As mathematics classrooms are becoming more and more diverse, teachers aiming to help all of their students learn are increasingly challenged. Pandemic-related learning gaps, the arrival of newcomers who may have experienced interrupted schooling, and the increase in the number of students with disabilities in general education classrooms have intensified performance differences among students. It is widely recognized that teachers require help and support to meet the varied needs of the different students they serve. There is less certainty, however, about the kind of support that will help teachers to make this happen.

When we ask teachers what they hope to learn to help them make math instruction more accessible for diverse learners, they often express a desire to learn strategies. The following quotes illustrate such expectations.

“I hope to learn strategies to better meet the needs of struggling learners and challenge those students [who are] exceeding standards.”

“I hope to learn strategies to better support student performance in the classroom.”

“I hope to learn more interventions to help my students with math.”

The belief in strategies as the solution for making mathematics more accessible is perhaps not surprising. Disability is often viewed as a medical condition and as a deficit that calls for expert interventions (cf., Lambert, 2016). Compounding this is the fact that mathematics is commonly perceived as a procedural subject, which may reinforce the belief that instructional procedures (strategies) are required to teach mathematical procedures.

Familiarity with a range of instructional strategies clearly is important for addressing the needs of diverse learners. Yet, acquiring new strategies alone doesn’t sufficiently prepare teachers for helping underperforming students be more successful in mathematics. Supporting teachers to learn and apply new instructional strategies without a deeper understanding of the learners in front of them is like teaching students algorithms without conceptual understanding. There is not one strategy that will likely work for all students who learn differently. This is because these students are enormously diverse. Within the subgroup of students with learning disabilities alone, individuals’ capacities can differ widely. This group may include students with attentional issues, those who struggle with visual or verbal processing, students who have difficulties with reading, or those who experience challenges when working with numbers. This group might also include students who have strong social-emotional skills, excellent motor coordination, or a well-developed visual-spatial sense. It is evident that one strategy would not fit all these students since they have different strengths and challenges. Just as solely teaching mathematical procedures to students is not sufficient for them to learn math, so sharing new instructional strategies with teachers is not sufficient to support them in teaching math. When it comes to procedures or strategies, both students and teachers should also understand why and how they work, and when it is appropriate to use them.

Let’s consider an example. Using timed activities is often recommended as a strategy for helping students to develop automaticity with previously learned math facts. Timed activities usually are brief and require students to generate as many correct responses as possible in a short amount of time. They may focus on basics such as addition, subtraction, multiplication, or division facts, and may be presented using flashcards, worksheets, or computer programs. Being able to automatically and accurately retrieve math facts is an important skill that helps students free up mental energy to solve more complex math tasks and engage in multi-step math problems. Just as mastering touch typing (knowing the locations of letters on a keyboard without having to think about it) helps to free our mental resources to focus on writing whole sentences and paragraphs quickly, so does knowing basic math facts, such as 5 + 5 = 10 or 4 * 4 = 16, help us to solve more complex problems such as x = (5 + 5) * 42 more efficiently.

Is the use of timed activities a strategy that teachers should use to help any student who might be struggling with retrieving math facts? The answer to this question is complex. One important question we must ask is why a student might be struggling. Being slow in processing math problems may not necessarily be due to a lack of knowing basic math facts but could be due to mental resources being unavailable for retrieving them. For example, a student who is an English learner may need to devote most of their working memory resources to processing language, such as reading and understanding a word problem, leaving very few resources for recalling math facts. Another student for whom handwriting is a challenge may need to devote much of their working memory capacity to writing numbers or letters, slowing down their processing and the retrieval of math facts while working on timed tasks that require a written answer. For these students, using timed activities may not be particularly helpful for increasing their processing speed. This is not to say that timed activities are not a useful strategy, but rather that deeply understanding individual students’ strengths and areas of challenge is very important for making proper decisions about what instructional approaches to use to support them.

Another important consideration is to think about the goals for math instruction and alternative approaches that may exist for accomplishing these goals. If the primary goal is to enable students to quickly and accurately recall basic math facts, the use of timed exercises is one way to support students in meeting that goal, but it is not the only strategy. Research has shown that timed activities can be successfully used to help some students meet this goal (Fuchs et al., 2021), but math educators (e.g., Boaler et al., 2015) have cautioned that performing a large number of repetitions of math problems under time pressure also can induce anxiety for other students and erode their confidence in their ability to learn and do math in the long term. Alternative approaches include learning number facts based on deep understanding of numbers and how they relate to each other—for instance, by having students learn to compose and decompose numbers, use number facts in a variety of mathematical situations, or engage in number talks. These alternative strategies have the added advantage of not only helping students to learn basic math facts and develop automaticity with them, but also to develop mathematical fluency, which is the ability to flexibly apply these math facts accurately and efficiently in various situations. Weighing the advantages and disadvantages of different instructional strategies is an important component in the process of making decisions about when and how to use them to effectively support students.

To help all students to be successful, educators must better understand the unique bundle of learning capacities each child brings to learning mathematics. Fundamental to making decisions about instructional strategies and when and how to use them is an understanding of individual students’ strengths and challenges. This is why our Math for All professional learning puts students at the center and focuses on helping teachers to deepen their understanding of how students learn and how different strategies might benefit them, rather than teaching teachers about instructional strategies in isolation. Similar to what is implied by the old saying “Give a man a fish , you feed him for a day; teach a man to fish and you feed him for a lifetime,” we believe that by giving teachers the tools to make thoughtful decisions about instructional strategies we are empowering them to improve mathematics education for all students in the long term.

For further reading:

Boaler, J., & LaMar, T. (2019). Valuing difference and growth: A YouCubed perspective on special education. YouCubed.

Boaler, J., Williams, C., & Confer, A. (2015) Fluency without fear: Research evidence on the best ways to learn math facts. YouCubed.

Fuchs, L. S., Newman-Gonchar, R., Schumacher, R., Dougherty, B., Bucka, N., Karp, K. S., Woodward, J., Clarke, B., Jordan, N. C., Gersten, R., Jayanthi, M., Keating, B., & Morgan, S. (2021). Assisting students struggling with mathematics: Intervention in the elementary grades (WWC 2021006). National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

Gregory, G. H., & Chapman, C. M. (2012). Differentiated instructional strategies: One size doesn’t fit all (3rd ed.). Corwin.

Lambert, R. (2016). ‘When I am being rushed it slows down my brain’: Constructing self-understandings as a mathematics learner. International Journal of Inclusive Education, 21(5), 521–531.

National Council of Teachers of Mathematics (2023). Procedural fluency in mathematics [Position statement].

Russel, S. J. (2007). Developing computational fluency with whole numbers in the elementary grades. TERC.