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Computer-based formative assessment for problem solving
Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. (LICR, Formative assessment)ORCID iD: 0000-0002-2863-0499
2023 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed) Epub ahead of print
Abstract [en]

This study focuses on computer-based formative assessment for supporting problem solving and reasoning in mathematics. To be able to assist students who find themselves in difficulties, the software suggested descriptions – diagnoses – of the encountered difficulty the students could choose from. Thereafter, the software provided metacognitive and heuristic feedback as suitable. The findings provide insight into how formative assessment can be designed to support students during their problem solving and indicate that diagnosis and feedback could be helpful for promoting students' creative reasoning. In other words, the feedback guided students in justifying, monitoring, and controlling their solution method.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2023.
Keywords [en]
Problem solving, reasoning, formative assessment, metacognitive feedback
National Category
Didactics Pedagogical Work
Research subject
didactics of mathematics
Identifiers
URN: urn:nbn:se:umu:diva-205036DOI: 10.1080/0020739X.2023.2178982ISI: 000934282000001Scopus ID: 2-s2.0-85148588469OAI: oai:DiVA.org:umu-205036DiVA, id: diva2:1738100
Available from: 2023-02-20 Created: 2023-02-20 Last updated: 2023-09-05
In thesis
1. Formative assessment and problem solving in mathematics
Open this publication in new window or tab >>Formative assessment and problem solving in mathematics
2023 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Formativ bedömning och problemlösning i matematik
Abstract [en]

In this thesis, the focus is on how reasoning in problem solving can be supported and which factors are associated with this support. In four studies, I investigated four aspects which address the overarching aim of the thesis. I report on two non-empirical studies and two intervention studies of formative assessment that deal with problem solving in mathematics.

Study 1 proposes a model based on different characteristics of feedback in mathematics education that have been studied in the literature. Study 2 addresses the effectiveness of different feedback types in mathematics. Study 3 investigates the usefulness of formative assessment in supporting students who engage in problem solving. Study 4 examines the relationship between a student’s self-efficacy, national test grade, motivation type, learning goal orientation, task-solving success, and the perceived usefulness of feedback.

I have used the concept of devolution of problem from Brousseau’s (1997) theory of didactical situations in mathematics to design a computer-based formative assessment support tool. The students were not provided with any solution method template to solve the tasks; instead, they were given the responsibility of constructing their own solution method with self-diagnosis and feedback support from the computer. The students determined where they had struggled and chose the diagnosis, and feedback was designed corresponding to each diagnosis. The feedback for each task starts at a relatively general metacognitive level; if it is insufficient, feedback is then provided in the form of general heuristic strategy suggestions.

Thematic analysis and systematic literature reviews were used in the first two studies. Participants in Intervention Study 3 were 17 first-year university students, whereas 134 students from upper secondary high school participated in Intervention Study 4. Think-aloud protocols have been used in this thesis analysis along with computer log files. In Study 4, structural equation model analyses were used.

The first study’s proposed model identified in which ways the characteristics of feedback both between and within feedback levels may be very different and thereby might affect students’ responses and learning differently. The results from Study 2 indicated that effective feedback provides to students sufficient motivational and cognitive support to use the feedback to engage in thinking about the mathematical learning targets. Such feedback characteristics are more often found in process-level feedback and self-ivregulation feedback than in task-level feedback. Study 3 showed how the use of computer-based formative assessment, including self-assessment and metacognitive and heuristic feedback, can support students to overcome difficulties in problem-solving by their own reasoning. The results from Study 4 showed that students’ mastery goals had a direct effect on the perceived usefulness of the feedback, but no such effects were found for students’ national test grades, self-efficacy beliefs, performance goals, intrinsic or extrinsic forms of motivation.

Abstract [sv]

I denna avhandling fokuseras på hur resonemang i problemlösning kan stödjas och vilka faktorer som är associerade med detta stöd. I fyra studier undersökte jag fyra aspekter inom det övergripande syftet med avhandlingen. Jag redovisar två icke-empiriska studier om formativ bedömning i matematik och två interventionsstudier med datorbaserad formativ bedömning som stöd till elevers problemlösning i matematik.

Studie 1 föreslår en modell baserad på olika egenskaper av återkoppling inom matematikundervisning som har studerats i litteraturen. Studie 2 behandlar effektiviteten av olika återkopplingstyper inom matematik. Studie 3 undersöker användbarheten av formativ bedömning för att stödja eleverna att engagera sig i problemlösning. Studie 4 undersöker förhållandet mellan elevers tro på sin egen förmåga, nationella provbetyg, motivationstyp, målorientering, uppgiftslösningsframgång och upplevd användbarhet av återkoppling.

Jag har använt begreppet ”devolution of problem” (delegering av ansvar för problemlösning) från Brousseaus (1997) teori om didaktiska situationer inom matematik för att utforma ett datorbaserat formativt bedömningsstöd. Eleverna försågs inte med någon lösningsmetodsmall för att lösa uppgifterna, istället fick de ansvaret att konstruera sin egen lösningsmetod med självdiagnostik och återkopplingsstöd från datorn. Eleverna identifierade var de hade svårigheter och de valde diagnos, och återkoppling var förutbestämd i enlighet med varje diagnos. Återkopplingen började på en relativt allmän metakognitiv nivå, och om den var otillräcklig gavs återkoppling som allmänna heuristiska strategiförslag.

Tematisk analys och systematiska litteraturöversikter användes i de två första studierna. Deltagare i interventionsstudie 3 var 17 förstaårs universitetsstudenter och 134 elever från gymnasieskolan deltog i interventionsstudie 4. Tänka-högt-protokoll har använts i studie 3 tillsammans med datorloggfiler. I studie 4 användes strukturella ekvationsmodellanalyser.

Den första studiens föreslagna modell identifierade på vilka sätt egenskaperna för återkoppling både mellan och inom återkopplingsnivåer kan vara olika och därmed kan påverka elevernas svar och lärande. Resultaten från studie 2 indikerade att effektiv återkoppling ger eleverna tillräckligt motiverande och kognitivt stöd för att använda återkopplingen för att tänka på de matematiskaviiinlärningsmålen. Sådana återkopplingsegenskaper återfinns oftare i återkoppling på processnivå och självregleringsnivå än i återkoppling på uppgiftsnivå. Studie 3 visade att användningen av formativ bedömning från datorn, baserat på självdiagnos och metakognitiv och heuristisk återkopplingen, kan användas på ett formativt sätt som ett stöd för att övervinna en svårighet under problemlösning. Resultaten från studie 4 visade att elevernas bemästrandemål (lärandemål) hade en direkt effekt på den upplevda användbarheten av återkopplingen, men inga sådana effekter hittades för elevernas nationella provbetyg, tron på sin egen förmåga, prestationsmål, inre eller yttre former av motivation.

Place, publisher, year, edition, pages
Umeå: Umeå University, 2023. p. 70
Series
Doktorsavhandlingar i pedagogiskt arbete, ISSN 1650-8858 ; 98
Keywords
Formative assessment, problem solving, reasoning, computer-based assessment, feedback, types of motivation, self-efficacy
National Category
Pedagogical Work Didactics
Research subject
educational work; didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-205703 (URN)978-91-8070-000-9 (ISBN)978-91-7855-999-2 (ISBN)
Public defence
2023-05-05, KBE301 (Lilla hörsalen), KBC-huset, Umeå, 09:00 (English)
Opponent
Supervisors
Available from: 2023-03-22 Created: 2023-03-16 Last updated: 2023-03-16Bibliographically approved

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