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.
While watching the video, I made a lot of connections to my own math experience. I majored in math in college and experienced similar situations to what Dan Meyer was talking about with math textbooks and problem-solving problems. The way that he redefined the problems by taking all the fillers out and adding real life examples makes them extremely more relatable and much easier to solve. The unproductive beliefs vs the productive beliefs chart caused me to stop and think. While reading through some of the unproductive beliefs, I found myself drawing connections to the ways that I taught the Math Expressions curriculum in prior years. After starting Illustrative Mathematics this year, I see many connections to the productive beliefs side of the chart. While it is hasn’t been smooth sailing teaching the new curriculum, I believe it will make a difference in how students solve tricky problems and result in more positive math experiences for all students.
ReplyDeleteThis is the second time I've seen the video and I am reminded of the power in the questions that we ask our students to get them to think about the concepts or situations that we are asking them to solve. Increasing student engagement and willingness to try new, challenging problems while feeling comfortable with productive stuggle is key. The more I work with our new Illustrative Math this year, the more my students are willing to work through productive struggle. I wish more of the questions in the new math is more like what Dan Meyer was sharing about getting the kids to identify the questions once they've bought into the situations...that said, what I'm seeing with student thinking, this is a really good move for providing students with positive and strong math experiences.
ReplyDeleteDan Meyer (and Jo Boaler) were two significant influences in my undergraduate math education through their drive for productive struggle, questions that advance rather than correct student thinking, and the derivation of formulas through discovery rather than through the classic "plug and chug". This phenomenon of "impatient problem-solving" seems only to be a greater battle in the classroom as students settle back into the routine of an in-person instruction and a return to pacing that may depend on the flow of the class as a whole, rather than one individual person. I often find myself repeating, "Just wait! Just wait! I promise we'll get to the answer in the end." Students, especially those who qualify as hi-cap, are desperate for the affirmation of a correct answer.
ReplyDeleteThe "visual-question-structure" model reminds me of the instructional routines I often do with students, including Dan's 3-Act Tasks and Estimation 180. We begin with a relatable visual element (either a still picture or video) and then begin to ask questions before I reframe the question in a way that aligns with the concepts we are currently exploring within our unit. The dialogue in these learning moments is rich and enables those quieter learners and shyer thinkers to shine as they no longer feel they are the last to arrive at a solution. Every student in engaged in meaning-making outside the strict confines of a traditional math problem. There is no expected formula or steps or procedure to follow.
I appreciated Dan's statement, "The math serves the conversation; the conversation doesn't serve the math." It reminds me that authentic math talk is often inexplicit to students in its connection to a unit and is only then revealed as organic questions crop up. When we begin with a question, our minds fixate our attention on the solution rather than the reality in which the problem is situated. We must continue to ask ourselves, "What really matters here?" when we approach our own curriculum because it allows our intuition, not a rigid formula, to guide our thinking. Every student feels they have something to contribute when we allow numbers, steps, and formulas to fall away.
The 8 Mathematics Teaching Principles were a useful reminder about where our energy as educators should be focused in instructional design and student engagement. Purposeful questioning and connecting mathematical representations are two areas I want to shift my attention toward as I reflect on my practice. A modified version of the Unproductive v. Productive Beliefs chart, in student-friendly language, would be an interesting attitudes survey to administer this year to my students and even their families. Where a person leans on the chart is quite revealing of their past math experiences and sense of self-efficacy. Ten years ago, as a student, much of my beliefs were similar to the left of the chart. My hope is that my students and colleagues see themselves on the right side today.
Erin - I'm glad you referenced, "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.
DeleteSo many things resonated with me while watching the video, I was struck by his claim that the way we teach math all but ensures students won't retain it. To me, that is an overwhelming and heartbreaking statement, that was my math experience, and not one I want for my students. The learning experiences described in the reading seem to describe the antidote to that problem. Productive struggle is something we value in our class and talk about, but I like Dan Meyer's term ' patient problem solving' even more! Such a powerful yet kid friendly term. I appreciated the textbook problem he demonstrated and how he stripped it down to eliminate all the sub information. I feel like that is something I can try right away. Finally, his recommendations to "ask the shortest question you can," and "be less helpful" reminded me of Building Thinking Classrooms and the ideas discussed in that book. I'm hopeful that our new curriculum will be a helpful tool in building the math class we wish we had in elementary, I'm excited to dig in!
ReplyDeleteIt is so true about how our students respond differently to "numberless", real events, thinking problem solving vs. strictly calculation and formula use. Definitely the first one create wider field for all students to get involve, help with visualization and learning math without even know it. I watched Dan Meyer's video few times and every time it gave me new ideas to use in my math groups. I love his blog and examples he presents there.
ReplyDeleteI've watched that video a couple of times, each time I have great take aways! One thing that stood out to me was the comparison of math problem solving to a sitcom, or in other words instant gratification. Second, was the question he posed, "What real world problem worth solving gives us all of the information?" This is so true, as I've taught and raised my own children, I've noticed that if all of the information isn't given then many children have great difficulty in knowing how to even ben problem solving. The third thing that really stood out was his advice to ask the shortest question possible. Absolutely! This allows the students to think of ask the question and serving as the hook to get buy in!
ReplyDeleteI also really like the chart with productive and unproductive beliefs around mathematics!
I enjoyed reading the chart from the reading and thinking about the shift from unproductive to productive beliefs. It makes me reflect on math fluency and how things have shifted from when I was in elementary school to now. Building fluency in the classroom goes beyond mastering a one minute “fluency” test, fluency encourages students to think flexibly and aligns with many of the productive beliefs in the chart. While watching the video it made me pause and think about the math experiences I am providing for my students, what ways am I engaging them? How am I answering and guiding their questions?
ReplyDeleteThe part that really resonates with me is all about asking the students questions that get them to think and come up with the answers on their own. It is so easy to “teach” by modeling and showing the steps or the strategies that we are trying to teach. Asking students questions and having them struggle to get there is the key to them not only understanding the skill but also retaining it. Looking at the chart from the excerpt, it is a good reminder that the role of the teacher is not to tell them the definitions, formulas, rules, etc. The students need to participate in engaging tasks in order to promote reasoning that moves students towards the understanding of the skill. It is also super important to challenge them and let them feel challenged. The importance of perseverance is taught and there are so many kids that give up when something is hard or they allow a group member to solve for them as they sit back and write down the answer. I am eager to gain more skills in this area in order to work with my students and help them learn and retain information.
ReplyDeleteYes! Productive struggle is where the magic happens. It's where the thinking happens. It's where the engagement happens. It's where the learning happens.
DeleteI love this video and have seen it a few times, and it never fails that every time I watch it, I think about how much more fun math would have been growing up if we had these open-ended questions that require true problem solving. This goes back to the last session I did which was creating math fluency, it is so easy to give students the exact answer or pathway to something, but is that really creating understanding? The questions in this video are obviously a lot higher than my grade level (kinder) but I am excited to keep going in this course and see maybe some examples that fit within my grade level. I understand the thinking behind it and know that it can be applied, but would love to see examples!
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