Through a singular case study, this research enquiry seeks to explore teacher perceptions about the development of a concept-based curriculum program (called as the Conceptual Curriculum by the school), in the context of an International Baccalaureate (IB) World school in the Middle East, and the intended and unintended outcomes of the initiative. The study employs Bernstein’s (1975) theories of classification and framing, and curriculum recontextualization, as an analytical framework to interpret findings. The study is informed through methods such as reading and analyzing of curriculum documents, conducting semi-structured interviews, and the distribution of a web-based questionnaire to teachers. Findings in this research inquiry revealed that, though teachers expressed the experience of creating and delivering the Conceptual Curriculum as sometimes being challenging and frustrating, a vast majority of the teachers prefer a flexible curriculum framework versus a prescriptive curriculum. However, findings also revealed that, though teachers seem to enjoy the freedom and flexibility of working with broad curricular frameworks as opposed to prescriptive curricula, there seem to be some fundamental questions pertinent to curriculum recontextualization remaining unanswered, for which perhaps teachers seek answers from qualified curriculum development personnel. Findings reveal that when broad curricular frameworks get recontextualized, the lack of consensus amongst teachers on what counts as essential knowledge is often a matter of concern. Findings reveal that in curriculum recontextualization, when having to negotiate between a “multiplicity of pedagogic fields” (Cambridge, 2011, p. 129) teachers seem to be inherently aligning to something that is a “crystal clear benchmark” such as the International Baccalaureate Diploma Programme (IB DP), as opposed to something that is more flexible and open-ended such as the International Baccalaureate Primary Years Programme (IB PYP). The disciplinary focus of the Conceptual Curriculum and the tendency of teachers to align more towards the IB DP rather than the IB PYP (even in lower grades such as 7 and 8) has thus resulted in a quick transition from the “weakly classified” (Bernstein 1971, p.49) inter-disciplinary IB PYP curriculum to a “strongly classified” (Bernstein 1971, p.49) Conceptual Curriculum with disciplinary focus. Findings from this study reveal that teachers see the value and purpose in teaching for conceptual understanding, but this, when coupled with having to choose curriculum content and developing a coherent curriculum has made the experience both challenging and burdensome for them. Findings also reveal that practical agendas of the school, such as addressing limited time and staffing issues assume priority over lofty ideals when the curriculum is recontextualized, thereby indicating that school-based curriculum initiatives lose rigor and form, in the cracks of everyday practice. Findings in this study thus suggest that when teachers are offered the possibility of working with flexible curricular frameworks, realities of everyday practice take over. This often leads to teachers self-prescribing the curriculum, thereby making the process self-mandated, which in effect defeats the very purpose of the school-based curriculum development initiative undertaken.

This study explored the development of student’s conceptual understanding of limit and derivative when specific computational tools were utilized. Fourteen students from a secondary Advanced Placement Calculus AB course explored the limit and derivative concepts from calculus using computational tools in the Maple computer algebra system. Students worked in pairs utilizing the pair-programming collaborative model. Four groups of student pairs constructed computational tools and used them to explore the limit and derivative concepts. The remaining four student pairs were provided similar tools and asked to perform identical explorations. A multiple embedded case design was utilized to explore ways students in two classes, a programming class P and a non-programming class N, constructed understandings focusing upon their interactions with each other and with the computational tools. The Action-Process-Object-Schema (APOS) conceptual model and Constructionist framework guided design and construction of the tools, outlined developmental goals and milestones, and provided interpretive context for analysis. Results provided insights into the effective design and use of computational tools in fostering conceptual understanding. The study found the additional burden of programming redirected students’ attention away from the intended conceptual understandings. The study additionally found, however, that pre-constructed tools effectively promote conceptual understanding of the limit concept when coupled with a mature conceptual model of development. Four themes influencing development of these understandings emerged: An instructional focus on skills over concepts, the instructional sequence, the willingness and ability of students to adopt and utilize computational tools, and the ways cognitive conflict was mediated.

The goal in mathematics has shifted towards an emphasis on both procedural knowledge and conceptual understanding. The importance of gaining procedural knowledge and conceptual understanding is aligned with Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000), which encourages fluency, reasoning skills, and ability to justify decisions. Possession of only procedural skills will not prove useful to students in many situations other than on tests (Boaler, 2000). Teachers and researchers can benefit from this study, which examined the effects of representations, constructivist approaches, and engagement on middle school students' algebraic understanding. Data from an algebra pretest and posttest, as well as 16 algebra video lessons from an NSF-IERI funded project, were examined to determine occurrences of indicators of representations, constructivist approaches, and engagement, as well as student understanding. A mixed methods design was utilized by implementing multilevel structural equation modeling and constant comparison within the analysis. Calculation of descriptive statistics and creation of bar graphs provided more detail to add to the findings from the components of the statistical test and qualitative comparison method. The results of the final structural equation model revealed a model that fit the data, with a non-significant model, p > .01. The new collectively named latent factor of constructivist approaches with the six indicators of enactive representations, encouragement of student independent thinking, creation of problem-centered lessons, facilitation of shared meanings, justification of ideas, and receiving feedback from the teacher was shown to be a significant predictor of procedural knowledge (p < .05) and conceptual understanding (p < .10). The indicators of the original latent factor of constructivist approaches were combined with one indicator for representations and two indicators for engagement. Constant comparison revealed similar findings concerning correlations among the indicators, as well as effects on student engagement and understanding. Constructivist approaches were found to have a positive effect on both types of student learning in middle school mathematics.

The purpose of this study was threefold: Examine middle school teachers' familiarity with, interest in, conceptual knowledge of and performance on light; Examine their ability to identify misconceptions on light and their suggested pedagogical ideas to address the identified misconceptions; and Establish the relationship between the middle school teachers' interest, familiarity, conceptual understanding, performance, misconception identification, and pedagogical ideas for light. Sixty six (66) middle school science teachers enrolled in three math and science teacher professional development projects at Southern Illinois University Carbondale participated in this study. This study used mixed-methods approach to collect and analyze data. The participants responded in writing to four different instruments: Familiarity and Interest Questionnaire, Conceptual Knowledge Test, Two-tier Performance Test, and Misconceptions Identification Questionnaire. Data was analyzed quantitatively by conducting non-parametric (Wilcoxon, Mann-Whitney U, and Kruskal-Wallis) and parametric (paired samples, independent samples, and One-Way ANOVA) tests. Qualitative data was analyzed using thematic analysis and open coding to identify emerging themes and categories. The results showed that the teachers reported high levels of familiarity with and interest in learning more about light concepts. However, they had low conceptual knowledge and performance on light concepts. As such, middle school teachers' perceived knowledge of light concepts was not consistent with their actual knowledge of light. To some extent, the teachers identified students' misconceptions expressed in some scenarios on light and also suggested pedagogical ideas for addressing such misconceptions in middle school science classrooms. However, most teachers did not provide details on their pedagogical ideas for light. Correlations among the four constructs (familiarity, interest, conceptual understanding, and performance) were only significant between performance and conceptual understanding, r (64) = .50, p = .000. There was no significant relationship between conceptual understanding and familiarity, and between performance and familiarity. In view of these findings, it is evident that some teachers did not have sound conceptual understanding and pedagogical ideas to effectively help their students develop the understanding of light concepts accentuated in the US national science education standards. These findings have implications on teacher education and science teaching and learning.

Low levels of learner performance in Mathematics in the Senior Phase (Grades 7-9) in South Africa is often attributed to insufficient mathematics content knowledge among teachers. Although this view might be justifiable, it is often incorrect to assume that content knowledge alone will solve the problem of low performance in mathematics. This study, therefore, argues that understanding learner misconceptions and/or errors and their underlying intricacies could provide the basis for instructional decision making, subsequently improved performance in mathematics. The purpose of the study was to explore the implications of teachers’ understanding of learner errors for mathematics learning. The study was guided by qualitative methods using a case study design which involved data collection from two schools, followed by in-depth data analysis. Two theoretical lenses, namely, Cognitively Guided Instruction (CGI) and Constructivist theory were used to explore the main research question: What are the implications of the teachers’ understanding of learner errors on the learning of school mathematics in the Senior Phase (specifically Grade 9)? Data was collected through lesson observations, analysis of learners’ test responses and interviews. The findings revealed that teachers’ understanding of learner errors from written responses differed notably from intricacies of same errors emanating from interviewing the learners as well as the same errors analysed by the researcher. The implications of these findings suggest the likelihood of a mismatch between teachers’ instructional decision making and learner misconception/errors and this may hamper effective learning of mathematics. / Dissertation (MEd)--University of Pretoria, 2020. / Science, Mathematics and Technology Education / MEd / Unrestricted

The purpose of this study is to explore the feasibility and effectiveness of a scalable concept map based navigation system for a digital textbook. A literature review has been conducted to identify possible methods to promote conceptual understanding in the context of a digital textbook, and these hypothesized solutions will be evaluated through a prototype tool. The primary method that has been selected for this study to promote conceptual understanding in textbooks is the concept map. When concept maps are used as advance organizers or navigation aids for hypermedia documents, they have been shown to promote conceptual understanding. Issues with scalability exist, however. When maps become too large or complicated, a phenomenon labeled "map-shock" occurs. Map-shock is a result of cognitive overload that nullifies the positive effects the concept map has on learning. In order to eliminate map-shock, one needs to manage the cognitive load imposed on the learner. This project proposes using information visualization techniques leveraged from the computer science domain to develop an interactive concept map based navigation system that will retain the positive effects of concept maps, and also present the visuals in a way that does not cognitively overload the user. This study seeks to answer the research question: "How can a large-scale concept map visualization tools be realized in a way that promotes conceptual understanding and manages cognitive load?" To answer the research question, a prototype tool, labeled the "Adaptive Map tool", was developed and populated with engineering statics content. This prototype contains content that is similar to the material in a traditional statics textbook, but the information is accessed through the proposed adaptive concept map visualization. The tool was then given to students in engineering statics class to be used as a supplemental textbook. The effects of the Adaptive Map tool were evaluated through a multiple case study approach that allowed researchers to understand how this tool fit into the larger learning context of a class. Results indicated that some students did integrate the Adaptive Map tool into the learning process, and furthermore that the tool did promote meaningful learning behaviors that lead to better conceptual understanding of the material. / Ph. D.

This dissertation reports on the secondary analysis of data obtained in 2013 about first-year university student’s conceptual understanding of concepts related to simple DC-circuits. The aim was to investigate the nature of conceptual understanding of students entering first-year physics at a South African university, and to explore how their conceptual understanding relates to contextual factors. Data collected from 815 participants comprise contextual data about each participant and responses in the DIRECT-instrument (Determining and Interpreting Resistive Electric Circuits Concepts Test). The conceptual framework for this study was based on a combination of the model about the effectiveness of science teaching and the critical outcomes related to electricity and electric circuits, which involve aspects of current, energy, potential difference and the physical aspects of circuits. The contextual data included information at personal, classroom and school level. Data were analysed using Rasch analysis. The study found that students entering a first-year physics module at a South African university have poor conceptual understanding about simple DC-electric circuits. The analysis of the DIRECT-instrument revealed that students had difficulties understanding concepts relating to parallel circuits, confusing terms such as voltage and current, and current and energy. They also struggled to relate a circuit diagram to an actual circuit and issues regarding short circuits were prominent. The analysis of the contextual data revealed that students’ degree of exposure to practical work does not imply conceptual understanding of DC-electric circuits. Factors that relate with conceptual understanding included students’ attitudes towards science, gender and previous achievement in Science, Mathematics, and English. Key terms: Conceptual understanding, DC-electric circuit, Misconception, Aptitudes / Dissertation (MSc)--University of Pretoria, 2021. / Science, Mathematics and Technology Education / MEd / Unrestricted

In an attempt to examine my practice of providing conceptually-based professional development on fractions to fifth grade teachers, I conducted a series of four one hour professional development workshops. I focused on the conceptual understanding of ordering, adding, and subtracting fractions. I examined the solution process that teachers used to solve fraction problems and their abilities to explain and justify their solutions in an attempt to interpret their understanding. My data showed the effects of this workshop series. The study helped determine the effects of conceptually-based professional development on fractions as demonstrated in the teachers' discussions, participation, and written explanations.

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