In early October, I presented at NCTM Hartford with the incomparable Heidi Fessenden (@heidifessenden / blog). Our session was called “Strategies for Cultivating Mathematical Thinking for All Learners.”
Slides available here.
In our various roles — as classroom teachers, inclusion specialists, coaches, etc. — we have observed a disconnect between what some teachers say they believe — that “all students can learn” — and how they structure learning experiences. Last year, on a tour of a school, the instructional coach informed Heidi that there was a lot of “I do, we do, you do” lesson structure and rote practice used. “Our kids need drill and repetition,” she explained.
Which kids are the ones she thinks need drill and repetition? …which aren’t?
Practice isn’t inherently a bad thing, but sacrificing all opportunities for students to be mathematical learners is incredibly damaging. Furthermore, it becomes a serious issue of equity when the students that are consistently lacking access to these opportunities are the students of color, the English language learners, the students with disabilities, the girls… etc.
“In the short term, explicit instruction is potentially effective to help students solve problems more quickly; however, this earlier introduction of explicit instruction may slow the progress of students with LD in becoming resilient, persistent problem solvers and developing deep conceptual understanding of topics.”
Hord, C.; Newton, J.A. Investigating Elementary Mathematics Curricula: Focus on Students with Learning Disabilities. Sch. Sci. Math. 2014, 114, 191–201.
Students need to develop procedural fluency, but the pathway towards this fluency can shape how students respond to problem solving situations.
Rachel Lambert, a researcher who looks into teaching math to students with learning disabilities, writes:
“It is ableist to assume that a student with LD cannot think conceptually, or cannot benefit from an engaging and rigorous inquiry curriculum. Much more is at stake than the multiplication tables; mathematics instruction that is authentic, relevant, and engaging allows students to construct identities as mathematical thinkers.”
Lambert, R.. “Indefensible, Illogical, and Unsupported”; Countering Deficit Mythologies about the Potential of Students with Learning Disabilities in Mathematics.” Educ. Sci., 2018, 8(2), 72.
Rachel adds that “these identities are particularly important for students from groups that have been underserved in mathematics, such as African-American, Latino and Indigenous students, as well as women and students with disabilities.”
And, in fact, these are the groups of people that are most likely to receive procedural instruction. They are often taught through rote practice such as “I do, We do, You do,” Math becomes more about answer getting than sense making, and students may not even realize all of the mathematical thinking that goes into what their peers do.
“Classroom environments that foster a sense of community that allows students to express their mathematical ideas—together with norms that expect students to communicate their mathematical thinking to their peers and teacher, both orally and in writing, using the language of mathematics—positively affect participation and engagement among all students (Horn 2012; Webel 2010).”
Principles to Actions, page 66
So although many educators believe that students who struggle in math class need to be taught one procedure to follow, many in the field have seen that, in fact, they need to come up with their own strategies and reason about math as much as other students.
Within the presentation, we offered three strategies.
- Naming the mathematical practices in student friendly language
to make clear what it means to think mathematically
- Assign competence
the practice of publicly identifying and praising times when students — especially low status students — are engaged in mathematical thinking
- Use high-leverage instructional routines
to give students opportunities to engage with tasks mathematically — focusing more on the content and less on the (already internalized) structure of the routine
I will publish another blog post about each of these three strategies (in the context of our presentation) this week (Tuesday, Wednesday, and Thursday). See links above.