Watch the video Math Class Needs a Makeover and read the excerpt from Principles to Actions. Pay close attention to the 8 Math Teaching Practices on page 10 and the chart on page 11 that outlines Productive and Unproductive Beliefs about Teaching and Learning Mathematics.
Consider
Respond and Interact
After watching and reading, 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 is resonating with you from this video and reading?
- What caused you to pause and think?
- What math experiences from your own classroom came to mind as you were watching and reading?
After watching and reading, 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.
As I was listening to Dan Meyer, I was struck by the number of parallels that exist between his thinking, the thinking of Peter Liljedahl, in Building Thinking Classrooms, and the principles guiding the new Illustrative Mathematics curriculum. For example, Meyer encourages the educator to “be less helpful,” and in the same regards, Liljedahl advises educators to acknowledge but not answer questions that cause student thinking to stop, or proximity questions students simply ask because the teacher is close by. Rather, Liljedalj encourages “keep thinking questions” where the educator gives hints and not answers. Each scholar highly regards students’ perseverance and active role in problem solving experiences. In implementing the Illustrative Mathematics curriculum in my classroom this year, I found “being less helpful” to be the most challenging, but most rewarding area of growth for me as an educator. Moving from a program taught primarily through direct instruction to a problem-based curriculum was very uncomfortable at first. I truly had to step back and figure out how to support my students and guide their understanding, in what initially felt like a new capacity. Trying to be “less helpful” turned into insecurities about not being helpful enough and I was so unsure of my effectiveness as an educator, but in staying the course and allowing my students to forge their own paths I saw and was amazed by their abilities to reason mathematically and problem solve.
ReplyDeleteThe idea to "be less helpful" in math seems really scary right now when I think about my group of students that have to meet me at the teacher table regularly for extra support. However, I am excited about this shift for students in their roles as math learners, as well as in my role as a math facilitator. I'm not looking forward to the uncomfortable-ness that will accompany this shift, but I know it is part of the process and will be worth it for my students. I am grateful to you, Kylie, for being brave and being an early implementer this year. It is really exciting to hear you share about how much your students have grown as mathematicians so far this year.
DeleteI agree! Being "less helpful" can feel really scary - especially with some of the kids in my current group. It makes me curious what Tier 2 interventions will need to be in place to support the kids who need the extra support and maybe a little "more" help.
DeleteWhat is resonating with you from this video and reading?
ReplyDeleteThe “5 symptoms” resonated most with me. I definitely notice these symptoms with some of my students. I have a habit of internalizing my students’ academic struggles in the classroom to my teaching (or the shortcomings in my teaching). There was some comfort to read this and realize that this is not something that only I experience. That said, clearly this indicates that something needs to be done.
What caused you to pause and think?
I really love Dan Meyer’s approach to teaching; making it so much more accessible for everyone to be part of the conversation. I hadn’t thought about using real world examples like videos and photos for math lessons like he has.
Dan Meyer also opened my mind to the rich conversations that can happen when the details are left out; allowing students the opportunity to think through the process on their own. I really like this.
I thought the reading was really interesting. I spent more time reading again through the “unproductive” vs. “productive” beliefs table. It’s such a large shift in thinking today, compared to when I learned math (which consisted of pretty much all of the “unproductive” beliefs!). After reading through this however, I’m left wondering if there is still some space for things in the “unproductive” column, like establishing a strong foundation by mastering basic skills and guiding students through steps in problem solving. Or, is this just completely unnecessary to mastery of math?
What math experiences from your own classroom came to mind as you were watching and reading?
I’m starting to think more about what I can do to ensure my students are being given plenty of opportunities like this. Perhaps on a smaller scale, I start math lessons with a warm-up which often involves a “math talk” of some sort. Today’s math talk was deciding which equation out of 4 did not belong. Rather than have students get hung up on the “correct” answer, I reiterate that there isn’t a right or wrong answer; it’s how you explain why a given equation does not belong.
Stacey, I also have the same wondering about space for those foundational skills. Am I holding onto it because that's how I was taught and basic skills that I use everyday? I still feel like there needs to be a balance of both. The challenge for me will be finding that balance.
DeleteWhat part made you pause and think?
ReplyDeleteThe part that made me stop and think were the comparisons of the Unproductive Beliefs versus the Productive Beliefs about teaching and learning math. The productive belief that an effective teacher provides students with appropriate challenge, encourage perseverance in solving problems and supports productive struggle in learning mathematics.
I know in our current math program when students’ struggle with a more difficult problem solver, I have taught problem solving by teaching them a step by step system to break down a problem, and a certain way to show their work. This practice was not allowing students to build the problem and reason mathematically on their own. I see how through Illustrative Mathematics, I’ll be posing purposeful questions to support students’ reasoning. I am eager to learn the questioning strategies and learn how to be more of a facilitator of math reasoning through using the new program.
One thing that resonated with me is "the math serves the conversation; the conversation doesn't serve the math." I was reminded of an Annie Fetter video that I watched years ago about creating genuine curiosity among our learners. It was in this video where I was first introduced to, "What do you notice?" and "What do you wonder?" These two simple questions have been game changers for me in launching a lesson.
ReplyDeleteI remember this also and do not use it enough! Tomorrow, I'm doing the first lesson in 5th grade math on analyzing numerical patterns and I'm going to start out with these questions. I'm also going to support the productive struggle and let them patiently problem solve. It's so hard to let them struggle and be less helpful to them in order for them to grow more. They'll have support from the discussion with their peers, but I'm really going to try to take a step back these next few months and let them drive the learning more.
DeleteI have been using those two questions a lot in class( What do you notice?, What do you wonder?) since starting this math journey. Sometimes I am surprise by their perspective and insight. I think this idea of more student involvement and less teacher talking at students will have a positive outcome. I know the first year will be challenging but I think it will also be rewarding to see student grow in confidence of their abilities and develop a deeper understand of the math content.
DeleteOne thing that immediately resonated with me was the five characteristics of students in a math class- lack of initiative, lack of perseverance, lack of retention, aversion to word problems and always looking for the formula. That was me as a math student 100%. Now, I thought this might be more typical in high school until yesterday when the teacher that has my 2021-22 students informed me they can't remember how to to multiply, divide, etc. fractions. My response was, "But that's what we did the entire year!!" Now, this wasn't all students, but it was very apparent my teaching had not made a lasting result on some. My immediate response, prior to watching the video and reading the article, was that something must not have connected fully for them, but what? I now think the more interaction and pathways to problem solving the students have, including Meyer's suggestions of using media, encouraging intuition, low level entry questions, and letting students build the problem are the key connections to long term understanding and mastery. This pairs with the article's idea of "using and connecting mathematical representations" and "pose purposeful questions" to name a few. The deeper we connect and create multiple brain pathways for mathematical understanding the better their conceptual knowledge and procedural fluency will be.
ReplyDeleteAimee, this also resonated with me. That's all we did in math was memorization. We never were taught strategies behind math. I often say if I only understood "the why" behind the math when I was younger I think I might have been a much better math student. Instead, I struggled with math for my whole education.
DeleteTwo things that resonated with me were to simplify and application. As a student and now a teacher, math problems can be overwhelming. Having too much information can be overwhelming for some people and interfere with problem solving. Where do I begin? On the flip side, I also have students who see the numbers presented and immediately move to solve without an understanding of the situation. One approach I've used in the past was to hide the numbers so students were "forced" to focus on the situation first. This was helpful in slowing down the process, make sense of the problem presented, and talk about what they would do to find a solution. However, I still had students who were not confident in math who were left intimidated and confused. I felt this way in a couple of my high school math classes. It wasn't until college that a professor helped me realize the importance of connections and application. This is similar to what resonated for me in Dan's TED talk.
ReplyDeleteAfter watching his presentation, I approached the next day's math lesson differently. I pulled back the curriculum's directions to circle groups of ten and count by tens and ones. Instead presenting just the large group of circles and asked students for the total. Students made a connection to our Star Student estimation jar activity from earlier in the year as a way to put the circles into groups of ten and then count them together. There was a difference though. We could physically group the items into groups of ten allowing for more accuracy. How would we do it with a picture? Through the discussion, they came to the conclusion they could mark the ones they counted before circling a group of ten and then count by tens and extra ones to find the total. There was a feeling of increased energy, engagement, and confidence that afternoon. :) I want so much more of that in our classroom for my students and as a teacher.
What resonated with me is my interest in seeing my first graders' response to Illustrative Mathematics next year. The freedom of approaching their math work more independently will definitely be challenging for many of them (and me, as well!). I see this approach connecting to my goal of challenging students to be more independent in general in the classroom. In the past few years, I find many students reluctant to solve small problems on their own, preferring to immediately ask for help. I am excited to see if/how broadening their approach to mathematical thinking will lead to increased confidence in themselves in general. It also changes my view of what an effective math teacher does, and I'm already wondering how this change in viewpoint can be applied to other classroom subject areas. I also feel some stress because an important part of this approach to learning seems to depend on the teacher being there to prompt/ask the right next question, and I'm wondering if I can do that effectively and reach all of my students. However, perhaps the struggle is part of the purpose and the learning and will lead to my students taking on greater control of their learning. There's a lot to consider! -Susan
ReplyDeleteThe table on page eleven in "Beliefs about Teaching and Learning Mathematics" resonates most with me. As I reflect on my experience in my classroom I have been enormously grateful for the math class I took last spring because it provided the background, skills and strategies to support student flexible and fluent mathematical thinking. As I reflect on the table of "Unproductive and Productive Beliefs" I feel excited to continue encouraging "productive struggle" with our new math curriculum. Student engagement, like the practices for fluency and flexible math thinking, has been high with the few Illustrative Math centers I have introduced so far.
ReplyDeleteWhat math experiences from your own classroom came to mind as you were watching and reading?
ReplyDeleteSome things that came to mind as I read the Mathematic Teaching Practices is how I've known for a long time that the way we've been teaching math according to our curriculum has been missing some key components. Although I try (we all try) to have meaningful discourse during lessons, for example, that gets pushed to the side often because of time constraints or the lack of confidence in the kids' ability to carry the conversation. I think that often several of those practices get touched on when we do math talks and warm ups, but during lessons, we go back to what's comfortable and quick, even though it's not always what's best for kids. I think that the 'productive struggle' kids need to go through will be interesting to watch happen. Considering the learned helplessness a lot of kids have adopted, I am hopeful that the perseverance needed will spill over into other areas during the school day.
The video and the reading reminded me of the learning I did last spring taking Renae's "Fast is not Fluent" math class. While it dives deeper and more broadly into the subject of math curriculum, I am still struck by the differences in how the math brains in my own family learned math when being taught the traditional way. My husband is an engineer and still remembers and uses formulas and algorithms and understands their practical use, and my three college-age children seem to have the same gift. I was an algorithm memorizer who got B's in high school math by figuring out what the textbook/teacher wanted, but retained only a skeletal understanding of what I was being taught. Thinking about my own students in the resource room, I can see how some of them are naturally able to see mathematical relationships easily, while for others it is a struggle. I am interested to see how the new curriculum will work for my diverse learners. Productive struggle seems like a really great concept, but I wonder about some of our slower processors and how we can help them without leading them to the answer and/or causing the struggle to be unproductive.
ReplyDeleteWhat caused you to pause and think?
What math experiences from your own classroom came to mind as you were watching and rea
What is causing me to pause and think about our new curriculum is something that Dan Meyer said, and I know what the new curriculum is encouraging us educators to do and that is to “be less helpful”. It feels daunting in ways – how will that look as we implement this new curriculum? However, as I listen to him speak about patient problem-solving and having students have conversations about “math so that math serves the conversation, and the conversation doesn’t serve math” it forces me to reflect on some of the most successful times in my classroom when students were having small group math work and doing problem solvers. They were truly leading their own discussions and taking their own steps to resolve the situation with me being less helpful. They not only enjoy those math lessons, but they truly are successful. I can only imagine with this new curriculum allowing for the students to not be led as much to the answers as previous math that they will be wildly successful and enjoy the process of learning through each other and using past schema to build on. The other idea that resonated with me was that when students believe that they are capable of learning mathematics there will be more of a willingness to persevere and solve challenging problems and I believe students get a great sense of belief in themselves when they can solve problems on their own and they are successful.
ReplyDeleteIt has been interesting talking to our grade level lead for Illustrative Math as she has walked through the process of "being less helpful." In September, she did feel a certain level of overwhelm with the process of increased student ownership. It is reassuring to learn from her that her students are absolutely more actively engaged in their own mathematical thinking and constructing their own strategies.
DeleteWhat caused me to pause and think was when Dan Meyer was talking about the structure of word problems and how they are basically leading to no thinking. I feel that I have seen that happen at times with my students who just start plugging in numbers but don't actually pause to think through what the problem is saying and asking. It also made me think of how I can start changing the questions that we have in our curriculum this year to have students construct meaning even more than they might be doing now. I think it will be an interesting shift to the new curriculum to see students have to make sense of the information in front of them instead of just following an algorithm or formula to solve. They will have to really be thinking about what is in front of them and start figuring out how to make sense of it. I am hoping that by having these conversations with peers and me when they construct meaning that the concepts will be more solid in their mind and they can access them with ease months after learning about it.
ReplyDeleteThe TedTalk with Dan Meyer was amazing. While I feel like I am no longer the "old school" math instructor that I was when I began teaching and haven't been for a while, it's still interesting how when I listen to teachers like him talk about challenging students and allowing that productive struggle, it tends to make me anxious and uncomfortable to some degree. It is definitely a challenge to picture math lesson, after math lesson where I'm not guiding my students in their thinking, but instead letting them decide where to take this math ship. At the same time, 5 minutes into his talk, I was super energized and ready to emulate his teaching style with my kids. The "Make sense of problems and persevere in solving them", has always spoken to me as a math instructor. At the end of the day, that is the skill I want my kids to walk out of the door with, in June. I would imagine that Dan Meyer's kids do just that.
ReplyDeleteSome experiences that come to mind in my own classroom and the age of students I teach are leading students into a mathematical structure by letting them be part of the formulation of a problem through discovery. Using real world examples, not diagrams and pictures, allows students to draw from their own experiences, learn through discovery and make sense of mathematic concepts. It promotes “buy in” and motivation. As the teacher, my role is to engage and guide students using purposeful questions. The role of the student is to be actively involved and make sense of problems.
ReplyDeleteAngela Moore
ReplyDeleteMy own Math experiences throughout public school mirror the way I have taught except for the incorporation of Math Talk when teaching problem solving tasks. I worry that I too have done a disservice to my students but know that I have also done a good job of instilling in them number sense as primary learners. I am nervous but excited to learn a better approach to helping students learn math. I know when we had our training with the new math, I found it very engaging! I felt a sense of accomplishment when I understood the concepts and could share this with my partner. I want this for my students as well. I also want my students to be ready for third grade and worry that the new math will be overwhelming to them. Thank you for helping us improve our teaching.
I absolutely loved this Ted Talk. My favorite quote was "Math should serve the conversation, the conversation should not serve the math". Often times we think that being a good teacher is asking the good questions but it should be that the students are asking the questions themselves. They should be steering the conversation. This leads to a lot more engagement and buy in from students. I think that our math routines and "notice and wondering" do a great job of allowing students to come up with ideas that are of interest to them. Many times they will wonder exactly what the problems intends them to, but now they have more ownership! I will say that getting students who are less confident or willing to participate sometimes are still timid to share their ideas. This is where celebrating mistakes is so incredibly important. I am really excited for our new curriculum because I think it will do a great job of helping students see the value in sharing their thoughts and curiosities about real world math problems!
ReplyDeleteI agree that celebrating mistakes is so important! I am looking forward to building that culture of mathematical thinking with our new curriculum.
DeleteThere are several things that resonated and stuck with me in watching this video and going through the reading. Two that I have been trying in my class are "being less helpful" and "asking the shortest questions I can". It is so easy to over explain or to push students to a solution before they are ready which doesn't allow them the time to come to solutions and understanding on their own. Keeping my prompting and questions simple not only allows more students to enter the conversation, it gives me a wider range of responses and allows my class to share their perspective. "Tell me more about that" has been a really great phrase to get my students to explain their thinking to both me and the class. I have also been thinking about math as a time for productive struggle and this makes me excited for a new curriculum that will allow students more time to explore and will be problem based learning. Allowing students to approach math more independently and giving them the time and space to arrive at their solutions definitely takes patience and has me reflecting on so many of my teaching habits. It is an adjustment for both the students and myself and I look forward to seeing how the new curriculum helps guide students and empowers them to take ownership of their learning.
ReplyDeleteI really liked the Dan Meyer video. One part of the video that caused me to pause and think was when he said we need to “be less helpful”. I definitely lean towards being the teacher who jumps in and helps or rescues. That productive struggle always felt frustrating to me as a math student and I think that because of that I tend to shy away from embracing those opportunities in my own classroom.
ReplyDeleteIn the Productive Beliefs section of the Beliefs about Teaching and Learning Math the last section really resonates with me, “An effective teacher provides students with appropriate challenge, encourages perseverance in solving problems, and supports productive struggle in learning mathematics.” It reminds me that I should go back to doing more work around growth mindset in my classroom related to mathematical thinking. Not only will being more intentional about growth mindset support my students, but it will also help to frame my own thinking around the productive struggle so that I see it as a part of our math community rather than something I avoid.
Ohhh! I forgot about that part, but that was one of my favorite parts. I need to keep that in mind, to ask the right questions and give them the time to do the work. I also found it frustrating but I think it is so powerful and with the right set up and questioning from the teacher, I think it can go a long way!
DeleteWhat resonate with you? I can really connect with his observations at the beginning where he talks about how we have forgotten much of the math we learned in school. Recently, my grandson brought home an assignment in multiplying fractions and wanted help. I had to sneak into the other room and take a refresher from google. Additionally, Kelley has my class from two years ago and will often mention that they don’t remember being taught long division, or multi digit multiplication. I have test scores that prove they did know what to do in third grade but they obviously were not secure in the knowledge, just in the procedures, but that did not stick with them as we changed units.
ReplyDeleteWhat caused you to pause and think? I loved the comparison to Three and a Half Men, and the impatience we have for instant solutions. I think some of that comes from the practice we do in the workbook that has 12 problems to solve. Students feel they must be fast and crank out those problems. I loved his strategy of breaking one problem down to just a simple question and having student discover what they need.
Another thought that stuck with me is “Be Less Helpful”. The other day a girl in class raised her hand for help. I went to help and she said she didn’t know what to do with problem number 6. I asked, Why don’t you read it to me. She was had not even read the problem. Just hoping for a quick fix. It has probably worked in the past because I am too helpful. All in all, really good food for thought.
This Ted Talk and reading made me pause and think about my teaching, about the new math curriculum and about the experiences for my students in my classroom. The part of the video in which he talks about the "impatience with irresolution" certainly made me stop and think about how I can connect to this statement. The desire to "jump in" and help students when they are struggling in math is (admittedly) something that I often struggle with in my teaching. I often think that it is something that I might have missed in my teaching or explaination in the material and this is why there is confusion. "Be less helpful" is a quote I would love to have printed on the wall for me to see. The math warm up at the beginning of our lesson provides the greatest opportunity for rich math discussions with student talk, discovery and questioning being the foundation of the math warm up block.
ReplyDeleteThis video and reading also made me think about the new math curriculum and how this seemed to summarize what the students and teachers will be experiencing in the upcoming years. Less scaffolding, more discovery, students using intuition in problem solving, redefining word problems and creating opportunities for productive struggle in our classrooms are all components of the new curriculum that I am really looking forward to!
What resonated with me????? Well several things. The TED Talk for one. The quote saying "Math should serve the conversation, the conversation should not serve the math". This is a long way from the math instruction I received in school. The idea that teachers talk less while not jumping in to save students.
ReplyDeleteI also really loved the the table on page eleven in "Beliefs about Teaching and Learning Mathematics" because everytime I read through it I see more and understand more of what the meaning id for math in the classroom.
What caused you to pause and think?
ReplyDeleteThe table with "Unproductive Beliefs" and "Productive Beliefs" made me pause and think, specifically "The role of the student is to memorize information that is presented and then use it to solve routine problems on homework, quizzes, and tests." This made me think about 'timed tests' which as a student I dreaded and would physically get sick before and have always struggled giving to students because I knew how they made me feel as a student. I am very excited at the opportunity to begin changing our instruction to allow students to become more "actively involved in making sense of mathematics tasks by using varied strategies and representations, justifying solutions, making connections to prior knowledge or familiar contexts and experiences, and considering the reasoning of others." I am excited to see a change in student understanding and their ability to understand math at a new level. Even talking with our teacher who is piloting the new program, she says it moves slower than our current curriculum but she has never heard her students discuss math concepts like her students do this year. I look forward to seeing these changes as we begin this new journey.
What is resonating with you from this video and reading?
ReplyDeleteI really liked the part of the video when it related a math problem to watching a sitcom, where you want an easy answer within a half an hour. The speaker also kept saying we don't want to solve a problem that is easy to solve and that also made me stop and think. Yes, it would be nice to get it right away but I can tell you from experience I grow more as person and learn more when I am challenged and pushed. I have been intrigued with starting my lessons with more of a question but I get panicky thinking I won't fit it all in. But what am I trying to fit in? Big questions for me to contemplate through this workshop and into next year.
What caused you to pause and think?
The part that really made me stop and pause was when the speaker said that we want involved kids, and that is the most clearly stated goal that I always am trying to do. I also stopped while reading the article where it talked about strategic competence. Recently my team has chosen a math practice as a common challenge and this part of the article was a really big clarification. I really had to read it slow and I still feel like I should review it a couple of times. It makes sense, it is just a lot of information but thankfully it is organized very clearly.
I loved the Ted Talk! Dan Meyer mentions how our teaching styles and curriculums often offer steps for students to make it over small cracks leading them to a formula that requires little thought. This reminded me of something I read from Jo Boaler. She wrote about the importance of productive struggle and provided a visual of a “math pit.” While in the pit students experience productive struggle, ask questions, interact with peers and teachers, and problem solve until they make their way out of the pit. She also provided another visual of the math pit with a ladder going across the top. It showed how teachers often provide too much scaffolding for students, helping them to the answers or formulas while robbing students of the chance to truly engage with the math. I believe Meyer’s encouragement of patient problem solving and suggesting that teachers be less helpful ties in nicely with Boaler’s “math pit” visual. In my own classroom, I have been using our new curriculum and I see so much of what Meyer’s encourages in it! My class has wonderful conversations about math, and they surprise me with the connections they make. I still find myself pulling out the ladder to help them over the pit from time to time, but feel encouraged and excited by my own growth and theirs.
ReplyDelete