Reflect after reading the Introduction and Chapter 1:
Why do the types of tasks matter in math classrooms? Why is the delivery important?
Consider the following questions:
- What is resonating with you from the reading?
- What caused you to pause and think during this section?
Respond and Interact
After reading these chapters, please post your response to one {or more} of the prompts above. Read our colleagues' reflections. Feel free to respond to someone by sharing a comment, insight or interesting possibility.
What caused me to pause was questioning how often are my students mimicking and not actually learning? Which made me feel like I need to make sure I am balancing non curricular tasks in. Needing to make sure that they a have actual full understanding of the concept and not just my directed lessons where it is easier to mimic understanding.
ReplyDeleteThere was so much to think about in this first chapter. Like Jessica, I thought about my students who are mimicking. As mentioned in the book, the students are working hard to do what they think is desired. The other behaviors, such as stalling and faking are ones I also see. It was interesting to see PL's data on these different behaviors in response to "now you try one."
ReplyDeleteAfter learning about the benefits of using engaging non-curricular tasks, a thought I had was, "What about the standards?" PL does address this and then goes onto explain the sequence of moving to curriculum thinking tasks only after using non-curricular tasks. The benefits PL mentions on page 91 make sense and he shares a lot of evidence for why we should not just skip to the thinking tasks that are part of the curriculum. I'm convinced ... however, my big question is about TIME! As I was unable to get through the IM units with my fifth graders this year, how will I fit in non-curricular tasks that are in addition to the curriculum??
One thing that resonated with me in this chapter was the pie chart on page 10 that shows the distribution of student behaviors on now-you-try-one tasks. I have seen these same behaviors in my classroom, and they are difficult to break. The structure of the traditional math class encourages and reinforces mimicking. I see that mimicking has its place in some skills, but when we emphasize and reinforce mimicking it shuts off student thinking. I like the way the Illustrative Math lesson structure flips this around and engages students in problem-solving at the beginning of the lesson. I noticed that it was hard for some students to break that mimicking pattern because it is so ingrained. I love the idea of starting with an engaging non-curricular task. I am thinking of ways to incorporate engaging tasks before the curriculum-based tasks at least during the first week of school. I think if chosen carefully, it would be a great way to establish math norms around “thinking” as opposed to mimicking. I also am concerned about time. I did not get through the fourth-grade curriculum last year. However, if these engaging tasks get students thinking about math more quickly, I know it will be worth it!
ReplyDeleteI was nodding as he was describing the "studenting" behaviors. I also felt convicted when I read, "Thinking is a necessary precursor to learning, and if students are not thinking, then they are not learning." It reminded me of so many math lessons where I just stood up there and asked kids to do what I was doing. They weren't thinking at all - they were just mimicking me. 😳 I hope they had a better teacher somewhere down the road. lol.
ReplyDeleteA part that stuck with me from the introduction was how an activity was reduced to "cookbook mathematics". I've done this a lot. Giving students a set of steps that lead them to completing a task, rather than letting them think and solve the problem in their own way, finding solutions and identifying patterns that work (or don't work) without me laying out a set of instructions that actually limit thinking. I'm so glad that, with help from colleagues and PD, I am able to steer away from this and really get the kids thinking.
ReplyDeleteAs the author said, “If we want our students to think, we need to give them something to think about – something that will not only require thinking but will also encourage thinking” (Page 19). To build a thinking classroom, the goals are making students think and problem solving, not just mimicking what we teach. Therefore, what types of tasks will play a big role for us to engage and encourage the students to think. In my small group of MAP students, my students are usually at different levels of their math skills. I would need to give them the task fitted to their skill level to encourage them to think. Otherwise, they will tell me it is too hard for them.
ReplyDeleteThe same things are resonating with me that have resonated with so many of you. The concept of "studenting" and mimicking are spot-on. It struck me to hear that 100% of students that were mimicking thought that was what the teacher wanted them to do. It makes complete sense that they would think this. On the other hand I am disheartened by this as I missed those opportunities with students to help them think for themselves and not just copy what I was doing. I was a student that was excellent at mimicking but definitely got lost when I had to do the thinking for myself because I only knew how to copy.
ReplyDeleteI absolutely love the idea of starting with those highly engaging, non-curricular thinking tasks. I can see how this creates a learning environment where it is okay to take risks and get stuck. When I was in the classroom, I loved putting tasks in front of students and seeing the different ways that they arrived at answers. Looking forward to seeing how this all unfolds in this book.
I always thought the "I do, we do, you do" style of teaching was the way to go. However, I and the teacher I partner with, have not been able to figure out why we have to spend so much time reviewing concepts and why are our students unable to remember how to solve problems. It is ever so clear now that this style of teaching only results in mimicking. Instead of telling the students how to solve the problems, I'll be asking them thought-provoking questions in hopes they'll be able to tell me how to solve the problems.
ReplyDeleteThough all of the content was interesting and very informative, one thing that specifically resonated with me was the study that Peter did - 40 classrooms in 40 schools. As someone who is very much data-driven, it was really enlightening to see the commonalities amongst the varying classrooms. The five categories that he was able to break the student behavior into, (Slacking, Stalling, Faking, Mimicking, and Trying it on their own) was very insightful. It caused me to reflect on students that I have taught and has given me a new mindset and understanding of their behavior. It also makes me think back to when I was a student and how relatable all of the categories are. I specifically remember being in a math class and mimicking what the teacher had demonstrated while I was working on a “try it on your own” problem.
ReplyDeleteSomething that caused me to pause and think was when he went over The Problem. It made me think about the responsibility I have in being intentional with my students; what I teach them and how. It also made me think about the relationship between the students mastering a broad understanding of the content and learning the process for computing problems.
There were so many ideas just in this first section! I was cringing when I was thinking about the studenting behavior and how I've always assumed students are learning when they are actually mimicking. The other behaviors (slacking, stalling, faking) are a bit more obvious, but I thought the kids mimicking were getting it. I was appalled by how few students were actually trying to reason on their own. One thing that made me pause was his statement that "teachers were planning on the assumption that students couldn't or wouldn't think" and I disagree with that. I see why under the context that he is speaking, but I always planned expecting students be engaged and think. What I did not realize is how little thinking they were doing given the curriculum provided, structure of the lessons and tasks students were being asked to do.
ReplyDeleteWhat made be pause and think about is how I will need to change my standard teaching routine and my students to becoming mathematical thinkers rather than mimicking steps on how to solve a math problem. Take the time, slow down and let the students think a task through which each student may use different steps but get's them to their final destination and may not always be correct but they are pushing themselves to think about the task or problem. Keeping students engaged and thinking about the task or lesson is something I always want to achieve.
ReplyDeleteI completely agree, JerriLee. I'm totally guilty of falling into the routine of keeping a schedule, following the pacing guide, having students mimick our teaching, and moving through daily lessons and activities, but this chapter was incredibly refreshing when the emphasis on NOT doing that was touched on right away. Being intentional by slowing down and MAKING the time for students to think independently about tasks will help them with every other activity and task we ask them to complete. Finding a sweet spot between teaching the curriculum and helping teach students HOW to think independently and problem-solve is the name of the game.
DeleteSorry about the late response. . . I thought this reading was very eye-opening, and it helped me reflect on my current teaching practices. I agree that we have traditionally focused on teaching students to mimic math strategies instead of engage in high-level thinking, but I truly believe that we've been moving in the right direction over the past few years, particularly with the math routines that we have added into our daily instruction. I think that's been a good first step. I like the concept of focusing more on open-ended questions that require deep level thinking. After all, we want our students to grow up to be critical thinkers - not only in math, but in all things. The questions the author raised about how to incorporate these tasks into our 180 days when we already have an extensive curriculum addressed my immediate reaction/question/concern. It's a practical issue that is not going to be resolved easily. From what I've seen, our new program does a pretty good job of providing students with opportunities to explore and think deeply before algorithms are introduced, so that's good. But, I wonder what we can do/add in that would accomplish what this first chapter describes. Like all teachers, I worry about having the time to find tasks to implement and the ability to choose the best ones to accomplish our goals. I look forward to reading more.
ReplyDeleteI too was struck by how much mimicking my kids do instead of thinking for themselves. And to think they thought that's what I wanted. :) I used the IM curriculum this year and it incorporates a lot of rich tasks that work with PL thoughts, which is nice, that I won't have to go out and find them. But I do worry about time, as always, because I didn't get through all the units this year. I can understand the importance of starting the non-curricular tasks as a way to set things up and get the year started. I am thinking already of when/where I might plug them into my day without taking my math block time because I know I am going to need that time.
ReplyDeleteposting this for Kelly Yvarra: There were a lot of eye-opening moments for me while starting this book. I found myself really thinking back to my math classroom when he talked about mimicking. There are so many curriculum based lessons that do require this and I agree with him that it is an addicting habit for students as they see it as success if they can mimic what we teach. As teachers, our goal is to get our students to be and feel successful. These true problem-solving skills he introduced that are not curriculum based problems cause children to grapple with concepts and sometimes fail. This naturally feels difficult as a teacher although allow students to truly think. I like the quote “problem solving is what we do when we don’t know what to do”. I also found the micro and macro moves are great to show implementation into the classroom.
ReplyDeleteI was impressed by how engaging the book is already, and had much to think about as everyone else said. As a K-3 resource room teacher, my first question was whether Liljedahl's research included the population I teach (specifically students with learning disabilities). Though I'm still not sure about that, I am excited to have the opportunity to push in with them for math during this coming school year. I am interested in his research on the results of using non-curricular tasks to jumpstart students' ability to think about curriculum-based thinking tasks. Though his research seems well-designed and the results are encouraging, I do wonder about the emotional effect of struggling with a task for some of my learners. When thinking about the value of mimicking, the one benefit that comes to my mind is that it can create more self-esteem when students are able to successfully apply an algorithm to solve a problem. I will be interested to see if "thinking tasks" provide that same boost for students with learning disabilities.
ReplyDeleteSomething specific from Chapter 1 that caused me to stop and think was in regard to the non-curricular tasks and their importance in aiding students in their ability to think independently, as well as how to practice problem-solving, especially when they are unsure of what to do initially. To be completely open and honest, this is something that I can improve in my instructional practice. I am intentional with using number talks and many other "thinking tasks" to open up daily lessons, however, those activities are also the first thing I cut out when I am short on time, or if I feel stressed about being behind the pacing guide or taking additional days to reteach and ensure comprehension of all students. I think this chapter was engaging and refreshing because it highlighted the importance of NOT doing that, and showed how non-curriculum-based activities are just as beneficial for our student's math fluency, problem-solving, and independent critical thinking skills. I am looking forward to using the IM curriculum this year which appears to lend itself nicely to the idea of thinking tasks and problem-solving.
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