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.
*"The formulation of the problem is more essential than its solution." Being an efficient, goal-orientated person by nature, I know I have been guilty of being an "impatient problem solver", with an "eagerness for the formula" -- and have likely taught in a way that reflects that. One of the most powerful changes in my classroom the last two years has been the use of number talks and witnessing the incredible conversations my students have had as a result. It has allowed me to see the value of "patient problem solving" and developing that mathematical reasoning with my students.
ReplyDeleteThe thing that resonated with me the most from this video and reading was the focus on the process of problem solving rather than finding the answer. The video encouraged genuine student curiosity and having students help to formulate the problem which is a switch from the ways in which we have taught math in the past. In the few IM lessons I have seen the main focus is on student problem solving and "helping less" which allows students to work together to make sense of problems. In the classroom, using our old curriculum, we would teach a few strategies to help students solve problems, essentially giving them the formula. I'm looking forward to switching this around and having productive struggles in which students work together to come up with their own strategies.
ReplyDeleteI also was struck by the emphasis on problem solving rather than learning formulas. This is contrary to how I learned math and how I was taught to teach math. The chart "Beliefs about teaching and learning mathematics" was eye opening for me. Reading down the columns, it initially looks like it is comparing the old way of teaching math and the new way of teaching math. Knowing that the columns are not "old vs new" but are "unproductive vs. productive" shifted my perspective. No teacher wants to waste time on unproductive methods.
ReplyDelete"Help less" resonated with me too. Especially with the preschoolers, I feel like they need less help and more opportunities for independence in most areas.
ReplyDeleteI have always loved math. At then end of the year, most of my students said math was one of their favorite parts of the day. I am looking forward to adjusting my teaching practices and instruction materials. I love how our new curriculum will have our students thinking critically and solving problems. When reading the passage Effective Teaching and Learning I enjoyed the portion that stated teachers should support constructive struggle. I have tried to implement this in small ways into my teaching practices in the past. Another portion of the passage that resonated with me was the importance of discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies. I am looking forward to allowing students to discuss their mathematical reasoning. I think this curriculum will support student learning and growth.
ReplyDeleteThe following quote from Effective Teaching and Learning, "“An effective teacher provides students with appropriate challenge, encourages perseverance in solving problems, and supports productive struggle in learning mathematics” really resonated with me after teaching our new IM curriculum this year. Fortunately for us, we won't need to rebuild math problems to support math reasoning and patient problem solving, as stated in the video. IM's lessons provide the platform for us to facilitate rich math discussions, allows multiple entry points for conversational intimidated students, and makes sure "the math serves the conversation, the conversation doesn’t serve the math" with students developing problem solving steps together, with a variety of solutions. As stated by many above, the true challenge is shifting your mindset to allow the struggle by "helping less", while developing the craft of questioning, I'm still learning how to do both!
ReplyDeleteFor part 1, the video and article were both interesting to relate to my one-year experience teaching IM in kindergarten. The 8 mathematical practices, 5 interrelated strands and the principles of learning all have their place in this new (to me) curriculum. I just finished my first year teaching it and went into it with an open mind and commitment to try all the parts as much as time allowed. Even though the video from this part was focusing on how problems are presented to high school math students, I can see how IM has taken the important ideas featured in the article and included them in the presentation of mathematical problems, even for kindergarteners. This year I did the best job yet in helping young learners become patient problem solvers. This occurred because of the way they were invited into math all year long. Because of the new curriculum, I offered daily experiences for students to use their intuition, explore problem solving options and construct knowledge socially. Another aspect addressed in the article is connecting new learning to prior learning. I experienced this in the units as they built on each other within units as well as unit to unit building and connections. I saw this in students' growth in some of the warmup routines used in IM. Students were able to use prior knowledge and skills to discuss and reason with new concepts. One barrier that has me thinking is how to support multi-language learners in an environment where proficiency in English is such a primary skill for moving math thinking forward.
ReplyDeleteIn part 1, the comment made in the video that "students are impatient" made me both chuckle and pause at the same time. Teaching in today's world of instant gratification, I encounter this impatient attitude in many areas, not just math. It really resonates with me in regards to math learning, though, as I have experienced many math lessons where students wanted to just quickly get the answer and cared less about the process. My kindergarteners are often frustrated when something requires effort. I am guilty of being that teacher who guides students through a problem step by step, to ensure that they are not frustrated or confused. IM math seems to have a much stronger focus on student inquiry and reasoning, about which I am both excited and a bit nervous! I also loved the suggestion made from the video to put everyone on a level playing field to begin with...allowing students to connect new learning with prior knowledge and to acquire that new knowledge through social discourse and interaction makes so much sense.
ReplyDeleteSomething that I frequently asked myself as a math student was "when am I ever going to use this in real life?". Dan Meyer's ideas about leading students towards questioning in math and towards formulating/solving related to things happening in real life (the ski lift and filling the container up with water" is something that resonated with me as a person who didn't really see the point in all of the math I was having to learn. The article further justified Dan Meyer's ideas by discussing the idea of "Strategic Competence", a student's ability to solve mathematical problems students might encounter in real life. I like that IM math will have students working in various ways to solve problems, whether working with manipulatives or working in small groups. I think this will be beneficial to students as they have an opportunity to ask and answer questions and find ways to connect what they are learning about to the world around them.
ReplyDeleteI loved in the TED Talk when he spoke about our neural pathways being wired to easy 22 minute bursts of small problems wrapped up in a tidy way. I'd love to begin Kindergarten this year with us committing to being "Patient Problem Solvers" in all areas. Since I am the beginning of school, I believe this mindset and way of thinking would greatly benefit my students in all areas. I also need to really try to not help too much. This year, our students came to us much less capable than in previous years, and looked to us to solve each problem for them. Even at the end of the year, we had students that would come and say "My shoe is untied" and stick their show in our faces. My question - "What are you going to do about that?" or "What is your next step?" helps empower my learners to know they are problem-solvers and can do it.
ReplyDeleteOne 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.
ReplyDeleteWe have been lucky at TES in that Rachelle (3rd Grade) introduced us to these questions a few years ago and they do get students to think and respond - even those with limited math confidence will get into the conversation :-)
Deleteone teaching practice that stands out to me is "building procedural fluency and conceptual understanding. In kindergarten, the beginning of addition and subtraction skills need lots of practice and repetition. one thing that stuck with me was how our parents were taught to do math. We are no longer looking for skill based on memorization and math drills. For example, the addition and subtraction skills are important, but there is lots of room to make this an engaging for students. For example, in my classroom this year, I created math centers. during the math centers students would work on conceptual understanding all week long on many math skills. for addition and subtraction students were taught games such as "shake and spills". This activity added manipulatives and some sensory items to help create and understand math equations. The students then represented the same concept in 5 or 10 frames which allowed students to translate into a drawing. i am interested in using the IM centers to help guide these math practices.
ReplyDeleteI was lucky to be one of the early implementers of IM math this past year. In my classroom, I have been able to observe students transition from looking to me to help them solve a problem in math in the beginning of the year, to being empowered to “construct knowledge socially, through discourse, activity, and interaction related to meaningful problems” as the year progressed. The quoted statement resonated with me because I witnessed it firsthand in my classroom. IM Math provides the platform for students to join in on math conversation daily. The warmups and activities demonstrated how students can have a range of strategies to solve problems, have a math conversation with their partner about their method, and allow them to take a risk and try something they may not have thought of. It is very encouraging and exciting to be a part of that.
ReplyDeleteI love how mathematical thinking is moving toward using real life experiences to help students understand the why. I believe that if students can see how these concepts can be used in their own lives, they are more apt to want to understand. Additionally, using manipulatives is essential for all learners to help solidify their comprehension.
ReplyDeleteIn the video, it was exciting to see how this teacher revised the order in which teaching usually occurs – asking the question first and letting the students formulate their own problem and allowing them to use what they know to help them develop their own path to the answer.
In this past year I have tried to incorporate more number talks as a warmup to encourage more student participation – especially with students who may typically be reluctant to jump into discussions. This was more apparent after our opinion writing unit – students loved to explain their why. Also creating an opportunity for students to comment on others explanations helped them see how there are multiple ways to achieve the solution.
I had an “aha” moment while reading the NCTM article when it pointed out that one unproductive belief in teaching math is guiding students step-by-step through problem solving to keep them from becoming frustrated. I know I have been guilty of this because I tended to think that shielding my students from frustration would help them like math more and thereby enable them to take more risks in math. I better understand now the importance of providing students with an appropriate level of challenge in order to develop perseverance in solving problems and to support productive struggle. I was inspired by the approach that Dan Meyers uses with his students for problem solving. As he stated in his TED talk, we can redefine math so that students are no longer intimidated, and in this way students can better develop math reasoning. Going forward, I am excited to actively teach my students that struggle can be productive and that we must be “patient problem solvers”. I look forward to the conversations that we will have in class that focus around mathematical reasoning and to using IM math to instill these concepts in my students!
ReplyDeleteSo many things to think about for the upcoming school year teaching our new math curriculum! The part where it says: "Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments." I think students having discussions with each other, explaining their thinking, reasoning how they arrived at their responses is super powerful! It deepens thinking and it's wonderful to see students learn from each other and know there are different ways to think about a problem/situation and come up with a reasonable answer. That reflects real life and that is important!
ReplyDeleteMy biggest takeaway from the Dan Meyer TED Talk and the article are the ideas behind mathematical reasoning and helping students to persevere through problem solving. As a kindergarten teacher, I often find that students already start school with that “impatience” or the notion that they are not good mathematical problem solvers. It is our job to pose questions and encourage their thinking through conversations as they formulate meaning and preserve to find ways to solve problems. I love the quote, “formulation of the problem is more essential than it’s solution.” When we pose questions and allow for mathematical conversations in the classroom, students use their prior knowledge, context, innate problem-solving abilities, reasoning, and more, to dive into a problem and find ways to develop meaning from the process of problem solving. Meyer spoke about breaking down problems by asking questions, using real life pictures and videos, and personal connections to level the playing field of intuition; all students to have an entry point when we focus our “teaching” of math in this way. “Students need to recognize the value of studying mathematics and believe that they are capable of learning mathematics through resolve and effort” (Schunk and Richardson 2011). My goal is to continue using the ideas behind cognitively guided instruction (CGI) to help my kindergarten students develop mathematical reasoning through patient problem solving. If we start a foundation of learning in this way, it will continue with them as they progress in school.
ReplyDeleteGrowing up I could memorize math facts and formulas but I never learned how to apply them or use them to problem solve. I had a negative attitude towards math and never fully understood it. Watching the video I wish I had had a teacher like Dan Meyers. I loved how he took the unnecessary words away and then showed the visual of the water tank. After I became a teacher I always ask students to explain their thinking so I could understand what they were thinking and how they were solving the problem. I am excited to jump into IM and learn more noticings and wonderings right along with the kids.
ReplyDeleteThe biggest thing that resonated with me in the video is that there is not retention of math reasoning because of the way math is taught. He talked about how people are looking for the fastest way to get the answer and needing to be a patient math teacher. The “unproductive vs. productive” about teaching and learning mathematics made me think about when I was a student in math classes and how I hope to teach math in my classes. Even taking math classes for my master’s a few years ago had me worried. In my class I want to teach more patient problem solving and hope to instill the beginnings of students coming up with their own strategies.
ReplyDeleteI agree with the article that dominant cultural beliefs around how to teach math is strong and hard to break mindsets. I think there is fear or uncomfortableness with change. However, I think so much good can come out of how Dan and the article describe teaching math. I found connections between the article and Peter Liljedahl's book Building Thinking Classrooms. I know most of my math teachers taught me with the "unproductive beliefs" and I started teaching the same way because that was the known experience. I am excited to try our new math curriculum and students collaborating with others to develop math skills.
ReplyDeleteI loved in the video when he said we are impatient with things that don’t solve quickly. Working on problem solving rather than learning formulas and going through a checklist. This will need to be a shift in my own classroom teaching, because I will need to shift my mindset and allow my students to struggle, to give them time to utilize their problem solving skills. I really liked the table on page 5 of the reading, it was a good check and balance for where I am, and where I want to go as a teacher.
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