To be successful in mathematics across grade levels, students must establish foundational mathematics skills because most newly acquired mathematics skills require the use and understanding of prerequisite skills. Longitudinal studies show that students who fall behind in as early as Grade 4 are likely to remain behind their peers as measured in Grade 8 (New Classrooms, 2019). In middle school, students with math difficulty or chronically low math achievement often have large gaps in mastery of prerequisite skills or unfinished learning. These gaps speak to the urgency to engage middle grade students, both those in special education for mathematics learning disabilities and those at risk for math difficulty, to avoid greater school failure (Romero et al., 2014). Furthermore, this unfinished learning often leads to more significant gaps with peers without mathematical difficulties. Educators and leaders recognize these challenges but often wonder where they can start in meeting the needs of students with math difficulty in middle school.
How can MTSS support students with math difficulty?
Schools have attempted to address the challenges and needs of students with and at risk for math difficulty by implementing a multi-tiered system of supports (MTSS) model. This model integrates data and instruction to maximize student achievement and support students’ social, emotional, and behavioral needs from a strengths-based perspective. It uses data to identify students at risk for poor learning outcomes, monitor student progress, provide evidence-based interventions, adjust the intensity and nature of those interventions depending on student responsiveness, and identify students with learning disabilities or other disabilities (according to state law).
Although the MTSS framework includes supplemental math support for students with math difficulty, at its foundation is high-quality core instruction that meets the needs of most students. In fact, research suggests that a supplemental class period is often not enough to close gaps and may not address the conceptual understanding to apply skills for middle school students with math difficulty (National Mathematics Advisory Panel, 2008; Stein et al., 2008). Furthermore, the impact of the COVID-19 pandemic illustrated in the most recent National Assessment of Educational Progress data, together with staffing shortages, suggests that we are not able to simply provide intervention to all students struggling with math difficulty; instead, we need to explore how we can bolster core math instruction.
What practices can educators implement to improve core instruction in middle school?
Rather than try to change all aspects of instruction, focusing on a few key practices may lead to greater impact and fidelity of implementation. The What Works Clearinghouse has identified a collection of evidence-based practices (EBPs) that can help all students improve math outcomes, especially students with math difficulty. When EBPs are coupled with scaffolds and specially designed instruction, they can lead to increased opportunities for students to master algebraic readiness (Agrawal & Morin, 2016) and increased math discourse (Miller & Hudson, 2007)! Specifically, the following three EBPs have been shown to support student learning in core instruction:
- Multiple representations
- Mathematical discussions using inquiry-based questions
- High student engagement
What do these practices look like in action?
- Multiple representations. When educators implement a concrete-representational-abstract framework in middle school, they increase students’ understanding of and flexibility in math. Using multiple representations helps students to build the conceptual understanding of the math and make connections to prerequisite skills. In addition, it provides needed scaffolds, additional practice opportunities, and supports, so that students with math difficulty can increase their discourse and ability to participate in core instruction.
- Inquiry-based questions. Promoting educators’ knowledge and use of questioning and inquiry-based activities could improve opportunities for students with math difficulty to increase their conceptual understanding. When teachers combine multiple representations with different types of questioning (e.g., generalization, flexibility, and reversibility; Dougherty et al., 2015) and support scaffolds (e.g., Universal Design for Learning guidelines), they can increase engagement, conceptual understanding, and procedural fluency for students with math difficulty. The teacher’s role is to create a positive discourse that involves scaffolding structures for student talk and engagement (Franke et al., 2007), rather than simply asking for the answer and using memorizing procedures.
- Student engagement. In middle school, math skills build upon earlier foundational skills, which lead to more multistep problems and a need for increased student engagement. Student engagement and practice are essential to increasing student understanding, especially for students with math difficulties because they may lack the prerequisite skills and/or conceptual understanding to be active in the learning of math. In middle school, the teacher needs to select math tasks that connect to earlier skills, include different entry points, and have the ability to scaffold the process for solving. High levels of student engagement increase practice time, understanding of skills, and overall achievement (Baxter et al., 2002; Hecht & Vagi, 2010; Hunt & Empson, 2015; Woodward et al., 2001).
Where can educators learn more about these practices?
Educators need support through professional development and coaching to increase the use of EBPs within core instruction that leads to greater student achievement. Teachers struggle to find time to learn about EBPs, practice new ways of teaching with the EBPs, and may lack time to collaborate with other math teachers and special education teachers (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010). A recent project, Teacher Instructional Practices for Algebraic Readiness (TIPS4AR), collaborated with general education teachers, special education teachers, and interventionists to create professional development modules that include opportunities for teachers to practice using EBPs and key examples to increase their own capacity to support all learners. Expert reviewers and teachers were integral in revising the modules to use for Tier 1, or core, instruction. Modules are free and available in PowerPoint format with sample scripting, resources, and handouts for easy school use.
The modules include the following:
- Embedding Multiple Representations in Middle School Mathematics Classrooms
- Increasing Inquiry-Based Questions in Middle School Mathematics Classrooms
- Increasing Student Engagement and Discourse for Students With Mathematics Difficulties and Disabilities
In addition, TIPS4AR facilitated a national book study using The Math Pact: Achieving Instructional Coherence Within and Across Grades, Middle School (Bush et al., 2021) with Grade 6, 7, and 8 math and general educators, speech and language pathologists, math coaches, and interventionists across 13 different states. The book study includes an overview of goals and activities, links to Jamboard with activities, and facilitation notes. The book study is designed to be completed over 6 to 9 months but can vary depending on how many times a group of educators meets. The book study includes the following components:
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This content was produced under U.S. Department of Education, Office of Special Education Programs, Award No. H326M17002. The views expressed herein do not necessarily represent the positions or polices of the U.S. Department of Education. No official endorsement by the U.S. Department of Education of any product, commodity, service, or enterprise mentioned in this website is intended or should be inferred.
References
Agrawal, J., & Morin, L. (2016). Evidence-based practices: Applications of concrete representational abstract framework across math concepts for students with mathematics disabilities. Learning Disabilities Research & Practice, 31(1), 34–44.
Baxter, J., Woodward, J., Voorhies, J., & Wong, J. (2002). We talk about it, but do they get it? Learning Disabilities Research & Practice, 17(3), 173–185.
Bush, S. B., Karp, K. S., & Dougherty, B. J. (2021). The math pact: Achieving instructional coherence within and across grades, middle school. Thousand Oaks, CA: Corwin.
Dougherty, B., Bryant, D. P., Bryant, B. R., Darrough, R. L., & Pfannenstiel, K. H. (2015). Developing concepts and generalizations to build algebraic thinking: The reversibility, flexibility, and generalization approach. Intervention in School and Clinic, 50(5), 273-281.
Franke, L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning. Information Age Publishing.
Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of educational psychology, 102(4), 843.
Hunt, J. H., & Empson, S. B. (2015). Exploratory study of informal strategies for equal sharing problems of students with learning disabilities. Learning Disability Quarterly, 38(4), 208-220.
Miller, S., & Hudson, P. (2007). Using evidence-based practices to build mathematics competence related to conceptual, procedural, and declarative knowledge. Learning Disabilities Research & Practice, 22(1), 47–57.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards: Mathematics.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education.
New Classrooms. (2019). The iceberg problem. How assessment and accountability policies cause learning gaps in math to persist below the surface…and what to do about it. Retrieved from https://newclassrooms.org/icebergproblem/
Romero, C., Master, A., Paunesku, D., Dweck, C. S., & Gross, J. J. (2014). Academic and emotional functioning in middle school: The role of implicit theories. Emotion, 14(2), 227–234.
Stein, M. K., Engle, R., Smith, M., & Hughes, E. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340.
Woodward, J., Monroe, K., & Baxter, J. (2001). Enhancing student achievement on performance assessments in mathematics. Learning Disability Quarterly, 24(1), 33–46.
