Accelerating Mathematical Learning in Elementary Students Through the Use of Mathematical Representations

Hou Chun Kuong, Ed.D.

School of Education

Morningside University, IA

Purpose of Study

• This action research examined the use of mathematical representations to accelerate learning in a 3^rd grade classroom
• Focused on understanding area through concrete, semi-concrete, and abstract representations: manipulatives, visual models, symbolic notation, and real-world contexts
• The goal was to support access to grade-level content using just-in-time scaffolds.

Acceleration vs. Remediation

• Acceleration provides targeted, just-in-time supports to help students access grade-level content.

​

• Remediation revisits below-grade-level content, often widening the achievement gap by keeping students behind.

Research Questions

• How does the use of mathematical representations influence accelerated learning?
• What types of representations do students choose and why?
• How does the use of representation impact engagement and confidence?

Methods / Procedures

​

• 23 third-grade students, most below grade level in reading and mathematics

​

• 10-week intervention on area concepts

​

• Weekly tasks required students to choose concrete, semi-concrete, or abstract strategies: tiling shapes, area models, symbolic equations, written explanations.

​

• Pre/post assessments, weekly performance tasks, teacher observation notes

Findings

​

Findings

​

Discussion of findings

• Accelerated Academic Growth
• Average math scores rose from 32% (pre) to 84% (post), with the greatest gains among students initially performing below grade level.

​

• Increased Confidence & Independence
• By Week 5, students chose their own representations (concrete, semi-concrete, or abstract), showing stronger problem-solving and conceptual understanding.

​

• Improved Engagement & Math Talk
• Students explained thinking with diagrams, vocabulary, and sentence stems, demonstrating deeper reasoning and higher engagement in math discourse.

Implications

• Representation as an Equity Tool�Diverse mathematical representations help bridge conceptual gaps for students performing below grade level, enabling equitable access to rigorous content.

​

• Support for Accelerated Learning Models�When students use just-in-time supports and choose representations that match their understanding, they can meet grade-level expectations without remediation.

​

• Classroom Practice Shift�Intentional integration of concrete, visual, and symbolic tools should be embedded in daily instruction to support all learners, particularly those who struggle with traditional methods.

Recommendations

• Integrate Representation Training in PD�Provide professional development for teachers on using multiple mathematical representations intentionally to support accelerated learning.

​

• Embed Choice in Instruction�Allow students to select concrete, semi-concrete, or abstract tools based on their comfort level, promoting agency and deeper understanding.

​

• Monitor and Reflect on Representation Use�Include formative assessments and student reflections to track how representation choices evolve and impact learning over time.

​

References

Bruner, J. (1966). Toward a theory of instruction. Harvard University Press.

Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science, and Technology (IJEMST), 9(1), 1-21. https://doi.org/10.46328/ijemst.1111

Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. The Roles of Representation in School Mathematics, 1-23.

National Council of Teachers of Mathematics (2020). Principles to actions: Ensuring mathematical success for all. National Council of Teachers of Mathematics.

Questions