| 1. |
- Bergwall, Andreas, 1972-
(author)
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Proof-related reasoning in upper secondary mathematics textbooks : Characteristics, comparisons, and conceptualizations
- 2021
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Doctoral thesis (other academic/artistic)abstract
- Proofs and proving are difficult to learn and difficult to teach. A common problem is that many students use specific examples as evidence for general statements. Difficulties with proofs are also part of the transition problems that exist between secondary and tertiary schooling in mathematics. As mathematics teaching often follows a textbook, the design of textbooks has been pointed out as one possible cause of the problems, and international textbook research suggests that proofs often have only a marginal place in textbooks.This thesis focuses on proofs and proving in upper secondary mathematics textbooks. It also addresses theoretical and methodological questions about what marks an opportunity to develop proving competence, and which properties of such opportunities are relevant to investigate and characterize. The thesis is based on data from four Swedish and Finnish textbook series for upper secondary school, and focuses on sections on logarithms, primitive functions, definite integrals, and combinatorics. It examines how addressed mathematical principles are justified, and whether the textbooks’ exercises offer opportunities to develop proof-related skills such as formulating and investigating hypotheses, developing and evaluating arguments, identifying and correcting errors, and finding counterexamples.The results show that just over half of the mathematical principles addressed in the analyzed textbook material are justified, and that only half of the justifications are general proofs. Few exercises are proof-related (10%), and those that include reasoning about general cases even fewer. General proofs are more common in the Finnish books, but proof-related tasks are more common and of a more varied nature in the Swedish ones. The most common form of proofs are direct derivations of calculation formulas, while reasoning about existence and uniqueness is unusual, as are contrapositive proofs and proofs by contradiction.Based on the results, explicit suggestions are offered as to what teaching can pay more attention to. For the analysis and design of proof-related activities, a framework consisting of four main categories is proposed: develop a statement, investigate a statement, develop an argument, and investigate an argument. Several properties that such activities may have, regardless of which category they belong to, are discussed. Finally, three areas for future research are suggested: how worked examples can support students’ learning of proof, how textbooks can be designed to stimulate formulation as well as the formal proving of hypotheses, and mapping of differences regarding proof between upper secondary and university textbooks.
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| 2. |
- Brehmer, Daniel, 1973-, et al.
(author)
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Facilities for Mathematics Teachers’ Learning from Professional Development Programmes : A Qualitative Systematic Review
- 2024
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In: Mathematics Teacher Education and Development. - 1442-3901. ; 26:2
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Journal article (peer-reviewed)abstract
- It is indicated that research on professional development programmes (PDPs) for mathematics teachers mostly concerns whether a programme affects the teachers’ practice or student learning, while the teachers’ learning is treated as a black box. Calls have been made for a shared body of knowledge on teachers’ professional learning and what supports such learning. In this article, 84 articles from mathematics education journals are examined with respect to facilities and catalysts for teacher learning from PDPs for mathematics teachers. Two main types of PDPs were identified—those that target teacher knowledge growth and those that target changed instruction—and it was determined that the types of facilities for catalysing learning linked to them differ. Typical of PDPs targeting teacher knowledge growth is that they emphasise knowledge of content and teaching, knowledge of content and students and specialised content knowledge; following insight and/or body of knowledge as facilities for catalysing the learning. Typical of PDPs targeting changed instruction is that they use more time and have a larger time span than PDPs targeting teacher knowledge growth, emphasise knowledge of content and teaching; and follow strategies by doing/experimenting when establishing them in the classroom as facilities for catalysing the learning.
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| 3. |
- Dahlén, Ewa
(author)
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Rektorn och den dubbla styrningen : en studie om gymnasierektors uppdrag i styrkedjan
- 2023
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Licentiate thesis (other academic/artistic)abstract
- In a global education policy context, school leadership has grown in importance in relation to improving school outcomes as well as equity in education. At the same time, during the last decades, the Swedish school system has undergone several large-scale national education reforms. Reforms that have changed the relations between the different levels in the decentralised Swedish school system and at the same time created debates about the purpose and goals of the school system. These debates are based in different perspectives and shaped by various school discourses. The result discourse connected to the perspective of marketization and the democratic discourse connected to the perspective of social inclusion and equality. These are two central discourses who proclaim different views on how challenges within the school system should best be solved. The purpose of this study is to contribute to knowledge about the mission and responsibilities of principals in upper secondary schools in the Swedish school system. The study takes its point of departure in observations of follow-up meetings between principals within upper secondary schools and the local education authority (LEA). This study has three theoretical contributions. The first contribution concerns knowledge of the principal’s mission, assignment, and work tasks. The second contribution is knowledge of how the result discourse and the democratic discourse are used in conversations about the principal’s mission, assignment, and work tasks. The third contribution is knowledge of the interaction between the principal and the LEA, different levels in the decentralised Swedish school system, in the context of follow-up meetings. The results show that LEAs describe the principal’s mission in three parts – economy, administration, and pedagogy. The two discourses are used in all three of the missions where they sometimes collide, creating a discursive conflict and sometimes co-exist without conflict. The results also show that the LEA and principals often have a common view of the purpose and goal of the school system, but there is seldom a common strategy for how these goals are to be achieved. This study contributes to an understanding how LEAs and political governance shape the role of the principals, but more studies are needed.
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| 4. |
- Eriksson, Kimmo, et al.
(author)
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Cultural Variation in the Effectiveness of Feedback on Students' Mistakes
- 2020
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In: Frontiers in Psychology. - : Frontiers Media SA. - 1664-1078. ; 10
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Journal article (peer-reviewed)abstract
- One of the many things teachers do is to give feedback on their students' work. Feedback pointing out mistakes may be a key to learning, but it may also backfire. We hypothesized that feedback based on students' mistakes may have more positive effects in cultures where teachers have greater authority over students, which we assume to be cultures that are high on power distance and religiosity. To test this hypothesis we analyzed data from 49 countries taking part in the 2015 wave of the TIMSS assessment, in which students in the 4th and 8th grades were asked whether their teachers in mathematics and science told them how to do better when they had made a mistake. For each country we could then estimate the association between the reported use of mistake-based feedback and student achievement. Consistent with our hypothesis, the estimated effect of mistake-based feedback was positive only in certain countries, and these countries tended to be high on power distance and religiosity. These results highlight the importance of cultural values in educational practice.
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| 5. |
- Eriksson, Kimmo, 1967-, et al.
(author)
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Higher-achieving children are better at estimating the number of books at home: Evidence and implications
- 2022
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In: Frontiers in Psychology. - : Frontiers Media SA. - 1664-1078. ; 13
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Journal article (peer-reviewed)abstract
- The number of books at home is commonly used as a proxy for socioeconomic status in educational studies. While both parents' and students' reports of the number of books at home are relatively strong predictors of student achievement, they often disagree with each other. When interpreting findings of analyses that measure socioeconomic status using books at home, it is important to understand how findings may be biased by the imperfect reliability of the data. For example, it was recently suggested that especially low-achieving students tend to underestimate the number of books at home, so that use of such data would lead researchers to overestimate the association between books at home and achievement. Here we take a closer look at how students' and parents' reports of the number of books at home relate to literacy among fourth grade students, by analyzing data from more than 250,000 students in 47 countries participating in 2011 PIRLS. Contrary to prior claims, we find more downward bias in estimates of books at home among high-achieving students than among low-achieving students, but unsystematic errors appear to be larger among low-achieving students. This holds within almost every country. It also holds between countries, that is, errors in estimates of books at home are larger in low-achieving countries. This has implications for studies of the association between books at home and achievement: the strength of the association will generally be underestimated, and this problem is exacerbated in low-achieving countries and among low-achieving students.
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| 6. |
- Eriksson, Kimmo, 1967-, et al.
(author)
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Socioeconomic Status as a Multidimensional Predictor of Student Achievement in 77 Societies
- 2021
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In: Frontiers in Education. - : Frontiers Media SA. - 2504-284X. ; 6
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Journal article (peer-reviewed)abstract
- We reassess the relation between students' socioeconomic status (SES) and their achievement by treating SES as multidimensional instead of unidimensional. We use data from almost 600,000 students in 77 countries participating in the 2018 PISA assessment of student achievement in math, science, and reading. The composite measure of SES that PISA uses can be broken down into six component variables that we here use as simultaneous predictors of achievement. This analysis yields several new insights. First, in the typical society, two predictors (books at home and parents' highest occupational status) clearly outperform the rest. Second, a new composite measure based only on these two components often reveals substantially larger achievement gaps than those reported by PISA. Third, the analysis revealed remarkable differences between societies in the relation between achievement and wealth possessions. In most societies, the independent effect of wealth possessions on student achievement was zero or even slightly negative-but in the least developed societies it was strongly positive. These findings have implications for how SES achievement gaps should be measured and interpreted.
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| 7. |
- Gustafsson, Patrik, 1974-, et al.
(author)
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Developing design principles and task types for classroom response system tasks in mathematics
- 2022
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In: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211. ; 53:11, s. 3044-3065
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Journal article (peer-reviewed)abstract
- This article reports on results from a design research project that implements a formative assessment practice with support from a classroom response system (CRS). Cumulatively building on earlier research and drawing on iteratively generated data from secondary schools in Sweden, the article elaborates on design principles and task types for constructing CRS tasks aimed at generating mathematical classroom discussions. The study generated three design principles, six task types and 31 empirically evaluated tasks useful for developing and using CRS tasks in classroom practices. The results are discussed in relation to earlier research, methodological considerations and the cultural context of Sweden.
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| 8. |
- Gustafsson, Patrik, 1974-
(author)
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Support for productive whole-class discussions in mathematics : Developing and exploring frameworks in the context of classroom response systems
- 2023
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Doctoral thesis (other academic/artistic)abstract
- In recent decades, research has stressed the importance of productive classroom discussions in high-quality mathematical instruction for all learners. However, after decades of attempts by professional development programs to support teachers in achieving these discussions, they are rarely reported on in the classroom context. Thus, there is still a need for support for teachers’ establishment of these discussions. One promising activity for achieving productive discussions involves using a classroom response system and implementing tasks in a multiple-choice format. However, there is little knowledge about whole-class discussions in secondary school mathematics using this approach. This thesis responds to this lack by contributing to knowledge about support for achieving productive whole-class discussions in mathematics using classroom response systems and multiple-choice tasks. The thesis particularly addresses knowledge about the key practices of constructing multiple-choice tasks and leading whole-class discussions. This is operationalized by applying an educational design research approach to 1) develop design principles for constructing tasks and a supplementary task type framework and further evaluate the potential of these design principles by characterizing whole-class discussions, and 2) explore frameworks for analyzing teachers’ leading of whole-class discussions and technology integration. In this work, data from interviews with teachers, reflection notes, and observations were used. The main results cover: characteristics of useful tasks in a multiple-choice format aiming at supporting teachers in achieving productive discussions; characteristics of whole-class discussions in the context of classroom response system in secondary school mathematics; the potential of applying the Structuring Features of Classroom Practice framework as an analytic tool to conceptualize and analyze teachers’ reasoning about classroom response system; and the suggestion of five new categories of teacher actions and enrichments of two existing categories in the redirecting, progressing and focusing framework. In the kappa of this thesis, these results are merged and discussed in relation to theories of ambitious mathematics instruction. The focus is on examining whether and how classroom response systems and multiple-choice tasks can support teachers in establishing this instruction. In summary, the main contributions of this thesis are: a tool for constructing multiple-choice tasks aimed at generating productive discussions in mathematics; an examination of analytical tools for analyzing teachers’ leading of whole-class discussions and technology integration; and suggestions for the development of these tools.
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| 9. |
- Kaufmann, Odd Tore, et al.
(author)
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Teachers’ Error-handling Practices Within and Across Lesson Phases in the Mathematics Classroom
- 2022
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In: International Journal of Science and Mathematics Education. - : Springer. - 1571-0068 .- 1573-1774.
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Journal article (peer-reviewed)abstract
- Multiple studies have been conducted regarding teachers’ error-handling practices, and how errors can be treated as opportunities for learning, albeit in the context of whole-class discussions. The aim of the present research is to continue to investigate teachers’ error-handling practices as they occur in different phases of maths lessons: introduction of the task, when students are working alone, and when students are working in pairs and finally, as part of the whole-class discussion. The study included 51 lessons from twelve teachers. A cross-case analysis was made across the individual teacher cases to look for similarities and differences between different teachers’ error-handling practices across the lesson phases in order to create teaching profiles with similar handling of student errors across the lesson phases. Five error-handling teaching profiles were identified; correcting errors throughout all phases, correcting errors during students’ work while few errors are brought up in whole class, correcting errors during students’ work while using a variety of practices in whole class, ignoring errors while using some of them in whole class, and discussing and explaining errors.
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| 10. |
- Kaufmann, Odd Tore, et al.
(author)
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Teachers’ framing of students’ difficulties in mathematics learning in collegial discussions
- 2022
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In: Scandinavian Journal of Educational Research. - : Informa UK Limited. - 0031-3831 .- 1470-1170. ; 67:7, s. 1069-1085
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Journal article (peer-reviewed)abstract
- This study investigates the diagnostic and prognostic framings of Swedishmathematics teachers regarding the difficulties experienced by studentsin mathematics learning. Collegial discussions among 65 mathematicsteachers in nine collegial groups were videotaped during a professionaldevelopment (PD) program entitled Boost for Mathematics for analysis.The results show that the diagnostic framings of the teachers weremainly attributed to the cognitive abilities of students, whereas theprognostic framings were mainly related to lesson organization suchthat students should collaborate. While the teachers emphasizecollaborate group work, they put little emphasis on how they could actin these learning situations. These results contribute to theunderstanding of Swedish mathematics teachers’ framing of students’difficulties in mathematics learning and to the role of collegialdiscussions in PD initiatives.
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