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.
There was a lot to unpack in this chapter, but what resonated most with me was the statement, "Problem solving is what we do when we don't know what to do". In third grade, our SGG is centered around problem solving, so this conversation was particularly relevant. When thinking about creating rich tasks to encourage thinking, we have to get comfortable with the idea of productive struggle. This sometimes feels contrary to our work as educators, especially when there is a sense of urgency to get kids "caught up", but allowing, and even encouraging students to get "stuck" and compelling students to think, experiment, and apply their knowledge in novel ways to get "unstuck" will lay the foundation for that new learning. There is difference between "problem solving" and "solving word problems", and if we want students to be able to make sense of problems and persevere in solving them, we need to be intentional about providing opportunities for non-curricular/rich problem solving tasks to engage students, welcome that disequilibrium, and get them thinking creatively. Then we can shift into those micro-moves that bring in the extensions of prior knowledge. The summary graphic on pg. 35 outlines this beautifully & I plan to share it with my team.
ReplyDeleteI thought the same thing about solving word problems and really diving deep into problem solving! Sometimes as educators it is hard to watch our students struggle to solve a problem, but that is were the deep learning really takes place!
DeleteI took a lot of notes while reading this selection; the description of "studenting" behaviors was spot on. I have felt the frustration of having students appear to do well during our lessons and then fall apart when it's time to do some independent work. I appreciated the way he defined problem solving and word problems, '...in word problems the problem is in the words.' I felt that one in my bones, hello 3rd grade unit 5! My pause and think moments were about lesson structure and how I might change my math block and they way we cover material. Investing time at the beginning of the school year setting up our math community and what that will look like/sound like is something I'm excited to do!
ReplyDeleteI was nodding as he was describing the "studenting" behaviors as well. 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.
DeleteI absolutely agree with both of you! His descriptions of studenting behaviors often felt like he was a fly on the wall in my classroom! Because of this, I think this will be a great read in preparation for not only a new school year, but navigating a new curriculum as well. I truly *hope* that I offer students more of their own opportunities to grow in the math rather than just do the steps because it's how they saw us do it.
DeleteThere is so much great information in the introduction and first chapter. My thinking is all over the place. First of all, having all the feels about students mimicking me and not thinking in class, as Renae mentioned in her reply to Angie! Like Kimberly and Angie both noted, the difference between "problem solving" and "solving word problems" needs to be realized by our teachers. It feels like our curriculum's "problem solving" is really "solving word problems". The definitions and types of tasks that promote student thinking was very helpful. It brought me back to when we were working on the creation and use of rich tasks in our buildings pre-COVID. This last year, after COVID's remote learning and shorter days, I felt like a lot of those practices and intentionality got lost as we were going along teaching from the book for the most part to stick to the pacing guide and fill in gaps! I'm excited to "start slow to go fast" by implementing non-curricular thinking tasks to start our year. I do tell my students that it is OK to get stuck & make mistakes, but they never seem comfortable with that. It sounds like the use of these engaging tasks will help our students learn that being "stuck" really is OK and they will want to get unstuck - building persistence and thinking as they engage in real problem solving, ("what we do when we don't know what to do.") One little worry buzzing around my brain is can & how will I be able to implement these practices as I also implement our new math curriculum... yikes... fingers crossed they are compatable.
ReplyDeleteYour excitement for bringing back those rich tasks and to start slow and go fast with these again in our teaching is contagious. I also feel that excitement! I am also excited to start the new curriculum because I have used Illustrative Math before to find rich tasks and great problem solving questions. It will be tricky to implement two new things, but your idea to go slow should work wonderfully!
DeleteYes, I can also agree with this. I did feel like I was teaching from the book and try to fill in the gaps that the kids missed during COVID. I also felt like I was trying to stick with the pacing guide and just teach them what they need to know. I am pretty excited about the information we will be learning from this book.
DeleteThere is quite a lot resonating with me after the intro and first chapter! It made me want to go in and complete change the way I do things right this moment, but I know it is all about baby steps and enjoying my summer ha! One line that continued to stay with me, just as others have said, was, “If students are not thinking, they are not learning”. I think of the students in my class this past year and the various levels of thinking they were involved in. Many students were masters at mimicking. I think it is also very important to put in context where they came from as far as remote learning how to get them unstuck from that way of learning. They wanted to be “done”, have the right answer, and get it turned in. Much like what it was like working on Google Classroom! I am excited to really dig into how to support my students in their thinking journey and how this connects to the idea of “productive struggle”. This upcoming school year I really want to start this way of thinking right away. I will admit that the beginning of this year I felt like I was just trying to survive and didn’t actually think about really diving into thinking tasks until about a month in. This was difficult for a lot of students. There were many frustrations, tears and comments about me “not helping” when I refused to give them the answer or show them a strategy. By the end of the year they became much more flexible in their way of thinking, but I know there is still so much more to be done. I think starting right away with these non-curricular tasks will be so beneficial. This chapter gave me so many ideas and I am excited to implement them!
ReplyDeleteI am struck by how much the readings so far have resonated with me! I have always tried to teach by the philosophy that I shouldn't be working hader that my students, but now I am going to rephrase that as "I should not be thinking more than my students". In a way it is painful to think that I have not always allowed for my classroom to promote thinking and learning in the way I thought I was. These chapters just make such sense and looking back at it I can see how kids were successfully mimicking the way to solve the problem instead of thinking on their own. Instead of beating myself up about it, I am excited to to learn new ways to increase thinking in my classroom.
ReplyDeleteThere several sections that cause me to pause and reflect. One section was when it talked about using these tasks to "prime" thinking and learning. This is what I have been working on in my class recently and in the past year. I would start with a rich task, knowing that this will prepare them for the lesson, but then after that go right into me do then you do what I did as a way to teach. I loved how in the book it gives you another way to touch on curriculum and still promote thinking. My thought has always been that there was no time to do all of this and still get to the required curriculum. I'm excited to read on and find more ways to do this!
You are so right! I've been operating (or so I thought) under the premise that I shouldn't be working harder than my students, but I need to reframe that into "I should not be THINKING harder." You're not alone in reflecting on past teaching, I had some cringing moments while reading this section.
DeleteWOW!! This book is really interesting and so 'right on'. It was really interesting about the 'mimicking' section. I found this to be really true in my class this year. They were pretty good at this and I really never thought about this until now. I also was intrigued by the institutional norms sections especially the classroom setup. I have always done flexible seating in my class and because of COVID, we really could not do that but this section made me really think about my classroom setup and how students bring their habits with them into class. However, if I make a change, I will have a chance to make something difference with their thinking. It just made me pause and reflect of the environment that I create in my classroom. Also, the questions on page 14 made me pause and reflect. I am really excited to continue with this book and try some of these new things in the upcoming year.
ReplyDeleteI agree jkim! I did a lot of thinking as I was reading about things I have done in the past in my classroom and the outcomes in terms of math thinking those created. I'm excited to hear about what changes you might make and what outcomes you hope to achieve!
DeleteMe too!
DeleteAs I concluded the first couple chapters of our book, I was left contemplating and critiquing the productive use of my students’ time in our instructional block. Though I have attempted to maintain high levels of engagement and sustain rigorous, diverse learning activities with low floors and high ceilings (in the words of the infamous Jo Boaler), I recognize that the countless hours I spend in the intentional design and construction of learning experiences result in a environment choked by "busyness”: instructional routines, partner work, group tasks, direct instruction, games, individual tasks, reviews, self-asssessments, etc. Liljedahl firmly distinguishes "business" from "thinking". A series of contextually-relevant, rich tasks only achieves the desired learning objective so long as the mental work behind the tasks is a result of the authentic challenges posed by the tasks. Often, as the author expressed based on his own observations of "good teachers", we subject our students to task after task after task in order to meet the expected progression of grade-level standards by the end of the year without pausing long enough to allow our students to fully process and immerse themselves in their conceptual understanding as it it developed. Effective instruction does not attempt to encourage students to "recreate the pattern of solutions" (p. 9), but rather invites students to formulate original thinking paths and blend novel concepts with individual or collaborative strategies for application. If we produce a classroom of "recreators" at the end of a school year, we have failed in our duty as educators. Instead, we must aim to produce classroom of creative thinkers who readily accept and embrace the "messiness" of math for the long term. As I begin to think about the tangible implementation of the ideas addressed in these chapters so far, I hope to increase my capacity to anticipate and predict when my students are ready to shift from non-curricular tasks to curricular tasks while maintaining an engaged "thinking" environment. As I always do, I aim to begin the school year with several days of non-curricular, collaborative tasks to gauge the readiness levels of my students to begin our curriculum and establish learning routines and expectations. As I read further, I look forward to reflecting on how I will reshape and reignite my mathematics instruction to effectively challenge and excite my students without defaulting to “busyness”.
ReplyDeleteThe introduction and chapter 1 were full of so much to think about! One sentence that I reread and thought a lot about was, "Begin by asking a question that is review of prior knowledge, then ask a question that is an extension of that prior knowledge." I love how the author gave examples of how to do this to introduce new content that could be tied to prior knowledge or learning of the students.
ReplyDeleteI also found the author's research about student thinking very interesting! Then he went on to talk about problem solving and how it is messing and cannot be routinized (students mimicking rather than thinking). This let me to really think about the 3 different types of lessons: non-curricular tasks, scripted curricular tasks and as-is curricular tasks. So many lessons in our classrooms could be changed to truly be thinking tasks!
The type of tasks matters in a math class for many reasons. First, it needs to be engaging and ‘hook’ the students in so when the task gets difficult, they are still motivated to keep trying. The task also needs to be relevant and relatable to the students. Delivery is important because students will pick up and feed on your energy. If you are excited about the lesson, most students will likely be excited as well. The opposite is true as well. If you are not excited about the lesson, students will be less likely to be engaged. Delivery is also important when it comes to activating prior knowledge. If you are presenting students with a problem-solving task, it is important to activate prior knowledge. This does not mean you have to show them how to solve it, but rather remind them of strategies and concepts they already know to get their brains thinking about the concepts.
ReplyDeleteMany others have shared ideas that resonated with me, too. The amount of studenting that I have seen in my classroom, for one. Reading the descriptions of each different type prompted names of students from the past like little bells. In the introduction they discussed how students bring all their prior habits and studenting norms with them when classes look similar. This was fascinating to read about how the lack of furniture for two weeks caused a disruption in their studenting norms. I would also like to cause a disruption in their studenting norms. I teach primary children, so to possibly be a part of spicing this up as we are laying the foundation for many years of education, I would like to.
ReplyDeleteStudenting. It seems like such a simple concept, but as I read through the intro and first chapter, I began to grasp just exactly that word meant. It isn't just the act of being a student. As I was reading the descriptions of each different type, I was thinking of this last year's class and how I could pinpoint students who were really good at, lets say, stalling (oh, the old pencil-sharpening-because-I-just-purposefully-broke-my-lead trick). As I continued through the first chapter, I found myself not just surface level reading. Honestly, I was trying to think my way through the rich thinking tasks that were presented. I'll be honest. My main pause and think was with the "card trick," which I tried numerous times with the kids playing in the backyard (and I still haven't figured out how to make it work!). What I came away with is really my need to let my students relish in that productive struggle we often talk about. I am very much going to push myself to place those thinking tasks first in my lessons!
ReplyDeleteOne of the things that resonated with me from the Intro and Chapter One was the idea of not if a math task is good or bad, but examining what it is good for. To that end, tasks and delivery matter because the type of task selected and how that task is delivered create an outcome. If the goal is to achieve the outcome of students who think about math in a way that will sustain them throughout their lifetime, attending to choosing thinking centered tasks and delivering them in a way that creates thinking classrooms is essential. For me personally as a student learning math who did so mostly by mimicking and didn't truly learn to think about math until I became a teacher, this would have been in a game changer! In addition, the macro and micro moves resonated with me as they are applicable changes that can be made in a classroom to move toward changing the outcome for students. Specific teacher moves that can be implemented to get students thinking more is such a great place to start!
ReplyDeleteA quote that I kept coming back to was, “Good problem-solving tasks require students to get stuck and then to think, to experiment, to try and to fail, and to apply their knowledge in novel ways in order to get unstuck.” This quote stood out to me because it emphasized the importance of creating a classroom community from day one that encourages risk taking and normalizes failing/trying again. I think it is so important for my young learners to really begin thinking flexibly and working through the problem-solving process. The chapter highlights in its Q/A that students can solve curricular thinking tasks without first being shown how to do them. There is an emphasis that using engaging non curricular tasks as a precursor to curriculum thinking tasks can increase the amount of students that are willing to think and increase the amount of time students are able to think for, both increasing students being successful at solving tasks. It makes me think about this Fall and the non-curricular tasks I can have my students engage in early so that they are set up for success.
ReplyDeleteI totally agree with the notion of risk taking and normalizing failing/trying again and again. It seems like non-curricular seems a lot like the number talks and routines we have been working on for a couple years. This just reinforces how we have been working towards.
DeleteKendall that same quote stood out to me as well. It is important for students to know that making mistakes is part of the learning process. It is how they grow. The environment that we create in the beginning of the school year is very important.
DeleteStudenting. What a funny word that is so spot on. I couldn't believe how accurate the descriptors were and how many times I have seen students with that behavior in my classrooms, Even when I thought my lessons were engaging, I didn't consider the mimicking aspect to them. I know we have been working diligently to change our instructions, especially with regards to thinking routines and number talks. I am excited to see how we look at our thinking of students differently after this book and how it meshes with our new teaching materials. I can't wait to think about my instruction differently and see kids responding differently and thinking more deeply.
ReplyDeleteThe types of tasks that matter in math classrooms are: non-curricular tasks, scripted curricular thinking tasks, and scripted curricular tasks that access, build upon and extend prior knowledge. The delivery is critical as student engagement is essential to increasing student thinking. Tasks are engaging to the point that students “cannot resist thinking” about them, and are based on the “reality that is relative to students’ lives”.
ReplyDeleteI was very inspired within the first couple of pages of our book. All of my wheels were spinning as I actively considered how to dramatically impact my students’ mathematical thinking and reinvent what it means to “student” in 2022. It is a bold move for Liljedahl to challenge the “legacy practices” within our educational system, he does so with steel focus and practicality, always centering his objective on creating a generation of thinkers.
The mental health of our children was also brought to the forefront early in our reading. When students live and learn in thinking classrooms they experience: everyone getting “stuck” - that it is a safe and normal part of learning. Through their engagement, they build their confidence based on what they were able to overcome, and in seeing their teacher’s confidence in them. These aspects thoroughly hit home for me as a mom of two little guys with “super powers”, my wish for them each school year is a richly inclusive classroom where their hearts are taken care of just as much as their minds.
As others have said, the section about student behaviors and how students are “studenting” really caused me to stop and think specifically about the students that appear to do well in class but when they took the test, they would struggle. Unable to use any strategy that might lead them to the correct answer. During class, they would watch what their teammate was doing and mimic those steps, thus not really thinking or learning the skill. In chapter 1, it states, “Good problem-solving tasks require students to get stuck…” This is challenging for most students. They don’t like the feelings that come with not knowing how to do something. Learning to problem-solve or think through different ways to solve a problem is an important growth mindset goal. Learning to be uncomfortable with what we don’t yet know how to do.
ReplyDeleteI agree, Amy. Becoming mathematical thinkers ties in well with everything we teach them about growth mindset. What a great opportunity for them to put it to good use. I think students are accustomed to being "rescued" when they're stuck and, like you said, they don't like those feelings that come along with not knowing what to do.
DeleteThe types of tasks matter in math classrooms because some encourage thinking, while others encourage mimicking. If a student is thinking, then they are engaged and invested in their own learning, while those who are mimicking are likely just going through the motions. I am excited to more intentionally implement the micro-moves noted on page 35, including starting with a non-curricular task and using scripted, curricular thinking tasks. Not only will this require a shift in my practice, but it will also cause a bit of discomfort for some of our learners. I believe that many of our mathematicians, when given a now-you-try-one task, think to themselves, "What does my teacher want me to do here?" Their goal seems to be to make the teacher happy rather than to acquire a new skill. I'm hopeful that using these "new" moves will ultimately result in giving my students more choice and more pride in their own accomplishments. As many of you have already noted, building a foundation of trust and acceptance in my classroom will be a necessary step to be successful in building thinking classrooms where it is okay to try, fail, and try again.
ReplyDeleteI spent a lot of time thinking about the "mimicking" behaviors that were discussed in these two chapters. The quote, "mimicking happens not alongside, but instead of, thinking" stuck with me as I realized how easy it is to mistake mimicking as learning. It also made sense that the longer students become habitual "mimickers" the more difficult it will be for them to truly understand mathematics. I feel hopeful that we can undo these learned behaviors and create lifelong mathematical thinkers.
ReplyDeleteAfter reading the first chapter and introduction, the thing that resonated with me the most is the importance of teaching students how to think and establishing an environment that allows them to do so.
ReplyDeleteI love the idea of giving students 3-5 highly engaging non-curricular tasks with “broad appeal and an open-middle” prior to beginning curriculum in order to drive students to want to talk and collaborate. I think creating a space for dialogue and teamwork, and setting the tone for joint effort, persistence, and thinking, right away will be so powerful. In reading, I felt assured that the investment of time and effort would set the tone for thinking and problem solving. I love that these tasks give students confidence by making “stuck,” an expected, safe place to be.
While attending a tech conference this summer I was introduced to the idea of using virtual escape rooms to encourage productive struggle. I think it could be a really powerful tool in propelling students toward thinking and making it a classroom norm to be “stuck” and move past whatever challenge may be in front of them. My hope is that this type of non-curricular task, along with mathematical ones, will help foster a willingness to think first, and build excitement around thinking this year.