In this study, the balance between conceptual and procedural teaching and its effect on the development of algebraic reasoning was examined. Participants included two seventh grade mathematics teachers and their students in targeted classes (N = 33). One video taped lesson from each teacher was selected for in-depth analysis of the balance between conceptual teaching, procedural teaching, and classroom time that included neither. Student participants took pretest and posttest algebra tests. Distribution of student responses and scores were analyzed for the degree of conceptual understanding demonstrated by students and then related to observed instructional practices. It was concluded that the students of the teacher with a more explicit conceptual emphasis in her lessons performed better on the test and were better able to exhibit flexible reasoning in unfamiliar contexts. Students whose teacher focused more heavily on procedural instruction without conceptual connections were less flexible in their reasoning and unable to apply some of the procedures taught in class.

In this study, the balance between conceptual and procedural teaching and its effect on the development of algebraic reasoning was examined. Participants included two seventh grade mathematics teachers and their students in targeted classes (N = 33). One video taped lesson from each teacher was selected for in-depth analysis of the balance between conceptual teaching, procedural teaching, and classroom time that included neither. Student participants took pretest and posttest algebra tests. Distribution of student responses and scores were analyzed for the degree of conceptual understanding demonstrated by students and then related to observed instructional practices. It was concluded that the students of the teacher with a more explicit conceptual emphasis in her lessons performed better on the test and were better able to exhibit flexible reasoning in unfamiliar contexts. Students whose teacher focused more heavily on procedural instruction without conceptual connections were less flexible in their reasoning and unable to apply some of the procedures taught in class.

The study employed Ernest (2006) Theory of Semiotic Systems to investigate the use of and exposure to multiple representations in a 10th grade algebra II suburban high school class located in the southeastern region of the United States. The purpose of this exploratory case study (Yin, 2014) was to investigate the role of multiple representations in influencing and facilitating algebra II students’ conceptual understanding of piece-wise function, absolute-value functions, and quadratic functions. This study attempted to answer the following question: How does the use of and exposure to multiple representations influence algebra II students’ understanding and transfer of algebraic concepts? Furthermore, the following sub-questions assisted in developing a deeper understanding of the question: a) how does exposure to and use of multiple representations influence students’ identification of their pseudo-conceptual understanding of algebraic concepts?; b) how does exposure to and use of multiple representations influence students’ transition from pseudo-conceptual to conceptual understanding?; c) how does exposure to and use of multiple representations influence students’ transfer of their conceptual understanding to other related concepts? Understanding the notion of pseudo-conceptual understanding in algebra is significant in providing a tool for examining the veracity of algebra students’ conceptual understanding, where teachers have to consistently examine if students accurately understand the meanings of the mathematical signs that they are constantly using. The following data collection techniques were utilized: a) classroom observation, b) task based interviews, and c) study of documents. The unit of analysis was students’ verbal and written responses to task questions. Three themes emerged from the analysis of in this study: (a) re-imaging of conceptual understanding; (b) reflective approach to understanding and using mathematical signs; and (c) representational versatility in the use of mathematical signs. Findings from this study will contribute to the body of knowledge needed in research on understanding and assessing algebra students’ conceptual understanding of mathematics. In particular the findings from the study will contribute to the literature on understanding; the process of algebraic concepts knowledge acquisition, and the challenges that algebra students have with comprehension of algebraic concepts (Knuth, 2000: Zaslavsky et al., 2002).

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Research has been undertaken to obtain a thorough understanding of the existence and degree of gender disparity in students' participation and performance in introductory university physics courses at the University of Edinburgh. The research on this topic has focused on three main subject areas: the proportion of male and female students enrolled in undergraduate physics courses and their reasons for choosing to study this subject, gender differences in student performance and, Finally, how students' attitudes and beliefs towards studying physics change after a period of instruction. Gaining an insight into students' attitudes towards studying and learning physics, as well as their conceptual understanding of the topics being assessed, can draw attention to potential areas of weakness which can be targeted in future teaching. This thesis comprises a comprehensive review of the current situation surrounding male and female participation in the undergraduate physics degree programme at the University of Edinburgh in comparison to other STEM subjects, as well as a description of factors potentially influencing the gender performance in physics. With respect to student performance, conceptual understanding tests have been used as evaluation tools to measure the effectiveness of introducing interactive engagement, such as Peer Instruction, into teaching environments in order to improve student performance, as well as a means by which male and female learning gains could be compared. Results indicate that female students show a lower level of conceptual understanding of Newtonian Mechanics than male students when entering the degree programme, and that this gender difference remains after a period of instruction. Qualitative interviews highlight the preconceptions of first year undergraduate physics students with regards to Newtonian concepts of force and motion and demonstrate the range of misconceptions held by both male and female students. The research presented here compares male and female performance on different forms of assessment; coursework, laboratory assessments, examinations and peer instruction in-lecture questions. Results indicate that while examination scores show no distinct gender trends, female students show consistently higher coursework scores compared to males across physics, chemistry and biology first year courses. Analysis of Peer Instruction questions implemented in the introductory physics lectures suggest that such teaching methodologies have had an overall positive effect on class performance, although there is evidence that differences exist between male and female performance on individual questions. Students' attitudes towards learning physics have been measured at under- graduate level in order to evaluate the level of 'expert-like' thinking of first year undergraduate students. One notable finding of this study has been the lack of decline in the `expert-like' thinking after a semester of teaching in recent years, where previously a decline had been witnessed in this expert-like thinking. This result coincides with a change in the format of lectures to a 'flipped- classroom' approach and may have implications for the introduction of new teaching methods. As well as focusing on the progression of undergraduate students' attitudes, this study has evaluated UK academics' attitudes towards physics. This has enabled a UK level of `expert-like' thinking to be established, with gender differences between male and female academics identified. Students' opinions of the transferable skills gained and their experiences during their degree programme are discussed. Each of the gender topics discussed in this thesis has provided a deeper insight into gender differences in student attainment at undergraduate level which could have implications for the further improvement of future courses.

There has been an influx of funding in science, technology, engineering and mathematics (STEM) allocated to adapting educational systems that engage, motivate and train learners with new and innovative techniques. This exploratory research project investigated the student outcomes associated with undergraduate biology learner' engagements in the ER Project. Thirty-one students interacted in small groups within an inquiry-learning environment supported by an innovative technology that introduced a database of images of green florescent endoplasmic reticulum and golgi apparatus. The aim of the ER Project was to increase learners' conceptual understanding of cell structure and movement and engage in scientific processes in an authentic inquiry setting. To identify relationships between and among independent and dependent variables in a causal model hypothesizing relationships among Prior Knowledge, Learning Preference, Attitudes toward Computers, Inquiry Task Performance and Conceptual Understanding were tested using path analysis. The study found that while prior knowledge was a strong predictor for conceptual understanding, it was not as effective for observing the inquiry task performance. But, the Motivation towards Computers and their Inquiry Task Performance indicated that learners understood the scientific processes and were able to communicate their results.

The purposes of this study were (a) to examine Zambian Junior high school pre-service science teachers' familiarity with, interest in learning more about electrochemistry, and their conceptual understanding and performance on electrochemistry (b) to examine the pre-service science teachers' ability to identify misconceptions on electrochemistry and their pedagogical ideas on how to address the identified misconceptions in junior high school classrooms, and (c) to establish the extent to which pre-service science teachers' familiarity with, interest in, conceptual understanding of, performance on, and pedagogical ideas for, electrochemistry are related. The electrochemistry concepts examined in this study were categorized into basic and advanced concepts. A sample comprised 66 junior high school pre-service science teachers at Mufulira College of Education in Zambia. The study used a mixed methods research design, and data were collected using a questionnaire, performance test, and interviews. The first two instruments collected quantitative data which was analyzed using non-parametric tests - Wilcoxon and Mann-Whitney tests. The third instrument collected qualitative data which was analyzed by identifying the emerging themes that formed categories. The pre-service science teachers reported high familiarity and interest in the electrochemistry concepts examined. There were statistically significant differences in familiarity with and interest in all concepts among all the groups. The year in college and level at which electrochemistry was learned showed statistically significant differences for both familiarity and interest. Results further showed low pre-service science teachers' conceptual understanding and performance on electrochemistry test. Between group comparisons on conceptual understanding and performance were statistically significant for year in college and levels at which electrochemistry was learned. The pre-service science teachers interviewed exhibited inability to identify misconceptions in most scenarios on basic electrochemistry concepts. Furthermore, teachers' suggested pedagogical ideas for addressing the misconceptions comprised both learner-centered and teacher-centered instructional practices. As such, the pre-service science teachers' self-reported knowledge of electrochemistry was not consistent with their actual knowledge. Correlational analysis of familiarity, interest, conceptual understanding and performance revealed statistically significant correlations between familiarity and conceptual understanding, r(64) = 0.56, p = 0.000 and between performance and conceptual understanding r(64) = 0.64, p = 0.000 only. These results have implications for teacher education and science teaching and learning.

Atmospheric Flight Mechanics (AFM) is one of the cornerstones of aeronautical engineering and includes subjects like aerodynamic prediction, stability and control, dynamics, and vehicle design. These topics are critical to the success of aircraft development, so AFM is considered one of the most important foundational knowledge areas for aerospace engineering. Unfortunately, students graduating from aerospace engineering programs are often underprepared to perform in AFM jobs. This ongoing research focuses on developing a blueprint for assessing conceptual understanding of AFM concepts. Since existing literature suggests that novices and experts organize knowledge differently, comparing students' and experts' mental models can shine a light on the alternative conceptions that students retain post-instruction. As such, framing the study around synthetic mental models can be advantageous. To explore these mental models, three types of data have been collected and analyzed. Document analysis was done on course documents to identify what concept relationships were being presented to the students. Class observations were conducted to analyze how concepts are introduced to students and what relationships are highlighted by the instructor. Finally, a concept mapping activity was facilitated to study the mental models that the students built after instruction. The results show a lack of synthetization between the knowledge introduced in the classroom and students' prior knowledge which translated into student mental models that do not meet some of the expectations of the course. Moreover, this study highlights the importance of the instructor's awareness of their own expectations for learning and knowledge synthetization in the design of an AFM course. / Doctor of Philosophy / Conceptual understanding research has often focused on how students develop their understanding of scientific concepts that are difficult to grasp. Through this research, many assessment techniques have been developed and implemented in the design of STEM courses. However, many of these techniques and implementations have been limited to K-12 or introductory engineering courses. Atmospheric Flight Mechanics (AFM) is an important part of the aerospace curriculum that has yet to be studied under the conceptual understanding lens. The goal of this study was to investigate how students develop AFM conceptual understanding using a synthetic mental model framework. This study focused on answering three questions, how are students being introduced to AFM concepts?, how do students' mental models develop throughout the semester?, and how do the students' and instructor's mental models compare?. Through the exploration of class documents, class observations, and concept mapping activities, this research found that students are having a hard time making sense of new knowledge based on their previous understanding of similar topics. By trying to integrate this new knowledge with their previous mental models, students are developing synthetic mental models that do not align with the scientific explanations of the topic. This study also found that instructors are often unaware of their own knowledge and expectations for learning which makes knowledge synthetization harder for the students. Therefore, addressing these issues during course design could make an AFM course easier to understand for students.

The purpose of this study is to inform instruction by increasing the body of knowledge regarding the relationship between college physics students' knowledge about models in science and their conceptual understanding with regard to electricity and magnetism. The data for this study was obtained through the administration of two instruments: Conceptual Survey of Electricity and Magnetism, a multiple choice assessment, and Student Understanding of Models in Science, a Likert-scale survey. Both traditional statistics and an innovative technique called Model Analysis were used to analyze the data. Analysis of the data revealed that there is a relationship between student understanding of models in science and conceptual understanding of electricity and magnetism topics. However, the results of this study also suggest that without specific instruction on models in science, overall understanding of models in science does not improve after a traditional electricity and magnetism course. Additionally, this study demonstrated that not only does student conceptual understanding of electricity and magnetism topics improve after a traditionally taught electricity and magnetism course, but also, students demonstrate more sophistication in their understanding of some electricity and magnetism topics. In the latter case, students showed improvement in their application of the expert rather than the naïve or null model of electricity and magnetism topics.