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Student Teachers' Knowledge of Students' Difficulties with the Concept of Function

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Title: Student Teachers' Knowledge of Students' Difficulties with the Concept of Function
Language: English
Authors: Borke, Mikael (ORCID 0000-0003-1170-5623)
Source: LUMAT: International Journal on Math, Science and Technology Education. 2021 9(1):670-695.
Availability: LUMA Centre Finland. University of Helsinki. A.I. Virtasen aukio 1, 00014 University of Helsinki, Finland. Tel: +358-50-348-0567; e-mail: editor@lumat.fi; Web site: https://journals.helsinki.fi/lumat
Peer Reviewed: Y
Page Count: 26
Publication Date: 2021
Document Type: Journal Articles
Reports - Research
Education Level: Secondary Education
Higher Education
Postsecondary Education
Descriptors: Mathematics, Secondary School Mathematics, Preservice Teacher Education, Preservice Teachers, Foreign Countries, Knowledge Base for Teaching, Student Problems, Secondary School Students
Geographic Terms: Sweden
ISSN: 2323-7112
Abstract: An important part of the mathematics syllabuses at the secondary school level in most countries is the concept of function. However, secondary school students often experience difficulties with this concept. These difficulties are well-known in the research literature. The study applies the mathematical knowledge for teaching (MKT) framework, including the category knowledge of content and students (KCS). Teachers' ability to anticipate students' difficulties is one aspect of KCS. The aim of this study is to investigate secondary mathematics student teachers' KCS regarding the concept of function. Ten mathematics student teachers participating in a Supplementary Teacher Education Program answered a questionnaire about fictive secondary school students' various difficulties with the concept of function. Follow-up interviews were conducted with four of the respondents. Compared to the findings of previous research on students' difficulties with the concept of function, the respondents in the study sometimes provide reasonable suggestions about the sources of students' difficulties. Some of the respondents demonstrate an aspect of KCS when they suggest that students can reason that a function must be defined by one algebraic expression only, and that students only know about continuous functions. However, no respondent suggests that one source of students' difficulties with a constant function with an implicit domain is the missing domain. In addition, some respondents take for granted that students can interpret the algebraic representation of a piecewise-defined function and translate it into a graph.
Abstractor: As Provided
Entry Date: 2022
Accession Number: EJ1327591
Database: ERIC
FullText Text:
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  Data: Student Teachers' Knowledge of Students' Difficulties with the Concept of Function
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  Data: <searchLink fieldCode="AR" term="%22Borke%2C+Mikael%22">Borke, Mikael</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-1170-5623">0000-0003-1170-5623</externalLink>)
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  Data: LUMA Centre Finland. University of Helsinki. A.I. Virtasen aukio 1, 00014 University of Helsinki, Finland. Tel: +358-50-348-0567; e-mail: editor@lumat.fi; Web site: https://journals.helsinki.fi/lumat
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  Data: <searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Higher+Education%22">Higher Education</searchLink><br /><searchLink fieldCode="EL" term="%22Postsecondary+Education%22">Postsecondary Education</searchLink>
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  Data: 2323-7112
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  Data: An important part of the mathematics syllabuses at the secondary school level in most countries is the concept of function. However, secondary school students often experience difficulties with this concept. These difficulties are well-known in the research literature. The study applies the mathematical knowledge for teaching (MKT) framework, including the category knowledge of content and students (KCS). Teachers' ability to anticipate students' difficulties is one aspect of KCS. The aim of this study is to investigate secondary mathematics student teachers' KCS regarding the concept of function. Ten mathematics student teachers participating in a Supplementary Teacher Education Program answered a questionnaire about fictive secondary school students' various difficulties with the concept of function. Follow-up interviews were conducted with four of the respondents. Compared to the findings of previous research on students' difficulties with the concept of function, the respondents in the study sometimes provide reasonable suggestions about the sources of students' difficulties. Some of the respondents demonstrate an aspect of KCS when they suggest that students can reason that a function must be defined by one algebraic expression only, and that students only know about continuous functions. However, no respondent suggests that one source of students' difficulties with a constant function with an implicit domain is the missing domain. In addition, some respondents take for granted that students can interpret the algebraic representation of a piecewise-defined function and translate it into a graph.
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        PageCount: 26
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      – SubjectFull: Secondary School Mathematics
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      – SubjectFull: Preservice Teacher Education
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      – SubjectFull: Foreign Countries
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      – SubjectFull: Student Problems
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      – SubjectFull: Secondary School Students
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      – SubjectFull: Sweden
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      – TitleFull: Student Teachers' Knowledge of Students' Difficulties with the Concept of Function
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