| 1. |
- Jäder, Jonas, et al.
(författare)
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Mathematical problem solving in textbooks from twelve countries
- 2020
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211. ; 51:7, s. 1120-1136
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Tidskriftsartikel (refereegranskat)abstract
- A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by mimicking available templates or whether a solution had to be constructed without guidance from the textbook. There were similarities between the twelve textbooks in the sense that most tasks could be solved using a template as guidance. A significantly lower proportion of the tasks required a solution to be constructed. This was especially striking in the initial sets of tasks. Textbook descriptions indicating problem solving did not guarantee that a task solution had to be constructed without the support of an available template.
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| 2. |
- Sidenvall, Johan, 1974-
(författare)
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Lösa problem : om elevers förutsättningar att lösa problem och hur lärare kan stödja processen
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Generellt sett domineras matematikundervisning av utantillinlärning och arbete med rutinuppgifter. Om undervisning till störst del görs på detta sätt kommer elever ha svårt att att utveckla andra viktiga förmågor i matematik såsom problemlösning, resonemang och begreppsförståelse. Tidigare forskning har visat om elever får jobba med problemuppgifter (dvs. skapa egna lösningsmetoder) i större utsträckning får de en ökad matematisk förståelse, än om de enbart arbetar med rutinuppgifter.Syftet med avhandlingen var att ge ökade insikter om varför utantillinlärning och arbete med rutinuppgifter fortsätter att vara vanligt samt undersöka och föreslå på vilket sätt elevers förutsättningar att jobba med problemuppgifter skulle kunna förbättras. Detta gjordes genom följande studier. (1) Relationen mellan vilka typer av lösningsstrategier (imitera eller skapa lösningsmetod) som krävdes och vilka som användes vid uppgiftslösning. (2) Relationen mellan elevers val av lösningsstrategi och uppfattningar om matematik. (3) Undersökning av andel problemuppgifter i läroböcker från 12 länder. (4) Karaktärisering av tidigare forskning med avseende på undervisning genom problemlösning och resonemang. (5) Interventionsstudie där ett lärarstöd, utformat för att stödja elevers problemlösning med hjälp av formativ bedömning, utvecklades, testades och utvärderades. Studierna fokuserade i första hand på skolans senare årskurser.Elevernas förutsättningar att lösa uppgifter genom problemlösning var begränsad: av att det var mycket ovanligt med problemuppgifter bland de enklare uppgifterna i läroböckerna, av elevernas val att använda sig av imitativa lösningsstategier och av att eleverna ofta kunde lösa uppgifter genom att lotsas fram till en lösning av en annan elev eller av läraren. Elevernas förutsättningar begränsades också av elevernas uppfattningar av matematik och av elever ibland arbetade med uppgifter som inte var inom räckhåll att lösas genom problemlösning. För att ge elever förbättrade förutsättningar att lösa problemuppgifter bör lärare låta elever arbeta med fler problemuppgifter i en lärandemiljö som innebär att elever faktiskt skapar egna lösningsmetoder och att lärarhjälp baseras på att stödja elever utifrån elevers svårigheter och inte lotsa fram till en lösning. Resultatet ger också implikationer för hur läroböcker kan struktureras och hur det testade lärarstödet skulle kunna vara en del av en proffessionsutveckling och en del av lärarutbildningen.
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| 3. |
- Sidenvall, Johan, 1974-, et al.
(författare)
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Supporting teachers in supporting students’ mathematical problem solving
- 2022
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis Group. - 0020-739X .- 1464-5211.
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of this intervention study was to develop and evaluate a support model for teachers, designed to assist them in diagnosing students’ (age 16–19 years) difficulties and providing feedback to support students’ mathematical problem solving. Reporting on an iteration in a design research project, the results showed that the support helped the teachers to provide less procedural information and instead help students construct solutions for themselves. Constraints in achieving this included the nature of some tasks, difficulties in making reasonable diagnoses, and students’ inability to communicate their difficulties.
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| 4. |
- Sidenvall, Johan, 1974-, et al.
(författare)
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Supporting Teachers to Support Students’ Problem-solving
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The purpose of this intervention study was to develop, test, and evaluate a teacher guide structured in line with central tenets of formative assessment in a real classroom setting. The teacher-guide was designed to support teachers’ diagnosis of student difficulties and their choice of feedback to help students to continue the construction of solution methods during problem- solving if they become stuck. By using an approach inspired by design research, five teachers used the teacher guide for two plus two weeks in 12 mathematics courses in upper secondary school with revisions of the teacher guide in between the iterations. Ninety-six teacher-student interactions were observed, and teacher interviews were conducted. The results showed that the teacher guide supported the teachers in providing less algorithmic information and instead focusing on the problem-solving process, and by that helping the students to themselves construct solutions during their problem-solving activity. The use of the teacher guide was sometimes constrained by the type of tasks the students were working on, by difficulties in making reasonable diagnoses of students’ difficulties, and by students’ insufficient ability and/or willingness to communicate.
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| 5. |
- Säfström, Anna Ida, 1984-, et al.
(författare)
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Developing a diagnostic framework for primary and secondary students’ reasoning difficulties during mathematical problem solving
- 2024
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Ingår i: Educational Studies in Mathematics. - : Springer Nature. - 0013-1954 .- 1573-0816. ; 115:2, s. 125-149
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Tidskriftsartikel (refereegranskat)abstract
- It is well-known that a key to promoting students’ mathematics learning is to provide opportunities for problem solving and reasoning, but also that maintaining such opportunities in student–teacher interaction is challenging for teachers. In particular, teachers need support for identifying students’ specific difficulties, in order to select appropriate feedback that supports students’ mathematically founded reasoning without reducing students’ responsibility for solving the task. The aim of this study was to develop a diagnostic framework that is functional for identifying, characterising, and communicating about the difficulties students encounter when trying to solve a problem and needing help from the teacher to continue the construction of mathematically founded reasoning. We describe how we reached this aim by devising iterations of design experiments, including 285 examples of students’ difficulties from grades 1–12, related to 110 tasks, successively increasing the empirical grounding and theoretical refinement of the framework. The resulting framework includes diagnostic questions, definitions, and indicators for each diagnosis and structures the diagnostic process in two simpler steps with guidelines for difficult cases. The framework therefore has the potential to support teachers both in eliciting evidence about students’ reasoning during problem solving and in interpreting this evidence.
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| 6. |
- Säfström, Anna Ida, 1984-, et al.
(författare)
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Initiating teacher-researcher collaboration to support students' mathematical problem-solving
- 2021
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Ingår i: Nordisk matematikkdidaktikk, NOMAD. - 1104-2176. ; :3–4, s. 131-151
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Tidskriftsartikel (refereegranskat)abstract
- Implementing teaching through mathematical problem-solving entails substantial challenges and calls for sustained teacher-researcher collaboration. The joint research and development project ”Teaching that supports students’ creative mathematical problem-solving” has a fundamental ambition to be symmetric in that both teachers’ and researchers’ needs and conditions are attended to and complementary in that their different areas of expertise are utilised and valued. In this paper we show how the interplay and development of symmetry and complementarity can function as a means for studying teacher-researcher collaborations.
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| 7. |
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| 8. |
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| 9. |
- Bergqvist, Tomas, 1962-, et al.
(författare)
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Mathematical reasoning in teachers' presentations
- 2012
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Ingår i: Journal of Mathematical Behavior. - : Elsevier. - 0732-3123 .- 1873-8028. ; 31:2, s. 252-269
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers’ ordinary task solving presentations. The characteristics of algorithmic and creative reasoning that are seen in the presentations are analyzed. We find that most task solutions are based on available algorithms, often without arguments that justify the reasoning, which may lead to rote learning. The students are given some opportunities to see aspects of creative reasoning, such as reflection and arguments that are anchored in the mathematical properties of the task components, but in relatively modest ways.
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| 10. |
- Bergqvist, Tomas, 1962-, et al.
(författare)
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Podcasting in School
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Podcasting is a new phenomenon in Swedish schools. This pa- per describes a project where the main goal is to analyze if the students’ interest in mathematics is affected if the mathematics is made accessible via podcasts and iPods. Teachers at eleven schools were encouraged to produce podcasts as a part of their mathematics teaching in school year eight. The results indicate an increased interest in mathematics and the learning of mathematics among the students. We also found that the tech- nical difficulties for the teachers were underestimated in the project, and that teachers had difficulties in finding time for the production of podcasts.
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