Advances in technology and the continued emergence of the Web as a major source of global information have encouraged tertiary educators to take advantage of this growing array of resources and move beyond traditional face-to-face and distance education correspondence modes toward a rich technology-mediated learning environment. Moreover, ready access to multimedia at the desk-top has provided an opportunity for educators to develop flexible, engaging and interactive learning resources incorporating multimedia and hypermedia. This study investigates pedagogical, individual and institutional factors influencing the adoption and integration of educational technology by academics at a regional Australian university for the purpose of developing interactive multimodal technology-mediated distance education courses. These courses include a range of multimodal learning objects and multiple representations of content in order to cater for different learning styles and modal preferences. The findings of this study revealed that a range of pedagogical, individual and institutional factors influence academics' development of interactive multimodal technology-mediated distance education courses. Implications for distance education providers and individual academics arising from these factors and subsequent recommendations are presented.

Students of chemistry encounter difficulties due to its abstract nature and the need to understand and communicate its concepts on macro, submicro, and symbolic levels using a range of representations and representational modes. Research suggests that when students are required to use multiple representations they have difficulties in understanding individual representations and in negotiating meaning through their use. This study sought to address these issues through the application of digital technologies. The main areas of research that provided a theoretical framework for this study were multiple representations in chemistry education and writing-to-learn in science. Other research in these areas has suggested that a better understanding of multiple representations might enhance students’ chemical literacy; however, limited research has investigated the impact of using digital technologies to create multimodal texts on students’ learning in chemistry, particularly the development of students’ skills in generating and integrating multiple representations. Until recently, much of the writing-to-learn research has focused on written composition. The knowledge-transforming model was proposed by Bereiter and Scardamalia (1987) to explain the influence of written composition on knowledge construction. However, having been developed prior to the time when students had ready access to digital technologies and a consequent capacity to create multimedia and digital texts, this model does not account for the production of such multimodal texts. This study examined the effect of learning experiences that utilised digital technologies to support students in using multiple representations and through writing-to-learn activities to create multimodal texts on learning outcomes in chemistry. The study was conducted in a metropolitan public co-educational high school in Queensland, Australia. Two Year 11 chemistry classes participated in the study, which was conducted in the first term of a 2-year course in which students learn chemistry as a separate discipline. The study consisted of a pilot study and an intervention study with two phases. The pilot study was used to trial the learning activities and data collection instruments and to gain an insight into instructional approaches that might be appropriate for the study. Phase 1 of the intervention study employed a pretest–posttest design. In this phase, students learned about chemical bonding and structure and their effects on the properties and behaviours of different materials. They also learned about the multiple representations used to understand and communicate about chemical bonding and structure. Within a modified crossover design, Phase 2 of the study employed mixed methods to compare the effects on learning outcomes when they created two different scientific texts: a digital poster and a laboratory report. Both text types required students to integrate multiple representations to report on their learning during laboratory investigations. These text types were chosen because they are commonly used by scientists to communicate their experimental findings. In Phase 1, students engaged in computer-based inquiries using both molecular modelling and simulation software to investigate phenomena such as intra- and inter-molecular bonding and their effects on properties, the differences between various types of bonds, the multiple representations used to describe and investigate bonding and structure, and to present their understanding to others. In Phase 2, students used a range of scaffolding resources to design and carry out two inquiries about the chemistry of biomaterials. In the first inquiry, students made and compared the properties of two different bioplastic films; in the second, students compared the relative fermentation rates of a range of carbohydrates. In both inquiries, students were required to report their findings and explain them on the submicro level using appropriate representations. Scaffolds included Science Writing Heuristics, which explicitly required students to consider which multiple representations would support their claims and explanations of data; digital resources for selecting, modifying, or creating representations; and genre templates. Pretest–posttest comparisons for both phases showed that the instructional approaches and resources used were effective for enhancing students’ learning outcomes. In all comparisons, the posttest performances were significantly higher. In the first phase, several of the identified alternative or missing conceptions about chemical bonding were effectively addressed, and in both phases, students’ conceptual understanding and their representational competencies were enhanced. The pretest–posttest comparisons for Phase 2 suggested that creating a diversified text – a digital poster – for explaining experimental results is at least as effective for enhancing understanding and representational competencies as creating a more traditional laboratory report. Other data were analysed to gain an insight into how or why the instructional strategies and resources used might have been effective. The student interviews revealed a number of advantages of using digital technologies, including promotion of higher order thinking, enhanced motivation and interest, the capacity of digital technologies to support and enhance visualisation, and the production of multiple representations in multiple modes. Students suggested that the digital resources allowed them to make links between macroscopic, molecular, and symbolic levels and to include a range of representations in their explanations. The evaluation questionnaire revealed similar trends. Analysis of the students’ texts suggested that the approaches used in Phase 2 were effective in supporting students’ content and rhetorical problem solving and the interactions between the two. Students utilised a range of representations, particularly structural diagrams, when making explanations of their macroscopic data on the submicro level. This study has implications for the instructional approaches used by chemistry teachers because it showed that integrating digital technologies into learning environments is effective when introducing students to the multiple representations used in chemistry and in the development of students’ chemical literacies. It also contributes to writing-to-learn research by focusing on multimodal communication and the benefits of creating multimodal texts for presenting, organising, and explaining data, and for representing knowledge. Significant findings of the study relate to the importance of digital technologies in generating multimodal texts and representations for instruction, scaffolding, and in student-centred inquiry-based learning. Further research might focus on the use of such resources for addressing other commonly identified alternative conceptions, the creation of other multimodal text types, the use of other digital technologies or authoring tools, or on the development of teachers’ technological pedagogical content knowledge, which is required for effective classroom implementation of these resources and strategies.

Students of chemistry encounter difficulties due to its abstract nature and the need to understand and communicate its concepts on macro, submicro, and symbolic levels using a range of representations and representational modes. Research suggests that when students are required to use multiple representations they have difficulties in understanding individual representations and in negotiating meaning through their use. This study sought to address these issues through the application of digital technologies. The main areas of research that provided a theoretical framework for this study were multiple representations in chemistry education and writing-to-learn in science. Other research in these areas has suggested that a better understanding of multiple representations might enhance students’ chemical literacy; however, limited research has investigated the impact of using digital technologies to create multimodal texts on students’ learning in chemistry, particularly the development of students’ skills in generating and integrating multiple representations. Until recently, much of the writing-to-learn research has focused on written composition. The knowledge-transforming model was proposed by Bereiter and Scardamalia (1987) to explain the influence of written composition on knowledge construction. However, having been developed prior to the time when students had ready access to digital technologies and a consequent capacity to create multimedia and digital texts, this model does not account for the production of such multimodal texts. This study examined the effect of learning experiences that utilised digital technologies to support students in using multiple representations and through writing-to-learn activities to create multimodal texts on learning outcomes in chemistry. The study was conducted in a metropolitan public co-educational high school in Queensland, Australia. Two Year 11 chemistry classes participated in the study, which was conducted in the first term of a 2-year course in which students learn chemistry as a separate discipline. The study consisted of a pilot study and an intervention study with two phases. The pilot study was used to trial the learning activities and data collection instruments and to gain an insight into instructional approaches that might be appropriate for the study. Phase 1 of the intervention study employed a pretest–posttest design. In this phase, students learned about chemical bonding and structure and their effects on the properties and behaviours of different materials. They also learned about the multiple representations used to understand and communicate about chemical bonding and structure. Within a modified crossover design, Phase 2 of the study employed mixed methods to compare the effects on learning outcomes when they created two different scientific texts: a digital poster and a laboratory report. Both text types required students to integrate multiple representations to report on their learning during laboratory investigations. These text types were chosen because they are commonly used by scientists to communicate their experimental findings. In Phase 1, students engaged in computer-based inquiries using both molecular modelling and simulation software to investigate phenomena such as intra- and inter-molecular bonding and their effects on properties, the differences between various types of bonds, the multiple representations used to describe and investigate bonding and structure, and to present their understanding to others. In Phase 2, students used a range of scaffolding resources to design and carry out two inquiries about the chemistry of biomaterials. In the first inquiry, students made and compared the properties of two different bioplastic films; in the second, students compared the relative fermentation rates of a range of carbohydrates. In both inquiries, students were required to report their findings and explain them on the submicro level using appropriate representations. Scaffolds included Science Writing Heuristics, which explicitly required students to consider which multiple representations would support their claims and explanations of data; digital resources for selecting, modifying, or creating representations; and genre templates. Pretest–posttest comparisons for both phases showed that the instructional approaches and resources used were effective for enhancing students’ learning outcomes. In all comparisons, the posttest performances were significantly higher. In the first phase, several of the identified alternative or missing conceptions about chemical bonding were effectively addressed, and in both phases, students’ conceptual understanding and their representational competencies were enhanced. The pretest–posttest comparisons for Phase 2 suggested that creating a diversified text – a digital poster – for explaining experimental results is at least as effective for enhancing understanding and representational competencies as creating a more traditional laboratory report. Other data were analysed to gain an insight into how or why the instructional strategies and resources used might have been effective. The student interviews revealed a number of advantages of using digital technologies, including promotion of higher order thinking, enhanced motivation and interest, the capacity of digital technologies to support and enhance visualisation, and the production of multiple representations in multiple modes. Students suggested that the digital resources allowed them to make links between macroscopic, molecular, and symbolic levels and to include a range of representations in their explanations. The evaluation questionnaire revealed similar trends. Analysis of the students’ texts suggested that the approaches used in Phase 2 were effective in supporting students’ content and rhetorical problem solving and the interactions between the two. Students utilised a range of representations, particularly structural diagrams, when making explanations of their macroscopic data on the submicro level. This study has implications for the instructional approaches used by chemistry teachers because it showed that integrating digital technologies into learning environments is effective when introducing students to the multiple representations used in chemistry and in the development of students’ chemical literacies. It also contributes to writing-to-learn research by focusing on multimodal communication and the benefits of creating multimodal texts for presenting, organising, and explaining data, and for representing knowledge. Significant findings of the study relate to the importance of digital technologies in generating multimodal texts and representations for instruction, scaffolding, and in student-centred inquiry-based learning. Further research might focus on the use of such resources for addressing other commonly identified alternative conceptions, the creation of other multimodal text types, the use of other digital technologies or authoring tools, or on the development of teachers’ technological pedagogical content knowledge, which is required for effective classroom implementation of these resources and strategies.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Esta pesquisa teve por objetivo analisar as contribuiÃÃes de metodologia desenvolvida, com suporte de tecnologias digitais, para o desenvolvimento do conceito de covariaÃÃo presente nas estruturas multiplicativas. Para isso, foram realizadas anÃlises das situaÃÃes presentes no campo conceitual multiplicativo, verificando a ocorrÃncia, ou nÃo, da covariaÃÃo. O desenvolvimento das atividades foi fundamentado em estudos relacionados Ãs contribuiÃÃes das mÃltiplas representaÃÃes para a aprendizagem e da abordagem seres-humanos-com-mÃdias. Utilizou-se, como metodologia, a pesquisa de intervenÃÃo. A investigaÃÃo foi realizada em uma Escola Municipal de Tempo Integral, localizada no municÃpio de Fortaleza - CearÃ, com estudantes de uma das turmas do 6 ano do Ensino Fundamental. A turma de alunos foi dividida em: Grupo Controle (GC), com 15 alunos e Grupo Experimental (GE), com 12 alunos. A investigaÃÃo foi dividida em trÃs etapas: prÃ-teste, intervenÃÃo e pÃs-teste. Todos os alunos, dos dois grupos, participaram do prÃ-teste e do pÃs-teste, aplicados individualmente e sem uso do computador. Tendo sido aplicados para diagnosticar os conhecimentos dos alunos em relaÃÃo à compreensÃo de situaÃÃes de proporÃÃo simples, de proporÃÃo mÃltipla, de proporÃÃo dupla, de interpretaÃÃo e construÃÃo de grÃficos lineares e compreensÃo de padrÃo de tabelas. A intervenÃÃo aconteceu apenas com o GE, no momento das aulas de MatemÃtica. Essa etapa teve duraÃÃo de 3 meses, com 18 encontros. As atividades desenvolvidas para esses encontros, utilizavam tecnologias digitais como: software Geogebra, recurso digital Equilibrando proporÃÃes, aplicativo online Cacoo, WhatsApp e blog. O GC manteve as aulas de MatemÃtica e de disciplinas eletivas, nos mesmos horÃrios do GE. Os dados foram analisados de modo a conhecer e compreender o desempenho dos alunos antes e apÃs as atividades; os teoremas-em-aÃÃo mobilizados durante a intervenÃÃo e suas evoluÃÃes; e as contribuiÃÃes das tecnologias usadas para a compreensÃo do conceito de covariaÃÃo. Os estudantes submetidos à intervenÃÃo apresentaram, estatisticamente, um desempenho superior, quando comparados aos estudantes do GC, demonstrando a eficÃcia da metodologia. Constatou-se, ainda, a modificaÃÃo de esquemas por meio de estratÃgias mais elaboradas, mesmo para situaÃÃes que jà eram conhecidas pelos estudantes do GE. As tecnologias digitais utilizadas contribuÃram para a compreensÃo da invariÃncia e da covariaÃÃo, ao relacionar mÃltiplas representaÃÃes de forma dinÃmica, possibilitar a produÃÃo de conhecimento e a significaÃÃo de contextos sociais e matemÃticos.

There has been a call to reform science education to integrate scientific thinking practices, such as data interpretation and modeling, with learning content in science classrooms. This call to reform has taken place in both K-12 science education through Next Generation Science Standards and undergraduate education through AAAS initiative Vision and Change in Undergraduate Biology Education. This dissertation work examines undergraduate students' learning of multiple scientific thinking skills in a curricular format called Teaching Real data Interpretation with Models (TRIM) applied to a large-enrollment course in Cellular and Developmental Biology. In TRIM, students are provided worksheets in groups and tasked to interpret authentic biological data. Importantly, groups are tasked to relate their data interpretations to a 2D visual model representation of the relevant biological process. This dissertation work consists of two studies with the overarching question: How do students use model representations to interpret data interpretations? In the first study, we primarily describe how students learn to navigate and interpret discipline-based data representations. We found the majority of groups could construct quality written data interpretations. Qualitative coding analysis on group discourse found students relied on strategies such as decoding the data representation and noticing data patterns together to construct claims. Claims were refined through spontaneous collaborative argumentation. We also found groups used the provided model to connect their data inferences to a biological context. In the second study, we primarily target our analysis on how individual students relate their data interpretations to different modeling tasks, including student-generation of their own model drawing. I interviewed students one-on-one as they worked through TRIM-style worksheets. From iterative qualitative analysis of transcripts and collected video on hand movements, I characterize the forms of reasoning at play at the interface of data and model representations. I propose a model at the end of Study 2 describing three modes of reasoning in data abstraction into models. I found when relating between data and models, students needed to link signs in both representations to a common referent in the real-world phenomenon. Establishing this sign-referent relationship seemed to depend on bringing in outside mechanistic information about the phenomenon. Once a mechanism was established, students could fluidly move between data and model representations through mechanistic reasoning. Thus data abstraction seems to rely on mechanistic reasoning with models. The findings from this dissertation work support the feasibility of student development of multiple scientific thinking skills within a large lecture course, and provide targets for curriculum and assignment designs centered on teaching higher order reasoning skills.

Calculus at the university level is taken by thousands of undergraduate students each year. However, a significant number of students struggle with the subject, resulting in poor problem solving, low achievement, and high failure rates in the calculus courses overall (e.g., Kaput, 1994; Szydlik, 2000; Tall, 1985; Tall & Ramos, 2004; White & Mitchelmore, 1996). This is cause for concern as the lack of success in university calculus creates further barriers for students who require the course for their programs of study. This study examines this issue from the perspective of Tall’s Three Worlds of Mathematics (Tall, 2004a, 2004b, 2008), a theory of mathematics and mathematical cognitive development. A fundamental argument of Tall’s theory suggests that connecting between the different mathematical worlds, named the Embodied-Conceptual, Symbolic-Proceptual, and Formal-Axiomatic worlds, is essential for full cognitive development and understanding of mathematical concepts. Working from this perspective, this research examined, through the use of calculus task questions and semi-structured interviews, how fifteen undergraduate calculus students made connections between the different mathematical worlds for the calculus topics of limits and derivatives. The analysis of the findings suggests that how the students make connections can be described by eight different Response Categories. The study also found that how the participants made connections between mathematical worlds might be influenced by the type of questions that are asked and their experience in calculus courses. I infer that these Response Categories have significance for this study and offer potential for further study and educational practice. I conclude by identifying areas of further research in regards to calculus achievement, the Response Categories, and other findings such as a more detailed study of the influence of experience.

Worldwide, an influx of immigration, has increased the heterogeneity of our classrooms. In light of today’s heightened teacher accountability, standards and high-stakes assessment, traditional ways of teaching need to change in order to effectively serve the needs of our culturally and linguistically diverse students. Therefore, a qualitative-interpretive study was conducted with ten science teachers working in six private, international schools based in Portugal, Spain, Switzerland, and Belgium with a focus on teacher perceptions, beliefs, teaching practices, and instructional resources used to teach science to English Language Learners (ELLs). Emphasis was placed on the specific teaching modalities and resources that science teachers use to support ELLs in their classrooms. It also addressed the needs of teachers to effectively teach science to ELLs. In response to the research questions, the thematic analysis revealed that the teachers working in these schools had a good awareness of ELL needs in science and wanted to make a difference for these learners. They perceived ELLs as quiet, but hardworking and motivated students. To some degree, the teachers used all seven modalities of teaching: reading, writing, speaking, listening, doing, interpreting, and representing, with or without the use of technology, and considered multimodality to be the most effective way to make science accessible to ELLs. Though not exhaustive, this research offers a set of pedagogical tools and resources for pre-service and in-service teachers to meet the needs of their ELLs in science. Furthermore, based on the teacher responses, the research identifies five key areas which are necessary for science literacy development of culturally and linguistically diverse students. These include: (i) teachers’ positive mindset and awareness towards ELLs in science; (ii) school leadership and administrative support for ELLs; (iii) time, multimodality, and specialized professional development (PD) to scaffold science for ELLs; (iv) the provision of realistic opportunities to collaborate with the ELL or English Language Development (ELD) teacher; and (v) co-teaching science with an ELL/ELD teacher. I would hereby like to share the findings of this thesis and make these accessible to fellow science teachers in the hope that they will refer and/or utilize the proposed strategies and resources in their daily practice.

abstract: The extent of students’ struggles in linear algebra courses is at times surprising to mathematicians and instructors. To gain insight into the challenges, the central question I investigated for this project was: What is the nature of undergraduate students’ conceptions of multiple analytic representations of systems (of equations)? My methodological choices for this study included the use of one-on-one, task-based clinical interviews which were video and audio recorded. Participants were chosen on the basis of selection criteria applied to a pool of volunteers from junior-level applied linear algebra classes. I conducted both generative and convergent analyses in terms of Clement’s (2000) continuum of research purposes. The generative analysis involved an exploration of the data (in transcript form). The convergent analysis involved the analysis of two student interviews through the lenses of Duval’s (1997, 2006, 2017) Theory of Semiotic Representation Registers and a theory I propose, the Theory of Quantitative Systems. All participants concluded that for the four representations in this study, the notation was varying while the solution was invariant. Their descriptions of what was represented by the various representations fell into distinct categories. Further, the students employed visual techniques, heuristics, metaphors, and mathematical computation to account for translations between the various representations. Theoretically, I lay out some constructs that may help with awareness of the complexity in linear algebra. While there are many rich concepts in linear algebra, challenges may stem from less-than-robust communication. Further, mathematics at the level of linear algebra requires a much broader perspective than that of the ordinary algebra of real numbers. Empirically, my results and findings provide important insights into students’ conceptions. The study revealed that students consider and/or can have their interest piqued by such things as changes in register. The lens I propose along with the empirical findings should stimulate conversations that result in linear algebra courses most beneficial to students. This is especially important since students who encounter undue difficulties may alter their intended plans of study, plans which would lead them into careers in STEM (Science, Technology, Engineering, & Mathematics) fields. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2019

This study explored instructional strategies that teachers in multilingual mathematics classrooms use to support the development of mathematical proficiency in algebra. The need for improvement of mathematics matriculation results in many multilingual schools is a well accepted concern in South Africa. The research method used was two case studies. In one case, the teacher shared a home language with all the learners. In the other case, the teacher did not share a home language with most of the learners. Data collected revealed that the teachers used language strategies as well as other strategies that would be used in any other mathematics classroom. These strategies were: Interactive Instruction; Scaffolding; Multiple Representations; Code-Switching and Language Modes. The data further revealed that the strategies were not used in isolation but in different combinations as needed, to support the learners.

The purposes of this study were to investigate sixth grade students&rsquo / understanding of multiplication of fractions in terms of the Pirie&ndash / Kieren Model of Understanding in the light of use of multiple representations and to improve mapping feature of the current theory to increase depicting power of the maps produced. One of the qualitative research methods, case study design was used. This study was conducted with two sixth grade students at a public school in Etimesgut, Ankara in the spring semester of 2009-2010. Students learnt fractions. They completed activity sheets during the lessons. They completed self-evaluation forms and wrote journals just after the instruction. After that semi- structured interviews were conducted with two students in order to analyze their understanding about multiplication of fractions. The data collected from interviews were used to reveal understanding maps of each student. Moreover, the data from activity sheets, student journals, observations, and self-evaluation forms were used to strengthen the findings from the interviews. This study showed that there was a relationship between students&rsquo / preference on the use of different type of representations and attained understanding level of multiplication of fractions. It was also found that establishing connection between multiplication of fraction concept and real life usage of these concepts and extending whole number multiplication to the multiplication with the fractions were acted as an obstacle for understanding the multiplication of fractions. In the current study, it was seen that there was a relationship between question type and students use of representations. Moreover, teachers should use different type of representations in their classrooms more frequently in order to help students to reach higher level of understandings. Teachers should also connect new ideas to what the students have already learned for deeper understanding of them.