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.
What resonates with me is just how important it is to connect into the students/ children's natural curiosity and questions. Kids naturally want to know how, when, why and that is what fuels their real and true learning. One of the things that really gave me a pause was the fact we do give them formulas and set learning patterns that don't seem to create real or true long term learning.
ReplyDeleteBe less helpful. That is such a difficult sentence for me. After observing an amazing lesson of the new math curriculum from Angie Houser, she showed me how to be less helpful correctly. Giving students more space to problem solve can be scary, but I saw and listened to such rich math conversations.I loved how sub-steps were taken out of the problem from the video, allowing the students to construct them, themselves. Taking out distractors and giving more ownership to the children, really appealed to me.
ReplyDeleteI also feel that it will be difficult to be less helpful and use short questions while teaching. It will take time to get use to. Students want to know if they are right or wrong. Our years of teaching to find an answer in a step by step way has caused the students to also look for our help. I am wondering if this change would have been better to start with maybe K-1. Then the next year add in 2-3 and then 4-5. This way the students could more gradually and more naturally learn this newer way of thinking. I think for students who have been programed to the other way of learning math will struggle more. Just a thought.
DeleteEven though I have watched Dan Meyers' video "Math Class Needs a Makeover" and read the Principles of Action pages several times in the past, I think it is so important to continuously remind ourselves of what type of environment and experiences we should be providing for our students to build their math foundation and find joy in learning math. I recorded several statements made by Dan Meyers that I felt were especially valuable and that uphold the structures and ideas present in our new curriculum, Illustrative Mathematics:
ReplyDelete1. "Math serves the conversation; the conversation doesn't serve the math." When we give students a situation and ask a question that allow students to develop their own questions or brainstorm ideas to formulate their own strategies to answer the question, it helps our students to own their learning, building reasoning skills, and productively struggle (persevere). Every lesson in Illustrative Math provides an opportunity for math discourse and sharing of ideas and reasoning.
2. Include students in the formulation of the problem - I saw this happen often as I was teaching Illustrative Math units this past year. One example is the first unit in fifth grade. Instead of giving students a formula to solve the volume of a rectangular prism, students were building prisms and developing their own ideas of how many cubic units were in the prisms. They were making sense of the vocabulary - base, layers, height, width, length, and depth - as they built the prisms with connecting cubes and discussing their ideas with peers. Eventually students were able to recognize that volume is the area of the base multiplied the number of layers AND the length x the depth (width) x the height of the prism. Discovering multiple formulas for volume and other math concepts (eg. mixed number multiplication) through conceptual understanding (hands-on, diagrams, models), math discourse, trial and error, and estimation really grounded students' understanding and reasoning.
3. Dan Meyers shared the thought that if math teachers continue to teach math with unproductive beliefs and tactics, bad things will happen to us. While this was meant to make us laugh, it is true that we should be providing experiences for our students that help them grow in their reasoning, perseverance, and joy at solving real-world math problems, so that our current students CAN take care of us in the future!
Julie,
DeleteYour first point in which you state "allow student to develop their own questions" is supported, as you know, by Illustrative Mathematics language routines. Specifically, MLR5 is "Co-Craft Questions" and it happens by presenting students with a hook—a context or a stem for a problem, with or without values included. The hook can also be a picture, video, or list of interesting facts. Next, students generate possible mathematical questions that might be asked about the situation. This was one of my favorite language routines for promoting discourse.
Impatient problem solvers versus patient problem solvers and their symptoms resonated with me. I do see most of the of the symptoms of doing math reasoning wrong which is a bit humbling. I am interested in learning how to create an environment in which kids become patient problem solvers. I do think I will need to work on being less helpful and asking the shortest questions. I am curious to see how this will work with sped students. Looking forward to learning more!
ReplyDeleteEach time I watch that Dan Meyer video, I am wowed. It's so good! 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.
ReplyDeleteOne thing that resonated with me was the idea of engaging students with visuals that get a conversation started and make the problem accessible to all students. This reminds me of many of the warm-ups from the fourth-grade curriculum. I found that the images and one simple question would get a conversation started based on student intuition. I noticed that all students were engaged, not just the students who feel confident as math students. This leads to students making sense of problems, constructing arguments, and critiquing the arguments of others right from the start of the lesson. I find it hard to ask the shortest question possible and be less helpful. One thing I am working on is listening to students more and thinking of the right question to move them forward if needed. I know how important the productive struggle is, but I can easily fall back into helping students to be more efficient. Efficiency does not result in thinking!
ReplyDeleteWhat stuck out the most to me is impatient problem solvers and lack of perseverance. I saw a lot of this in my students at the beginning of the school year. Students were so used to being told “what to do” if they didn’t understand a problem. It was so ingrained in them from years previous, that I even had students coming up to me during tests asking me to show them how to solve a problem! I also saw students turning in work where they obviously knew that their answer didn’t make sense, but they didn’t attempt to come up with other solutions, because they had tried it once and “that was enough.” It was a serious struggle.
ReplyDeleteHowever, using the new curriculum really forced my students to become more patient problem solvers. With no strategies given at the beginning of new learning, they had to really push their thinking and work together to use what they knew to problem solve through each unit.
The kids worked so hard on this all year and the BEST example of this was mid-year. I had a student who was intent on persevering through a pre-unit question our team had created for some SGG data. He refused to give up and worked all day on a single problem. He would take a break for our other core subjects and the minute he finished his required tasks, he was asking to work on the problem. When he finally completed it, the whole class was invested and everyone wanted to know if he had found the correct solution with his strategy. When I announced he had indeed solved for the correct answer, the whole class was cheering for him and he felt SO accomplished!
I am excited to continue to stretch myself and my students again next year by being a little less “helpful” and helping them to be comfortable with being patient problem solvers.
I really like the idea of putting math concepts into real life problems so the kids can see how to solve it and understand it. Also that we are not just focusing on fact fluency but also concepts and procedures.
ReplyDeleteThe first thing that pops into my head while watching and reading part 1 is that this change seems to be moving away from a teacher centered approach to a more child centered one. The Montessori approach also comes to mind. I connected this to the "building math fluency" class a took. I have used the grade level sites as a resource during my MAP lessons in order to build more fact fluency. I can see how the "Fluency" and "Number Routines" areas would also help in continuing to build connections. I really like using the "math flips", "number strings", "subitizing activities", "make it Monday", and the "WODB?" areas as ways to get my students thinking mathematically and become more motivated. I feel the "Convince me that...", "Same or Different?", and the "Would you rather" sections would also help support this approach to teaching math. What is making me pause and think is... do I need to create a bunch of problems for this different approach to math? Or does this new program provide enough support for both the classroom and the MAP program to use? In MAP my time for planning and productive struggle is limited. Will I be able to offer enough opportunities for my students to grow?
ReplyDeleteOne thing that resonated with me from the reading is this productive belief: "The role of the teacher is to engage
ReplyDeletestudents in tasks that promote reasoning and problem solving and facilitate discourse that moves students toward shared understanding of mathematics." In teaching with the Illustrative Mathematics curriculum, I noticed how crucial productive student discourse is to this shared understanding. Relating this to the video, it ties in to Meyers' suggestion to encourage student intuition. In order to get students talking about problem-solving, we have to level the playing field by appealing to students' background knowledge and interests. I remember one lesson in which students were comparing 400 meter track race times. As they were ordering the place of each finisher, a question came up about who would come in first, the person with the greatest time or the lowest time? This wasn't something I reminded them of before they tried to solve the problem, but was a piece of information students needed to move forward. Without the discourse between students, this question may not have been asked aloud and highlighted for shared learning.
One thing that resonates with me through these resources is the shared belief in helping our students engage in and providing rich task that promote reasoning and problem solving for our students. We have been working so hard the last several years to begin this work with some of our neediest students. In our small groups we do so much work around building a strong foundation for our students around numbers sense, reasoning, problem solving, and thinking flexibly about number relationships. We are doing great work and seeing growth! One thing on my mind is how we can continue the great foundational work we are already doing while increasing the the students engagement, productive struggle, and important student discourse around their learning that will help bring about mathematical understanding.
ReplyDeleteThe thing that resonated with me the most was as many others stated, the quote, "Math serves the conversation; the conversation doesn't serve the math." It is so important to get our students talking about math so that they are invested in it and fully understand what they are doing. I also love his point about making the playing field level for all students to be able to access the math. Even if they don't know the formula or if the feel they are not a good math student, they can still talk about what they are seeing in the visual or in the video. These conversations almost always lead to the question you want them to be solving. But it ends up coming from them and not you, so they are more vested in the math!
ReplyDeleteOne thing that resonated with me is to give them a task that put's every student on the same playing field to talk about what they see or think what would be the answer. Getting all students to participate in the conversation creates that concept of thinking math.
ReplyDeleteI love the idea of patient problem solving. This is a big shift from the traditional operational math with explicit steps. It makes so much more sense to me. To me it seems to give math more of a gray area feel rather than a black and white formula. It opens up room for discussion and allows for creativity amongst the students. I do worry a bit that with the Special Education population this will be a tough shift. I am so used to explicit instruction and repetition that I often miss the essence of math, which is to creatively solve real life problems.
ReplyDeleteAlong with many others, what resonated most with me is the concept of impatient vs patient problem-solving. This is something I see over and over again in my students, particularly their lack of perseverance and willingness to try, mess up, dig deeper, and keep going! The example that Dan Meyer provides where he takes a word problem and removes the steps and almost all of the information required his students to ask themselves "what matters here" when they are solving problems. In order for our students to become patient problem solvers, we also need to be patient in the process of their perseverance, which is something that I am continually working towards. I am excited about the new IM curriculum and the opportunity for thinking and problem-solving it provides.
ReplyDeleteI liked his analogy about how students are like consumers forced to buy something they don't want to buy. What resonated with me is impatient problem solvers versus patient problem solvers.
ReplyDeleteAs a person who always needs to know the "why" to any answer, I found this video very meaningful. I often struggled as a kid to stay engaged when it came to math and I think a large part of it was due to the fact that I was given standard algorithms to follow and didn't get to the why. Breaking a problem down to something that a child might see every day could really get them thinking. After all, they are led to believe that once they are out of school, they will never use these practices again. This is an example of how to debunk that.
ReplyDeletePlaying catch up here! The concept of "be less helpful" stood out to me the most. Our fourth grade math team has done an amazing job of creating routines in our lessons that offer opportunities for student discourse and entry points for all, but I do find that I may jump into the conversation offering my own thinking a little too often. It is hard to balance the "I'm going to model how to share my thinking" idea with "be less helpful," but that did cause me to pause and think a bit!
ReplyDeleteI also enjoyed the concepts in the article. On page 11, the author provided a chart of beliefs about teaching and learning mathematics. I appreciate how they explained how to unravel these beliefs, "beliefs should be understood as unproductive when they HINDER the implementation of effective instructional practice or LIMIT student access to important mathematics content and practices." This makes me think I will really slow down and evaluate each instructional practice this year utilizing this lens.
What's resonating with me is the part about being less helpful. I find I front load so much for my students because I don't want them feeling so overwhelmed they shut down and don't try. But the most engaged my students are with math is when we've done number talks and they are able to have conversations given little information. They get so impatient to get to the choice boards that they take shortcuts to get the answers. It really is so important to help students become "patient problem solvers." I am so excited to see how the new curriculum sets that up.
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