What, if any, kind of inferential reasoning can be a legitimate source of justified aesthetic belief? Looking at deductive and inductive reasoning respectively, this paper concludes that only the latter can be formulated so that there is reason to accept the premises as true and thus justify the conclusion. This follows from considerations about the type of generalisations that the arguments rely on. Universal generalisations, on which the type of deductive reasoning under consideration relies, are always victim to counterexamples. Also, they are incompatible with a reasonable conception of the relationship between an aesthetic property and its correlating set of non-aesthetic properties. The generalisations that inductive aesthetic reasoning relies on, however, evade the problems faced by deduction as well as are compatible and a natural complement to the common aesthetic practice of acquaintance having epistemic authority over reasoning. These considerations lead to the conclusion that inductive, while not deductive, aesthetic reasoning is a legitimate source for justified aesthetic belief.

This study assessed the knowledge structure of undergraduate participants related to previously determined critical concepts of Analysis of Variance (ANOVA) by using Pathfinder networks. Three domain experts’ knowledge structures regarding the same concepts were also elicited and averaged to create a referent knowledge structure. The referent knowledge structure served as a basis for formative feedback. Then, each participant’s knowledge structure was compared with the referent structure to identify common, missing, and extraneous links between the two networks. Each participant was provided with individualized written and visual, and multi-media feedback through an online Concept Mapping tool based on the principals of formative assessment and feedback in an attempt to increase their conceptual knowledge of ANOVA. The study was conducted with 67 undergraduate participants from a mid-size university in the United States. Participants completed two data collection tools related to the critical concepts of ANOVA. Later, three different types of feedback around the critical concepts were given to participants in three stages. First, each participant was given visual feedback as a result of the comparison between their own knowledge structures and the referent knowledge structure to highlight similarities and differences between the two. Then, participants were provided with individualized written and multi-media feedback to emphasize conceptual understanding behind ANOVA procedures. This procedure was followed by the re-assessment of participants’ reasoning ability related to ANOVA and knowledge structures related to critical concepts to measure the effect of the intervention. Results suggest that participants both in control and intervention groups had the same level of statistics experience and anxiety before this study indicating that randomization of participants into two different groups was successful. Moreover, women participants reported a statistically significant higher level of statistics anxiety than men, however, it seems that this small difference did not limit their ability to perform required statistical tasks. Further, findings revealed that participants’ conceptual knowledge related to critical concepts of ANOVA increased significantly after the individualized feedback. However, the increase in the conceptual understanding did not help participants to transform this knowledge into more formal understanding related to procedures underlying ANOVA. Moreover, even though, previous similar studies suggest that participants are consistent in using a single strategy for making inferential reasoning across datasets, in the present study, qualitative data analysis revealed that statistics learners demonstrate diverse patterns of inferential reasoning strategies when they were provided with different size of datasets each with varying amount of variability. As a result, findings support the use of an extended framework for describing and measuring the development of participants’ reasoning ability regarding consideration of variation in statistics education.

Informell statistisk inferens ses som ett sätt att undervisa statistik i framtiden för att ge elever möjlighet att utveckla de  statistiska förmågor som krävs i en teknologiskt utvecklad värld. Informella statistiska inferenser handlar om att ge eleverna möjlighet att engagera sig i statistiska diskussioner och problemområden utan att ha den bakomliggande formel statistiska kunskap som krävs för att göra statistiskt säkerställda påståenden. Informella inferentiella resonemang ses som de resonemang som förs av elever, på ett informellt vis, för att i slutändan göra dessa informella inferenser. Syftet med denna studie är att undersöka på vilket sätt, samt i vilken utsträckning aktiviteten: svarta lådan möjliggör  elevers uttryck av ISI och IIR. De två frågeställningarna som fungerar som bas för arbetet är: 1. Vilka aspekter av ISI och IIR kommer till uttryck hos en klass förstaårselever på IB-programmet under aktiviteten med den svarta lådan? Samt 2. I vilken utsträckning? Forskningslitteraturen som använts i denna studie är hämtad ifrån UniSearch och ERIC. Informell statistisk inferens är ett relativt nytt forskningsområde. Således har det inte studerats i någon omfattande mening i en svensk kontext. Dessutom har, så vitt författaren till denna studie vet, ingen forskning genomförts på elever i gymnasieskolan i Sverige. Därav är det svårt att jämföra resultatet av studien med andra studier. Således kan inte heller några generella slutsatser om aktiviteten: svarta lådans möjliggörande för elevers uttryck av ISI och IIR dras.  Studien fann dock att elever uttryckte alla definierade aspekter av ISI under aktiviteten, samt att de använde sig av informella resonemang (IIR) vid konstruktionen av dessa inferenser. / Informal statistical inference (ISI) is emerging as a way to teach statistics in the future in order to give students the opportunity to develop the statistical abilities required in a technologically developed world. ISIs are about giving the students opportunity to engage in statistical discussions and problem areas without the underlying formal statistical  knowledge required to make statistically sound claims. Informal inferential reasoning (IIR) is seen as the reasoning that is given by students, in an informal way, and that leads to these informal statistical inferences. The aim of this study is to examine in what way, and to what extent, the activity: Black Box enables students  expressions ISI and IIR. The two research questions that work as a base for the study are: 1. What aspects of ISI and IIR are expressed by a class of first-year students attending the IB-program during the activity: Black Box? And 2.  To what extent are these aspects expressed? The research literature used in this study was found on UniSearch as well as ERIC. Informal statistical inference is a relatively new research area. Therefore, it has not been studied in any extensive way in a Swedish context. Furthermore, as far as the author of this study is aware, no research at all regarding ISI and IIR  has been made on students attending upper secondary school in Sweden. As a result of this it is difficult to compare the of this study with that of other studies. Furthermore, no general conclusions can be made of the activity: Black Box and its enabling of students expressions of ISI and IIR. The study did, however, find that students expressed all defined  aspects of ISI during the activity and that they used IIR to construct these inferences.