| 1. |
- Bengtsson, Anna
(författare)
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When mathematics teachers focus discussions on slope : Swedish upper secondary teachers in a professional development initiative
- 2014
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The shift towards collegiality is a new setting for many teachers. Most teachers work alone, in isolation from their colleagues and collegial collaboration requires organisational structures. The aim of the study is to describe and analyse upper secondary mathematics teachers’ collective practice,developed in a professional development initiative. This study is a case study and the empirical data is generated through observations and an interview of a group of four teachers at a school who met on a weekly basis throughout a term. Their discussions focused on the mathematical concept of slope in a setting of learning study. This thesis is the case of when mathematics teachers focus discussions on slope and draws on Wenger’s Communities of Practice Perspective, as a unitof analysis, and addresses the question: What are the characteristics of practice when upper secondary mathematics teachers focus discussions on slope in the setting of a learning study? The analysis accounts for characteristics of the aspects of practice, through the coherence of mutual engagement, joint enterprise and shared repertoire in the community of practice. The teachers are engaged around finding small changes in their teaching that could give major effect in students learning. They negotiate what the students need to know in order to understand the relation between Δy and Δx. The characteristic of practice is a conceptual mapping of the concept of slope. It reveals students’ partial understanding of related concepts due to how they were given meaning through previous teaching. The conceptual mapping of slope goes back as far as to the student’s partial understanding of the meaning of subtraction. However, what emerges is in relation to the teachers’ experience of avoiding students’ difficulties with negative difference when teaching slope. It turns out to be a negotiation and a renegotiation of teaching slope for instrumental understanding or conceptual understanding. An overall characteristic of practice is that it develops in a present teaching culture.
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| 2. |
- Berggren, Elin, 1979-, et al.
(författare)
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Praxeologies-in-action during struggle with problem-solving
- 2023
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Ingår i: <em>Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13).</em>. - : ERME. - 9789637031045 ; , s. 2267-2274
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Konferensbidrag (refereegranskat)abstract
- Engaging in productive struggle during problem-solving activities can be viewed as critical to learning mathematics. In this paper, we explore how mathematical praxeologies can be utilized to describe students’ struggle with mathematical problem-solving. The results indicate that the students’ productive struggle with an optimization problem involving functions, graphs, and derivatives, contains long sequences where the students switch rapidly within and between mathematical praxeologies. During the work session as a whole, the students mix coherent arguments with tentative and on occasion unproductive arguments focusing on technology. One notable exception among these attempts is a theoretical moment where the students reduce the complexity of a previous subtask by deducing a general equation which provides them with key ideas on how to solve the given task.
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| 3. |
- Bergström, Tove, et al.
(författare)
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The importance of flow for secondary school students’ experiences in geometry
- 2023
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211. ; 54:6, s. 1067-1091
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Tidskriftsartikel (refereegranskat)abstract
- This article is intended to contribute to greater knowledge regarding the importance of flow and the time used to perform an activity, with a focus on students’ mathematical experiences of 3D bodies. Thirty-one 9th-grade students took part in the study. Flow and variation theory was used in the analysis of lesson observations, submission tasks, audio recordings, logbooks, tests and nationwide tests. The results indicate that the selected mathematics problem is characterized by seven components, which serve as the basis for identifying intended critical aspects; a variation is evident in the balance between skills and challenges that is characterized by the critical aspects that the students discern; a variation is evident in the experience of flow that is dependent upon the students’ approach to their work on various activities; the students’ mathematical experiences are based, both short- and long-term, on discerned critical aspects and on the time spent on the activity that generates flow. Theoretical contributions as well as implications for teaching are presented at the end of the article.
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| 4. |
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| 5. |
- Holmqvist Olander, Mona, et al.
(författare)
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Bridging the gap between theory and practice by the use of iterative processes
- 2013
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Ingår i: Journal of Education and Learning. - : Canadian Center of Science and Education. - 1927-5250 .- 1927-5269. ; 2:1, s. 230-239
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this study is to study learning the positional ten base notation by the increase of students’ test scoresduring the learning study process. Five teachers, one researcher and 53 students participated. Three researchlessons in three different groups of students were conducted. The improvement in the third lesson (C) correlateswith the more developed theoretical based assumptions the design is made, which resulted in a pattern ofvariation that stronger pointed out the aspect needed to discern to understand the object of learning in a new andmore developed way. The differences in the third research lesson (C) was significant** p=0.005 while thedifferences in research lessons A and B were not significant.
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| 6. |
- Karlsson, Natalia, et al.
(författare)
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Teachers and student-teachers' challenges with addition and multiplication strategy problems
- 2019
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Ingår i: Proceedings of the 43rd Conference of the International Groupfor the Psychology of Mathematics Education. - : IGPME. - 9780639821566 - 9780639821573 ; , s. 53-53
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Konferensbidrag (refereegranskat)abstract
- The Swedish National Agency for Education emphasizes that students in grades 1-3 should be able to develop addition and multiplication strategies based on the properties of these operations before focusing on standard algorithms. This means that teachers need to understand student perceptions of these concepts in order to be able to develop instructions for promoting such strategies. According to Ball, Thames and Phelps (2008) teachers need mathematical knowledge to be able to meet such a demand. Other researchers recommend carrying out qualitative studies investigating a field experience of pre-service and in-service teachers. Since the in-service teachers’ knowledge depends on what they were taught in school themselves, we studied the teaching process in grade 3 in order to learn how they were initially introduced to addition and multiplication (Van Dooren, De Bock, & Verschaffel, 2010).The teaching process and teachers’ understanding of problems with multiplication content was studied in 3rd grade mathematics classrooms. This study investigated challenges faced by teachers when they went from interpretation to formulation of the multiplication problems. Data is drawn from three main sources: observation, interviews, field notes and video recordings. The data was analysed in a qualitative way, using variation theory (Marton, 2015). The analysis reveals that the participating teachers were more successful in using addition strategies than multiplication ones in problem development. For example, most teachers identified multiplication as a repeated addition. Consequently, they often missed important multiplication structures and their link to division. The results explain some reasons for difficulties in elementary mathematics experienced by in-service teachers and the consequences they lead to in their teaching. Teachers' understanding of mathematical concepts is crucial for their interpretation and setting of the example problems.
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| 7. |
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| 8. |
- Lennerstad, Håkan, et al.
(författare)
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Kvadreringsregeln
- 2014
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Annan publikation (övrigt vetenskapligt/konstnärligt)
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| 9. |
- Lennerstad, Håkan, et al.
(författare)
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Åtta IKT-projekt för matematiken i skolan : empiri och analys
- 2012
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Rapport (refereegranskat)abstract
- Denna rapport presenterar empiri och analys av en granskning av åtta projekt som mottagit medel från Skolverket för att tillämpa IKT i skolans matematikundervisning. Empirin är organiserad enligt aktivitetsteorin, vilken sätter relationerna mellan människa, miljö, aktiviteter och mål i förgrunden. Empirin som presenteras är till stor del sammanställda repliker från lärare och elever vid intervjuerna, organi¬sera¬de för att belysa verksamhetens olika relationer. Det betyder att presentationen är till stor del på de verksammas villkor, och på deras språk.Ett stort antal konkreta slutsatser framkommer ur detta material. En av dem är att klass¬upp-sätt¬ningar av datorer är sällan framgångsrika, på grund av att teknisk support ofta var otillräcklig, och att lärarna inte kan veta hur mycket eleverna använder datorerna till icke-skol-verk¬sam¬het. Dessa problem finns inte för interaktiva skrivtavlor. De framstår däremot som ett socialt verktyg, som gör utbyte och dialog om ämnet lättare att få till stånd. I flera fall framkom indirekt, men ändå tydligt, att utbildningen på tekniken hade varit otillräcklig, trots att lärarna inte uttryckte ett tydligt missnöje med den. Skrivtavlan ökade lärarnas motivation för samarbete. En framåtriktad slutsats är att en lärargrupp som har ett fungerande samarbete och goda didaktiska, ämnesmässiga, ledar- och relationella kompe¬tenser med en interaktiv skrivtavla har en möjlighet att komma längre med elevernas måluppfyllelse.
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| 10. |
- Lövström, Anna, 1972-
(författare)
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Delaktighet för elever med olika förkunskaper i matematik : en interdisciplinär studie om betydelsen av undervisningens utformning och genomförande för elevers lärande
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation is about developing our knowledge of teaching and student learning through examining teaching that has been designed and implemented with in a learning study. Applying an interdisciplinary approach, this research builds knowledge of how teaching can be designed and implemented for young students with different prior knowledge of mathematics. The focus is on inclusive education and, in particular, on inclusive learning environments. Teaching and learning about whole numbers for students in grades 2 and 3 were studied.The empirical material, mainly comprising videotaped lessons and the results of identical knowledge tests that the students completed before and after the lessons, was collected in a learning study and used in two steps. First, the teaching characteristics were analysed at a collective level, mainly based on test results used to measure learning outcomes, i.e.,students’ ability to expand their number range from natural to whole numbers. The extent to which the teaching characteristics were transferable to new teaching contexts was also investigated. Second, an interdisciplinary approach was followed, applying knowledge and theories from special needs education and mathematics education. Examining teaching characteristics in relation to outcomes, the research perspective expanded from the collective to the individual level, emphasizing participation and learning among students with different prior knowledge according to test results. Notably, at a collective level, teaching was characterized by being based on the identification of critical aspects. Analyses of teaching outcomes at the individual level revealed a mixed picture of student learning and participation in the learning study lessons. Concerning one studied lesson, an analysis of student test results revealed considerable diversity in student achievement, indicating that some students learned what was intended while others did not. However, test results from another lesson indicated that all students progressed in learning about whole numbers. During this lesson, the teacher-guided mathematical discourse incorporating several routines seemed to be central to facilitating student participation as well as change in the discourse on whole numbers.The main conclusion is that the interdisciplinary research approach helped foster deeper insight into teaching design and its outcomes regarding individual students’ learning and participation. In addition, the findings emphasize the importance of teachers taking responsibility for inviting the students into the mathematical discourse in relation to the access aspect of participation, and then, through challenging questions, facilitating progress to the collaborative aspect of participation.
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