In many classrooms, educators face similar challenges: students arrive with vastly different mathematical backgrounds. Some students have special needs, some are multilingual learners developing their English skills, or some perform below grade level in math.
There are many reasons students might need different support in mathematics. Multilingual learners, for example, can sometimes find word problems and vocabulary challenging; however, research has found that providing many experiences in solving, discussing, and writing word problems can support them.
Additionally, learning disabilities are a pervasive challenge in our nation’s classrooms. According to the American Psychiatric Association, an estimated 5 to 15% of school-age children have a learning disability, which can affect their ability to build essential foundational skills in mathematics. One of those disabilities is dyscalculia, or difficulties with learning number-related concepts, processing numerical information, learning arithmetic facts, or using the symbols and functions to perform accurate or fluent math calculations.
Although these challenges can be significant, they can also be addressed through early intervention and adequate support for both teachers and students. One way to address these challenges is to use Multiple Strategies, which involves helping students develop mathematical skills in varied ways, ensuring they can all build number sense and mathematical reasoning.
Using Multiple Strategies, such as modeling, engaging in discussions, and viewing and creating visual representations to teach mathematics, ensures that students have a deep understanding of math, rather than a shallow or incorrect notion.
Common Challenges Multiple Strategies Address
Rigid Thinking
Rigid thinking in mathematics occurs when students rely on memorization rather than understanding. This might happen if students are taught only one approach to solve a problem, which might hinder them if they forget a step or if the method doesn’t work efficiently, and they have no other approaches to use.
One-Size-Fits-All Instruction
Students don’t all learn the same way and at the same pace. A one-size-fits-all approach to teaching doesn’t account for individual learning needs, including dyscalculia, multilingual learners who need additional language support, and students with varying levels of prior knowledge. Offering multiple access points in math allows all students to engage with and understand math.
Limited Number Sense
Number sense is the ability to understand numbers and how they relate and connect with one another. When instruction centers on memorization without building conceptual understanding, students are at risk of developing limited number sense. Without strong number sense, students struggle to estimate, reason, or apply their knowledge to solve real-world problems.
Students must learn that math is not about one right way or memorization, but about reasoning and adaptivity, which is what Multiple Strategies provide.
What Research Says about Multiple Strategies
Using Multiple Strategies is backed by research. For example, multiple means of content representation, expressing learned content, and content engagement are cornerstones in the Universal Design for Learning, a framework to improve and optimize teaching and make learning universally accessible to all learners based on what we know about the human brain.
Also, one of the National Council of Teachers of Mathematics’ “Effective Mathematics Teaching Practices” states, “Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.”
Specific instructional strategies within Multiple Strategies are also well-researched. The National Council of Supervisors of Mathematics recommends that teachers consistently use manipulatives to build conceptual understanding of mathematics. Additionally, plenty of research has found that games can support intrinsic motivation, or the self-determined drive to act out of interest, enjoyment, and natural curiosity. Research also shows that students who use accurate visual representations are six times more likely to correctly solve mathematics problems than are students who do not use them. Studies show that visual representations are especially helpful for students with learning disabilities and for low-achieving students.
Best Practices to Implement Multiple Strategies
Some educators may believe that Multiple Strategies confuse students. Additionally, others face implementation challenges and feel overwhelmed by too many methods. The following tips can help educators effectively incorporate Multiple Strategies:
- Start small and build gradually. Introduce two strategies for solving a problem and build over time as students gain confidence.
- Compare strategies to build flexibility. Inquiry-based research shows that having students compare different approaches develops mathematical reasoning.
- Showcase student thinking. Use student work to demonstrate how strategy comparison deepens understanding. Facilitate discussions about how each approach leads to the same answer.
Multiple Strategies in Practice
One program that effectively implements Multiple Strategies is Do The Math, which has been proven successful in addressing the key challenges that students face by incorporating concrete manipulative materials and games, selected children’s literature, and visual representations.
New York City Public Schools, like many other districts nationwide, has many students with special needs, multilingual learners, and students performing below grade level in math. According to data from New York City Public Schools, students with disabilities account for 21.6% of students enrolled in the district, and 16.3% of students are English learners. Additionally, the most recent National Assessment of Educational Progress (NAEP) data indicate that approximately two-thirds of NYC’s fourth graders were not proficient in math, and roughly 77% of eighth graders were below grade level in math.
Researchers identified six schools and implemented Do The Math in small-group or whole-class settings. Plus, teachers received two days of training from Math Solutions.
The results were significant: Students at all six schools, including those designated as special education as well as general education, showed significant gains. Surveys revealed that students’ confidence improved from the time they began to use Do The Math until they completed it, and they began using mathematics vocabulary consistently and correctly because of the program’s explicit emphasis on the teaching and use of mathematics vocabulary. Teachers reported that Do The Math students were teaching the strategies to classmates not in the program. Overall, teachers gained a deeper understanding of the common misconceptions that their students experience. In addition, teachers reported finding the lessons easy to teach and the program easy to use.
Beyond New York Public Schools, other school districts have seen positive results with Do The Math. Teachers from the Miami-Dade County Public School District felt that the games in Do The Math played a large part in student success because students had fun while learning. At one school in the San Marcos Unified School District, economically disadvantaged Do The Math students and multilingual learners outperformed their peers at another school in the same district. The other school had similar demographics but did not use Do The Math.
When students with different mathematical backgrounds are given multiple entry points to access math concepts, the results are clear: more confidence, stronger number sense, and greater growth.
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Download the full Research Foundations: Evidence and Efficacy Report to explore how Multiple Strategies drive meaningful math learning and discover how Do The Math can support your students’ success.
Read the research behind Do The Math’s intervention strategies.
