Reflect
Read the two summaries linked below to get a better understanding of the design principles and key structures of Illustrative Math. Then watch the short video to learn more about the 5 Practices for Orchestrating Productive Math Discussions.
Consider
- What is resonating with you from these readings or this video?
- What caused you to pause and think?
- What principles or structures from your own math classroom align with some of these beliefs or components?
Respond and Interact
After reading and watching, 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 these readings or this video?
ReplyDeleteThere were several parts of the readings that resonated with me, including that for teachers, there are exemplar videos that demonstrate these new routines. This will make it much easier to ensure that I am delivering content to my students in the most effective way possible.
I also really enjoyed reading about the practices for “orchestrating productive discussions”. These discussions are so important for moving students from just going through the motions of solving mathematics problems to truly understanding what they’re doing and why. This, I believe, will allow for a much deeper understanding of math concepts, as well as make math much more fun for students.
One other part of the reading that really stood out are the “teacher moves” to support the math community in my classroom. This is a fabulous resource that I will refer to any time I need ideas on how to best support my students as mathematicians.
What caused you to pause and think?
The journal writing is really interesting to me. I hadn’t considered journaling for math before, but after reading the rationale for it, I am looking forward to including it in our math routine. The more I can foster connections to math in my students’ lives, the better. Also, journaling offers students another way to have a “voice” and share their thinking.
What principles or structures from your own math classroom align with some of these beliefs or components?
The primary objective in my math instruction is not finding the correct answer, but rather a deep understanding of the content. This deep understanding gives students the tools they need to arrive at the correct answer. I try to foster class discussions on a regular basis; encouraging students to share with each other the how and the why of solving problems. I’m excited about what Illustrative Mathematics has to offer because it seems to align very well with my goal as a math teacher for my students.
I've never used math journals either, but I'm now more intrigued by it too. I can see it being beneficial for processing their learning and an opportunity to share their understanding. My understanding is that this would be a notebook and that is isn't part of the student workbook. It will be interesting to see if the time needed to do so can be built into the 60 minute lesson block.
DeleteWhat caused you to pause and think?
ReplyDeleteThe Design Principles makes me anticipate building a math learning community with my students next fall and how I can better build a math community with my students this year. It is always my intention to build a community where all students feel valued as individuals. As it says in this section, we want our students to feel known, heard and seen. In developing a math community I am excited to help my students think and communicate mathematically. I am anticipating I’ll learn ways to assess and advance student thinking. I liked all the questioning strategies to guide discussions.
I appreciate Renae sharing her math talk questions. What do you notice? What do you wonder? I can see using those same questions to open a math discussion for the day. Really, you can use those questions in any subject, but they provide an entry point for any student no matter their understanding of the math concept for the day.
I have the same intention and am looking forward to learning how to build my math learning community better and stronger. While I do have a few confident, risk takers, most of my students this year are shy and afraid to share or make a mistake. I am looking forward to learning how to encourage more risk taking and collective learning.
DeleteI feel similarly that this curriculum is going to help set up a really strong mathematical learning community by following consistent routines. The structure of the lessons will encourage engagement from all students on a daily basis.
DeleteOne idea that is resonating with me is how well thought out and organized this curriculum is from design principles, to routines, to expectations, community building- it's all here! I like that each unit, lesson and activity has the same overarching design structure that allows for coherence. Another thing I'm impressed with is the community building that takes place within the program that is taught through mathematics and not as something separate. On another note, being a PLC activator, I'm intrigued to see the program offers ideas and structures for how PLC groups could work together to support math instruction. I'll be interested to see how the suggestions closely align with our current PLC model. I think it could be very helpful, as coming up with pre-assessments, additional teaching resources to use and a plan is sometimes difficult! This could streamline the process for sure.
ReplyDeleteI teach first grade. One structure I tried last year (and didn't maintain) was an interactive math journal. It required a lot of prep and although it did have it's pros, the purpose was enough for me to warrant the investment in time. After reading the articles, I like the idea of a journal to reflect and connect instead and wondered what it could look at this age. Initially, pictures/verbally sharing with a partner or small group makes sense. Then moving into more writing as the year progresses and their writing skills have strengthened. At this age, they get excited when they can make a personal connection. With some of these reflecting questions, it'll help encourage them to make those connections with math and get that metacognition flowing. :)
ReplyDeleteI appreciate the "teaching moves to support math community" portion of one of the articles. I would love to learn more about the assigned rotating roles. What are the roles?
I appreciate that same section of "teaching moves to support math community"! I really like the sentence stems that are provided and will be relying on those especially at the beginning of next year!
DeleteIn the video she says “Stop talking. Observe. Listen.” This is an intimidating part of this new math curriculum for me and is going to take intentionality and patience and trust for me to shift my instruction in this way. I am looking forward to this challenge because I see the value and I look forward to being able to be several months into the curriculum so I can see the benefit of this shift. I am also looking forward to the future math talks I will be having with my students. I am eager to cultivate a math community because this is something that I am lacking in my current classroom. We have an established reading and writing community and I intentionally work to build my students positive identities as readers and writers. Starting on page 6 of the IM Key Structures reading there is a chart with suggested teacher moves for establishing a math community. I like that there are sentence frames included. This is definitely a resource that I will be referring to and relying on to support me as I become more comfortable in my own instructional abilities for cultivating a math community.
ReplyDeleteOne idea that is resonating with me is helping to make students believe they are mathematical thinkers and their ideas and perspective are worthwhile. Using the structure of this new math curriculum will really help engagement and empower each student to take risks and participate regardless of their level. After seeing it at our Illustrative training, I have been taking student ideas and posting them in a strategy bank for the class to reference. It has been so powerful to not only acknowledge student ideas, but to help students find a way to get started when they are "stuck" or are not how to begin a problem. They can reference this list and use their peers strategies to get started. I have noticed that making their ideas and thinking visible really boosts their confidence and has helped engage some of my lower students in a new way. My second take away from these readings and the video is the power of purposeful planning and anticipation that will help me in being able to present solutions and student thinking that will most benefit the lesson and progression. The new curriculum is going to challenge me and will definitely take some getting used to, but I am really excited for the math community that it will help me build and for all the reflection and growth I will also gain as a teacher.
ReplyDeleteI love that the Key Structures of IM includes suggestions for PLC work. I also appreciated the table with teacher moves & questions that will support building a math community in our classrooms. Good stuff!
ReplyDeleteJackie Decker talks about the 5 Practices based on Smith and Stein's book 5 Practices for Orchestrating Productive Math Discourse to Support Student Learning. I stopped to pause and think several times throughout the video. Starting a new math curriculum feels overwhelming. I am expecting it to be difficult initially to anticipate where the students are in their learning, what different strategies students might use, and which representations students might use because the lesson progression is so different from what I have become used to. I paused again to think about monitoring in the second stage. I love the idea of vertical non-permanent surfaces. Do we have access to these, Renae? I recall learning about this last year. It resonated with be to be a quiet, listening observer during this time. Observing Decker sequence student possible solutions made me wonder why I had never thought of doing this! How brilliant! In Key Structures for IM my takeaway was the journal ideas for reflecting on the content/practice as well as student feelings towards math. I loved the higher-level thinking prompts which I would most likely use in a closing discussion in first grade - perhaps an exit ticket in the later part of the year.
ReplyDeleteCherie - when teachers complete the Building Thinking Classroom book study, they get a set of non-permanent vertical surfaces! 🎉 Sign up for the summer book study...it will change your math life! I'm serious - it's SO good!
DeleteI would say that two things that were resonating with me most were the Student Journal Prompts and the Building Math Community.
ReplyDeleteI love the idea of a journal prompt, especially as they ask students about their thoughts and feelings about math. I think this is so important as man times we may not work through these feeling with our students with all the pressures of "getting it done". My favorite question was "In math class, it’s important to listen to other people’s ideas. Describe a time when you learned". Having students reflect of different points of view helps develop their conceptual understanding and holds them accountable. I am curious, as others are, when, where, how to fit this in the lessons.
something by listening carefully to someone in your class.
I am really excited that there are lessons built in our new curriculum that helps us develop our community as a class. Having norms is so important to a successful math lesson especially when the math lessons have a lot of moving parts and require deep, complex thinking. I often see some negative math attitudes at the beginning of the year. With a community these students as well as others can feel seen, heard, and understood. The teacher talking moves were also a helpful reminder!
I was excited to think about a math journal, I would love to see examples of the journal from early implementers. How do they set it up and are their tabs dividing the different units? I also am also excited to build a math community. Because I have the highly capable learners they are really connected in their love for math, they love learning new concepts, and have a natural curiosity when faced with a math challenge.
DeleteAngela Moore
ReplyDeleteThe articles spoke to my philosophy of teaching and I found great comfort in that. I feel like the use of math talk, hands on activities and student-centered learning has been missing for a while, especially in Math. When the Common Core came, there was a strange expectation that students do more sitting and listening while the teacher lectures. This has lowered student buy in significantly. I know my second graders will love the new approach which is so much more age appropriate, too. Center time will also provide students with movement lacking in our current Math program. I really paused to think about the inclusion of an equity focus which we are just beginning to both understand and use. It is the question of equity that made me want to teach in the first place so I hope to learn how to better acknowledge and teach to students of all socioeconomic backgrounds.
Having used Student Math Journals for a while in the Enumclaw SD and it helped provide insight into student thinking for those that were strong enough writers. Many years have passed since then and second graders are much better writers now. I believe a regular routine of journaling will be useful. Journalling does take time and I feel it may be more useful for teachers the second year of teaching the new curriculum.
The item that I am most interested in at the moment is the PLC information:
"To support teacher collaboration around planning and teaching, we have identified an activity in every unit
section as a PLC activity. This activity was chosen because it is either a key mathematical idea of the section
or requires a more complex facilitation. We also organized a structure for teachers to use as they work
together in professional learning communities."
My PLC team is considering using the new curriculum for our final PLC topic this year. I believe the curriculum provided PLC topics will help us really focus our goals and give insights into how we can help all our students and our instruction. I am excited and nervous about how much time learning and planning with the new curriculum will involve. Knowing the PLC ideas are imbedded to help us is a relief.
Quite a few things were running through my mind as I read and watched the video. There are things that excite me about the new curriculum, especially when compared to M.E. I loved reading that there are instructional routines that allow all students to engage and contribute to our daily math conversations. The energy in the classroom when you have those rich discussions where everyone is involved in some way is always memorable. I loved reading that instructional routines are just that, routine. That they are used so frequently within I.M. that students become comfortable with them and that they become second nature. Lastly, I loved reading that students are given the opportunity to bring their own experiences to lessons and "see themselves in the material". This is the intent of every lesson that we teach, regardless of the content or subject. Easiest way to get buy-in, in my experience.
ReplyDeleteTwo parts of the video really spoke to me. "Stop talking and listen". Always a good reminder. I tend to learn the most about my students and their thought processes, when I stop talking and listen. This also tends to bring to light any mathematical misconceptions students may have. I also love the idea of vertical non-permanent surfaces for problem solving. I have always used the Fish Bowl method of share out, but I really like how doing it this way allows students to see everyone's thinking at a glance.
Mel - a set of non-permanent, vertical surfaces is the fantastic prize for teachers when they complete the "Building Thinking Classrooms" book study. 🎉 Sounds like some great summer reading if you ask me. 😏
DeleteWhat is resonating with you from these readings or this video? I am really excited to learn how to teach in a way that encourages productive struggle. I currently teach math to ten 3rd grade students with learning disabilities in a pull-out model. This is a very large group for math with one teacher in the resource room, and with our current curriculum I am always looking for ways for them to explore concepts that don't involve me lecturing. I am excited that our new curriculum comes with this guidance built in. This is especially important for many of my students who have challenges with receptive and expressive language, and "telling" them about a concept is just not effective.
ReplyDeleteWhat caused you to pause and think? The journal writing ideas caused me to pause and think, as the students I work with all struggle with writing. We will need to be mindful of accommodating writing in math in a way that makes expressing their ideas accessible for these students.
What principles or structures from your own math classroom align with some of these beliefs or components? As I have gone through the current 3rd grade math curriculum this year, I have paused in various spots to focus more on students' understanding of what we are doing rather than getting the correct answer. We don't focus on memorizing math facts with these students, so I have had more time to help them see what multiplication is by doing activities with equal groups, for example. As we are starting to work on rounding, I am seeing which students are struggling with the concept because their number sense is still developing, and thinking of different ways I can help those students see the big picture rather than focus on the algorithm and/or correct answer.
When I was reading and watching the video there were a few things that stood out. In the video it said observe, stop talking, and listen. I think this was a great reminder for me because sometimes I just want to help right away but needed that reminder to really listen to the students and see what they are doing. This went along with the readings because in the reading it mentioned how students learn by doing and not being told what needs to be done. I also liked how they mentioned the vertical work boards. I have incorporated those a bit into my units and have found it extremely helpful when I am selecting the work I want to have a class discussion about. I would like to be more intentional in the order that I call on students, and I think the vertical boards will help because I can actually see the students work instead of trying to remember who said what or who had specific work in their journals.
ReplyDeleteThis resonated with me also Teagan. I believe listening will be my biggest challenge. I am trying to practice now letting students lead math discussions and pretending I don't know the answers so that they can figure out the strategies. It is a difficult skill not to want to jump in.
DeleteSame here Teagan! I also think that with the new curriculum we are going to have a lot on our mind since it is new. But something I keep thinking about is what the lady said at our training. I forget the exact wording but it was something like focus on the integrity not the efficiency.
DeleteWhat caused you to pause and think? What stood out the most was that I have used three act tasks by Graham Fletcher often, but I hadn't seen the gear problem before. That one is a bit above my kids, but I usually enjoy the conversations my students have around the three act tasks and how productive they feel. They are also high engagement because I'm not talking 'at' them. I have run across several instances where a student thinks of a strategy that I didn't anticipate and I think it's so fascinating how their brains can work-- both in a good way and not so good way. Sometimes, though, kids can twist their thinking into knots to try to be unique or sound smart, and I am a little apprehensive about this happening. Not that they can't make mistakes, but sometimes that sort of discussion can confuse rather than give insight to others. I know that vertical surfaces will/would be helpful with this curriculum, but they're expensive if you want ones that will last. How will the district help us with that?? I liked the journaling idea. I've always wanted to be able to do that, though I know time is an issue with the lessons, so I'm wondering how I might fit that in.
ReplyDeleteTeaching some of our youngest learners , Kindergarten really is a hands on math space. A space where children use manipulatives and grapple with math problems. I really loved, "All Students are Capable of Learning in Math". The Design Principles lay it out beautifully. Learning by Doing, Rigor, Conceptual Understanding, Procedural Fluency and ability to Apply to Concepts. All of these principles bring out mathematical thinking. I am looking forward to see how IM lays this out for Kinders. I know much of the math in Kinderis center based, so I am looking forward to see where this will take my students next year.
ReplyDeleteThere are a few things that stuck out to me in the reading and they all seemed to be related. The first was, "Students learn mathematics by doing mathematics, rather than by watching someone else do mathematics
ReplyDeleteor being told what needs to be done." This makes so much sense and I see this in my class. My students really respond to playing games where they get to practice the skills instead of watching a lesson. I have been more intentional in bringing in more games which correlates to our current unit.
Two other statements that stood out to me are "Community is central" and "In order to extend the invitation to all students to do mathematics, we must work to explicitly develop the math learning community." This seems to fall in line with classroom community in general. I feel this is important for a classroom in general and look forward to being more intentional with math time.
Lastly, the last thing that stood out to me was "Getting better at teaching requires teachers to
plan at the course, unit, and lesson level, and to reflect on, and improve on, each day’s instruction. Equitable
instruction requires teachers to develop both their knowledge of mathematics and the socio-cultural
contexts of the students they teach in order to deepen learning for all students." I like this because it falls in line with my beliefs that we can always learn and strengthen our ability as teachers.
I had several of the same thoughts. I have started some of the IM games with my class this spring. I was hesitant to let go of the older math games, but after seeing my students respond to the IM ones, I feel refreshed and excited.
DeleteThe first principle that resonates strongly with me is that every student can learn math. It is important to me that I can present the material in various ways that each student in my class has an opportunity to connect with the material in their learning style. I already do some vertical work in my class with problem solvers and small group work. The students really enjoy this activity and I find it very valuable for learning. The one take-a-way that I will be implementing going forward is making sure that roles are switched throughout the process. Usually, each group assigns the roles on who does what and then solves the problems together, but I like the idea of giving different colored pencils/pens to students so that others have an opportunity to write, and you assure they are all actively involved in the process. In addition, for early finishers I liked the idea of them “revising their explanation so more students will understand it”. This is a great way for them to add on to their thinking and add to the class discussion while other groups finish. The other idea that resonated with me and caused me to pause and think was reflection. Our class reflects on their learning on Fridays, but I really liked the idea of specifically having students reflect on their mathematical learning with prompts to reflect on their own experiences, what they learned, what they found difficult or how they were successful. It would give them a chance to ask a question that they may have struggled to ask during class time or think about the strategy. This was exciting to me and something I am going to begin implementing now.
ReplyDeleteThe section discussion in the video of "select & sequence" reminded me of how powerful it can be to pre-select what students/strategies you would like to highlight rather than asking for random volunteers. I know I have found myself choosing at random and often wishing I would have been more thoughtful. Additionally, the importance of sequencing your selections in a way that meets the goal you have in mind - whether that is starting with some sort of direct modeling then moving toward something more abstract, or you're trying to make connections between two or more strategies. The amount of time you have to keep kids engaged in the part of the lesson where different strategies are shared cannot last too long, so I think it's important to be mindful about selecting and sequencing.
ReplyDeleteI appreciate this approach, especially with our youngest learners. These practices parallel my philosophy and style as a Kindergarten teacher. Discussion and expression are so important and I believe leads to better and deeper understanding of concepts as students explore and expand their thinking as they listen to their peer’s perspectives. I think this approach allows all students the opportunity and access to share whether they have formulated an approach to solve a problem or not, students can all learn from each other. I also appreciate the principle that every student can learn math and they learn by doing math.
ReplyDeleteIn the video, the first step of taking time to anticipate reminds me to take the time to think through students' possible reactions and solutions, sometimes I don't take enough time for this valuable test. I also appreciated the monitoring step where it was suggested to "stop talking and listen." This has been a goal of mine for quite a while to do less talking and allow students to do the exploring and thinking. The step of selecting work to share and sequencing the order in which that work is shared is one which I have found very useful when students share their mathematical thinking!
ReplyDelete
ReplyDeleteThe first summary had a lot of good information. It was like a lot of information so I tried to slow down and really take in what was being said. One part that I really connected with was the part where it talked about the usefulness for particular mathematical learning goal. We are currently doing something in our PLC that really made me realize that this is a really strong piece to bring to the group. Another thing that stood out was where t talked about the journaling. That would be super powerful, but what I loved even more was that there was a list of real questions I can have in front of me as sort of my go to questions. I feel like I need to laminate a trifold of these useful questions. On that trifold I could also include the part where it had the student moves and the teacher moves. This was really awesome to look over because I could actually visualize what that would look like in my classroom. Oh and another thing I would have on my trifold toolkit would be the 5 practices for orchestrating productive mathematics. The way this is set up makes a lot of sense but it also is very intimidating since there is a lot before and in the moment. One thing that makes me feel better is that I truly believe that this is a great way to teach learners. It will take a lot of practice but it is important work that really matters.
This week's reading was especially interesting to me. I love the way that it was taken directly from our new curriculum as I had a chance to read some more about the lesson structure and some o the "why's" that we will be working with and teaching next year.
ReplyDeleteFirst, the phrase that stood out to me was that students are "Learning math by doing math". Not listening to or watching as someone else is talking and/or problem solving while the rest are watching. Students are truly building their conceptual understanding throughout the lesson(s) and are engaging in mathematical conversations to build their understanding.
I have been dipping my feet in to the new curriculum and exploring these lessons with my current students. Some noticings that are aligned with this reading include the conversations around math, the opportunity for exploration in math concepts and the community building within the classroom.
Another thing that jumped out at me while reading was the use of math journals. I have implemented math journals in my classroom, but have not used these consistently (especially this year) and seeing the journal prompts inspired me to use these in my math lessons next year. I love the idea of students reflecting on their learning in their math journals and responding to a short prompt based on the lesson, what they are learning (quick formative assessment) or just a reflection of how they are feeling about the lessons. I love this idea and can't wait to use math journals in my classroom again.
Kristina I agree with you! The idea of students "learning math by doing math" seems like a natural way of teaching. Yet, for many years, students have been trying to learn math by observing another person, most often the teacher talk, model and solve. As a previous kinder teacher who utilized manipulatives, games and a constructivism approach in math, I'm beyond excited to dig into this new curriculum.
DeleteAfter reading the Illustrative Math design principles and key structures, what resonates with me is the belief that all students are capable of learning. I firmly believe that fostering a positive student perception is crucial for their success. As a teacher, it is my responsibility to create a classroom environment where students are aware of my unwavering confidence in their abilities, enabling them to develop self-assurance. It is a place where negative self-talk is replaced with a positive growth mindset and the necessary support is provided. This self-confidence acts as a catalyst for perseverance and strengthens their problem-solving skills. When students believe in themselves, they can achieve great things.
ReplyDeleteOne idea that made me pause and reflect is the concept of building a "math" community. While I have always strived to create a sense of community within our classroom, the notion of extending it specifically to math resonated with me. It is essential because my students will continue to be classmates as they progress to fourth and fifth grade discovery classes. We emphasize the idea that we are a team, encouraging collaboration, mutual support, and fostering personal connections. However, incorporating math into this community-building process is an exciting prospect. This year, I have fully embraced the morning meeting as a means to strengthen these connections. As part of our morning slides, I include math-related activities such as "Would You Rather?" or "Which One Doesn't Belong?" Additionally, I review math concepts we have covered. This integration has been well-received by my students, and they thoroughly enjoy this connection time.
Furthermore, I have implemented game time as a structured activity during our math lessons. Allotting a dedicated portion of our math time for playing games that reinforce our math content has been incredibly effective. Through playing these games together, students become teachers themselves, correcting misconceptions and actively engaging with the concepts. This approach has proven to be an excellent method of positively reinforcing math concepts and strategies.
What resonates with me is that all students come with their own unique background knowledge and learning needs. Furthermore, that every student is a capable learner that can actively engage and provide input in their own way. By implementing math instruction that supports this concept you create and foster students who can potentially view themselves as math learners and/or mathematicians if you will. This is a powerful move in cultivating a safe classroom that promotes risk taking, math talks and the ability to take part in productively struggling through math concepts/problems. I'm excited to see this in action.
ReplyDeletethat teachers will have daily opportunities to learn about and leverage their students’ understandings and
experiences and how to position each student as a capable learner of mathematics.
From the readings, one thing that resonated with me was the importance of building a math community. As teachers, most of us work hard to build a classroom community where students feel safe and cared about, however I had never spent a lot of time with this in math class specifically until starting the new math curriculum. I think starting the year with math class norms is really powerful and encourages risk-taking, participation, and exploring new concepts that may feel uncomfortable. I will say that although I referred to our norms from time to time, I read that IM encourages reviewing these once per week. I will implement this next year as a weekly routine and reminder for my students. Another thing that resonated with me was the chart of teaching moves that support the math community. The suggested teacher moves are a way to engage all students and the questions are a good resource for us as we move away from, “I do, we do, you do” teaching.
ReplyDelete