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Bridging the Gap: Understanding Students' Struggles with Algebraic and Graphical Representations of Functions

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Title: Bridging the Gap: Understanding Students' Struggles with Algebraic and Graphical Representations of Functions
Language: English
Authors: Santosh Pathak
Source: Mathematics Teaching Research Journal. 2025 17(6):340-359.
Availability: City University of New York. Creative Commons. 205 East 42 Street, New York, NY 10017. Web site: https://mtrj.commons.gc.cuny.edu/
Peer Reviewed: Y
Page Count: 20
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Grade 12
High Schools
Secondary Education
Descriptors: Mathematics Instruction, Mathematical Concepts, Algebra, Graphs, Problem Solving, Grade 12, High School Students, STEM Education, Foreign Countries, Barriers, Cognitive Processes, Metacognition
Geographic Terms: Nepal
ISSN: 2573-4377
Abstract: Students often find it challenging to move between algebraic and graphical representations of functions, which can lead to a fragmented understanding and make problemsolving more difficult. Research and classroom observations suggest that putting too much emphasis on algebraic procedures may limit students' ability to think graphically and connect different representations. In this study, we looked at how well students could use both algebraic and graphical approaches to solve function-related problems. We also explored their preferences for different representations and how aware they were of alternative strategies. To do this, we gave a five-question survey to 300 Grade 12 STEM students in Nepal. The survey included a variety of function types and required students to reason both symbolically and visually. The results showed a strong preference for algebraic methods, while performance on graph-based tasks was significantly lower. Many students were not even aware that graphical strategies were an option and had trouble transferring their knowledge between the two forms. These findings point to a clear need for changes in teaching and curriculum design. A better balance between symbolic and visual reasoning--including more graph-based tasks, the use of visualization tools, and training to build metacognitive skills--could help students develop a more flexible and deeper understanding of mathematics.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1507433
Database: ERIC
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  Data: City University of New York. Creative Commons. 205 East 42 Street, New York, NY 10017. Web site: https://mtrj.commons.gc.cuny.edu/
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  Data: Students often find it challenging to move between algebraic and graphical representations of functions, which can lead to a fragmented understanding and make problemsolving more difficult. Research and classroom observations suggest that putting too much emphasis on algebraic procedures may limit students' ability to think graphically and connect different representations. In this study, we looked at how well students could use both algebraic and graphical approaches to solve function-related problems. We also explored their preferences for different representations and how aware they were of alternative strategies. To do this, we gave a five-question survey to 300 Grade 12 STEM students in Nepal. The survey included a variety of function types and required students to reason both symbolically and visually. The results showed a strong preference for algebraic methods, while performance on graph-based tasks was significantly lower. Many students were not even aware that graphical strategies were an option and had trouble transferring their knowledge between the two forms. These findings point to a clear need for changes in teaching and curriculum design. A better balance between symbolic and visual reasoning--including more graph-based tasks, the use of visualization tools, and training to build metacognitive skills--could help students develop a more flexible and deeper understanding of mathematics.
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      – Text: English
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        PageCount: 20
        StartPage: 340
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      – SubjectFull: Grade 12
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      – SubjectFull: Foreign Countries
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      – SubjectFull: Barriers
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      – SubjectFull: Cognitive Processes
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      – SubjectFull: Metacognition
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      – SubjectFull: Nepal
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      – TitleFull: Bridging the Gap: Understanding Students' Struggles with Algebraic and Graphical Representations of Functions
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