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Exploring student collaboration during Data Generation in the Statistics Classroom: An Inferentialist Perspective
Örebro universitet, Institutionen för naturvetenskap och teknik.ORCID-id: 0000-0002-4185-3208
2019 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This dissertation explores student collaboration during data generation in statistics. The first aim is to put the semantic theory of inferentialism to work and develop a theoretical lens for exploring student collaboration during data generation. The second is to use the previously developed inferentialist lens regarding collaboration to better understand data generation processes in the statistics classroom. Two studies were conducted in Swedish 5th and 7th grade classes. The first involved 7th-grade students collaboratively engaged in experimentation with paper helicopters and their flight durations. The second study involved 5th graders experimenting with paper frogs and their jump lengths. The analyses reveal that inferentialism is a meaningful perspective for exploring student collaboration. One salient theoretical contribution of this thesis is that the inferentialist concept of norms helps avoid the dichotomy between social and individual facets of collaboration and learning that have plagued research on collaboration. However, by using the inferentialism lens, the social and individual can be regarded in their intertwined and dynamic natures. The thesis also illustrates how the formulation of tasks, social conditions, and norms mutually condition students’ learning opportunities. It is also demonstrated that data generation processes can also involve conceptual learning opportunities. The results offer ideas concerning which classroom conditions and manners of formulating tasks may contribute to such conceptual learning opportunities

Abstract [sv]

I denna avhandling utforskas elevers samarbete under datagenerering i statistik. Avhandlingens första syfte är att operationalisera en semantisk teori, inferentialismen, och skapa en teoretisk lins för att utforska elevers samarbeten är de genererar data. Det andra syftet är att utnyttja denna inferentialistiska lins för att förstå datagenereringsprocessen i statistikklassrummet bättre. Två klassrumsstudier har genomförts. Elever i årskurs 7 fick arbeta tillsammans för att undersöka pappershelikoptrar och hur länge de kunde flyga. Elever i årskurs 5 fick samarbeta i ett experiment med pappersgrodor och undersöka hur långt de kunde hoppa. Analyserna visar att inferentialismen är ett värdefullt perspektiv för att utforska elevers samarbete. Ett framträdande teoretiska bidrag från denna avhandling är att det inferentialistiska sättet att konceptualisera normer kan användas för att undvika den dikotomi mellan individuellt och socialt perspektiv som har varit framträdande i tidigare forskning om samarbete i matematikklassrum. Genom att analysera samarbete med hjälp av inferentialistisk teori kan den dynamiska interaktionen mellan det individuella och det sociala undersökas i sin sammanflätade natur. Avhandlingen illustrerar också hur formulering av uppgifter, sociala villkor och normer tillsammans skapar förutsättningar för vilka begrepp som kommer i spel och därmed blir möjliga att lära sig. Det visas också att processen att generera data kan involvera begreppsliga lärandesituationer. Resultaten ger därför indikationer på vilka slags klassrumssituationer och vilka uppgiftsformuleringar som kan bidra till sådant konceptuellt lärande.

sted, utgiver, år, opplag, sider
Örebro: Örebro University , 2019. , s. 134
Serie
Örebro Studies in Mathematics ; 1
Emneord [en]
Inferentialism, Collaboration, Data generation, Statistics
HSV kategori
Identifikatorer
URN: urn:nbn:se:oru:diva-74660ISBN: 978-91-7529-295-3 (tryckt)OAI: oai:DiVA.org:oru-74660DiVA, id: diva2:1322973
Disputas
2019-09-27, Örebro universitet, Teknikhuset, Hörsal T, Fakultetsgatan 1, Örebro, 13:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2019-06-11 Laget: 2019-06-11 Sist oppdatert: 2019-09-05bibliografisk kontrollert
Delarbeid
1. An inferentialist account of students’ collaboration in mathematics education
Åpne denne publikasjonen i ny fane eller vindu >>An inferentialist account of students’ collaboration in mathematics education
2019 (engelsk)Inngår i: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050XArtikkel i tidsskrift (Fagfellevurdert) Epub ahead of print
Abstract [en]

Collaboration is an increasingly popular topic in mathematics education due to its potential to foster students’learning. The purpose of this article is to draw attention to the semantic philosophical theory of inferentialism and its value for investigating students’ collaboration. We suggest that Brandom’s inferentialism can serve as a valuable theoretical resource to overcome certain issues of existing theoretical view-points on student collaboration. In particular, we argue that inferentialism may help to understand the individual and social nature of collaboration as intertwined. We illustrate our inferentialist approach using data from two scenes taken from video-recorded group work sessions from a fifth and seventh grade primary school class in Sweden. The topic in both classes was data generation in statistics.

sted, utgiver, år, opplag, sider
Springer, 2019
Emneord
Collaboration, Data generation, Inferentialism, Norms, Philosophy
HSV kategori
Identifikatorer
urn:nbn:se:oru:diva-76042 (URN)10.1007/s13394-019-00267-0 (DOI)
Forskningsfinansiär
Swedish Research Council, 2012-04811
Tilgjengelig fra: 2019-09-04 Laget: 2019-09-04 Sist oppdatert: 2019-09-04bibliografisk kontrollert
2. Informal Inferential Reasoning and the Social: Understanding Students’ Informal Inferences Through an Inferentialist Epistemology
Åpne denne publikasjonen i ny fane eller vindu >>Informal Inferential Reasoning and the Social: Understanding Students’ Informal Inferences Through an Inferentialist Epistemology
2018 (engelsk)Inngår i: Topics and Trends in Current Statistics Education Research / [ed] Gail Burrill, Dani Ben-Zvi, Springer, 2018, s. 153-171Kapittel i bok, del av antologi (Fagfellevurdert)
Abstract [en]

Informal statistical inference and informal inferential reasoning (IIR) are increasingly gaining significance in statistics education research. What has not sufficiently been dealt with in previous research is the social nature of students’ informal inferences. This chapter presents results from a study investigating seventh grade students’ IIR in an experiment with paper helicopters. It focuses on students’ reasoning on the best rotor blade length, addressing statistical correlation. We study how students draw inferences when working in a group; and how their inferences emerge socially in their IIR. For grasping the reasoning’s social nature and its normativity, we use inferentialism as background theory. The results illustrate how students’ informal inferences are socially negotiated in the group, how students’ perceived norms influence IIR, and what roles statistical concepts play in students’ IIR.

sted, utgiver, år, opplag, sider
Springer, 2018
Serie
ICME-13 Monographs, ISSN 2520-8322, E-ISSN 2520-8330
Emneord
Generalization from data, Inferentialism, Informal inferential reasoning (IIR), Informal statistical inference (ISI), Informal statistical reasoning, Norms, Social
HSV kategori
Identifikatorer
urn:nbn:se:oru:diva-76043 (URN)10.1007/978-3-030-03472-6_7 (DOI)978-3-030-03471-9 (ISBN)978-3-030-03472-6 (ISBN)
Forskningsfinansiär
Swedish Research Council, 2012-04811
Tilgjengelig fra: 2019-09-04 Laget: 2019-09-04 Sist oppdatert: 2019-09-04bibliografisk kontrollert
3. Designing for responsibility and authority in experiment based instruction in mathematics: The case of reasoning with uncertainty
Åpne denne publikasjonen i ny fane eller vindu >>Designing for responsibility and authority in experiment based instruction in mathematics: The case of reasoning with uncertainty
2017 (engelsk)Inngår i: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10) / [ed] Dooley, T.; Gueudet, G., Dublin, Ireland: Institute of Education, Dublin City University, Ireland , 2017, s. 3740-3747Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

This study examines principles of task design concerning the concept of uncertainty in the area of statistics. A purpose is to promote and support students reasoning competency involving the aspects authority and responsibility. By using inferential role semantics as a background theory, we examine students' reasoning by means of how they show authority and responsibility for statements in the reasoning process. Statistical tasks where students generate and analyze their own data formed the basis for this pilot study conducted with seventh grade students in Sweden. The students were able to reflect on how their actions and consequences of their actions influence their reasoning with uncertainty. The study describes the findings, and presents principles to inform the design of innovative learning environments that promote authority and responsibility in reasoning in the domain of uncertainty.

sted, utgiver, år, opplag, sider
Dublin, Ireland: Institute of Education, Dublin City University, Ireland, 2017
Emneord
Design principles, uncertainty, responsibility, authority
HSV kategori
Identifikatorer
urn:nbn:se:oru:diva-76044 (URN)000467053304094 ()978-1-873769-73-7 (ISBN)
Konferanse
10th Congress of the European-Society-for-Research-in-Mathematics-Education (CERME10), Dublin, Ireland, February 1-5, 2017
Tilgjengelig fra: 2019-09-04 Laget: 2019-09-04 Sist oppdatert: 2019-09-04bibliografisk kontrollert
4. Data generation in statistics – both procedural and conceptual: An inferentialist analysis
Åpne denne publikasjonen i ny fane eller vindu >>Data generation in statistics – both procedural and conceptual: An inferentialist analysis
2018 (engelsk)Inngår i: Perspectives on professional development of mathematics teachers: Proceedings of MADIF 11 / [ed] J. Häggström, Y. Liljekvist, J. Bergman Ärlebäck, M. Fahlgren, & O. Olande, Göteborg, Sweden: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2018, s. 191-200Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

Data generation in statistics education is often conducted by the students them-selves; however, the question of what learning opportunities the data generation process offers has only been studied to a small extent. This paper investigates to what extent data generation is an observational and procedural vs. a conceptual activity. We inquire into this question based on an empirical study where eleven year old students measured the jump lengths of paper frogs. Our analysis draws on stu-dents’ discussions in group work, and it uses inferentialism as a background theory. Our results indicate that students’ discussions are conceptual to a certain extent and provide various learning opportunities for the students.

sted, utgiver, år, opplag, sider
Göteborg, Sweden: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2018
Serie
Skrifter från Svensk Förening för MatematikDidaktisk Forskning, ISSN 1651-3274 ; 13
HSV kategori
Identifikatorer
urn:nbn:se:oru:diva-76045 (URN)978-91-984024-2-1 (ISBN)
Konferanse
The eleventh research seminar of the Swedish Society for Research in Mathematics Education (MADIF11), Karlstad, Sweden, January 23–24, 2018
Tilgjengelig fra: 2019-09-04 Laget: 2019-09-04 Sist oppdatert: 2019-09-20bibliografisk kontrollert
5. Authority in students’ peer collaboration in statistics: an empirical study based on inferentialism
Åpne denne publikasjonen i ny fane eller vindu >>Authority in students’ peer collaboration in statistics: an empirical study based on inferentialism
2019 (engelsk)Inngår i: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 24, nr 2, s. 25-47Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Students’ peer collaboration efforts in mathematics and statistics is a topic that has increasingly gained attention in research. In any collaboration, authority relations play a role for how meaning is constituted: Whenever things are discussed and decision sare made, authority is involved in a sense that some arguments or persons may be more convincing and powerful than others. In this article, we investigate how authority changes dynamically in type and in distribution as groups of fifth grade students collaborate in data generation processes. We identify and categorize authority using an epistemological framework, which is based on the philosophical theory of inferentialism. The results show that the three different types of authority described in inferentialism are all identifiable in students’ collaborative work. We also find and categorize further types of authority connected to the statistics group work, some of which are hardly addressed in previous research.

sted, utgiver, år, opplag, sider
Göteborg, Sweden: NOMAD, 2019
HSV kategori
Identifikatorer
urn:nbn:se:oru:diva-76046 (URN)
Tilgjengelig fra: 2019-09-04 Laget: 2019-09-04 Sist oppdatert: 2019-09-05bibliografisk kontrollert

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