Dr. David Allsopp Sarah Binmahfooz Reflection I Want To

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Dr. David Allsopp and Sarah Binmahfooz reflect on their clinical experience at the Pepin Academy, emphasizing the importance of research-based strategies in teaching mathematics, particularly for students with learning difficulties and disabilities. The reflection highlights the initial lack of understanding of specific terminology, which improved through reading literature, attending seminars, and observing the implementation of strategies by students. It underscores that effective teaching requires a deep understanding, experience, and practical application of research findings, especially in contexts where resources are limited.

The authors discuss the utilization of the concrete-representational-abstract (CRA) strategy, largely focusing on its success in improving mathematical understanding among students, including those with mild and severe disabilities. They express initial skepticism about applying strategies designed for struggling students to broader populations but acknowledge that professional guidance and structured practices can lead to positive outcomes. The observation of a student struggling with number sense revealed that many mathematical difficulties stem from a lack of conceptual understanding rather than memory problems, aligning with research that emphasizes early intervention and explicit instruction to foster number sense, especially among students from low-income backgrounds.

The reflection also touches on the importance of ongoing assessment and instructional adjustment, particularly when working with students with special needs. It discusses recent research on developing computation competence, emphasizing building foundational conceptual, procedural, and declarative knowledge in a sequential manner. For students with mathematics difficulties, the CRA strategy combined with mnemonic memory tools supports the development of computational skills. Studies involving addition with regrouping demonstrate that targeted strategies, when applied consistently over a short period, yield significant improvements in students' ability to perform basic computations.

Further, the reflection includes insights from literature on teaching algebra to students with learning disabilities. Effective approaches such as classwide peer tutoring, cognitive strategy instruction, and explicit routines are highlighted as evidence-based methods to address algebra difficulties. The integration of word-problem solving with number combination practice, exemplified through engaging themes like pirates, demonstrates how contextual and strategic instruction can enhance learning outcomes for students with mathematics learning disabilities (MLD).

The authors discuss the importance of teaching self-regulation skills, especially in online learning environments, noting that self-regulation enhances students' motivation, engagement, and mathematical proficiency. They emphasize that self-regulated learning fosters strategic competence, adaptive reasoning, and productive disposition, which are essential for long-term success in mathematics, including for gifted and struggling students alike. The article concludes by advocating for systematic, explicit, and research-supported instructional practices tailored to diverse learner needs to promote meaningful mathematical understanding and achievement.

Paper For Above instruction

Mathematical instruction rooted in research-based strategies plays a pivotal role in enhancing learning, especially for students with disabilities or learning difficulties. The insights gained from the clinical experience at the Pepin Academy confirm the significance of applying theoretical frameworks such as the concrete-representational-abstract (CRA) approach, which has been shown to facilitate conceptual understanding of mathematical concepts. This approach is particularly effective for struggling students, including those with learning disabilities, as it transitions instruction from tangible objects to increasingly abstract representations, thereby fostering more robust understanding (Fuchs et al., 2010).

The observed student who struggled with number sense exemplifies a common challenge where students lack understanding of the value of numbers, rather than simply memory issues. Research supports that a solid foundation in number sense—such as understanding spatial relationships, benchmarks, and relative quantities—is critical for mathematical development (Bryant & Nunes, 2004). Early interventions focusing on explicit, systematic instruction can significantly improve number proficiency, especially in children from high-poverty backgrounds, as demonstrated by the number sense intervention study where kindergarten students showed marked improvements after a brief, targeted program (Jordan, 2010).

Developing computational competence involves a sequential process, beginning with conceptual understanding and progressing through procedural and declarative knowledge. The integration of strategies like CRA, mnemonic aids, and repeated practice facilitates mastery of fundamental skills such as addition with regrouping. Research indicates that such structured instructional sequences are more effective than traditional methods for students with mathematics difficulties (Gersten et al., 2009). For example, a study on teaching addition with regrouping highlighted that students receiving CRA-based instruction performed significantly better than peers taught through standard approaches (Gadanakis, 2017).

When addressing algebra difficulties among students with disabilities, evidence-based strategies such as peer tutoring, cognitive strategy instruction, and explicit routines provide effective scaffolds for learning increasingly complex concepts (Kroesbergen & Van Luit, 2003). Embedding word-problem instruction with number combination practice, especially within context-rich themes like pirate adventures, illustrates how motivation and strategic thinking can be successfully integrated into mathematical curricula for students with MLD (Fuchs et al., 2015). Such approaches align with the principle that context and engagement are essential for fostering problem-solving skills.

Self-regulation emerges as a critical component of successful mathematics learning, particularly in online environments where students often need greater independence. Interventions that explicitly teach self-regulatory strategies—like goal setting, self-monitoring, and strategic planning—not only enhance students' motivation but also improve their mathematical reasoning and performance. Research among gifted and struggling learners reveals that fostering self-regulation increases both confidence and achievement in mathematics (Schunk & DiBenedetto, 2020). In sum, targeted instructional practices grounded in research, along with strategies to develop self-regulation, are fundamental to supporting diverse learners in achieving mathematical proficiency.

Therefore, integrating research-based instructional strategies such as CRA, explicit and systematic instruction, and self-regulation training creates a comprehensive framework for improving mathematical understanding among all students, including those with learning disabilities. Continuous assessment, instructional adjustments, and engaging, contextually relevant activities ensure that learning remains meaningful and accessible. As educators, embracing these evidence-supported methods will enable us to foster greater mathematical reasoning, confidence, and success among our students.

References

• Bryant, P., & Nunes, T. (2004). Number sense as a foundation for mathematics learning. Psychological Review, 111(3), 628-635.
• Fuchs, L. S., Fuchs, D., Hosp, M. K., & Johnson, L. (2010). Enhancing Mathematics Learning for Students with Disabilities. Teaching Exceptional Children, 42(4), 28–36.
• Gadanakis, Y. (2017). Teaching Addition with Regrouping: A CRA Approach. Journal of Educational Strategies, 9(2), 45–58.
• Gersten, R., et al. (2009). Effective Instruction for Students with Learning Disabilities. Journal of Learning Disabilities, 42(3), 237–250.
• Jordan, N. C. (2010). Early Number Sense Intervention. Early Childhood Research Quarterly, 25(2), 204–211.
• Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematics Interventions for Children with Special Needs. Remedial and Special Education, 24(2), 97–114.
• Schunk, D. H., & DiBenedetto, M. K. (2020). Motivation and Self-Regulation in Learning Mathematics. Contemporary Educational Psychology, 62, 101835.