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Navigating Methodological Challenges: A Quantitative Exploration of Students' Mathematics Self-Beliefs
Luleå University of Technology, Department of Health, Education and Technology, Education, Language, and Teaching.ORCID iD: 0000-0002-7587-7152
2024 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Att navigera metodologiska utmaningar : En kvantitativ undersökning av studenters självuppfattning i matematik (Swedish)
Abstract [en]

Mathematics self-beliefs influence students’ self-image, classroom behavior, engagement, and motivation. However, current research faces challenges due to overlapping constructs, which can lead to high correlations and ambiguous findings. For instance, while mathematics self-efficacy is often defined broadly in educational research, task-specific mathematics self-efficacy refers specifically to confidence in completing particular tasks. To enhance the credibility of predictions regarding mathematics achievement, it is crucial to distinguish between different types of general mathematics self-beliefs. This thesis aims to provide new insights into these beliefs by refining methodologies for their measurement.

An exploratory factor analysis of upper-secondary student data, utilizing both quantitative and qualitative reasoning, revealed a clear distinction between mathematics self-concept and generalized mathematics self-efficacy beliefs. A key difference between these two constructs is that the latter significantly influences student engagement. Additionally, the identified factor structure included two constructs related to mathematics anxiety. One noteworthy finding is that the worries of providing incorrect answers in the classroom significantly contribute to gender differences and diminish students’ agentic engagement. Overall, these findings underscore the importance of removing variables with substantial intercorrelations from the analysis, provided this procedure is supported by qualitative reasoning. The findings of this thesis support a pragmatic approach to investigating mathematics self-beliefs, ultimately offering new insights into the significant role of autonomy-supportive teaching in shaping students’ general mathematics self-beliefs.

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2024.
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
Keywords [en]
Mathematics Self-efficacy, Mathematics Self-concept, Operationalization challenges, Exploratory Factor Analysis, Student Engagement and Motivation
National Category
Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:ltu:diva-108623ISBN: 978-91-8048-614-9 (print)ISBN: 978-91-8048-615-6 (electronic)OAI: oai:DiVA.org:ltu-108623DiVA, id: diva2:1890282
Public defence
2024-10-17, C305, Luleå University of Technology, Luleå, 13:00 (Swedish)
Opponent
Supervisors
Available from: 2024-08-19 Created: 2024-08-19 Last updated: 2024-09-26Bibliographically approved
List of papers
1. An Analysis of High and Low Intercorrelations between Mathematics Self-Efficacy, Anxiety, and Achievement Variables: A Prerequisite for a Reliable Factor Analysis
Open this publication in new window or tab >>An Analysis of High and Low Intercorrelations between Mathematics Self-Efficacy, Anxiety, and Achievement Variables: A Prerequisite for a Reliable Factor Analysis
2020 (English)In: Education Research International, ISSN 2090-4002, E-ISSN 2090-4010, Vol. 2020, article id 8878607Article in journal (Refereed) Published
Abstract [en]

This paper draws on data from a quantitative study of upper secondary students' general mathematical self-efficacy, anxiety towards mathematics, and their relationship to achievement in mathematics. The main objective of this article is to discuss the type of information that may be lost if potential problems of validity and extreme multicollinearity in exploratory factor analysis would be solved by only removing variables without doing a profound analysis. We also describe a method that treats Likert items in the questionnaire as ordinal variables that may represent the underlying continuous variable. Our study shows, for example, that removal of problematic variables without a profound analysis leads to a loss of significant information about test anxiety. Our qualitative analysis of problematic variables also led to an unexpected finding regarding the relationship between general mathematical self-efficacy and motivational values in mathematics.

Place, publisher, year, edition, pages
Hindawi Publishing Corporation, 2020
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:ltu:diva-81566 (URN)10.1155/2020/8878607 (DOI)000598470100001 ()2-s2.0-85106820566 (Scopus ID)
Note

Validerad;2020;Nivå 2;2020-11-27 (alebob)

Available from: 2020-11-25 Created: 2020-11-25 Last updated: 2024-08-19Bibliographically approved
2. Relations Between Mathematics Self-Efficacy and Anxiety Beliefs: When Multicollinearity Matters
Open this publication in new window or tab >>Relations Between Mathematics Self-Efficacy and Anxiety Beliefs: When Multicollinearity Matters
2024 (English)In: Journal of Experimental Education, ISSN 0022-0973, E-ISSN 1940-0683Article in journal (Refereed) Epub ahead of print
Abstract [en]

This article reports on an investigation among 156 upper secondary students who self-evaluated their general mathematics self-efficacy and anxiety beliefs. After minimizing the influence of extreme multicollinearity, an exploratory factor analysis revealed a clear four-factor pattern. Two of the factors were interpreted as self-concept-like factors; one representing student’s overall confidence in mathematics labeled mathematics self-concept, and the other labeled generalized mathematics self-efficacy, concerned with student’s future-oriented perception of their competence in mathematics. The other two factors are students’ anxiety when they give wrong answers in mathematics class (in-class anxiety), and students’ anxiety and stress when they must do mathematics homework (assignment anxiety). Although no gender differences were found in previous mathematics achievement, the analyses indicated that all latent factors differed between genders. However, further analyses of logistic mixed models with all latent factors and prior mathematics achievement as predictors revealed that reported in-class anxiety was the primary discriminating factor between male and female students. 

Place, publisher, year, edition, pages
Taylor & Francis, 2024
Keywords
Factor analysis, mathematics anxiety, mathematics self-concept, mathematics self-efficacy, multicollinearity
National Category
Other Mathematics
Research subject
Mathematics and Science Education
Identifiers
urn:nbn:se:ltu:diva-105046 (URN)10.1080/00220973.2024.2338545 (DOI)001200035000001 ()2-s2.0-85190431776 (Scopus ID)
Note

Full text: CC BY license

Available from: 2024-04-10 Created: 2024-04-10 Last updated: 2024-08-22
3. An inquiry of different interpretations of programming in conjunction with mathematics teaching
Open this publication in new window or tab >>An inquiry of different interpretations of programming in conjunction with mathematics teaching
2022 (English)In: Bringing Nordic mathematics education into the future: Proceedings of Norma 20, The ninth Nordic Conference on Mathematics Education / [ed] Nortvedt, G. A.; Buchholtz, N. F.; Fauskanger, J.; Hähkiöniemi, M.; Jessen, B. E.; Naalsund, M.; Nilsen, H. K.; Pálsdóttir, G.; Portaankorva-Koivisto, P.; Radišić, J.; Sigurjónsson, J. Ö.; Viirman, O.; Wernberg, A., Svensk förening för MatematikDidaktisk Forskning - SMDF, 2022, , p. 234p. 17-24Conference paper, Published paper (Refereed)
Abstract [en]

This article discusses computational thinking and programming in mathematics teaching and aims to shed light on different interpretations of what programming entails. The literature review revealed that there are mainly two ways of approaching programming in an educational context either by a narrow interpretation or a broader interpretation of programming. These different interpretations of programming are manifested in different ways in mathematics teaching. The narrow interpretation is manifested in an activity that focuses on learning to write code on a computer, while the broader interpretation of programming is displayed in activities with a focus on learning how solve problems in such a way it can be executed by a computer or by a human. Also, this article explores an appropriate programming activity within the context of mathematics education in Sweden. 

Place, publisher, year, edition, pages
Svensk förening för MatematikDidaktisk Forskning - SMDF, 2022. p. 234
Series
Skrifter från Svensk förening för MatematikDidaktisk Forskning, ISSN 1651-3274 ; 17
Keywords
Mathematics education, computational thinking, programming, coding, self-efficacy
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:ltu:diva-94989 (URN)
Conference
The ninth Nordic Conference on Mathematics Education (NORMA 20), Oslo, Norway [Online], June 1-4, 2021
Note

ISBN för värdpublikation: 978-91-984024-6-9

Available from: 2022-12-23 Created: 2022-12-23 Last updated: 2024-08-19Bibliographically approved
4. Predicting Student Engagement: The Role of Generalized Mathematics Self-Efficacy
Open this publication in new window or tab >>Predicting Student Engagement: The Role of Generalized Mathematics Self-Efficacy
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This study explores how generalized mathematics self-efficacy and mathematics self-concept influence students' engagement across behavioral, emotional, cognitive, and disengagement dimensions. Conducted during an advanced mathematics course in Sweden, the study assessed students' self-beliefs in mathematics at both the beginning and the end of a course segment where they solved mathematically complex and contextually realistic problems. Path analysis revealed that generalized mathematics self-efficacy is a stronger predictor of engagement than gender, prior achievement, mathematics self-concept, or mathematics anxiety. Mathematics anxiety was measured through students' reported stress about not being able to complete assignments at home (referred to as assignment anxiety) and their reported concern about giving incorrect answers in class (referred to as in-class anxiety). Notably, self-concept had minimal impact on agentic engagement, with its effect mediated by generalized mathematics self-efficacy and in-class anxiety. Prior achievement influenced cognitive engagement primarily through generalized mathematics self-efficacy, while assignment anxiety played a key role in cognitive disengagement.

National Category
Learning Didactics Psychology
Research subject
Mathematics Education
Identifiers
urn:nbn:se:ltu:diva-108614 (URN)
Available from: 2024-08-19 Created: 2024-08-19 Last updated: 2024-09-07

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