A math classroom full of “sweaty brains”

By Michelle Sirois

A classroom teacher currently engaged in Zeroing in on Math’s Deeper Learning work and former EdVestors’ Math Fellow.

Over the past few weeks, my fourth-grade math class at the Oliver Hazard Perry Elementary School worked together on multiplication. We tackled word problems that challenge students to connect relevant components of questions, apply mathematical thinking and knowledge to their approach, and prove their answers through alternative solutions. The curriculum recommends a lesson plan that first presents a problem to the students, then allows the students to solve the problem, and finally provides more problems for students to work on.

We often tell students to take risks and make mistakes because they lead to learning. Yesterday, my own mistake led to lots of learning, excitement, challenges, and opportunities for more learning.

We recently encountered our first word problem that involved division and I decided to slightly alter the introduction of the problem. I did this by removing the questions, to see what students would notice and wonder about the problem. However, in doing so, I accidentally removed the total numbers of apples too.

The question read:

Mrs. Santos owns a neighborhood grocery store. She has some apples to arrange in rows for her window display. She has room for 4 rows in her window.

(The scenario I meant to give them read that Mrs. Santos had 52 apples to arrange in 4 rows.)

Productive curiosity

Upon hearing the lively chatter around the room, I decided not to share the original problem with the total number of apples.  I challenged my fourth graders to think about how many apples there might be in total and how they might go about representing the situation. In our classroom, we have a range of math proficiency from one student working at a first-grade level to students far above grade-level. Students played with various approaches to a solution: some worked with cubes, some tried factors of 16, others pushed themselves to multiply with larger and larger numbers they haven’t multiplied before!

We reconvened as a class after fifteen minutes to discuss what different groups tried. I began the conversation with the notion that many groups wrestled with: that Mrs. Santos only had 16 apples. Half of the class was convinced 2 rows of 8 apples was possible until their classmates pointed out the problem stated she had 4 rows to work with. Group after group presented their work around multiplication until one student came to the revolution that “this is a division problem!” He explained his reasoning and I saw light bulbs go off in their heads and hands shot up with excitement!

One group who placed 98 apples on each row shared their work and found 98 x 4 = 392. Their classmates were intrigued by the large numbers and mentioned how large the windows must be to fit all the apples,

I promised the class more time to work on the problem after lunch and cheers erupted across the classroom, “My head is exploding with ideas!” One student who often confuses mathematical concepts whispered, “This is the best math class ever – it’s starting to make sense now!”

 “Sweaty Brains”

At the Perry, we celebrate “sweaty brains”. A sweaty brain happens when students challenge themselves with harder problems than what is asked of them. Exercising their brains furthers their conceptual knowledge.

After lunch, I wrote out key questions: How many apples are in each row? How many apples does Mrs. Santos have in all? Where does this concept show up in their work? Where does this show up when writing both the multiplication and division equations of this situation?

Students challenged themselves with more and more 3-digit numbers and checked in with me to see if they were right. I asked them to prove their work by using another strategy, so they kept multiplying and dividing with more and more large numbers!

Engaged and joyful learning

When it was time to wrap up, the students groaned and wished they had more time – I was ecstatic to hear it!  Before leaving class, each student had to solve the original problem that stated Mrs. Santos had 52 apples to arrange equally in 4 rows. I was impressed that all but 5 students correctly solved the problem using multiplication and division concepts they learned and retained. For the 5 students who didn’t solve the problem correctly, I now have a targeted approach to talk through their misconceptions.

As any teacher will tell you, teaching can be mentally, emotionally, and physically. But yesterday, it was just pure joy. Every kid stayed engaged with one problem for over an hour – one problem! This lesson reminded me that kids don’t need to do ten, twenty, or hundreds of problems to learn. They just need the right context and questions to explore – and with that, learning is engaging, invigorating, and joy-filled.

 

To learn more about Zeroing in on Math, click here.

The Oliver Hazard Perry K-8 School was a 2018 School on the Move Finalist, click below to learn more about the Perry K-8.

Apply to the 2020 Zeroing in on Math Fellowship!

Applications are now open to join the Math Fellows – a cohort of math teachers and coaches with a commitment to improving access to effective math instruction and a willingness to dream big, think creatively, and implement practically. Find more details on the Fellowship and application here. Applications are due Tuesday, January 7 at 4pm.

 

By Teachers For Teachers: Changing the Culture of Math Class

By Heidi Fessenden (Learning Specialist, Mozart Elementary School), Maggie Roth (Second grade teacher, Match Community Day Public Charter School), and Michelle Sirois (Learning Specialist, Perry Elementary School)

This blog post is the second in a series of blogs written by the six teachers who designed and led a five-session class for Boston math teachers. Please check out the first post here.

At an early session of our teacher-led math course, Bridging Classrooms, we began by asking, “Please share something you’re thinking about connected to math in your classroom.”

Here’s a sampling of what we heard:

  • How do I make sure I’m not over-scaffolding?
  • I am trying to get my students to work more independently in math class.
  • I want my students to be more engaged and motivated to do math.
  • I want students to think, “does that make sense?” when they solve problems, so they’re not just using procedures.

If you’re a math teacher, you’re probably nodding your head right now.  

We have to do it all as math teachers: know content well, differentiate, motivate, play catch-up. It can be overwhelming. Often, we find that math PDs we attend don’t help. In creating this PD, hosted by the Boston Teachers Union, we were hoping that teachers would feel better supported and prepared for their classrooms. The teachers who took the class, special and general educators in grades 2-8, came from charter and public schools in the Boston area. Most took the class with a colleague from their school so that they could plan together and observe each other in between sessions.

Today we’ll share the effect Bridging Classrooms had on teachers. In our next post, we’ll explore why they think Bridging Classrooms altered their teaching.

What they got out of our class (how their classrooms changed):

During our final class we asked teachers to use the sentence stem “I used to _______, now I ______” to reflect on what they used to do to teach math and how that has changed. One teacher started with, “I used to rely on my comfortable bag of tricks and talk a lot.”

We could relate. It’s easy to get into a comfort zone and forget the myriad of strategies that push student thinking and engagement. As teachers reflected on what changed in their classrooms, a few themes emerged. Taken together, these themes could be summarized in one way: the culture of math changed in their classrooms. Below, we use the voices of participants to explain the many ways their math classes changed after this course.

Student-led, interactive lessons

Many of the teachers in the group spoke about making more space for student voices and group work. They found themselves talking less in order to increase student thinking.

  • I used to teach, teach, teach, teach math and never facilitate.
  • I used to be terrified of doing any kind of group work or partner work because I was nervous there would be one student doing all the work or they wouldn’t get along.
  • Now I step back and let my students take the lead in their learning, let them struggle.
  • Now I find that my students have been working with each other better than ever. They are using motivational language with their table groups and partners while also asking great mathematical questions to better understand their peers’ work.

Open-ended tasks (less focus on right answers)

Another common theme was that teachers began using more open-ended tasks in their classes, where the focus was on reasoning rather than on getting the right answer. Many of these were modeled on tasks we had done in our course, such as visual number talks, numberless word problems, noticing and wondering, and Three Act Tasks.

  • Now my students have started having positive conversations about math. Students became comfortable sharing their thinking, regardless if they were right or wrong.
  • Now I make a conscious effort to implement strategies that I learned from this class, particularly strategies in which there is no definitive right or wrong answers (i.e. “Give me a number that you think is too big to be the sum.”).
  • Now I start every math class with a visual without a question and allow students to notice and wonder before giving them a question.

Increased support for students with special needs

Retha Reynolds, a fifth grade teacher of a substantially separate classroom for students with learning disabilities at the Sumner Elementary School in Roslindale, shared how she entirely changed the structure of her math lessons, turning the leadership of the class over to the students, primarily through using Three Act Tasks. (Read a summary of the structure of a Three Act Task here, and see how Dan Meyer breaks one down here.) Early in the course, Retha talked about her doubt about how to increase discourse among students with special needs. “They kept saying, ‘less teacher talk,’” she explained. “I didn’t know how to do that in a special ed class.”

After Bridging Classrooms, she explained, “when I plan I think about how am I going to get them talking about the math before we get to the math we’re going to do.” She does this using images or scenarios and asking students what they notice and wonder before giving them a math problem to solve. When district administrators visited her class on a walk-through, they “couldn’t believe it was a special education class” because of the level of dialogue and engagement with the math content. “I don’t know what I would have done without Three Act Tasks,” Retha reflected. Other teachers mentioned that they also felt better equipped to support students with special needs after taking our course, even if they didn’t entirely adopt a new structure like Retha did.

As we listened to teachers describe how their classrooms were changing, we wondered what it was about this relatively brief course that had such an impact. We asked them, and in our next blog post we’ll share some of what we found out.

Melissa Frascella (Math Dept Chair / Eighth grade math teacher, Boston Collegiate Charter School), Meredith Hart (Sixth grade teacher, Haley Pilot School), and Alia Verner (Math Director / Instructional Coach, TechBoston Academy) also contributed to this blog post.

To learn more about Zeroing in on Math, click here.