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Supporting Teachers to Support Students’ Problem-solving
Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). (Lärande genom imitativa och kreativa resonemang (LICR))ORCID iD: 0000-0002-9691-1995
Umeå University, Faculty of Social Sciences, Department of applied educational science, Interactive Media and Learning (IML). Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). (Lärande genom imitativa och kreativa resonemang (LICR))
Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. (Lärande genom imitativa och kreativa resonemang (LICR))
Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. (Lärande genom imitativa och kreativa resonemang (LICR))
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keywords [en]
teacher-guide, problem-solving, formative assessment, design research
National Category
Didactics
Identifiers
URN: urn:nbn:se:umu:diva-157561OAI: oai:DiVA.org:umu-157561DiVA, id: diva2:1299150
Available from: 2019-03-26 Created: 2019-03-26 Last updated: 2019-04-09
In thesis
1. Lösa problem: om elevers förutsättningar att lösa problem och hur lärare kan stödja processen
Open this publication in new window or tab >>Lösa problem: om elevers förutsättningar att lösa problem och hur lärare kan stödja processen
2019 (Swedish)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[en]
Solving problems : on students’ opportunities to solve problems and how teachers can support this process
Abstract [sv]

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.

Abstract [en]

In mathematics education, there is generally too much emphasis on rote learning and superficial reasoning. If learning is mostly done by rote and imitation, important mathematical competencies such as problem-solving, reasoning, and conceptual understanding are not developed. Previous research has shown that students who work with problems (i.e. constructs a new solution method to a task), to a greater extent increase their mathematical understanding than students who only solve routine tasks.

The aim of the thesis was to further understand why teaching is dominated by rote learning and imitation of procedures and investigate how opportunities for students to solve tasks through problem-solving could be improved. This was done through the following studies. (1) Investigating the relation between types of solution strategy required, used, and the rate of correct task solutions in students’ textbook task-solving. (2) Studying the relationship between students’ beliefs and choice of solution strategy when working on problems. (3) Conducting a textbook analysis of mathematics textbooks from 12 countries, to determine the proportions of tasks that could be solved by mimicking available templates and of tasks where a solution had to be constructed without guidance from the textbook. (4) Conducting a literature review in order to characterize teaching designs intended to enhance students to develop mathematical understanding through problem solving and reasoning. (5) Conducting an intervention study were a teacher guide, structured in line with central tenets of formative assessment, was developed, tested, and evaluated in real classroom settings. The teacher guide was designed to support teachers in their support of students’ in their problem-solving process. Studies I, II and V were conducted in Swedish upper secondary school settings. 

The students’ opportunities to solve tasks through problem-solving were limited: by the low proportion of problems among the easier tasks in the textbooks; by the students' choice of using imitative solution strategies; and by the guidance of solution methods that students received from other students and their teachers. The students’ opportunities were also limited by the students' beliefs of mathematics and the fact that a solution method of problem tasks was not always within reach for the students, based on the students' knowledge. In order to improve students’ opportunities, teachers should allow students to work with more problems in a learning environment that lets students engage in problem-solving and support students' work on problems by adapting their support to students' difficulties. The results also give implications for the construction and use of textbooks and how the use of the teacher guide could be part of teachers’ professional development and a tool that teacher students may meet within their education.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2019. p. 74
Series
Umeå Studies in the Educational Sciences ; 33
Keywords
problem solving, reasoning, beliefs, textbook, teaching, formative assessment, design research, secondary school, problemlösning, resonemang, uppfattningar, lärobok, lärare, undervisning, formativ bedömning, designforskning, gymnasieskola
National Category
Didactics
Identifiers
urn:nbn:se:umu:diva-157557 (URN)978-91-7855-049-4 (ISBN)
Public defence
2019-05-17, N420, Johan Bures väg 16, Umeå, 12:30 (Swedish)
Opponent
Supervisors
Projects
Lärande genom imitativa och kreativa resonemang (LICR)
Available from: 2019-04-16 Created: 2019-04-09 Last updated: 2019-05-14Bibliographically approved

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Sidenvall, JohanGranberg, CarinaLithner, JohanPalmberg, Björn

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