Many of us have strong literacy workshops up and running. We are supporting our readers and writers through modeling, rich conversations, conferences and independent work. But what about our math time? Are we supporting our young mathematicians in a similar way? Kassia Omohundro Wedekind shows us the power of small-group instruction through a math workshop approach in her new book, Math Exchanges.
Math Exchanges stands on the shoulders of great literacy thinkers such as Regie Routman, Lucy Calkins and Debbie Miller, as Kassia shows us how conversation and reflection through the workshop approach in math is as powerful for teaching and learning with young mathematicians as it is for young readers and writers. Teachers will see how creating math workshops with “community, rigor, and joy” can be a powerful (and fun!) way to teach math in this book that is a joy to read. Filled with practical examples, glimpses into the minds of expert teachers interacting with students, and real life “kid talk” from mathematicians in grades K-3, this book will be a welcome addition to all teacher’s bookshelves.
We have the honor of kicking off this blog tour and sharing more of Kassia’s deep thinking about math with you. Enjoy our conversation with Kassia Omohundro Wedekind!
1. I love how you connect Lucy Calkins’ advice “teach the writer, not the writing” to math. “Teach the mathematician, not the math” is such a powerful way to think about our small group instruction, or “math exchanges” as you call them. In this day and age of pacing guides, curriculum maps and standards, how do you advise teachers to stay true to these words and focus on our young mathematicians, not what our pacing guide dictates?
This is such an important question…and such a hard one! I think the bottom line is that if you are teaching for true and deep understanding, you must teach responsively. If you’re teaching from a place that is way beyond a child’s understanding or you’re teaching only for surface-level understanding, a child may learn to mimic understanding or pass a test, but she won’t really understand mathematics. And unfortunately, we already have a society with a lot of people who don’t really understand or even like math. So, I think we, as teachers, can make a powerful choice to teach responsively, even in the difficult time in which we teach. We can show the amazing true understanding that comes from teaching a child to construct understanding rather than memorize isolated facts and procedures. We can change how people view mathematics in their lives and in the world.
Even the best curriculum resources, maps, standards, and pacing guides (and there are some useful ones out there) cannot replace the knowledge the teacher has of the child. So, my best advice is to become an expert on your students. Learn more about how children construct numeracy in their minds and take responsive steps based on that information. When people challenge you, use your unique understanding of each child and your understanding of how math is learned to lead the conversation. Bring your data (qualitative and quantitative) of what the child knows and what the next steps are. I think people respond to teachers who are experts on their children and have carefully crafted instruction for their specific learners.
2. Throughout your book you highlight the importance of meaningful talk amongst our young mathematicians. Pat and I agree that talk is the foundation for powerful learning. How do you go about establishing this at the beginning of the year?
Giving yourself permission to go slowly at the beginning of the year to establish a culture of talk in your classroom is critical. You will have (or at least I do!) those moments of “I should be moving faster!” or “I didn’t have time to get to…” Just keep telling yourself that the time you’re taking to establish a community in which children actively listen to one another, respond to each others’ ideas and push each others’ thinking is well worth the investment of time.
In the beginning of the year I spend a lot of my planning time thinking about how I will facilitate talk in the focus lesson, math exchanges, and the reflection parts of my math workshop. We chart and practice some language that helps us explain our thinking (“I think…because…), connect our thinking to that of our classmates (“I agree/disagree with Jeremy because…”, “My strategy is similar to/different from Marta’s because…”) and summarize one another’s thinking (“When my partner solved that problem first she…”). We practice looking at the person speaking. We learn to turn and talk and then explain the ideas of our partners. These are the kind of dialogue skills that are useful across the content areas (not to mention in life!).
These kinds of conversations look a little different at each grade level, but I truly believe all kids are capable of this. In my kindergarten class in which about 80% of students are English language learners, we have been having these kinds of conversations from the first week of school. I won’t say that it’s always easy or that we always have profound conversations, but we are learning how to talk math with each other. During our reflection time children share what they have worked on during their independent (well, in September we’re working towards independent!) math stations. As part of a focus on sorting and patterning, last week Jenny brought a sorting tray of pom poms she had sorted according to color and size to the circle for reflection. She explained “I put the same color together.” We opened the floor for discussion. “You also sorted by big, medium, small, and really small. It’s size and color,” said Kara. “Big blue,” responded Patricia, a girl whom I had never previously heard say a single color word or size word in English. Talk differentiates itself naturally. Everyone learns to bring something to the conversation.
3. One of my favorite quotes from your book is “Imagine if, at the end of the school year, all kindergarteners left understanding math as a medium through which to wonder about and investigate their world. Imagine if each child left kindergarten with a sense of ownership and agency in the world of mathematics. Imagine if all kindergarteners viewed mathematics as a place for play, creativity, and imagination. Imagine the possibilities for these young mathematicians. Endless.”
As someone who truly hated math all through school and for much of my teaching career, this book has changed how I view math and how I teach math. It’s now one of my favorite times of the day! I never knew it could be this fun. What advice do you have for teachers who don’t enjoy teaching math? How can they change their thinking and become better math teachers?
I’m right there with you! I was not someone who loved math. (Side story: A high school friend of mine who I recently reconnected with asked me “Kassia, you wrote a math book? Do you remember eighth grade algebra when about half way through the school year you decided you’d just retake the class the next year so you spent the rest of the year napping in the back of the class?” Yes, I remember…)
I did not see myself as a mathematician until I started to really study how young children construct mathematical understanding. I read about these amazing studies that have been done with babies as young as a few weeks old (some of which are explained in my book) that prove that we are hardwired from birth to think mathematically. In one study babies were shown images on two screens of one and two dots. One or two drum beats were played. When one drum beat was played, the babies spent more time looking at the one dot image. When two dots were played, babies spent more time looking at the two dot image. We are born with capacity for numeracy and problem solving that we need to learn how to better teach to. When a baby is born we assume that this child will develop linguistic fluency. We assume the baby will learn to speak her language fluently, to read it and write it. We assume linguistic competence because we know we are hardwired for language. We are just as hardwired for mathematical fluency, and yet, when a baby is born we don’t necessarily assume that he will be as mathematically strong as we assume he will be linguistically. We need to change that.
Go into a preschool or kindergarten class and watch children play. You can’t help but be amazed by what they do. They sort, they arrange items in order of size, they count, they combine groups, they estimate. No one has taught them to do this. Children come to us with intuitive strategies for math and problem solving. They use math to make sense of and organize the world. And that’s great news. It means that it is not our job to impose a foreign system of understanding and facts on these children. It is our job to be curious about what they know, understand the strategies they comes to school with, and build on these strategies as children learn about more formal mathematics.
I think what makes me love kindergarten so much is that, as the kindergarten teacher you cannot be cynical about the world. You just can’t. When you sit beside a child to read, to play, to count, amazing things happen. And not just once in a while, amazing things happen every single day. So if there is any place to feel great hope and endless possibility for the future of mathematics, it is in the kindergarten classroom.
Wow. This is definitely a book that will change how you view math, and how you teach your young mathematicians. It’s a much needed addition to professional resources for elementary teachers. Please follow this blog tour at the following sites to enjoy more interviews with Kassia about Math Exchanges, and have the chance to win a free book.
Our Camp Read-A-Lot, hosted by Laura Komos (October 4th)
Reflect and Refine, hosted by Stenhouse author and first grade teacher, Cathy Mere (October 5th)
Elementary, My Dear, Or Far From It, hosted by Jenny Orr (October 6th)
Please leave us a comment or a question about Kassia’s interview or her book – or your thoughts on this post. We will be raffling off a free copy of Math Exchanges (or another Stenhouse book if you already have Math Exchanges) at the end of the tour. Enjoy!
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I loved reading your thoughts and questions in regards to Math Exchanges! Hearing what other people think (and wonder) really helps me to move forward in new directions. It’s exciting to hear that Math is now one of your favorite times of the day! And of course, I enjoyed reading Kassia’s responses as well.
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Sounds like a great book. I’ll be curious when I read it, to see how it differs from books like Show and Tell: Representing and Communicating Mathematical Ideas in K-2 Classrooms, by Dacey and Eston.
Thanks, Laura. Looking forward to the blog tour stop at Our Camp Read A Lot!
Sue–Thanks for commenting! Show and Tell by Dacey and Eston is a great one! (As is Dacey and Eston’s Growing Mathematical Ideas in Kindergarten.) I think one difference is that my book addresses the math workshop structure and focuses on teacher language and small groups.
Reading this leaves me feeling so inspired to get started making changes to my math block. I have been feeling uncomfortable with the routine and structure that is imposed on my students by the program that I use. I do like the program but I want more flexibility. I see a math workshop as a flexible way to create deep mathematical thinkers and problem solvers. I am not very far along in my reading of the book yet but I can’t wait to read more and begin making changes to the way my students and I use our math time.
I devoured this book at the Stenhouse website. It belongs on a very short list of great books that have totally transformed the way I think and teach a subject. Since reading it, have been building math minilessons around mathematician statements and have found that they often parallel the work we are doing and writing workshop. My students make stronger connections when they learn that mathematicians make a movie of the problem in their mind and make a plan for how they will solve just as readers and writers visualize and plan. During math exchanges, my students draw on the work from our minilessons as they decide how to tackle a problem. I think this book really sets teachers up well for the work of the common core as we attend to math content and practices. The book is buzzing through our school and making its way into staff development already.
I’d love to get this book. My school has started Intervention and Enrichment groups for Math and I think this would give me lots of great ideas for my own classroom teaching and my small group teaching. 🙂
Jill–I think you bring up a great point about flexibility. Teaching must be flexible and loyal to the student’s understanding, not to following a program to the letter. I hope you’re able to use the book to find some flexibility you’re looking for.
Courtney–Thank you for your kind words. I’m so glad the book has meant something to you. I’d love to hear more about the mathematician statements you’re using and learn more about he work your kids are doing in math workshop.
This looks like just the book I must read next! I am a first grade teacher who has spent the last year trying to figure out how to be a better mathematics teacher. I think less children are coming to school with a background of playing domino and dice games. I think that there is a gap opening up of students who have those subitizing skills and those you need our help.
I recently previewed Math Exchanges on Stenhouse and absolutely love it! It is one of few great books I have dedicated to math and I hope to use it as I transform my math block. While I have many questions, something I would like to know more about it the Math Boxes. How do they work? What exactly are they doing?
I read bits and pieces on the Stenhouse website and got so excited! I am going to buy a copy for the other 4 teachers at my grade level. Each year I say I’m moving slower than my colleagues because I don’t think my first graders are getting a real understanding of…. (you name it) I feel so thrilled to see research and problems and language that relates to how we are teaching reading and writing. This has the power to change so many things we do in our classrooms. Keep these conversations coming!
Congratulations Janet! You’re the lucky winner of a free copy of Math Exchanges (or another Stenhouse title if you already have it). Enjoy!
I love it all but the first question tugged at my heart and the third question made me think how lucky I am to teach K. Thank you.
What great thinking and comments you all have! Thanks so much for writing!
Suzanne–I think you’re right that, just as in literacy, there is a great gap between children who have had exposure to counting, games with dice, and having mathy talk at home and those who don’t. For those children the role of math in early childhood education is even more critical!
Amy–Math boxes is one structure for math workshop (I talk about a couple of different ones in the book). It’s similar to a book box in that it holds “just right” material for each child. Sometimes it might be a couple of story problems to work on independently, a math game to play with a friend, or a collection of items to be counted and recorded in a counting journal.
Thanks for the prompt response. I liked the ideas you presented in the book and inquired because I am in need of something for students to work on independently at the beginning of math workshop. I have been trying to incorporate work stations as well. I started with a rotation system similar to one mentioned in your book, but I am finding it hectic. I would prefer something more independently run where I can call groups as needed. I might try something like your structure. I currently teach a 1/2 split and I am finding it challenging to meet the needs of both groups when outcomes are so different. Have you seen/used this approach in combined grades? Any tips? I feel like the math exchanges would help me reach both grades more effectively. Regardless, I am going to purchase the book tonight and I will most definitely be sharing it with colleagues this week as we meet for our PLC. Thank you, thank you, thank you!
Thank you for all the thoughtful comments and replies! We will be raffling off the free book on Friday, after the blog tour ends. Make sure you’re checking in on all the other sites – great math thinking out there!
@Amy–I taught a 2nd/3rd grade multiage class a few years ago and had a structure similar to what you described:
5-10 minute routine (count around the circle, dot cards, quick images)
10-15 minute focus lesson
10-15 minute independent task (math box time)
15-20 minute partner task (partner game, problem solving on chart paper, etc)
5 minute reflection
It really fit my needs that year with a wide range of learners. It allowed independent time to practice what the individual needed to focus on and also a lot of collaboration and learning from one another. It also had a more peaceful feeling for me that year over stations. I’ve found when it comes to structure, what works for one teacher or one group of kids may not work for another. I think flexibility with structure is important as long as you have all the “essential elements of math workshop.”
Good luck this year!!
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I am in the middle of reading Math Exchanges and love it. Unlike Kassia, I did love math in school, but soon lost that excitement when I started teaching whole group lessons and followed the book lesson by lesson. Now that I use a math workshop, I absolutely love teaching math again! I am learning a lot from Math Exchanges and know that I will be tweaking my workshop based on the book.
Does your 5-10 minute routine tend to correlate with the independent task they’ll be doing? We are in the 2nd year of our math adoption, so I feel there is less flexibility, however, I’m at a school that encourages and embraces small group math instruction and using the comprehension strategies in all areas (including special areas; music, etc.). Unfortunately, there just hasn’t been the model set for what the math block should looks like and how much we need to tie our instruction to exactly what’s coming from our curriculum. We all know the bigger picture is to make mathematicians, but we’re all scared to jump GoMath ship. 😉
The thought of teaching math workshop invigorates me. I just haven’t found a way to make it work (just like others have said). I think this book is the one for me!