As a new school year begins, teachers and leaders are already planning intervention support for students who are not currently meeting grade-level math standards. Rather than defaulting to traditional remediation practices that have produced disappointing results and failed to position students for future success, let’s cultivate the learning habits our students need to engage in rigorous mathematics and take ownership of their math learning long after they’ve left our classrooms.
This three-part blog describes why it is essential to grow students’ habits of mathematical thinking alongside their math content knowledge in both intervention and core instruction settings. It outlines easy-to-implement strategies to build empowering math habits in all students.
Part 1: Teaching Up for the Math Practices
Teaching up – the opposite of “dumbing down” – rests on the conviction that every student is smart and benefits from being taught as “smart kids” are taught. Teaching up supports each learner in “reaching up.” –Carol Ann Tomlinson (2023, p. 1)
“Teaching up” in the math classroom is an approach to instruction that engages all students in challenging mathematics while providing each student with the scaffolding needed to be successful with this challenge. Also called “accelerated math instruction” (Almarode et al., 2024; Newton, 2023), teaching up provides all students with instruction on their grade-level math content while simultaneously differentiating that instruction for individual students to build not-yet-solidified prerequisite skills and understandings.
Teaching up is both a mindset and a skillset. It is only possible when educators believe all students are capable of learning high-level mathematics with understanding, given appropriate support. It requires teachers to have a deep understanding of the mathematics curriculum across strands and grade levels, strong expertise in formative assessment, and an extensive toolkit of strategies for scaffolding learning.
Teaching up is a vehicle for enacting equity in our classrooms (Gonzalez, 2023; Newton, 2023; Tomlinson, 2023; Safir & Dugan, 2021). It helps students explore and stretch their capacity for learning. Teaching up strengthens students’ math identities by demonstrating that they are mathematically capable. Tomlinson states, “When students master skills and content that initially seem beyond them, they also build self-confidence and sense of themselves as capable learners” (2023, p. 1).
As educators plan for teaching up in mathematics, they typically focus on the mathematics content they are charged with teaching, the concepts and skills students are expected to learn at their grade level (e.g., two-digit subtraction in second grade; fraction computation in sixth grade). Less attention is given to growing our underperforming students’ mathematical practices, their habits of mathematical thinking. According to Rachel Lambert, author of Rethinking Disability and Mathematics, “As soon as a student is seen to be “struggling,” the focus of their education tends to narrow to content and skills alone” (2024, p. 80). The mathematical practices, however, are an equally important focus for our teaching up work because they are key to developing our students’ mathematical agency.
The math practices articulate what it means to learn and do math. They are cognitive tools that allow our students to “self-scaffold” their mathematics learning now and in the future. If our goal is to help students become self-directed math learners who are positioned for continued success in mathematics, we must teach up for the mathematical practices in addition to teaching up for our math content.
The Mathematical Practices
The math practices are a critical and required part of our math curriculum. They are mathematical habits of thinking that define how learners should engage with mathematics. In many states, they are called the Standards for Mathematical Practice.
The Standards for Mathematical Practice:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically including mental math.
- Attend to precision.
- Look for and make use of structure.
Look for and express regularity in repeated reasoning (NGA & CCSSO, 2010).
Many educators did not experience the math practices as learners in elementary and secondary school (Gonzalez, 2023). It is difficult to teach for proficiencies we have not yet developed in ourselves. Yet, it is essential that we do so. The math practices are key to developing our students’ mathematical agency.
Mathematical Agency
Mathematical agency is a person’s self-directedness in learning and using mathematics. When students have agency, they initiate action to support their own learning; they are active agents in their learning rather than passive recipients of this learning. Students with math agency engage enthusiastically with mathematical problems, relishing the chance to grapple with challenging tasks. They ask questions, share their math thinking, and make use of mathematical tools. They expect math to make sense and see themselves as mathematical sense-makers. (Burwell & Chapman, 2024)
A Strategic Plan to Grow the Math Practices
Teachers have been provided with little guidance on how to grow students’ mathematical practices. In Parts 2 and 3 of this blog series, we outline concrete steps teachers can take to teach up for the math practices and student agency, positioning struggling students to catch up and keep up with grade-level math expectations. This instructional blueprint involves initial explicit teaching about each practice followed by strategic coaching to help individual students internalize the math practices as habits.
Try It Out
How do these ideas relate to your context? How do they affirm and/or challenge your current beliefs about teaching and learning mathematics? Prior to reading Part 2 of this blog series, we encourage you to consider one of the following ideas:
- Think about your current math intervention practices. What role does “teaching up” play in your intervention work? How might you strengthen this aspect of your math instructional program?
- Observe your students’ use of the mathematical practices. Which of your state’s math practices do your students employ naturally and confidently? Which are not yet habits that students can call on as needed? Why are the math practices important to your students’ math learning?
- Observe for mathematical agency. Which of your students demonstrates healthy mathematical agency? Which students would benefit from stronger math agency? Why is mathematical agency important to your student’s math learning?
References
Almarode, J., Thunder, K., Shin, M., Fisher, D., & Frey, N. (2024). The mathematics playbook: Implementing what works best in the classroom. Corwin.
Burwell, H. & Chapman, S. (2024). Power up your math community: A 10-month practice-based professional learning guide. Corwin.
Gonzalez, L. (2023). Bad at math? Dismantling harmful beliefs that hinder equitable mathematics education. Corwin.
Lambert, R. (2024). Rethinking disability and mathematics: A UDL math classroom guide for grades k-8. Corwin.
Newton, N. (2023). Accelerating k-8 math instruction: A comprehensive guide to helping all learners. Teachers College Press.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2024). Mathematics standards. Common Core State Standards Initiative. http://www.corestandards.org/Math
Tomlinson, C. A. (2023). “Teaching up” to reach each learner: Quick reference guide. ASCD.
Safir, S., & Dugan, J. (2021). Street data: The next-generation model for equity, pedagogy, and school transformation. Corwin.
