need to be pushed further.
3. Having all the questions to ask students on one page, keeps the stress of forgetting the questions out of my head. It lets me focus more on the students than the questions. The columns of who and what lets me remember which students used the strategies listed. While the order allows me to make the sequence. This sheet allows me focus more on the students than the questions I need to ask.
Jenelle Jarnagin
ReplyDelete1) Working the problems ahead of time would put me into the students mindset of the problem. It prepares me for the direction students might go with the problem and be prepare to direct through questions and lessen the time that will take during the classroom time. This should help me be more efficient with me classroom time. I don't routinely solve all the problems the students do. I have solved every problem at least once but with 5 preps it is almost impossible to solve every problem every year. There is just not enough time. If I do solve the problem I only solve it once and always as a math teacher and not as the student.
2) Trying to come up with all the different solutions will help me understand the students thinking. It gives me a chance to begin the process of coming up with both assessing and advancing questions. Also coming up with inaccurate approaches will give me a chance to come up with questions to advance the students' thinking while just not giving them an approach/answer and stopping their thinking altogether. It will help me keep all the students actively engaged.
3) A monitoring chart would help me organize the different solution possibilities along with having a place to write out the assessing and advancing questions. It is also can be continually added to and improved over time. It is also a good jumping off point for the selecting, sequencing, and connecting of the 5 practices.
1) . I have to solve the task and/or problem myself before the students to make sure I understand the goal of the problem and how I would think about it. Once I have a way of solving the task, then I am more comfortable in identifying and working with students on other possible approaches. It gives me confidence in my facilitation of the problem.
ReplyDelete2) . Trying to come up with different solutions will be a challenge... I will have to use resources to help with this. I enjoy finding multiple ways of solving a problem so it will be interesting. I also anticipate learning from the students the first year and then recording their ways of solving the problem to use in the anticipation step next year.
3)The monitoring chart will be a critical organizational tool for me. I anticipate making it my own and changing as necessary -- but it is a great template to start with.
Advantages of solving the task ahead of time is that you can find where students may make mistakes and prepare the right questions to help them overcome those mistakes. It should also help you understand where they may get stuck and you can come up with questions to help them move forward. I have been to both math conferences that focused on the “Principles in Action” book and I have done a few activities/tasks last year in my class. Students and I both enjoyed them, but I definitely did not have clarifying and advancing questions nor did I have the different possible solutions thought out ahead of time with the order I would like them presented in. I don’t routinely use tasks to introduce- reinforce-expand students’ understanding of standards. I think the biggest reason is that this is a fairly new idea for me and I am learning how to do it. I feel like many times we as teachers are pulled in so many directions that it is easy to lose focus. Finally, its helpful if you have someone who you can collaborate with and that is not always the case in every school district.
ReplyDeleteAs stated previously, if you can anticipate both the correct and incorrect approaches, then teachers will be better prepared to ask the questions necessary to help students on their math discoveries.
Using a chart can help you keep track of approaches that are being demonstrated along with reasons why. It can also add to the chart approaches that are new and unusual. Also, you can star the questions that you feel helped students or write down the questions that you came up with in the moment that helped students move on.
1. To be honest, I do not routinely solve the problems my students are given. I solve their homework problems in one way to create an answer key. I worked the problems my first year with the students and since then I have remember a lot, but not everything. The benefits to solving the problem first are huge. I wish that I would have been better with this. When you solve the problems first you are able to get an idea on how students will be thinking which can help guide the entire class. I can walk around an know what work is being done and learn about student understanding instead of student tasks.
ReplyDelete2. Being prepared for both correct and incorrect is important because it helps to prepare the questioning we might need to phrase. I sometimes forget about finding the incorrect solutions, but this is just as important as correct answers. It is not bad for students to get wrong answers. It is important though to make sure that we can understand where the students got off the path and how to get them back to the right direction.
3. I LOVE the idea of using a chart. I think that it will help keep me focused during a lesson. It is easy to get caught up in one students thinking or another. It is also easy to lose track of who has shared, who might need extra help, and which order you would like students to work in. Using a chart can help keep all of that organized for you. It is easy to have the majority filled out before class so that all I will need to write down is who did which strategy and which order I would like them to present. I am visual person, and this will help SO much to keep track and make sure I stay on the math goal.
Amanda Thorsen
1. I used to work through problems before students worked them, but the longer I have taught the less I tend to do that. I feel like I know that math and know where students are going to struggle. I do see the importance of working through a task and trying to realize the different ways students might approach the task. I feel if you don't you will just be flying by the seat of your pants and your lesson will end up like Mr. Crane's with learning going off in many directions. I don't think I would be as focused in the moment when my students are working on the task and I'd be trying to figure out what questions to ask and how to guide this group, etc.
ReplyDelete2. Again, I think it is just part of being prepared. I think it might help you learn how to use student's mistakes and misunderstandings to help them and others in your classroom learn. I've been reading a book by Jo Boaler and she talks about how important mistakes are in the learning process. If I don't plan for those mistakes I would quickly guide them in a different direction and not help them focus on the fact the it is ok to make mistakes.
3.I think the monitoring chart has two important components. It's for planning, planning, and planning!! The more that I plan up front I feel the more successful the task is going to be in meeting my mathematical goal. I particularly like the columns with the questions. I feel like it is difficult to come up with really good questions on the fly. The other aspect is that once the task is complete you have a lot of information recorded to use for your reflection on the lesson and to use next time you use the task so you don't have to start from square one every year, therefore you don't have to spend as much time planning the next time around.
1) It seems clear that solving the task that I'm asking students to solve is critical. It will make me think through ways to solve the problem, and consider misconceptions students will have as well as mistakes that they'll make. This work up front becomes critical during the lesson, as I will notice immediately when looking at student work where they're heading, what questions to ask them, and potential problems they'll run into. If I don't work the task first, my time during monitoring becomes laborious and inefficient! As I mentioned in class, I haven't taught math yet (at least not at this level & not for the past 7 years), but I plan to do this every time!!
ReplyDelete2) Considering correct AND incorrect responses really helps me to ask the right questions. If I notice that someone is on an incorrect path, I can ask assessing questions to get them to understand their own thinking. Once they see where they're on the wrong track, I can then ask some advancing questions to get them headed in the correct direction. Additionally, if someone is on the right track, I can then ask them some advancing questions to get them to understand the math more deeply.
3) Again, it seems clear that a monitoring chart would be a vital tool for facilitating a lesson using this protocol. I am not mentally organized enough to simply remember what students did what, including how they explained their thinking, and what direction I nudged them in. Also, a chart like this would be a great place to jot down great things that students tell you as you monitor. Then you can ask them to repeat what they said to you, to the whole class. (I've found that some of the best thoughts on how to explain things seem to come from students...)
Kate Wonders
ReplyDelete1. I think it's very important for a teacher to solve a task before presenting it to students. Teachers need to experience the task/problem for themselves. Working on the task will help the teacher ensure that students are engaged in the mathematics centered around a specific goal, will help the teacher identify and anticipate student struggles, and will help teachers plan for questioning.
2. Considering both correct and incorrect responses will help teacher sequence work to be explained to the class, will help the teacher plan for questioning, and will allow the teacher to be more prepared for monitoring. Considering student answers will also allow the teacher to plan for differentiation- plan for how to help students struggling with the task and plan for how to enrich the task for early finishers.
3. A monitoring chart will help teachers remember and record which individual students were doing different strategies. You can use the chart to help sequence work and write down names of students to present to the class. You could also keep the monitoring forms to look back on to see individual student growth from task to task.
I do think working out problems using multiple strategies is important and is something that I do when leading a math class. It allows me to anticipate potential answers (both correct and incorrect) and plan purposeful questions that allow students to reflect on their work the validity of their answers. It helps create a clearer path for teachers to lead students on.
ReplyDelete2. Again, I think considering both correct and incorrect answers will allow teachers to mediate incorrect and extend/challenge correct solutions. Differentiation is higher when all possible solutions are anticipated.
3. I think it could be very helpful and allow teachers to keep track of strategies that are being used and have those strategies presented in a logical order to deepen connections. It should help monitor student learning and help students build knowledge from one task to another.
1. What do you see as the advantages of solving the task in which students will engage? Is this something you routinely do? Why or why not?
ReplyDeleteI do this pretty often but not as much as I should. There are come concepts that I feel more confident about. If it is an activity/task,I think it is important to work it through before asking the students so I can anticipate responses and questioning.
2. Why might you want to anticipate both correct and incorrect approaches to solving a task?
I think anticipating incorrect approaches helps in noticing where they are going wrong and I can come up with questions to ask them to help them see their mistakes. Anticipating correct approaches allows me to have questions ready to further their understanding in the concept.
3. How might a monitoring chart such as the one shown in figure 4.5 be useful to you in your work?
I love this chart to aide in monitoring a task. This is a great way to organize different responses and be prepared on what order you want to present these to the class.
Kelsey Burger
1. What do you see as the advantages of solving the task in which students will engage? Is this something you routinely do? Why or why not? I almost always work the students problems out in advance for three reasons: 1) I never want to be caught with my pants down, 2) I want to see where problems may arise, and 3) I like to work math problems
ReplyDelete2. Why might you want to anticipate both correct and incorrect approaches to solving a task? I believe it even with incorrect approaches there is something to learn there..
3. How might a monitoring chart such as the one shown in figure 4.5 be useful to you in your work? I believe it could be very valuable for me as I believe I have my good students and I gravitate toward their work.
Jackie
ReplyDelete1. I think trying to get into their "math mindset" would help us prepare in the long run. Plus, it might reinforce if their thinking is in line with what we are thinking. I don't usually do this as I don't usually teach math so I really haven't had to anticipate their possible solutions and processes.
2. Correct solutions would verify that they are understanding the concept. Incorrect would be in order to disspell and prior misconceptions.
3. This chart figure 4.5 would be a great tool in helping monitor my students progress and in which order to select them for sharing their solutions.
1. I routinely do the problems I ask my students to complete, especially if we are going to focus on them in class discussion. I do this to make sure I know the correct process and answer so I feel confident and fresh with the material. I also do it to recognize any issues my students might have thinking through or completing the problem. It helps me to think of the questions I should be asking them along the way.
ReplyDelete2. It is important to anticipate both correct and incorrect solutions so that these ideas can be recognized quickly and I know what questions to ask students to understand their thinking. If I have ideas of their process I can spend the time with my students asking them questions that pertain to their thoughts not clarifying or probing questions so that I can figure out their thinking and wasting their time. I also should have follow up questions prepared to push their thinking.
3. The monitoring chart is a smart way to keep everything you are observing in your classroom organized. It should contain the anticipated solutions as well as thoughtfully crafted questions to push and support their learning. It should help me keep my thoughts in order so I am prepared to select and connect during the student presentations. It also keeps me accountable to keep moving and make it to all of my groups instead of finding just one correct solution I should be looking for other options to help my students connect to the different levels and representations of the mathematics.