| 1. |
- Söderström, Sharmin, 1987-
(författare)
-
Formative assessment and problem solving in mathematics
- 2023
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 2. |
- Sidenvall, Johan, 1974-
(författare)
-
Lösa problem : om elevers förutsättningar att lösa problem och hur lärare kan stödja processen
- 2019
-
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.
|
|
| 3. |
- Jäder, Jonas, 1971-
(författare)
-
Med uppgift att lära : om matematikuppgifter som en resurs för lärande
- 2019
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Elevers möjligheter att utveckla sin kunskap i matematik påverkas av de uppgifter de arbetar med. Det är möjligt att göra en distinktion mellan rutinuppgifter och matematiska problem. En rutinuppgift är en uppgift som en elev kan lösa genom att använda en välbekant metod, eller genom att imitera en förlaga. För att lösa ett matematiskt problem behöver däremot eleven konstruera en för henne ny lösningsmetod. För att utveckla sin matematiska kunskap behöver elever möta såväl rutinuppgifter som matematiska problem. Problemlösning kan skapa förutsättningar för en elev att utveckla såväl en kreativ problemlösningsförmåga, som en konceptuell, matematisk förståelse.Avhandlingen består av fem studier med ett fokus på matematikuppgifter, där studie 1-3 syftade till att undersöka vilka möjligheter att arbeta med matematisk problemlösning som elever i gymnasieskolan erbjuds. Detta undersöktes genom läroboksanalyser, studier av elevers arbete med uppgifter och av elevers uppfattningar om matematik. Uppgifter i läroböcker från 12 länder analyserades (studie 1) och ungefär 10 procent av dessa var matematiska problem. Eleverna arbetade (studie 2) nästan uteslutande med de uppgifter som av läroboksförfattarna kategoriserats som enkla och utan att arbeta problemlösande. Bland dessa uppgifter var andelen matematiska problem 4 procent. Inte heller bland uppgifter som kategoriserats som till exempel ’problemlösning’ eller ’utforska’ var matematiska problem i övervikt. Resultaten var relativt lika för de tolv ländernas läroböcker. Elevers uppfattningar om att rutinarbete är säkrare och något som är rimligt att förvänta sig i matematik (studie 3) kan ha en ytterligare påverkan på deras möjligheter att arbeta problemlösande. Med tanke på de positiva effekter som påvisats för elever som arbetar med problemlösning verkar elevers möjligheter att arbeta med problemlösning begränsade. Det finns potential i att såväl utveckla innehållet i läroböckerna för att öka andelen matematiska problem, som i ett medvetet uppgiftsurval från dessa läroböcker.Syftet med studie 4 och 5 var att fördjupa förståelsen för problemlösning. Ett analytiskt ramverk har utvecklats för att identifiera kreativa, konceptuella och andra utmaningar i elevers problemlösning. Respektive utmaning karaktäriserades för att ytterligare fördjupa förståelsen för dessa och för problemlösning. Elevers arbete med matematiska problem (studie 4) och lärares förväntningar på de utmaningar elever möter vid problemlösning (studie 5) studerades. Konceptuella och kreativa utmaningar visade sig vara de mest centrala vid elevers problemlösning. Genom den karaktäristik som knöts till respektive utmaning kan svårigheter med att identifiera, framför allt kreativa utmaningar, och relationen mellan uppgift och utmaning diskuteras.
|
|
| 4. |
- Vinnervik, Peter, 1971-
(författare)
-
När lärare formar ett nytt ämnesinnehåll : intentioner, förutsättningar och utmaningar med att införa programmering i skolan
- 2021
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In March 2017, programming was introduced in the Swedish school curriculum. The reform was formally enacted in July 2018. Research shows that teachers enacting curriculum reform practices encounter various challenges. For this particular reform, few teachers had prior experience of programming, and research further suggests that programming is difficult to teach and learn. It is therefore important to study teachers’ perceptions and experiences of what they should teach, why, and how, as this can provide valuable insight into how new policies influence teachers’ work, and how new policies are implemented.This thesis explores circumstances that may influence teachers’ integration of programming in school mathematics and technology education and consists of three studies. Study 1 and 3 draw on teachers’ perceptions and experiences collected before and after formal enactment of the reform. Study 2 draws on textual data from formal curriculum documents. The studies address three questions: (1) What challenges do teachers perceive prior to the introduction of programming? (2) What message about programming is communicated in the intended curriculum? (3) How do teachers transform programming into teaching content in technology education and what challenges do they face?The results show that teachers face several intrinsic and extrinsic challenges during the process of integrating programming in their teaching. A perceived lack of professional knowledge and understanding of programming among the teachers emerged as a prominent challenge both prior to and more than two years into the reform. Additional challenges are related to teaching materials, time for preparation and professional development. In technology education, teachers mainly see programming as a medium to explore and understand technological systems and construction work. They are uncertain of what programming means in terms of practices and concepts, and about learning progression and assessment. The results further reveal that the curriculum texts are sparse on details about what programming knowledge entails. Important strategic decisions are left entirely to the teachers without any clear guidance. In addition, the results indicate that many technology teachers work in isolation and that interdisciplinary work around programming, as intended in the curriculum, is generally lacking. It is concluded that there is a risk of inequality among schools and that the children’s experience of programming becomes fragmented, despite good intentions. The current implementation model needs to be improved, and this thesis presents two possible actions.
|
|
| 5. |
- Jonsson, Bert, Professor, 1961-, et al.
(författare)
-
Creative Mathematical Reasoning : Does Need for Cognition Matter?
- 2022
-
Ingår i: Frontiers in Psychology. - : Frontiers Media S.A.. - 1664-1078. ; 12
-
Tidskriftsartikel (refereegranskat)abstract
- A large portion of mathematics education centers heavily around imitative reasoning and rote learning, raising concerns about students’ lack of deeper and conceptual understanding of mathematics. To address these concerns, there has been a growing focus on students learning and teachers teaching methods that aim to enhance conceptual understanding and problem-solving skills. One suggestion is allowing students to construct their own solution methods using creative mathematical reasoning (CMR), a method that in previous studies has been contrasted against algorithmic reasoning (AR) with positive effects on test tasks. Although previous studies have evaluated the effects of CMR, they have ignored if and to what extent intrinsic cognitive motivation play a role. This study investigated the effects of intrinsic cognitive motivation to engage in cognitive strenuous mathematical tasks, operationalized through Need for Cognition (NFC), and working memory capacity (WMC). Two independent groups, consisting of upper secondary students (N = 137, mean age 17.13, SD = 0.62, 63 boys and 74 girls), practiced non-routine mathematical problem solving with CMR and AR tasks and were tested 1 week later. An initial t-test confirmed that the CMR group outperformed the AR group. Structural equation modeling revealed that NFC was a significant predictor of math performance for the CMR group but not for the AR group. The results also showed that WMC was a strong predictor of math performance independent of group. These results are discussed in terms of allowing for time and opportunities for struggle with constructing own solution methods using CMR, thereby enhancing students conceptual understanding.
|
|
| 6. |
- Jonsson, Bert, Professor, 1961-, et al.
(författare)
-
Gaining Mathematical Understanding : The Effects of Creative Mathematical Reasoning and Cognitive Proficiency
- 2020
-
Ingår i: Frontiers in Psychology. - : Frontiers Media S.A.. - 1664-1078. ; 11
-
Tidskriftsartikel (refereegranskat)abstract
- In the field of mathematics education, one of the main questions remaining under debate is whether students’ development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students’ math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students’ performance on practiced test tasks and transfer test tasks. Cognitive proficiency was shown to have an effect on students’ learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension.
|
|
| 7. |
- Karlsson Wirebring, Linnea, 1979-, et al.
(författare)
-
An fMRI intervention study of creative mathematical reasoning : behavioral and brain effects across different levels of cognitive ability
- 2022
-
Ingår i: Trends in Neuroscience and Education. - : Elsevier. - 2452-0837 .- 2211-9493. ; 29
-
Tidskriftsartikel (refereegranskat)abstract
- Background: Many learning methods of mathematical reasoning encourage imitative procedures (algorithmic reasoning, AR) instead of more constructive reasoning processes (creative mathematical reasoning, CMR). Recent research suggest that learning with CMR compared to AR leads to better performance and differential brain activity during a subsequent test. Here, we considered the role of individual differences in cognitive ability in relation to effects of CMR.Methods: We employed a within-subject intervention (N=72, MAge=18.0) followed by a brain-imaging session (fMRI) one week later. A battery of cognitive tests preceded the intervention. Participants were divided into three cognitive ability groups based on their cognitive score (low, intermediate and high).Results: On mathematical tasks previously practiced with CMR compared to AR we observed better performance, and higher brain activity in key regions for mathematical cognition such as left angular gyrus and left inferior/middle frontal gyrus. The CMR-effects did not interact with cognitive ability, albeit the effects on performance were driven by the intermediate and high cognitive ability groups.Conclusions: Encouraging pupils to engage in constructive processes when learning mathematical reasoning confers lasting learning effects on brain activation, independent of cognitive ability. However, the lack of a CMR-effect on performance for the low cognitive ability group suggest future studies should focus on individualized learning interventions, allowing more opportunities for effortful struggle with CMR.
|
|
| 8. |
|
|
| 9. |
|
|
| 10. |
- Norqvist, Mathias, 1971-, et al.
(författare)
-
Shifts in student attention on algorithmic and creative practice tasks
- 2023
-
Ingår i: Educational Studies in Mathematics. - : Springer. - 0013-1954 .- 1573-0816.
-
Tidskriftsartikel (refereegranskat)abstract
- In mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior during repetitive practice, an eye-tracking study was conducted with 50 upper secondary and university students. Their eye movements were analyzed to study how the two groups shifted their gaze both within and across 10 task sets. The results show that when a solution method was present, the students reread this every time they solved the task, while only giving minute attention to the illustration that carried information supporting mathematical understanding. Students who practiced with tasks without a solution method seemed to construct a solution method by observing the illustration, which later could be retrieved from memory, making this method more efficient in the long run. We discuss the implications for teaching and how tasks without solution methods can increase student focus on important mathematical properties.
|
|
