Till Örebro universitet

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.

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.

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.

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.

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.

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.