Understanding fractions is fundamental for expanding number knowledge from the whole number system to the rational number system. According to the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics (2000), learning fractions is an important mathematical goal for students in grades three through five in the U.S. Moreover, the NCTM suggests that fraction instruction start in Pre-K and continue through 8th grade. At the same time, the Common Core State Standards for Mathematics (CCSSM) suggests that fraction instruction should occur from Grade 3 to 7. In contrast to the time spent on learning fractions in the U.S., students in China spend a relatively short time learning fractions (Zhang and Siegler, 2022). According to the Chinese national curriculum standards, the Chinese National Mathematics Curriculum Standards (CNMCS) for five-four system, the fundamental fraction concepts are taught in grades 3 and 5 only. However, Chinese students continue to have higher performance on fraction items in international assessments when compared with American students (Fan and Zhu, 2004). Consequently, over the last several years, researchers have investigated subject content knowledge and pedagogical content knowledge of Chinese in-service teachers and pre-service teachers via fraction division (e.g., Li and Huang, 2008; Ma, 1999). There are also studies exploring Chinese written curricula of fraction division (e. g., Li, Zhang, and Ma, 2009). Recently, a quantitative study from Norton, Wilkins, and Xu (2018) investigated the process of Chinese students' construction of fraction knowledge through the lens of fraction schemes, a model established by western scholars Steffe (2002) and his colleague Olive (Steffe and Olive, 2010). However, there is a lack of qualitative research that attempts to use fraction schemes as an explanatory framework to interpret the process of Chinese students' construction of fraction knowledge. The main purpose of this study was to investigate Chinese students' understanding of the fundamental fraction knowledge in terms of their understanding of the "fraction unit," referred to as a "unit fraction" in the U.S., using Steffe and Olive's (2010) fraction schemes as the conceptual framework. A sequential mixed methods design was used in this study. The design included two consecutive phases, namely a quantitative phase followed by a qualitative phase (Creswell and Plano Clark, 2011). During the quantitative phase, five hundred and thirty-four Chinese fourth and fifth grade students were administered an assessment. The quantitative data was first analyzed using a Cochran's Q test to determine if the Chinese participants in this study follow the same progression of fraction schemes as their American peers. Results indicate that the development of fractional schemes among Chinese 4th and 5th grade participants in this study is similar to their U.S. counterparts and the Chinese participants in Norton et al.'s (2018) study regardless of the curricula differences across countries or areas in the same country, the textbook differences, and the language differences. Next, two different analysis of variances (ANOVA), a three-way mixed ANOVA and a two-way repeated measures ANOVA were conducted. The three-way mixed ANOVA was used to inform the researcher as to the fraction schemes these students had constructed before the concept of fraction unit is formally introduced and after the concept of fraction unit is formally introduced. The results showed that the fraction knowledge of the students in this study developed from 4th grade to 5th grade. The analysis of clinical interview data confirmed this conclusion. The two-way repeated measures ANOVA was used to determine which model (i.e., linear, circular, or rectangular) is more or less problematic for Chinese students when solving fraction tasks. The results suggest that generally students' performance on linear model tasks was better than their performance on circular model tasks, but there was no statistically significant difference between performance on circular model and its corresponding rectangular model tasks. The results from the quantitative analyses were also used to screen students to form groups based on their highest available fraction scheme for a clinical interview in the second phase, the qualitative phase. In the qualitative phase, a clinical interview using a think-aloud method was used to gain insight into the role of students' conceptual understanding of the fraction unit in their construction of fraction knowledge. In this phase, students were asked to solve the tasks in the clinical interview protocol using the think aloud method. Two main findings were revealed analyzing the clinical interview data. First, a conceptual understanding of fraction units as well as a conceptual understanding of a unit whole play a critical role in the construction of Chinese students' fraction knowledge. Second, the lack of the understanding of a fraction unit as an iterable unit may be one of the reasons that obstructs students move from part-whole concept of fractions to the measurement concept of fractions. This study also demonstrates that a conceptual understanding of fraction units and the unit whole are a necessary condition for constructing of a conceptual understanding of fraction knowledge. Thus, implications of this study suggest that teachers not only should help students build a conceptual understanding of fraction units, but also need to confirm that students have constructed the concept of what the unit whole is before asking students to identify the fraction units for the referent whole. On the other hand, the tasks used in the present study only include continuous but not discrete wholes. Therefore, future research may focus on investigating how students identify fraction units and in what way the iterating operation could be used when students encounter a discrete whole. / Doctor of Philosophy / Understanding fractions is fundamental for expanding number knowledge from the whole number system to the rational number system. According to the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics (2000), learning fractions is an important mathematical goal for students in grades three through five in the U.S. At the same time, the Common Core State Standards for Mathematics (CCSSM), suggests that fraction instruction should occur from Grade 3 to 7. In contrast to the time spent on learning fractions in the U.S., students in China spend a relatively short time learning fractions (Zhang and Siegler, 2022). According to the Chinese national curriculum standards, the Chinese National Mathematics Curriculum Standards (CNMCS) for five-four system, the fundamental fraction concepts are taught in grades 3 and 5 only. However, Chinese students continue to have higher performance on fraction items in international assessments when compared with American students (Fan and Zhu, 2004). Consequently, over the last several years, researchers have investigated fraction knowledge of Chinese in-service teachers and pre-service teachers via fraction division (e.g., Li and Huang, 2008; Ma, 1999). There are also studies exploring Chinese written curricula of fraction division (e. g., Li, Zhang, and Ma, 2009). Recently, Norton, Wilkins, and Xu (2018) collected and analyzed numerical data from Chinese students and investigated the process of how Chinese students learn fraction knowledge through a model established by western scholars Steffe (2002) and his colleague Olive (Steffe and Olive, 2010). However, there is a lack of research study that attempts to seek an in-depth understanding of how Chinese students learn their fraction knowledge. This study used both numerical data and data gathering from interviewing 29 4th and 5th grade Chinese students. It aimed to investigate Chinese students' understanding of the fundamental fraction knowledge in terms of their understanding of the "fraction unit," referred to as a "unit fraction" in the U.S., using Steffe and Olive's (2010) fraction schemes as the conceptual framework. This study demonstrates that a comprehensive and practical understanding of fraction units and the whole of a given fraction are a necessary condition for building a comprehensive understanding of fraction knowledge. The implications of this study suggest that teachers not only should help students build a comprehensive understanding of fraction units, but also need to confirm that students have built the concept of what the whole of a given fraction is before asking students to identify the fraction units for the referent whole.

abstract: Geoscience educators commonly teach geology by projecting a photograph in front of the class. Geologic photographs often contain animals, people, and inanimate objects that help convey the scale of features in the photograph. Although scale items seem innocuous to instructors and other experts, the presence of such items is distracting and has a profound effect on student learning behavior. To evaluate how students visually interact with distracting scale items in photographs and to determine if cueing or signaling is an effective means to direct students to pertinent information, students were eye tracked while looking at geologically-rich photographs. Eye-tracking data revealed that learners primarily looked at the center of an image, focused on faces of both humans and animals if they were present, and repeatedly returned to looking at the scale item (distractor) for the duration an image was displayed. The presence of a distractor caused learners to look at less of an image than when a distractor was not present. Learners who received signaling tended to look at the distractor less, look at the geology more, and surveyed more of the photograph than learners who did not receive signaling. The San Antonio area in the southern part of the Baja California Peninsula is host to hydrothermal gold deposits. A field study, including drill-core analysis and detailed geologic mapping, was conducted to determine the types of mineralization present, the types of structures present, and the relationship between the two. This investigation revealed that two phases of mineralization have occurred in the area; the first is hydrothermal deposition of gold associated with sulfide deposits and the second is oxidation of sulfides to hematite, goethite, and jarosite. Mineralization varies as a function of depth, whereas sulfides occurring at depth, while minerals indicative of oxidation are limited to shallow depths. A structural analysis revealed that the oldest structures in the study area include low-grade to medium-grade metamorphic foliation and ductile mylonitic shear zones overprinted by brittle-ductile mylonitic fabrics, which were later overprinted by brittle deformation. Both primary and secondary mineralization in the area is restricted to the later brittle features. Alteration-bearing structures have an average NNW strike consistent with northeast-southwest-directed extension, whereas unaltered structures have an average NNE strike consistent with more recent northwest-southeast-directed extension. / Dissertation/Thesis / Ph.D. Geological Sciences 2011

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As the notion of digitalisation make its way further into our lives and society, the educational system must modernise – digitalise – in order to stay relevant. But where is the digitalised school heading? Drawing on governmental policy documents associated with Sweden’s national digitalisation strategy, the study aims to emphasise the political dimension of the strategy in order to analyse more fundamental questions regarding the idea and ideological function of the Swedish educational system in the late modern age. Thus, the analysis follows a conceptual framework of mainly Giddens (1991) late modernity theory in order to shed light on the strategy from the angle of Giddens institutionalised tripartite dynamics of social change: time-space distanciation, disembedding mechanisms and institutional reflexivity. Key findings are that the concept of digitalisation often is formulated as an incentive for stimulating market dynamics, retaining reflexivity and disembedding knowledge. In other words, to preserve and proceed the very nature of the late modern state, through the educational system and its student.

This dissertation is focussing on students’ experiences of assessments, which means that the assessments are related to studying. The assessments particularly investigated are the main types of assessments used in the application and selection for higher education in Sweden – the grading in schools on secondary level, and the Swedish Scholastic Aptitude Test (SweSAT). The literature review is an analysis of previous knowledge, resulting in a model of orientations to studying. The empirical investigation consists of interviews with 100 students in upper secondary school, municipal adult education and folk high schools. The interviews are analysed with a phenomenographic approach, and the analysis results in categories describing ways of experiencing what it means to study, ways of experiencing the grades, and the SweSAT. In addition to this, the analysis gives a description of relations between components within categories, relations between categories, and relations between phenomena. The main patterns in the students’ experiences of the assessments are the following: The different categories, describing the experiences of the assessments per se, are focussing on assessment of performance, assessment of personal qualities (including developed knowledge), or uncertainty in relation to the assessment. There are four main aspects of the students’ experiences of the value of assessments, i.e., the relation to future plans, the relation to the student’s personal context, the possibility to influence your result, and the relation to other assessments used in the selection. The final result of the empirical investigation is a reconstructed model of five orientations to studying, where the empirical results are integrated with previous knowledge. The five categories are the knowledge orientation, the duty orientation, the participation orientation, the qualification orientation, and the resistance orientation. These orientations are also described as adaptive and/or non-adaptive in relation to the demands of the education. A further analysis in relation to three social science perspectives shows how assessments can contribute to the colonization of the educational lifeworld, how assessments can be seen as instruments of discipline, and how assessments can be seen as disembedding mechanisms.