| 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. |
- Jäder, Jonas, et al.
(författare)
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Reasoning requirements in school mathematics textbooks: an analysis of books from 12 countries
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- A selection of secondary school textbooks from twelve countries in five continents is used as an indicator of the opportunities to learn mathematics through different forms of reasoning, in particular with respect to the distinction between rote learning and deeper learning. One aspect that is fundamental to the development of conceptual understanding as well as problem solving ability is the opportunity to learn how to construct mathematically well-founded reasoning. This study compared textbook tasks to the information provided previously in the book, determining if it is possible and reasonable to mimic available solution templates, or if a solution has to be constructed. The results show that the percentage of tasks where it is possible to mimic available templates is on average 79 %, but that this percentage varies widely within the books depending on the textbook authors own labeling of the tasks, and on the mathematical content. 13 % of the tasks can be solved mainly by mimicking provided templates but require some minor modification, and the remaining 9 % of the tasks require that the main parts of the solution are constructed without the guidance of a template. Although these distributions are relatively similar in all textbooks, the twelve countries perform differently in international tests such TIMSS and PISA.
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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
- 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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| 8. |
- Jäder, Jonas, et al.
(författare)
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Mathematical Reasoning and Beliefs
- 2014
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Ingår i: Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (Vol. 6). - Vancouver : PME. - 9780864913661 ; , s. 114-114
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Konferensbidrag (refereegranskat)abstract
- We present a research project on students’ mathematical reasoning and how beliefs are indicated in their arguments. Preliminary results show that students express beliefs that task solving does not include reflection or much struggle. The results underpin earlier studies stressing expectations as a theme of belief.
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| 9. |
- Jäder, Jonas, et al.
(författare)
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Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving
- 2017
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Ingår i: International Journal of Science and Mathematics Education. - : Springer Science and Business Media LLC. - 1571-0068 .- 1573-1774. ; 15, s. 759-776
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Tidskriftsartikel (refereegranskat)abstract
- Beliefs and problem solving are connected and have been studied in different contexts. One of the common results of previous research is that students tend to prefer algorithmic approaches to mathematical tasks. This study explores Swedish upper secondary school students’ beliefs and reasoning when solving non-routine tasks. The results regarding the beliefs indicated by the students were found deductively and include expectations, motivational beliefs and security. When it comes to reasoning, a variety of approaches were found. Even though the tasks were designed to demand more than imitation of algorithms, students used this method and failed to solve the task. © 2016 Ministry of Science and Technology, Taiwan
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| 10. |
- Sidenvall, Johan, 1974-
(författare)
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Att lära sig resonera : om elevers möjligheter att lära sig matematiska resonemang
- 2015
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Students only learn what they get the opportunity to learn. This means, for example, that students do not develop their reasoning- and problem solving competence unless teaching especially focuses on developing these competencies. Despite the fact that it has for the last 20 years been pointed out the need for a reform-oriented mathematics education, research still shows that in Sweden, as well as internationally, an over-emphasis are placed on rote learning and procedures, at the cost of promoting conceptual understanding. Mathematical understanding can be separated into procedural and conceptual understanding, where conceptual understanding can be connected to a reform oriented mathematics education. By developing a reasoning competence conceptual understanding can also be developed. This thesis, which deals with students’ opportunities to learn to reason mathematically, includes three studies (with data from Swedish upper secondary school, year ten and mathematics textbooks from twelve countries). These opportunities have been studied based on a textbook analysis and by studying students' work with textbook tasks during normal classroom work. Students’ opportunities to learn to reason mathematically have also been studied by examining the relationship between students' reasoning and their beliefs. An analytical framework (Lithner, 2008) has been used to categorise and analyse reasoning used in solving tasks and required to solve tasks.Results support previous research in that teaching and mathematics textbooks are not necessarily in harmony with reform-oriented mathematics teaching. And that students indicated beliefs of insecurity, personal- and subject expectations as well as intrinsic- and extrinsic motivation connects to not using mathematical reasoning when solving non-routine tasks. Most commonly students used other strategies than mathematical reasoning when solving textbook tasks. One common way to solve tasks was to be guided, in particular by another student. The results also showed that the students primarily worked with the simpler tasks in the textbook. These simpler tasks required mathematical reasoning more rarely than the more difficult tasks. The results also showed a negative relationship between a belief of insecurity and the use of mathematical reasoning. Furthermore, the results show that the distributions of tasks that require mathematical reasoning are relatively similar in the examined textbooks across five continents.Based on the results it is argued for a teaching based on sociomathematical norms that leads to an inquiry based teaching and textbooks that are more in harmony with a reform-oriented mathematics education.
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