Making Sense of Abstract Algebra: Exploring Secondary Teachers’ Understandings of Inverse Functions in Relation to Its Group Structure

Wasserman, Nicholas H.

doi:10.1080/10986065.2017.1328635

Cited by 34 publications

(26 citation statements)

References 14 publications

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“…Failure to define and show patterns and relationships between concepts governing inverse functions likely to affect the teacher's ability to clear misconceptions and would negatively affect the teacher's ability to effectively teach the concept. This finding is consistent with many studies that found pre-service teachers with insufficient knowledge of aspects inverse functions (Even, 1992;Wasserman, 2017).…”

Section: Discussionsupporting

confidence: 93%

“…There is sufficient evidence in literature which shows that prior research about the concept of a function focused on pre-service teachers' knowledge of inverse and composite functions (Even, 1992;Karahasan, 2010;Kontorovich, 2017;Paoletti, 2020;Wasserman, 2017).…”

Section: Pre-service Teachers' Knowledge Of Inverse and Composite Functionmentioning

confidence: 99%

“…Their inability to demonstrate mathematically strong understanding of inverse functions coupled with failure to recognize patterns and connections involving inverse functions (Even, 1992;Wasserman, 2017) implies that there is serious need to pay attention to their difficulties during teacher training and this could affect their ability to teach because effective MPCK could come about when a teacher has a strong subject matter knowledge background. This is consistent with the views of Weber et al, (2020) who found that teachers better respond to pedagogical issues regarding inverse function concepts that they are likely to encounter in future.…”

Section: Pre-service Teachers' Knowledge Of Inverse and Composite Functionmentioning

confidence: 99%

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Pre-service Teachers’ Knowledge of Identifying and Clearing Pupils’ Misconceptions about Inverse and Composite Functions via Vignettes

Sintema

Prieto

2021

EURASIA J Math Sci Tech Ed

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The purpose of this study was to investigate pre-service teachers' knowledge of content and students vis-à-vis their ability to anticipate, identify and clear high school students' misconceptions about inverse and composite functions. To accomplish this goal a case study research design was used to examine one fourth year mathematics education pre-service teacher from one of Zambia's public universities. A case study strategy was preferred for this study because it enables the researcher to focus and have an in-depth investigation of an individual subject in a natural setting. As a data collection tool, the study used a questionnaire containing 7 vignettes comprising 4 inverse function vignettes and 3 composite function vignettes. Data were analyzed based on Ebert's framework for characterizing the level of proficiency of functions and graphs. Findings revealed that the pre-service teacher's level of proficiency of identifying and clearing students' misconceptions was mostly good. Results suggest that vignettes might be useful in mathematical pedagogical courses in teacher education.

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Section: Discussionsupporting

confidence: 93%

Section: Pre-service Teachers' Knowledge Of Inverse and Composite Functionmentioning

confidence: 99%

Section: Pre-service Teachers' Knowledge Of Inverse and Composite Functionmentioning

confidence: 99%

See 1 more Smart Citation

Pre-service Teachers’ Knowledge of Identifying and Clearing Pupils’ Misconceptions about Inverse and Composite Functions via Vignettes

Sintema

Prieto

2021

EURASIA J Math Sci Tech Ed

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“…One student (Fira) uses the metaphor "( ∘ ) "# " which is illustrated by wearing socks ( ) then wearing shoes ( ), in reverse (inverse) is removing shoes ( "# ), then the socks ( "# ). In this case, students categorized as relational-identity, in accordance with a developed genetic decomposition model (Marmur & Zazkis, 2018;Paoletti et al, 2018;Wasserman, 2017)., Namely the scheme "inverse function as coordination of two functions to obtain identity "and" inverse function as the act of exchanging and and completing it for ". Wasserman (2017) asserts that the existence of an element of identity can help students in abstract algebra, where inverses are considered descriptors in Group concepts and recognize the function identity of ( ∘ "# )( ) = ( "# ∘ )( ) = = ( ).…”

Section: Category Of Reversible Reasoningmentioning

confidence: 99%

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

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Researchers have argued that reversible reasoning is involved in all topics in mathematics. The study employed a qualitative research approach, consisted of three sessions (pre-assessment, thinking-aloud, and interview), and involved eight participants enrolled in Algebra class. The aim was to explore the potential role of reversible reasoning on students' inverse functions. The result of study indicated that there three categories of reversible reasoning that refer to the consistency of students in completing inverse function tasks, which are relational-harmonic, relationalvisual, and relational-identity. Mental activities performed by the students in constructing and reasoning inverse functions were also explained. In addition, potential aspects of the students' reversible reasoning created during the process of constructing meaning were highlighted. These findings provide perspectives on reversible reasoning, students' understanding of inverse functions, and areas of future research

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“…Functions is regarded a very important topic in the Zambian secondary mathematics curriculum and a deeper understanding of the concept of a function creates a solid foundation for learning several other mathematics topics and advanced mathematics concepts. However, there is research evidence suggesting that both preservice and in-service teachers are struggling and exhibit limited knowledge of many aspects of the topic (Cho & Moore-Rosso, 2014;Kontorovich, 2017;Malambo, 2016;Ubah & Bansilal, 2018;Wasserman, 2017).…”

Section: Significance and Scope Of The Studymentioning

confidence: 99%

Pre-service mathematics teachers’ knowledge of functions: a mixed methods sequential explanatory study

Sintema¹

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Making Sense of Abstract Algebra: Exploring Secondary Teachers’ Understandings of Inverse Functions in Relation to Its Group Structure

Cited by 34 publications

References 14 publications

Pre-service Teachers’ Knowledge of Identifying and Clearing Pupils’ Misconceptions about Inverse and Composite Functions via Vignettes

Pre-service Teachers’ Knowledge of Identifying and Clearing Pupils’ Misconceptions about Inverse and Composite Functions via Vignettes

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Pre-service mathematics teachers’ knowledge of functions: a mixed methods sequential explanatory study

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