| 1. |
- Bergwall, Andreas, 1972-
(författare)
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Proof-related reasoning in upper secondary mathematics textbooks : Characteristics, comparisons, and conceptualizations
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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. |
- Eriksson, Kimmo, et al.
(författare)
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Cultural Variation in the Effectiveness of Feedback on Students' Mistakes
- 2020
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Ingår i: Frontiers in Psychology. - : Frontiers Media SA. - 1664-1078. ; 10
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Tidskriftsartikel (refereegranskat)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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| 3. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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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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Ingår i: Frontiers in Psychology. - : Frontiers Media SA. - 1664-1078. ; 13
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Tidskriftsartikel (refereegranskat)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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| 4. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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Socioeconomic Status as a Multidimensional Predictor of Student Achievement in 77 Societies
- 2021
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Ingår i: Frontiers in Education. - : Frontiers Media SA. - 2504-284X. ; 6
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Tidskriftsartikel (refereegranskat)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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| 5. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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Using TIMSS items to evaluate the effectiveness of different instructional practices
- 2019
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Ingår i: Instructional Science. - : Springer Science and Business Media LLC. - 0020-4277 .- 1573-1952. ; 47:1, s. 1-18
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Tidskriftsartikel (refereegranskat)abstract
- Can instructional quality be measured using TIMSS items on how often certain instructional practices are used in the mathematics classroom? We focused on three instructional practices that have been the topics of longstanding debates in the educational literature: memorizing formulas, listening to the teacher, and relating mathematics to daily life. In a multi-level multiple regression analysis, we examined how class-level responses to these items predicted mathematics achievement. In Sweden, across four waves of TIMSS, relating to daily life was a negative predictor of achievement, whereas memorizing formulas and listening to the teacher were positive predictors. This was also the typical pattern of results across all countries participating in two waves of the international TIMSS. Our findings are in line with certain positions on the abovementioned debates. Although conclusions are limited by the correlational nature of the data, we argue that TIMSS is a promising tool for evaluating the effectiveness of different instructional practices. We also suggest several improvements.
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| 6. |
- Lindvall, Jannika, 1987-, et al.
(författare)
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Does the duration of professional development programs influence effects on instruction? : An analysis of 174 lessons during a national-scale program
- 2023
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Ingår i: European Journal of Teacher Education. - : Taylor & Francis Group. - 0261-9768 .- 1469-5928. ; , s. 1-19
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Tidskriftsartikel (refereegranskat)abstract
- We examine the effects of a year-long national-scale professional development (PD) program on mathematics instructional quality. In contrast to previous studies examining the effects of this program on instruction by comparing before and after participation or parti-cipants and non-participants, we examine whether instructional quality changed during the program. More specifically, we conduct an analysis of 174 video-recorded mathematics lessons given by 52 teachers during their year of participation. Contrary to previous studies, the results demonstrate that the instructional quality did not improve over the course of the PD. We suggest that the explanations for the diverging results concern how, when, and to what extent instructional quality changes in PD programs. Specifically, we discuss how the explanations may illuminate the significance of PD duration for PD effects, and how these effects may be mediated by features concerning the PD content and the scale at which the program is implemented.
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| 7. |
- Lindvall, Jannika, 1987-, et al.
(författare)
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Impact and Design of a National-scale Professional Development Program for Mathematics Teachers
- 2022
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Ingår i: Scandinavian Journal of Educational Research. - : Informa UK Limited. - 0031-3831 .- 1470-1170. ; 66:5, s. 744-759
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Tidskriftsartikel (refereegranskat)abstract
- By examining the effects of a national-scale teacher professional development (PD) program on instructional practices and student mathematics achievement, we contribute to calls for empirical studies investigating the impacts of such programs conducted at scale. The program corresponds well with core critical features of high-quality teacher PD and mathematics instruction identified in the literature, and the results indicate that it has had a small but statistical significant impact on teachers' instructional practices. However, no effect was found for student achievement. These results raise questions as to the importance of the critical features and how programs incorporating all of them affect instructional practices and student achievement.
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| 8. |
- Ryve, Andreas, 1973-
(författare)
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Approaching Mathematical Discourse : Two analytical frameworks and their relation to problem solving interactions
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The driving force of conducting the two studies presented in this thesis is to examine ways that conceptual understanding and problem solving could be part of mathematics teaching, and through that, part of students' mathematical knowledge. The specific aims of the thesis are: 1) to characterize the classroom discourse of two, apparently similar, problem solving courses in teacher education and 2) to discuss the possibilities of developing two analytical approaches - the communicational approach to cognition and the dialogical approach - used for studying mathematical discourse. The two aims are elaborated on by means of data collected through audiotaped recordings and field notes from observations of problem-solving activities in engineering and teacher education. In relation to the first aim, the analysis of the classroom discourse within the two courses makes it clear that both courses displayed different kinds of discourse that could be broadly categorized in terms of: subject-oriented, didactically oriented, and problem solving oriented discourses. However, the comparisons between the two courses reveal a marked difference in the distribution of these categories of discourse. It is suggested that the introduction of explicit conceptual frameworks in teaching is of crucial importance for the topical focus of the classroom discourse, and for prospective teachers' opportunity to engage in mathematical productive discourse. The analyses of the two approaches for studying mathematical discourse reveal that the two frameworks can be further developed and the study also indicates ways in which such development can be achieved using a theory of contextualization and theories of mathematical learning. Finally, the thesis discusses theoretical and practical implications of the results, foregrounding issues of importance for the research on mathematical discourse, and for teachers and teacher educators involved in designing instructions for mathematical problem solving.
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