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.
Resonating with me was the fifth strand called productive disposition. I'm excited to create an environment where students have resolve and see themselves as mathematicians. By developing this sense of self students then will become motivated, will be willing to persevere and will have an interest in math. I cause learning!!!
ReplyDeleteThe second part of the article that will linger with me, is the chart on page 11 Unproductive / Productive beliefs around the teaching and learning of mathematics. Knowing that my beliefs impact my teaching practices I would like to focus on active participation and purposeful questioning/facilitation which will support the lesson design of IM. Let's grapple mathematicians!
I loved the video. I actually stopped and read the transcript so i really understood what he was talking about too. The concept of real-world math makes so much sense in the world today. Really looking at real life objects, like the tank, and having the kids get to the point where they are generating the mathematical questions is so powerful. I think the open middle concepts and three act tasks we have been using in the past few years really lend to this too. They help all kids have an access point, like the teacher mentioned is a bigger issue if a student doesn't engage because they know someone else in the group knows the formula already. I think our new math curriculum has a structure that lends to exploration and allows all students to access the math. Reasoning is hard for mathematicians and finding ways to better teach how to do so is a great move in the right direction.
ReplyDeleteA few things that resonated with me...
ReplyDeleteFirst was the “lack of perseverance” which I saw in many of my students this year. They just want to get to the right answer fast. If they didn’t get an answer fast enough, they expected me to show them how to get to that answer quickly. The try and try again wasn’t in their repertoire.
Second, was Dan Meyer comment in his video about writing down the thoughts and ideas students shared with their name by their thought as well as when he mentions how you can “get people (students) arguing against each other, friend versus friend, in pairs, journaling, whatever.” I heard there is a lot of math talk in IM and saw posts on the IM Facebook group about partner talk and small group math talk having a positive role in helping students share their ideas in a safe space.
Third, is using multimedia, objects, or bringing real life examples into the classroom to help students relate and connect to a problem. The article mentions having students make connections to prior knowledge and familiar contexts and experiences which I feel will help students be more actively involved in math talk.
I am hoping as I begin teaching the IM curriculum in the fall that I can help guide my students who have the “lack of perseverance” grow their strategies through math talk with classmates in different ways.
I agree with you Beverly on the 'lack of perseverance' that I saw in most of my kids. If they did not know what to do, they would wait for me to explain again or want me to provide them with the answer... Usually it was " Do I need to add?....pause... or Do I need to subtract?" So I totally know how you feel and can relate to you on this issue/ problem.
DeleteI am also hopeful that the new math will help with the problems that we see many kids face today in our classroom. I want to see the engagement, the conversations, the perseverance, and just the excitement. Can't wait to try this out!
What resonated with me is that we need more patient problem solvers! I for sure fall into this category too. :)
ReplyDeleteI want to make math as real world as possible. I see how showing just the photo/video and ending question makes students think about the "in between" questions and steps. No formula or strategy is given at the beginning. THIS is what I think will push my students the most. Many of them are very good at learning algorithms, but are not necessarily good problem solvers. So I need to be LESS helpful to promote perseverance. This is something I learned more about in the book Building Thinking Classrooms too.
Posing purposeful questions that promote reasoning and problem solving is so important. But must be supporting productive struggle. It can be a bit tricky to know when it is productive and when it is just overwhelming... for me too! This is why students (and teachers!) need a variety of strategies and a low floor so everyone can get started.
There was quite a bit that resonated with me during both the video and the reading. One thing that stuck out was the concept that math facts and rules are easy to forget over the years, but are easy to pick back up if you have a deep grounding in reasoning. To do this we need to give students more opportunities with real math that, as shown, doesn't just feed them numbers they will use. I so often see students understanding that "this unit is on double digit addition," see two numbers, and add, without really comprehending the problems. (Side note, this is also why I get so upset when kids don't label). There is a lack of initiative to ground reasoning because we don't give students enough time to explore. There is pressure from making sure we get all of the curriculum done, pressure from families to just teach them the old way, and internal pressure to make sure kids do well on tests which often means telling them the steps to get the answers. Because of this there is a lack of perseverance as students age because they are used to teachers giving them the "tricks".
ReplyDeleteI especially appreciated the idea we eliminate large portions of word problems and have kids solve one larger problem without giving an algorithm. The examples presented reminded me of Fletchy Three Act Tasks, and it might be nice to have those listed as enrichment activities depending on lessons.
Finally, and perhaps more controversially, is the idea of our standardized tests. If we are not looking for mastery of topic presented, but are looking to build logic and reasoning as a spiral, this needs to be demonstrated in the way we distribute grades. While I haven't taught the new math curriculum, I have seen teammates do it, and have been a parent of a student taking it. These tests do not reflect the proposed ideals of a spiraling curriculum. I have seen HUGE growth in my own child's conceptual understanding of fractions and his reasoning behind computation. (This is coming off of just teaching 5th for years and him being in 5th). His reasoning was far beyond what my previous students understood by looking at Math Expressions, yet he got 1's and 2's on tests. If we are not looking for mastery in skills, I think our end of unit assessments need to show that. Luckily, Sam was able to demonstrate his thinking in various ways, but the section of reading today on the role of teacher looking at assessments made it clear our ideas need to change.
Jennifer I am inspired to hear your success story for your son and at the same time concerned over the testing. It is true this type of learning will allow students to challenge themselves and create meaning. It will work really well for some and I fear will still leave some behind. My own son in 7th grade was part of the pilot for both middle school options. He is a rule follower and like to know the expectations. He candidly expressed that he didn't like having to figure out all the steps and wished the teacher would just show him how to complete the problems. I think this will challenge him in a way that will be good for him, but it is a shift. With this shift in mind, we will have to help students and families understand the process and know how to interpret their child's success.
DeleteI appreciated your candor about the experience of your son, and having mine move into middle school, where I will have less "control" makes me nervous as well. As a teacher, my team discussed sending home an email and letter at the beginning of the year explaining the shift, and then a letter with the first assessment explaining why scores might look different. I believe Amy O. (2nd CRES) created a letter that was used for sending home the first test. I am EXTREMELY lucky that my son's teacher did not just use standardized tests to decide his grade, because he only got 1's and 2's, but his teacher looked at his work as a whole and his math talk discussions. I fear that with so many students in middle school, the same opportunities won't be provided. (I've also never taught middle school, so could be completely wrong.)
DeleteThe math class experience that came to mind was my own class most of the time. It is like what the article mentions as an obstacle: review, demo, practice. I think we have taken strides to get out of this with other mathematical practices being encouraged. However, there is so much content to get through and so little time. I feel I have let the drudgery creep into the math class. Admittedly, it is clear some students are left out, as they don't connect with the direct instruction and are challenged very little on a daily basis.
ReplyDeleteHowever there is hope. In the moments when games are played, number talks inserted and problem solving with 3 act tasks enter into math time students are lively and engaged. I know this is what's needed and I have so much hope for this new math practice & curriculum. It will challenge me to be a better leader by allowing students to lead their own learning. At least that is my goal.
As I was watching the video and reading the article, it does make me think about my classroom kids but also the way I grew up in school. For instance, looking at the back for the answers (I remember that they would have the odd number answers) , trying to remember the formula (not really understanding but just wanting to get to the answer) and always knowing that someone in class would answer the question in class. WOW! That was straight on. Then it reminded me of my own class and what I see in kids. I see lack of perseverance and also kids who always said.."Do I add?...or do I subtract?..."
ReplyDeleteI am really excited to try this new math curriculum for next year. I want to see the engagement, the math conversations, the questioning or defending their reasoning... However, I am a little nervous just because this is something new and I grew up in the math word where it was practice drills and memorization.
I really enjoyed how the math teacher talked about engaging his kids by using real life objects and where ALL kids could participate in the math conversations and not feel intimidated. The water tank was soo hilarious and it even made me really interested and I even laughed so hard. I would love to see and use more real life situations and objects in our class and can't wait. I am excited that we won't be seeing the story problems ( that you would never use in real life or even hear about) that my kids had to answer in the math curriculum. Can't wait!!
Several things resonated with me from both the video and article. First of all, in the video the teacher's advice was to be less helpful in order to create more patient problem solvers. I think it's difficult to watch our students struggle and it is human nature to want to jump in and help them. In contrast, we need to create situations where students have to make sense of the problem themselves and identify what they need to know in order to solve it. When we provide them with everything they need to be successful we are not allowing them to engage in that productive struggle that creates flexible and persistent problem solvers who are able to reason and apply their conceptual understanding in real world situations. I believe this is what has been missing in our previous math classrooms.
ReplyDeleteSomething else that resonated with me is the shift in the role of the teacher and student. Rather than being a dispenser of knowledge and telling students what they need to know, there is a much greater payoff when the teacher acts as a facilitator allowing the students to assume a more active role in their learning. Another important piece is the importance of feedback from not only adults, but also peers.
As an early adopter of our new math curriculum, standing back and not "jumping in" has been one of the most difficult pieces for me. I've had to learn to trust in the process and allow students the opportunity to make their own connections and engage in productive struggle. This allows them to learn in meaningful and active ways through collaboration with their peers.
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.
ReplyDeleteSo many ideas resonated with me in both the video and the article, especially the idea of the need to be patient with problem solvers. I was an early implementer of the IM math this year and although I found if challenging in the beginning, I came to love it. The kids did take time to "figure stuff out," but, because they were invited into the math before demonstration, many became better at using math discourse - talking with a partner and struggling - although I believe it WAS productive struggle for many. Of course there were still a lot of kids who DID just ride the coattails of stronger mathematicians - trusting their partners thinking and still shy or afraid of saying the wrong thing.
ReplyDeleteI was excited when in the video, he stated that a better way to introduce math is visual/question/structure, as well as using real world problems to create a productive disposition. So much of the warm-up for IM lessons introduces the lesson with a visual and that exact questioning... "What do you notice, What do you wonder" I love this way of starting math - It really is a great way to start that allows access to every student... there is no wrong answer, this is when the most hands go up in class. He also said, "let students build the problem" . Often something they "wonder" leads to the math they are about to engage in. As for myself, I need to be "less helpful" and ask the students more questions when they ask me what to do, in order to continue for them to be problem solvers and build perseverance.
The very first thing that resonated with me after watching the video was I wish he would have been my math teacher. Wow, he just brought to light so many things that I was seeing but didn’t know how to rework or wish I would have learned.
ReplyDeleteWhen he was talking about how all the information is given to the students and that there isn’t any real need to problem solve, I thought man that is so true. I hate to say it but I have tried to show my kids that all these problems have patterns. So if they see the pattern they just have to plug in the numbers to be successful. I have always been taught to look for the pattern or formula and you can solve the problem. Well guess what it’s time to shake it all up.
I’m always selling how wonderful story problems are from the very start of teaching math. Mostly, because I always hated them and got so lost in all the words. I noticed this with my students too. So it was especially insightful to me how he (Dan Meyer) just rewrote the problems without all the extra words that we have been teaching kids to ignore. And how by doing this we prompted students to ask questions because now their minds are free to wonder. They are way more involved in the process instead of just looking for a quick answer or just giving up because they can’t read the story problem.
I can't wait to read and learn more!!
Linda, I totally agree it is so hard to get out of the habit of being to helpful. I think though the way that our program is set up we are going to learn a new way to be helpful. This new way won't be that we give the answer but that we present the problems. It should be a fun but bumpy ride.")
ReplyDeleteOne thing that resonated with me was students becoming "patient problem solvers". As many of you have said already, I see this in my kids. They see numbers and just start doing math...not taking time to think it through. With an abundance of information at our fingertips and the expectation of immediate results, patience has become a scarce commodity at times in my students (and myself).
ReplyDeleteAs an early adopter of IM, I saw math conversations greatly increase this year in my room. Students were engaged in conversations, this did not come easy for some students, it took lots of revisiting what their job was in a math conversation, but we got there over time!
Another thing that stood out to me was to be "less helpful", this is an area of growth for me for sure. Learning and becoming skillful at asking them questions to help prompt them into thinking mathematically and in a way that will move them forward. I found myself reminding them of my job too as I tried this more and more, that I was not going to solve the problem for them, but my job was to help them find a way to solve it by asking questions. My class had many conversations about this too, because in their minds asking me meant getting the problem solved, and they would become frustrated or think I wasn't helping them because they didn't get the answer to the problem.
I resonated with many aspects that others have mentioned. Teaching math is one of my favorite subjects because of the math talk and math discourse that students engage in. When they reach that "Aha" moment it's wonderful. It's also fun to witness the different problem-solving approaches and the unique ways in which students' minds tackle math problems. It's a way for me to see what makes sense to them.
ReplyDeleteReflecting on my early days as a teacher (a long time ago), I used to demonstrate the steps to solve a problem solver and expected students to replicate the process with similar problems. However, simply providing them with the formula that made the most sense to me didn't make it meaningful or understandable for some. Now, we encourage students to explore various strategies, articulate why their approach makes sense, and actively listen to and give feedback to their peers. This makes math time more productive and a sense of life long learning.
Developing their sense of productive struggle and cultivating a willingness to take risks has taken longer since Covid, since I'm sure some parents may have provided answers or shared formulas that made sense to them when they were younger. This isn't their fault since I know that's how we were taught in the past.
I am excited to continue teaching in this manner and foster a community of mathematicians who embrace taking risks, sharing ideas, and posing questions to one another.
I related to this post a lot thinking about how I can apply real world problems to the math that I teach in my classroom. I actually always think about how I can apply real world situations to all subjects because I think it makes the content so much more relatable. I also think that kids have a hard time when there is grit involved in problems solving. A lot of the time students quit before they put in real time and try to attack the problem from different angles. I am excited for the new math curriculum because I have heard that it builds problem solving skills.
ReplyDeleteSomething I have been working on for the past couple of years is working on asking meaningful questions to my students that guide them into problem solving and lead them to ask questions of themselves. I think this leads students to be better problem solvers and helps them become stronger self starters.
One thing that really resonated with me was being less helpful. I have been reading “Building Thinking Classrooms in Mathematics” this summer. In the very beginning, it talks about how good problem solvers need to get stuck. It is often difficult as a teacher to watch students struggle when we know the one tip that might help them get unstuck. As an early implementer of the IM curriculum, it was very challenging in the fall to watch students struggle, but students were almost always able to work through it and this helped their confidence. In turn they were less likely to give up as quickly the next time.
ReplyDeleteThe chart with productive and unproductive beliefs was eye opening. I felt like this year I started to move my teaching into the more productive beliefs. I was the teacher that would give students an equation and then walk them through the steps of solving it. This year, as I listened to students explain their thinking and modeled it on the board, I tried not to jump in with my ideas or thoughts and often they got to the correct answer. By the end of the year, the math conversations in my class were the best I have ever experienced in my teaching career.
I smiled the whole time reading this reflection, Amy. "the math conversations in my class were the best I have ever experienced in my teaching career..." I couldn't love this more. ❤
DeleteAs I reflect on my first two years of teaching, one of the biggest lessons I have learned is to be patient. As an educator it is difficult to watch your students struggle. It can be awkward at times for those students and other students in the classroom to sit and wait as others struggle. One of my focuses at the end of the year last year was to work on allowing students to struggle and working through that struggle. As I watched the video one of the things that stood out to me was that Dan mentioned, "be less helpful". As difficult as that may be for me, it is something I want to continue to work on. Allowing students to work through their struggle and push themselves to continue the difficult math conversations that may arise from their own personal or group struggles.
ReplyDeleteAs 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, Liljedahl 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 past 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.
ReplyDeleteThere were many things that resonated with me. I dabbled with the new curriculum a bit at the end of the year since it felt “safe” with my students from last year. It was a challenge to allow the productive struggle. I am so used to showing them how to do things, or providing a formula after many concepts are built. It will be such an amazing learning experience for them and us. I want to allow my students to build their own understanding while guiding them. From the bit I did dabble it will take growth and learning on my part in regards to when to question and push and when to allow them the struggle.
ReplyDeleteI connected with the white discussion about problem solving. So many times my students have grumbled and back away from problem solving. I think connecting to real world problems and breaking them down into smaller chucks while they build their understanding will help. I have dug into the curriculum deep enough to see how they are presented but I have heard it is more 3 read style which excites me.
Several things resonated with me. The first one I know will be the hardest for me is to be "less helpful" while my students are struggling with a problem. I understand the benefits for them, and I want them to be better problem solvers, but I will need to work hard on this one. The second one is to use visuals from the real world to help invite conversation. What a powerful idea! At the end of the year, I did a few practice lessons with IM to see how it will feel for the fall. I saw how much the student's enjoyed talking about the different ways a problem could be solved. It was amazing to watch all of the math student-talk going on. I am looking forward to using our new math curriculum.
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