By Andrew Gael, posted June 20, 2016 —

I notice proponents of sense making in math class—such as Dan Meyer and The Math Forum —encouraging teachers to present a perplexing scenario to students and let them develop questions where math can be useful. As a special education math teacher, I often wonder how much to explain or “front-load” for my students before engaging in the problem-solving process.

Some students, however, may need scaffolding, language support, culturally relevant pedagogy, or skill reinforcement before they are ready to grapple with a truly perplexing problem-solving situation. This highlights a major dilemma for special education math teachers, who must balance these ambitious and sense-making teaching practices with the learning needs of their diverse student populations. How much scaffolding is too much? How much scaffolding takes the process of solving the problem out of the hands of the student? A specific instance of this is when teachers are deciding what information to present to students during the problem-solving process. Maybe you can help me figure it out.

One of my favorite blog posts is from Joe Schwartz, an elementary school math coach in New Jersey. In his post, Joe describes how to build a better worksheet. The main idea is to eliminate extraneous stuff that exists on curriculum activity sheets, but doesn’t lead to mathematical thinking. Joe’s post proves to me why he would make a great special education teacher, because it illustrates what most special education teachers do on a daily basis: We have to identify the most mathematically essential pieces of a activity sheet or task and eliminate the rest of it that might cause obstacles to students’ executive functioning. Such teachers must create easy access to hard math. That’s the goal. Joe does an amazing job exemplifying this in his post.

By taking Joe’s advice to build better activity sheets, teachers can limit overscaffolding. For example, earlier this school year, I was perusing some EngageNY activity sheets to use for our measurement unit, and my SMARTboard was also on, projecting my computer screen to the classroom. After several minutes of watching me scrolling, my assistant teacher exclaimed, “That would make a good ‘notice and wonder’!” She was referring to an activity sheet in one of the EngageNY modules.

I asked her to tell me more.

“Well, you just give them that picture and ask what they notice.”

The picture was of a paintbrush seemingly being measured by squares, which were lined up with gaps in between each square—an exercise in error analysis.

I use the instructional routine “I notice/I wonder,” with some regularity; so, I was pleasantly surprised to hear her use it during our planning time. I notice/I wonder creates access to sense making by scaffolding the aspects of expressive communication that students with disabilities may struggle with, without overscaffolding their mathematical thinking.

So, we came up with this activity sheet work-around by adding the structure of noticing and wondering to the image.

The title may also be unnecessary, but giving students a hint as to what direction the lesson is headed and giving a frame to some of what they notice seems fine to me. What do you think? Is this new activity sheet still too scaffolded? How would you introduce this or a similar situation to your students to create easy access to hard math?

We hope that after students are given the opportunity to take ownership of their mathematical thinking, a conversation about how to appropriately measure the paint brush using the cubes will come up organically. Susana Davidenko and Patricia Tinto (2003) highlight that listening to your students will promote equitable teaching practices in mathematics for all learners:

In classrooms that promote meaningful understanding, teachers pose questions that encourage students to think beyond how to find an answer. The focus is on the processes and concepts involved in the problem situations. Questions such as “Did anyone solve it another way?”; “Tell us about what was going through your mind when you were working on this problem?”; and “Can you explain how you solved it?” promote student communication and validation of their thinking. This conversation, in turn, helps promote equity in the classroom (Campbell and Langrell 1993; Whitin and Whitin 2000).

And maybe, just maybe, if you allow them to take ownership of their mathematical thinking by using sense-making routines like I notice/I wonder, your students will surprise you and wonder something that is just as important mathematically as the original direction in which the lesson was meant to go.

Reference

Davidenko, Susana, and Patricia Tinto. 2003. “Equity for All Learners of Mathematics: Is Access Enough?” in Access to Academics for ALL Students: Critical Approaches to Inclusive Curriculum, Instruction, and Policy. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Andrew Gael has worked in education for more than ten years and as an educator of students with disabilities for the last six. He was born and raised in New York City, receiving his Master’s in Education from Brooklyn College. Gael now teaches math at the Cooke Center Academy, a school for students with developmental, learning, and physical disabilities in Manhattan. He has spoken nationally to advocate for equitable access to the highest quality math instruction for the typically under-served student population of students with disabilities. He writes about the intersection of math education, special education, and disability rights on his blog, The Learning Kaleidoscope.