"We are all Math People"- Collaboration and Preparation in our Middle School Math Classrooms
I like to strike a balance of productive struggle.
This is where having a co-teacher is great - we have more people for feedback so we can send students to try something, even if they may not have it 100% correct.
- Ms. Graul
In education, we often take for granted that getting all students to love reading is a worthy goal. Somehow, this same principle doesn’t always transfer to math. Not true at Springfield Prep. Helping students embrace their identity as math people is at the heart of Ms. Graul and Ms. Sela’s practice alongside deep knowledge of mathematical standards, thorough intellectual preparation for every lesson, and consistent effort to connect content to real life examples and transferable mathematical practices.
In this post we will…
Share how Ms. Graul unpacks each unit she plans and teaches
See how she prepares for individual lessons and uses this preparation to effectively collaborate with Ms. Sela
Share video clips that show students grappling with unit rates as part of a larger exploration of ratios, see the real life connections Ms. Graul and her students make, how Ms. Graul connects to mathematical practices, and how she and Ms. Sela collaborate during the lesson to meet all students’ needs.
Include links to lessons and other resources that you can use at your school!
We’ll start by hearing from Ms. Graul. How do you unpack a unit prior to teaching it?
I use a protocol to help me organize my thinking and to situate each lesson within our assessment system. For example, I want to know how each lesson contributes to the way students will be assessed on various assessments. That said, the physical product that comes out of this is not nearly as important as the process.
Even if I’m unpacking a unit that I’ve already taught in previous years, I do the unpacking just the same because the process itself is a huge part of my intellectual preparation. It helps me craft the story that guides each lesson and creates a throughline of meaning for students.
How do you prepare for individual lessons and how does our co-teaching model inform your approach to preparation?
I lead with the belief that the children are brilliant. (credit here to Dr. Danny Martin who presents this belief as an axiom!) This influences my approach because I try to plan lessons that don’t tell students what to do but instead guide them to use the tools they have and their own experiences to make meaning and solve problems.
I depend on the throughline that I established during the unit unpacking to provide context for every lesson. I ask myself “What do students already know that will support them in this new inquiry? What purpose does this lesson serve for the overall story of the unit and how will I ensure students succeed at achieving this purpose?” Rather than just planning to do what is in the curriculum, I really try to strike a balance of productive struggle. This is where having a co-teacher is great - we have more people for feedback so we can send students to try something even if they may not have it 100% correct. We have more eyes on great student thinking and can discuss what the next step should be rather than talking too much on the front end. Sometimes it works well, sometimes we flop! But we learn from it and adjust our approach so that every day is responsive to the students we have in the classroom.
Seeing is believing. The following video clips show how this level of preparation and collaboration translates into classroom instruction that helps students see themselves as math people.
See the lesson come to life. In this lesson students are continuing to build their conceptual foundation for ratios and proportions by learning how to calculate equivalent ratios between prices and quantities and exploring the idea of unit rates.
In this clip, see how Ms. Graul uses familiar contexts to introduce complex mathematical ideas.
Next, see how students share a variety of strategies for determining the price of different quantities of avocados when eight avocados cost $4. You’ll also see how Ms. Graul authentically connects to Mathematical Practices during the discussion.
Finally, see some examples of how Ms. Graul and Ms. Sela collaborate throughout the lesson to meet students' needs.
We covered a lot of ground in this post-- here Meaghan shares one last piece of advice for new Middle School Math teachers on how to get started helping students see themselves as math people.
I would advise new middle school math teachers to deeply reflect on their own purpose and how that purpose influences practice. The most daunting and inspiring part of my job is that I am very aware that the problems I present to students are not themselves the end, but a means to an understanding and the understanding is the goal. Success in 6th and 7th grade is NOT “exceeds standards” MCAS results if those results don’t build the foundation for student learning in 8th grade and beyond. The understanding is what students will carry with them and apply to every aspect of their lives. Because of this, the standards (including the Standards for Mathematical Practice) are infinitely more important than the problems that assess the standards. Ask yourself constantly not “did they earn the point?” but instead “do they understand the concept?”. There’s a big difference.
Interested in more resources from Springfield Prep’s Math Team? Check out the following resources:
