This is a bittersweet post, as it marks the final set of videos from my Math Routines video series from this past school year. I learned so much over the course of the year while filming and working with teachers and students across grades K-4 on these Number Routines:
As I watched each filmed class routine, I reflected a lot on the types of questions I asked students, the way I structured the problem(s), the math the students knew, and the many interesting student ideas I didn’t anticipate in my planning. This process was an incredible experience in professional growth.
Seeing math routines through the lens of every grade level has been such an amazing experience. While I’ve remained fairly consistent in the types of routines filmed in the kindergarten, third, and fourth grade classrooms, I’ve introduced a new routine to this first grade collection called Choral Counting.
Choral Counting is an activity in which students count together by a given number as the teacher records the count on the board. The purpose of a choral count is not just to practice rote counting, but to engage students in reasoning, predicting, looking for patterns, and justifying things they notice in the count.
I’m always fascinated by math in the early grades. In kindergarten especially, it can be so challenging for teachers when students come into school with varying exposures to both language and mathematics, yet all of their ideas are incredibly intuitive, informal, complex, and foundational to the math they will encounter in later grades.
After reading a great deal of work by Doug Clements and this research study by Greg Duncan — indicating that early math skills are one of the best predictors of later success in both math and literacy — I really began to wonder… what is it about early math that makes it such a powerful predictor?
One of the most powerful things about routines in the math classroom is the structure of the activity stays the same while the content can change each time. Since the teachers in my building use these routines in all of the K-5 classrooms, it creates a structural coherence that is beneficial for both teachers and students.
When you hear the word argument, you might think of a heated dispute or a clashing of opposing sides. In the mathematics classroom, however, the practice of argumentation involves making claims, supporting them with evidence, evaluating the reasoning of others, and making sense of mathematical ideas. This mathematical practice is identified by the Common Core Standards as central to the work of K-12 mathematics. It’s the practice through which a mathematical community determines what will be accepted as true.
While students in the upper grades may engage in more formal argumentation and deductive proof, young children can and do engage in supporting their reasoning with evidence, making sense of the arguments of their peers, and making conjectures about mathematical relationships. For example, students might argue that 5+3 is the same thing as 3+5 by modeling both expressions using unifix cubes.
Or students might move toward making more general statements about how and under what conditions a mathematical relationship is true. For young students, this might sound like, “It doesn’t matter what order you add the numbers in, you will always get the same amount.” This is related to, and perhaps builds on the claim above, but implies this relationship will be true for any number.
I couldn’t be more excited about the launch of this Teaching Channel project — it’s so near and dear to my heart. Over the past five years, much of my work in the classroom and with teachers has centered around math routines that generate student discourse and help us learn more about our students’ understandings. All of this work has been inspired by books I’ve read, conversations with colleagues in person and on Twitter, and the amazing student mathematical discussions I’ve heard, sparked by these routines. With this project, I have the opportunity to share all of the hard work of my colleagues, showcase the safe culture they have established in their classrooms, and highlight all of the wonderful mathematical ideas of their students.
This entry is the second post in the series Getting Better Together: A Lesson Study
In my first Lesson Study post, I discussed choosing a mathematical goal and task. In ending the post, I invited you to take some individual think time to work out the four questions posed. This was your time to think about how you would plan the lesson for your class, what sequence you would use, and what questions you would ask. You were also tasked with choosing a warmup to engage your class and a formative assessment strategy. Now it’s time to think about the math and the lesson plan.
This entry is the first post in the series Getting Better Together: A Lesson Study
Don’t you just love those days when a math lesson goes really well? A lesson where, at any given moment, you could look around and see students engaging in a task, persevering through problems, talking with one another about the mathematics, making connections, and in the end, be able to demonstrate understanding of the mathematical goal for the day? While it’s an amazing experience we probably wish we could have every day, there’s also much to be learned when a lesson doesn’t go quite as well.
In math class, we often see students pull numbers out of math problems and operate on them without thinking about the context. Many students arrive at an answer, but don’t realize their answer doesn’t make sense within the context of the problem.
When this happens, we’re left wondering many things that are extremely important in our future planning:
- Are they struggling with the math?
- Are they struggling with comprehension of the text?
- Are they making sense of the problem as mentioned in SMP1?
After reading Brian Bushart’s blog post, I’ve found that taking the numbers and questions out of the problem itself engages students in making sense of contexts. Students are then able to notice and wonder about the context without the worry of having to solve for something.
We’ve found collaboration with one another to be an invaluable component of our professional learning. In every conversation we have around the math, the lesson, and student work, we learn so much. Since we know it’s not always easy to find the time to meet, especially living on opposite coasts, we’ve found ways to be creative in our scheduling, planning, tools, and technology to make it happen.
We were fortunate to begin our journey together over two years ago when we worked on a project supported by Illustrative Mathematics, Smarter Balanced Assessment Consortia, and Teaching Channel. The project connected educators from around the country in a planning, teaching, and reflection cycle unlike anything we had ever experienced. Recently, NCTM’s publication Teaching Children Mathematics, published an article on this work and hosted a Twitter chat that generated an energetic conversation about collaboration that sparked a new idea for us to try.