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.
At the end of the school year, I always find myself in such a weird space. I’m exhausted, need a breather, and know I should take some time to get off the runaway train that is teaching.
However, that need to disconnect, decompress, and check out of education thinking for a bit is quickly followed with the excitement of finally having time to catch up on all the great educational reads I can’t seem to get through during the school year. As I start to make my list — and question whether I’m a workaholic unable to disconnect from teaching — I find so many teachers and coaches on Twitter asking for book recommendations. Whether it be recommendations for the following school year’s professional learning or simply for personal learning, I’m relieved to see I’m not alone!
A day in my classroom is filled with inquiry, deep questioning, hands-on learning, and student-driven discussions. Yet, for all aspects of my teaching that I’m proud of, I’m also continuously reflecting on my instructional practices that need improvement.
This past year, I’ve lived the mission of Getting Better Together by sharing my experiences with others and allowing their advice/feedback to guide my instruction. From engagement in book studies, to Twitter chats, to receiving video feedback, I’ve been amazed at the growth of my online professional learning community and consequently, my growth as an educator.
My growth continues, alongside you, the Teaching Channel community, in three new videos. You’ll see me try out instructional strategies that are aimed at reaching all learners and differentiating the learning experience in the classroom. And you’ll also see me work to elevate every student’s voice through designed tasks and groupings. (Read my accompanying blog post, Three Ways I’ve Become A Better Listener.)
“When you talk, you are only repeating what you already know; but when you listen, you may learn something new.” Dalai Lama
What does it really take to be a good listener? My entire life I’ve struggled to answer this question.
In elementary, middle, and high school I won either “most talkative” or “most social.” I loved public presentations so much that I got a degree in broadcasting and intended to spend my life narrating stories from the field. After a career transition to teaching, I quite enjoyed the feeling of being on stage. I created and sang songs, gave incredibly entertaining lectures, and presented ideas in a logical fashion to my students.
About four years ago, I began reading about focusing on student voice within the classroom and elevating this as the predominant voice. As I began to think about how my classroom could transition to meet this focus, I had to let go of part of my practice. Not only did I enjoy the presentations, but they defined my teaching style. (My Nicki Manaj integer song was a classroom stopper!) Yet, as I gained more experience and redefined my role as an educator, I realized I needed to elevate student voice and minimize my own.
I’m a huge fan of writing in math class! While I was teaching, I had my 5th graders write in their math journals every single day. Whether they used the journals before the lesson to write down estimations, during class to show their reasoning through a problem, or at the end of class for an exit prompt, the journals were always a safe and not-graded place for students to jot down their thoughts. No matter the prompt, I always learned so much about what they understood by reading their entries each day.
This year, as a math specialist, I get to see student writing in math classes across many grade levels, and it’s so incredibly interesting. I’m able to see where it all begins, in kindergarten, before students are even writing explanations in words, to 5th grade, where the writing becomes very articulate. In each lesson I plan with teachers, we incorporate a writing aspect that we use for reflection after the lesson. The students’ written pieces, in addition to our classroom observations, help to ground our reflective conversation after the lesson.
Imagine going to school each day and entering a classroom filled with students who are eager to explore mathematical ideas, willing to embrace failure and struggle, and persistent with any math problem you give them. As teachers, we have often been led to believe that the greatest math lessons come about when we have good curriculum materials and interesting tasks — those are important, without doubt, but the new science of the brain is telling us that engaged and successful students come about when students believe they have unlimited potential and that they can learn anything.
Studies even show that our brains grow the most when we’re struggling and challenged, and if you believe in yourself, as a teacher or a student, your brain will grow more when you encounter challenge than if you doubt your potential (see a 1-minute video explaining that below).
When I started teaching, I remember being overwhelmed by the many things I was “supposed” to do during a lesson. Grab students’ attention, check for understanding, make sure everyone had an opportunity to share their thinking… the list went on!
Sometimes it felt like I spent more energy making sure I checked off each part of my lesson than actually teaching. But over time, I learned to internalize all these different strategies and plan lessons using a variety of effective techniques.
In our new video series, funded by Cisco Systems and created in partnership with the Rodel Foundation of Arizona, we get to explore the approach of the Rodel Math 20/20 Initiative. Included in this approach is a three-phase lesson structure (adapted from Teaching Student-Centered Mathematics) that helps teachers make sure they are covering — and then internalizing — the parts of an effective and engaging real-world math lesson.
Modeling with mathematics is the practice of making sense of the world through a mathematical perspective. Take a moment to look around and get curious: How do you use mathematics to make decisions in your everyday life? Maybe you’re deciding what to make for dinner. Does the recipe have enough servings to feed everyone or will you need to modify it, perhaps by doubling or halving the amount of each ingredient? When should you start making dinner if you’d like to eat at 6?
These questions can be viewed from a mathematical perspective. There is something to count, measure, or quantify and the answers to these questions have real and interesting implications for our lives.
Children also need opportunities to identify mathematical problems in their world, determine what information will help them solve a problem, develop mathematical models of situations, and revise their models to more closely predict real world phenomena. This is the work of modeling with mathematics, a mathematical practice identified by the Common Core State Standards as central to the work of K-12 mathematics.