Students' Mathematics Conceptual Challenges: Exploring Students' Thinking, Understanding, and Misconceptions in Functions and Graphs
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| Title: | Students' Mathematics Conceptual Challenges: Exploring Students' Thinking, Understanding, and Misconceptions in Functions and Graphs |
|---|---|
| Language: | English |
| Authors: | Isaac Gyan Ayeh (ORCID |
| Source: | European Journal of Science and Mathematics Education. 2025 13(3):191-206. |
| Availability: | European Journal of Science and Mathematics Education. Eastern Mediterranean University, Farnagusta, TRNC, Mersin 10, Turkey. e-mail: editor@scimath.net; Web site: http://www.scimath.net |
| Peer Reviewed: | Y |
| Page Count: | 16 |
| Publication Date: | 2025 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Grade 11 High Schools Secondary Education |
| Descriptors: | Grade 11, High School Students, Mathematics, Mathematical Concepts, Mathematics Education, Graphs, Comprehension, Misconceptions, Thinking Skills, Interviews, Barriers, Mathematics Skills |
| ISSN: | 2301-251X |
| Abstract: | Functions and graphs are fundamental mathematical concepts in mathematics and are vital to helping students comprehend the relationship between variables and other advanced topics in higher-level mathematics. Research has shown that students continually possess misconceptions and inaccurate thinking about functions and function representations. Function concepts such as variations, covariations, and function notations are challenges students face in conceptualizing function concepts in the classroom. Sources of these misconceptions may stem from the way students think about functions. The contributing factor to this problem is the teaching approaches or methods teachers use in mathematics classrooms, which focus on students demonstrating their skill in solving mathematics problems without helping students develop the conceptual understanding of the mathematics they teach. Although function forms the foundation of understanding higher mathematics, students' and teachers' understanding of function concepts appears to be mixed with many misconceptions and wrong assumptions. The researcher engaged the student in five clinical interview sessions to assess the student's conceptual understanding of selected topics on functions and graphs. The researcher developed and implemented an instructional intervention to strengthen such understanding. A qualitative research method through clinical interview was used to engage a senior high school student in grade 11 in five one-hour meetings to assess the student's conceptual understanding of selected topics under functions. Over the five clinical interview sessions, the interviewer engaged the student's conceptual understanding of topics on functions, such as the meaning of functions, variations, covariations, and function notations. The researcher developed function assessment questions and validated them by experts for restructuring. All clinical interview sessions were voice recorded and transcribed, and photocopies of the student's worksheets were collected and analyzed quantitatively to support the results and findings of this study. Findings from the study show that students continually develop procedural competencies over conceptual understanding in the mathematics classroom. The student over-relied on the "vertical line test" concept to determine whether a graph diagram represents a function. The student's solutions to the covariation task showed a graphic representation of discrete points with a line drawn through the points to represent a continuous covariation. The designed interventions strengthened the students' understanding and provided a means of testing/validating assumptions about the function concepts and understanding. |
| Abstractor: | As Provided |
| Entry Date: | 2025 |
| Accession Number: | EJ1484071 |
| Database: | ERIC |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=EJ1484071 Name: ERIC Full Text Category: fullText Text: Full Text from ERIC |
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| Items | – Name: Title Label: Title Group: Ti Data: Students' Mathematics Conceptual Challenges: Exploring Students' Thinking, Understanding, and Misconceptions in Functions and Graphs – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Isaac+Gyan+Ayeh%22">Isaac Gyan Ayeh</searchLink> (ORCID <externalLink term="https://orcid.org/0009-0007-8346-0465">0009-0007-8346-0465</externalLink>) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="SO" term="%22European+Journal+of+Science+and+Mathematics+Education%22"><i>European Journal of Science and Mathematics Education</i></searchLink>. 2025 13(3):191-206. – Name: Avail Label: Availability Group: Avail Data: European Journal of Science and Mathematics Education. Eastern Mediterranean University, Farnagusta, TRNC, Mersin 10, Turkey. e-mail: editor@scimath.net; Web site: http://www.scimath.net – Name: PeerReviewed Label: Peer Reviewed Group: SrcInfo Data: Y – Name: Pages Label: Page Count Group: Src Data: 16 – Name: DatePubCY Label: Publication Date Group: Date Data: 2025 – Name: TypeDocument Label: Document Type Group: TypDoc Data: Journal Articles<br />Reports - Research – Name: Audience Label: Education Level Group: Audnce Data: <searchLink fieldCode="EL" term="%22Grade+11%22">Grade 11</searchLink><br /><searchLink fieldCode="EL" term="%22High+Schools%22">High Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink> – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22Grade+11%22">Grade 11</searchLink><br /><searchLink fieldCode="DE" term="%22High+School+Students%22">High School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+Concepts%22">Mathematical Concepts</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Education%22">Mathematics Education</searchLink><br /><searchLink fieldCode="DE" term="%22Graphs%22">Graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Comprehension%22">Comprehension</searchLink><br /><searchLink fieldCode="DE" term="%22Misconceptions%22">Misconceptions</searchLink><br /><searchLink fieldCode="DE" term="%22Thinking+Skills%22">Thinking Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Interviews%22">Interviews</searchLink><br /><searchLink fieldCode="DE" term="%22Barriers%22">Barriers</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Skills%22">Mathematics Skills</searchLink> – Name: ISSN Label: ISSN Group: ISSN Data: 2301-251X – Name: Abstract Label: Abstract Group: Ab Data: Functions and graphs are fundamental mathematical concepts in mathematics and are vital to helping students comprehend the relationship between variables and other advanced topics in higher-level mathematics. Research has shown that students continually possess misconceptions and inaccurate thinking about functions and function representations. Function concepts such as variations, covariations, and function notations are challenges students face in conceptualizing function concepts in the classroom. Sources of these misconceptions may stem from the way students think about functions. The contributing factor to this problem is the teaching approaches or methods teachers use in mathematics classrooms, which focus on students demonstrating their skill in solving mathematics problems without helping students develop the conceptual understanding of the mathematics they teach. Although function forms the foundation of understanding higher mathematics, students' and teachers' understanding of function concepts appears to be mixed with many misconceptions and wrong assumptions. The researcher engaged the student in five clinical interview sessions to assess the student's conceptual understanding of selected topics on functions and graphs. The researcher developed and implemented an instructional intervention to strengthen such understanding. A qualitative research method through clinical interview was used to engage a senior high school student in grade 11 in five one-hour meetings to assess the student's conceptual understanding of selected topics under functions. Over the five clinical interview sessions, the interviewer engaged the student's conceptual understanding of topics on functions, such as the meaning of functions, variations, covariations, and function notations. The researcher developed function assessment questions and validated them by experts for restructuring. All clinical interview sessions were voice recorded and transcribed, and photocopies of the student's worksheets were collected and analyzed quantitatively to support the results and findings of this study. Findings from the study show that students continually develop procedural competencies over conceptual understanding in the mathematics classroom. The student over-relied on the "vertical line test" concept to determine whether a graph diagram represents a function. The student's solutions to the covariation task showed a graphic representation of discrete points with a line drawn through the points to represent a continuous covariation. The designed interventions strengthened the students' understanding and provided a means of testing/validating assumptions about the function concepts and understanding. – Name: AbstractInfo Label: Abstractor Group: Ab Data: As Provided – Name: DateEntry Label: Entry Date Group: Date Data: 2025 – Name: AN Label: Accession Number Group: ID Data: EJ1484071 |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1484071 |
| RecordInfo | BibRecord: BibEntity: Languages: – Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 191 Subjects: – SubjectFull: Grade 11 Type: general – SubjectFull: High School Students Type: general – SubjectFull: Mathematics Type: general – SubjectFull: Mathematical Concepts Type: general – SubjectFull: Mathematics Education Type: general – SubjectFull: Graphs Type: general – SubjectFull: Comprehension Type: general – SubjectFull: Misconceptions Type: general – SubjectFull: Thinking Skills Type: general – SubjectFull: Interviews Type: general – SubjectFull: Barriers Type: general – SubjectFull: Mathematics Skills Type: general Titles: – TitleFull: Students' Mathematics Conceptual Challenges: Exploring Students' Thinking, Understanding, and Misconceptions in Functions and Graphs Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Isaac Gyan Ayeh IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2025 Identifiers: – Type: issn-electronic Value: 2301-251X Numbering: – Type: volume Value: 13 – Type: issue Value: 3 Titles: – TitleFull: European Journal of Science and Mathematics Education Type: main |
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