This study examined the use of ranking task exercises in physics as a means to elicit student's quantitative and/or qualitative understanding of four different physics concepts. Each ranking task exercise in physics asked students to examine several different scenarios that contain a number of quantitative features and then arrange the scenarios in an ordered sequence according to some other quantitative feature. In this study, students completed four different ranking task exercises as part of their coursework in their high school physics class. The responses of students to these ranking task exercises were scored, analyzed, and categorized according to the extent to which a student's response was primarily quantitative or primarily qualitative in nature. The results show that while students relied on a combination of both qualitative and quantitative representations as they completed the exercises, the majority of students used qualitative representations in their solutions to the ranking task exercises in physics. While the students' qualitative and quantitative representations supported the students' rankings of the scenarios in each ranking task exercise, the qualitative representations used by the students provided insight into the student's current understanding of the physics concepts being investigated. The findings suggest that regardless of the representation used by the student to complete the ranking task exercise, students had difficulty in correctly ranking the scenarios in all of the ranking task exercises used in this study. While the students used both quantitative and qualitative representations in their solutions to ranking task exercises in physics that contained two quantitative variables, the study found that students relied exclusively on qualitative representations in their solutions to the ranking task exercise in physics that contained four quantitative variables. / CITE/Mathematics and Science Education

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Validating claims from misinformation is a highly challenging task that involves understanding how each factual assertion within the claim relates to a set of trusted source materials. Existing approaches often make coarse-grained predictions but fail to identify the specific aspects of the claim that are troublesome and the specific evidence relied upon. In this paper, we introduce a method and new benchmark for this challenging task. Our method predicts the fine-grained logical relationship of each aspect of the claim from a set of multimodal documents, which include text, image(s), video(s), and audio(s). We also introduce a new benchmark (M^3DC) of claims requiring multimodal multidocument reasoning, which we construct using a novel claim synthesis technique. Experiments show that our approach significantly outperforms state-of-the-art baselines on this challenging task on two benchmarks while providing finer-grained predictions, explanations, and evidence. / Master of Science / In today's world, we are constantly bombarded with information from various sources, making it difficult to distinguish between what is true and what is false. Validating claims and determining their truthfulness is an essential task that helps us separate facts from fiction, but it can be a time-consuming and challenging process. Current methods often fail to pinpoint the specific parts of a claim that are problematic and the evidence used to support or refute them. In this study, we present a new method and benchmark for fact-checking claims using multiple types of information sources, including text, images, videos, and audio. Our approach analyzes each aspect of a claim and predicts how it logically relates to the available evidence from these diverse sources. This allows us to provide more detailed and accurate assessments of the claim's validity. We also introduce a new benchmark dataset called M^3DC, which consists of claims that require reasoning across multiple sources and types of information. To create this dataset, we developed a novel technique for synthesizing claims that mimic real-world scenarios. Our experiments show that our method significantly outperforms existing state-of-the-art approaches on two benchmarks while providing more fine-grained predictions, explanations, and evidence. This research contributes to the ongoing effort to combat misinformation and fake news by providing a more comprehensive and effective approach to fact-checking claims.

The literature on analogical reasoning has established several main points of consensus, or rules about how the process works and what behaviors it produces. The first rule is that the process is employed almost universally. Second, its utilization is extremely prominent in novel situations, such as foreign policy decisions. These rules being established, it must be inferred that almost all foreign policy makers utilize analogical reasoning to some extent when faced with a unique situation. Another rule established is that once a person has defined a situation in terms of the analogy and developed an appropriate policy, he/she will rarely change his/her opinion. However, it has been well established by the groupthink theory that, when placed in a group setting, individuals can be dissuaded from their original assessments of the necessary responses to a situation. Thus it must be inferred that group processes, at least the groupthink syndrome, and analogical reasoning interact. Consequently, in order to fully understand a policy failure, which has been credited to groupthink, it is necessary to examine what cognitive processes led to both the original formulation and the adoption of the policy. Exactly how these processes interact remains unstudied. Although the literature reviewed in this study is not comprehensive on either subject, it covers the more authoritative and critically reviewed literature. Also, extensive efforts to find a similar argument to the one presented here offered few results. This implies that the correlation, if any, remains relatively understudied. Therefore, there is a need for the work at hand, in order to further understand how these prevalent cognitive processes have affected foreign policy decisions and the implications for the future.

<p>Students’ use of superficial reasoning seems to be a main reason for learning difficulties in mathematics. It is therefore important to investigate the reasons for this use and the components that may affect students’ mathematical reasoning development. Assessments have been claimed to be a component that significantly may influence students’ learning.</p><p>The purpose of the study in Paper 1 was to investigate the kind of mathematical reasoning that is required to successfully solve tasks in the written tests students encounter in their learning environment. This study showed that a majority of the tasks in teacher-made assessment could be solved successfully by using only imitative reasoning. The national tests however required creative mathematically founded reasoning to a much higher extent.</p><p>The question about what kind of reasoning the students really use, regardless of what theoretically has been claimed to be required on these tests, still remains. This question is investigated in Paper 2.</p><p>Here is also the relation between the theoretically established reasoning requirements, i.e. the kind of reasoning the students have to use in order to successfully solve included tasks, and the reasoning actually used by students studied. The results showed that the students to large extent did apply the same reasoning as were required, which means that the framework and analysis procedure can be valuable tools when developing tests. It also strengthens many of the results throughout this thesis. A consequence of this concordance is that as in the case with national tests with high demands regarding reasoning also resulted in a higher use of such reasoning, i.e. creative mathematically founded reasoning. Paper 2 can thus be seen to have validated the used framework and the analysis procedure for establishing these requirements.</p><p>Paper 3 investigates the reasons for why the teacher-made tests emphasises low-quality reasoning found in paper I. In short the study showed that the high degree of tasks solvable by imitative reasoning in teacher-made tests seems explainable by amalgamating the following</p><p>factors: (i) Limited awareness of differences in reasoning requirements, (ii) low expectations of students abilities and (iii) the desire to get students passing the tests, which was believed easier when excluding creative reasoning from the tests.</p><p>Information about these reasons is decisive for the possibilities of changing this emphasis. Results from this study can also be used heuristically to explain some of the results found in paper 4, concerning those teachers that did not seem to be influenced by the national tests.</p><p>There are many suggestions in the literature that high-stake tests affect practice in the classroom. Therefore, the national tests may influence teachers in their development of classroom tests. Findings from paper I suggests that this proposed impact seem to have had a limited effect, at least regarding the kind of reasoning required to solve included tasks. What about other competencies described in the policy documents?</p><p>Paper 4 investigates if the Swedish national tests have had such an impact on teacher-made classroom assessment. Results showed that impact in terms of similar distribution of tested competences is very limited. The study however showed the existence of impact from the national tests on teachers test development and how this impact may operate.</p>

Students’ use of superficial reasoning seems to be a main reason for learning difficulties in mathematics. It is therefore important to investigate the reasons for this use and the components that may affect students’ mathematical reasoning development. Assessments have been claimed to be a component that significantly may influence students’ learning. The purpose of the study in Paper 1 was to investigate the kind of mathematical reasoning that is required to successfully solve tasks in the written tests students encounter in their learning environment. This study showed that a majority of the tasks in teacher-made assessment could be solved successfully by using only imitative reasoning. The national tests however required creative mathematically founded reasoning to a much higher extent. The question about what kind of reasoning the students really use, regardless of what theoretically has been claimed to be required on these tests, still remains. This question is investigated in Paper 2. Here is also the relation between the theoretically established reasoning requirements, i.e. the kind of reasoning the students have to use in order to successfully solve included tasks, and the reasoning actually used by students studied. The results showed that the students to large extent did apply the same reasoning as were required, which means that the framework and analysis procedure can be valuable tools when developing tests. It also strengthens many of the results throughout this thesis. A consequence of this concordance is that as in the case with national tests with high demands regarding reasoning also resulted in a higher use of such reasoning, i.e. creative mathematically founded reasoning. Paper 2 can thus be seen to have validated the used framework and the analysis procedure for establishing these requirements. Paper 3 investigates the reasons for why the teacher-made tests emphasises low-quality reasoning found in paper I. In short the study showed that the high degree of tasks solvable by imitative reasoning in teacher-made tests seems explainable by amalgamating the following factors: (i) Limited awareness of differences in reasoning requirements, (ii) low expectations of students abilities and (iii) the desire to get students passing the tests, which was believed easier when excluding creative reasoning from the tests. Information about these reasons is decisive for the possibilities of changing this emphasis. Results from this study can also be used heuristically to explain some of the results found in paper 4, concerning those teachers that did not seem to be influenced by the national tests. There are many suggestions in the literature that high-stake tests affect practice in the classroom. Therefore, the national tests may influence teachers in their development of classroom tests. Findings from paper I suggests that this proposed impact seem to have had a limited effect, at least regarding the kind of reasoning required to solve included tasks. What about other competencies described in the policy documents? Paper 4 investigates if the Swedish national tests have had such an impact on teacher-made classroom assessment. Results showed that impact in terms of similar distribution of tested competences is very limited. The study however showed the existence of impact from the national tests on teachers test development and how this impact may operate.

This exploratory case study was undertaken to obtain a greater understanding of the difficulties that physics students face when solving image-object projections in optics problems. This was carried out by studying the students’ reasoning when facing new kinds of problem settings using the refraction of light and the position of the virtual image and the real object as the frame for the research. The results show that there is more than one reasoning possibility that is feasible for students to use when dealing with the same problem. The results also illustrate how several different ways of reasoning may be simultaneously needed to solve a refraction problem. The different kinds of reasoning have been referred to as reasoning categories in this study. The analysis illustrates how the categories complement each other, and the use of many reasoning categories is shown to be fruitful. However, the vast majority of the participants made contradicting answer selections when solving similar problems by using contradicting reasoning approaches. This lack of consistency in the participants’ reasoning could indicate that they have a fragmentary understanding of optics in general. Both the capability to link reasoning approaches together, as well as the affordances that different modes of representations offer, are needed for the construction of a better conceptual understanding. Only mastering a few ways of reasoning and a few modes of representation could lead to fragmented knowledge, which, in turn leads to making problem solving really challenging. One purpose of this study was to find out if reasoning categories and modes of representations are essentially linked. If so, then the reasoning categories would be determined by the representation of the problem. The analysis shows that there is a connection, but that there are also other factors at play.

Syftet med denna studie är att undersöka hur lärare ser på förmågan att föra och följa matematiska resonemang och hur lärares matematikundervisning kan organiseras för att möjliggöra för elever att främja denna förmåga. Vi har använt oss av ett ramverk beskrivet av Herbert m.fl. (2015) om lågstatielärares uppfattning om matematiska resonemang. Vi har även utformat ett eget ramverk baserat på vad forskning visar främjar elevers matematiska resoenamngsförmåga och utifrån det genomfört en deduktiv innehållsanalys. Genom semisturkturerade intervjuer har 12 lärare i årskurs 2-3 gett sin syn på matematiska resonemang och hur de organiserar undervisningen för att främja elevers matematiska resonemangsförmåga. Resultatet visar att lärare ser resoneamng som svårdefinerat men att de ändå bedriver en undervisning som möjliggör för eleverna att främja denna förmåga. Vidare visade resultatet att undervisningen lärarna bedrev visade på djupare uppfattning av matematiska resonemang än vad de själva uttryckte. Däremot ser de flesta lärare att matematikboken inte ger eleverna möjlighter till matematiska resonemang. Några lärare lyfter materialet Sluta räkna-serien av Ulla Öberg som särskilt gynnsamt för att utveckla elevers matematiska resonemangsförmåga. Det som dominerar lärarnas undervisning i arbetet med matematiska resonemang är problemlösning, öppna uppgifter, arbete i par eller grupp samt arbete med konkret material. / The aim of this study is to examine how teachers view the ability to make and follow mathematical reasoning and how teachers' mathematical lessons can be organized to enable students to develop this ability. We have used the framework described by Herbert et al. (2015) for primary teachers' perceptions of mathematical reasoning. We have also created our own framework based on what research shows fosters students' matehematical reasoning ability and based on this made a deductive content analysis. Through semi-structured interviews 12 teachers in grades 2-3 gave their views on mathematical reasoning and how they organize their lessons to foster students' mathematical reasoning ability. The results show that teachers view reasoning as hard to define but that they still conduct lessons that make it possible for students to foster this ability. Furtthermore, the results show that the lessons the teachers conduct show a higher perception of mathematical reasoning than what they themselves express. Most of the teachers express that the mathematical textbook does not give students the possibility for mathematical reasoning. Some teachers mention the material Sluta räkna-serien by Ulla Öberg as especially effective to foster students' mathematical reasoning ability. What dominates the teachers' lessons when working with mathematical reasoning are problem solving, open tasks, working in pairs or groups and working with concrete material.

Skolverket (2022a) betonar vikten av att elever utvecklar sin resonemangsförmåga, som är en av de fem angivna förmågorna i matematikens kursplan. Trots kursplanens betoning visar forskning att elever ofta spenderar mycket tid på självständigt arbete med läroböcker under matematikundervisningen. Därför undersöker vår studie hur elever i årskurs 1 resonerar när de arbetar med uppgifter som anses främja ett kreativt matematiskt resonemang (KMR). Vidare undersöktes möjligheter och utmaningar med att använda sådana uppgifter. Som teoretiskt ramverk användes Lithners (2008) kategorisering av olika resonemang samt Gray och Talls (1994) teori om proceptuellt tänkande för att besvara studiens frågeställningar. Utöver dessa teorier användes aven Vygoskijs teori för bredare förståelse av studiens resultat (Säljö, 2020). Studien identifierade möjligheter med att använda arbetssättet som metod, om den anpassas och stöttas på rätt sätt. Detta kan hjälpa eleverna att utveckla djupare matematiska insikter samt förbättra sin resonemangsförmåga. En utmaning med arbetssättet var att hitta en uppgift som betraktas utmanade för alla elever trots skillnaderna i deras förkunskaper. Metoden som användes för att samla in empirin var "task-based interviews". Eleverna engagerades i matematiska aktiviteter och ombads tänka högt för att synliggöra deras tankeprocess. Resultaten visade att trots att det var utmanade att tillämpa Lithners (2008) ramverk på yngre elever så kunde de flesta föra KMR. / The Swedish National Agency (2002a) for Education emphasizes the importance of students developing their reasoning skills, which is one of the five competencies outlined in the mathematics curriculum. Despite the curriculum's emphasis, research shows that students often spend a lot of time working independently with textbooks during mathematics instruction. Therefore, our study examines how first-grade students reason when working on tasks designed to promote creative mathematical reasoning (CMR). Additionally, the study explores the opportunities and challenges associated with using such tasks. To answer the research questions, Lithner's (2008) categorization of different types of reasoning and Gray and Tall's (1994) theory of proceptual thinking were used as theoretical frameworks. Vygotsky's theory was also employed for a broader understanding of the study's results (Säljö, 2020). The study identified opportunities for using this approach as a method, provided it is adapted and supported appropriately. This can help students develop deeper mathematical insights and improve their reasoning skills. One challenge with this approach was finding a task that is challenging for all students despite differences in their prior knowledge. The method used to collect empirical data was "task-based interviews." Students engaged in mathematical activities and were asked to think aloud to reveal their thought processes. The results showed that although it was challenging to apply Lithner's (2008) framework to younger students, most were able to engage in CMR.

Designing and developing complex engineering systems is a collaborative effort. In Model-Based Systems Engineering (MBSE), this collaboration is supported through the use of formal, computer-interpretable models, allowing stakeholders to address concerns using well-defined modeling languages. However, because concerns cannot be separated completely, implicit relationships and dependencies among the various models describing a system are unavoidable. Given that models are typically co-evolved and only weakly integrated, inconsistencies in the agglomeration of the information and knowledge encoded in the various models are frequently observed. The challenge is to identify such inconsistencies in an automated fashion. In this research, a probabilistic (Bayesian) approach to abductive reasoning about the existence of specific types of inconsistencies and, in the process, semantic overlaps (relationships and dependencies) in sets of heterogeneous models is presented. A prior belief about the manifestation of a particular type of inconsistency is updated with evidence, which is collected by extracting specific features from the models by means of pattern matching. Inference results are then utilized to improve future predictions by means of automated learning. The effectiveness and efficiency of the approach is evaluated through a theoretical complexity analysis of the underlying algorithms, and through application to a case study. Insights gained from the experiments conducted, as well as the results from a comparison to the state-of-the-art have demonstrated that the proposed method is a significant improvement over the status quo of inconsistency identification in MBSE.