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Doctor of Philosophy / Curriculum and Instruction Programs / David S. Allen / Margaret G. Shroyer / Ongoing, effective professional development is viewed as an essential mechanism for eliciting change in teachers’ knowledge and practice in support of enacting the vision of NCTM’s Principles and Standards of School Mathematics. This case study of the Infinite Mathematics Project, a Title IIB MSP professional development initiative, seeks to provide a qualitative examination of the characteristics and strategies used in the project and their impact on teacher learning and practice. The project embodied many features and strategies of effective professional development such as: mathematics content focus; sustained over time; reform activities (e.g., lesson study, teacher collaboration); active learning opportunities (e.g., implementing an action plan; developing differentiated instruction activities for a mathematics classroom); coherence with NCTM and state standards; and collective participation by IHE facilitators and participant K-12 teachers from partner districts. The findings reveal teachers gained both content knowledge (knowledge about mathematics, substantive knowledge of mathematics, pedagogical content knowledge, and curricular knowledge) and pedagogical knowledge (knowledge about strategies for differentiating instruction in a mathematics classroom, for supporting students’ reading in the content area, for fostering the development of number sense, for implementing standards-based teaching, and for critically analyzing teaching). The study also provides some evidence that the project had an impact on teaching practice. In addition, an implication of the study suggests the positive impact of Title IIB MSP partnership requirements.

Doctor of Philosophy / Department of Educational Leadership / Royce Ann Collins / In an era of increasing demand for a limited budget, more universities are turning to adjunct faculty to fill the need and to address the student load. Adjunct faculty members are hired for their content knowledge and close association to the business world and industry. This study was conducted to investigate whether a relationship exists between (a) technological pedagogical content knowledge (TPACK); (b) pedagogical training; and (c) personal technology; and to determine which variables have the greatest influence in the willingness of adjunct faculty at a Midwestern higher education institution to choose and integrate digital technology into curriculum and expand to the discussion of TPACK into graduate level education. TPACK is both a framework and an instrument to measure the level of integration of the primary components of the TPACK framework. TPACK is a term that describes what a teacher must know to integrate technology effectively into curriculum or teacher practices and represents the combination of teacher content knowledge, pedagogical knowledge and technology knowledge as interrelated. TPACK allows educators to consider what knowledge is required to integrate technology into teaching and how they might develop that knowledge within themselves. The study was conducted with a sample (n=30) of adjunct faculty members from two extension campuses from a Midwestern, Tier 1 university. The data revealed significant relationships between pedagogical training and selection of appropriate technology, and between personal technology use and selection of appropriate technology. The data also revealed that TPACK was a significant predictor; however, the subdomains of TPACK masked the true impact because of the high presence of covariance.

This thesis focuses on how school textbooks and teachers present models of chemical bonding in upper secondary schools in Sweden. In science, as well as in science education, models play a central role, but research has shown that they often are difficult for students to understand. In science education, models are presented to students mainly through textbooks and teachers, and textbooks influence teachers’ teaching. The aim of this thesis was to investigate how textbooks and teachers present models of chemical bonding with respect to students’ difficulties in understanding. To analyze representations of models, an analytical framework based on research reports of students’ difficulties in understanding related to models in general and chemical bonding in particular was developed. The chapters of chemical bonding in five chemistry textbooks were analyzed. Further, ten Chemistry teachers’ lesson plans about chemical bonding and semi-structured interviews with the teachers concerning their teaching were analyzed. This analysis concerned teachers pedagogical content knowledge (PCK) of teaching chemical bonding, with focus on knowledge of students’ difficulties in understanding and teaching strategies that take these difficulties into account. The results show that the teachers could specify examples of students’ learning difficulties, but the teaching strategies to promote the students’ understanding were limited. This indicates a deficient interaction between knowledge of difficulties in understanding and teaching strategies, two essential components of teachers’ PCK. Further, the models of chemical bonding represented in the textbooks and by the teachers might cause students’ difficulties in understanding. This indicates a gap between research of students’ difficulties in understanding and teaching practices as well as textbooks’ development. Further, the teachers’ representations of models were strongly influenced by the textbooks. Implications for textbooks’ authors, pre-service as well as in-service teachers are addressed. / <p>Papper 2 "Upper secondary teachers knowledge..." ingick i lic.uppsatsen som manuskript med titeln: "Swedish upper secondary teachers’ pedagogical content knowledge to teach chemical bonding". Nu publicerad. </p>

Despite the growing importance of science and technology in society, school students consider these subjects irrelevant and hard to learn. Teachers must therefore know how to teach science in ways that enhance students’ understanding and interest. This thesis explores various aspects of the teaching and learning of chemical bonding, an important topic in school chemistry that is primarily taught using models. Research has shown that students find chemical bonding difficult to understand, and that the use of models in science education contributes to this difficulty. I therefore investigated teachers’ knowledge of how to teach chemical bonding and ways of developing it to improve students’ understanding. To this end, I analysed chemistry textbooks and teachers’ lesson plans, and conducted semi-structured interviews with teachers about their teaching of chemical bonding. This revealed that the representations of chemical bonding used in textbooks and by teachers can cause students difficulties. The teachers were generally unaware of how these representations might affect students’ understanding, implying that their pedagogical content knowledge (PCK) could be improved. To explore ways of incorporating research findings into teaching practice and developing teachers’ PCK, I conducted a learning study in which three secondary science teachers together explored and reflected on their own teaching practice. CoRe, a method for creating detailed descriptions of what, how, and why specific content is taught, was used to enhance the reflections and make the teachers’ PCK explicit. As a result, the teachers developed their representations of chemical bonding, became more aware of students’ understanding, and were better able to motivate their actions and choices of content and strategies. This thesis shows how professional development can bridge the gap between research and teaching practice, and how teachers’ PCK can be developed to improve students’ understanding. / Many complex real-world phenomena can only be understood using models that make the abstract visible and provide explanations, predictions, descriptions, or simplifications. However, research has shown that students have difficulties understanding models used in science education in general, and particularly chemical bonding models. This thesis examines various aspects of the teaching and learning of chemical bonding, and its presentation in textbooks and by teachers. It is shown that the representations used by teachers and in textbooks can cause students to have difficulties in understanding, which teachers were generally unaware of. Teachers rarely justify their choices specifically to overcome students’ difficulties, suggesting that their knowledge of how to teach chemical bonding could be improved. A learning study in which teachers collaboratively explored and reflected on their own teaching practice significantly improved their presentation of chemical bonding, their awareness of students’ understanding, and their ability to justify their choices. Overall, this work shows that there is a gap between research and teaching practice, and that effective ways of incorporating research results into teaching practice are needed to improve teaching and learning in chemistry.

Doctor of Philosophy / Curriculum and Instruction Programs / David S. Allen / This study examined pedagogical content knowledge (PCK) and Mathematics knowledge for teaching (MKT) from a perspective that blends existing definitions, questions, and methodologies into a unique method of collecting and analyzing data. Many studies on MKT have been done using qualitative methodology, usually with the researcher interviewing or testing individual teachers and analyzing that data using qualitative methods. A smaller number of studies have attempted to measure MKT using a quantitative approach, often times involving paper pencil tests with multiple choice and some open ended questions. Current research is also heavily weighted towards pre-service elementary teachers in the area of MKT for division by fractions (Depaepe et al, 2013). Although it may be true many pre-service elementary teachers have difficulties with division by fractions (Li & Kulm, 2008; Ma, 1999; Tirosh, 2000), we do not know if these problems persist for in-service elementary teachers or with secondary teachers at any stage. This study used a survey created by the researcher as a synthesis of existing questions from research on MKT with regards to division by fractions. This survey was delivered through an online format. The qualitative data in this research was then coded into quantitative data using a rubric developed by the researcher producing MKT scores that could be analyzed using statistical methods and generalized to a larger population. This study examined the Mathematical Knowledge for Teaching held by elementary, middle, and secondary in-service teachers in the domain of division by fractions. In particular this research asked if there was a relationship between the educational background, training, and experience of teachers and their MKT. Multiple analysis including independent t-tests, independent one-way ANOVAs, and Multiple regression analyses revealed that Middle school teachers and teaching at a middle school were significant predictors of increased MKT scores when compared with other groups of teachers. The type of teaching license, the type of degree held, total experience, and grade level experience were all found to have no significant relationship to MKT scores.

This mixed methods case study investigated mathematics teachers‘ perspectives of the effects of the Lesson Study Process on their content knowledge, pedagogical knowledge, and the potential for students‘ achievement. The population was 55 teachers from elementary, middle, and secondary schools in a metropolitan area. The three research questions guiding this study were: (1) What are the perspectives of teachers on the impact of the Lesson Study Process on their mathematical content knowledge? (2) What are the perspectives of teachers on the impact of the Lesson Study Process on their pedagogical knowledge? (3) What are the perspectives of teachers on the potential impact of the Lesson Study Process on their students‘ achievement? Literature pertaining to constructivism, teacher professional development, and Lesson Study was reviewed. Data from surveys, questionnaires, and focus group sessions were examined both quantitatively and qualitatively to determine common categories, themes, and connections to each of the research questions. The teachers believed that their mathematics content knowledge was positively affected in the areas of deeper understanding which led to an increase in self-confidence. The teachers also believed that their pedagogical knowledge was enhanced in the areas of planning and attention to student thinking. Finally, the teachers mentioned five areas for potential improvement in students‘ achievement. They included: students‘ increased conceptual understanding of the topics taught during the research lessons, planning lessons more thoroughly by making them relevant to the students‘ daily lives and planning it within the context of the state‘s curriculum, shifting the focus of an in-class observation from the teacher‘s performance to student thinking, and a similar shifting of the manner in which students are assessed—from right/wrong answers to seeking thought processes whereby the student may correct misunderstanding.

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Humanities, School of Education, 2012 / Reflection about lessons delivered is a practice widely encouraged in teaching. Reasoning, particularly about transformation of subject matter knowledge of lessons yet to be taught, is an internal process and a speciality evident largely in expert teachers. The study investigates the feasibility of fast-tracking its development in pre-service chemistry teachers. It focuses on developing this specialty within a specific topic, as a theoretical construct called Topic Specific PCK (TSPCK). Five knowledge components of TSPCK are identified as the enablers that transform subject matter knowledge. The components are: (1) students’ prior knowledge, (2) curricular Saliency, (3) what is difficult to teach (4) representations, including powerful analogies, and (5) conceptual teaching strategies. These components are identified, with reference to literature, as aspects specific to the subject matter knowledge of the teacher and useful in its teachability. A new tool to measure the quality of TSPCK is developed. The procedure for developing the tool consists of the following steps: (i) confirming the characteristics of the test items fitting the Topic Specific PCK construct, (ii) production of test items, (iii) judgment of items, (iv) construction of the instrument (v) piloting and (vi) validation of the instrument. Care is taken to ensure presentation of multiple evidence and discussions, addressing the interpretive and arguments as requirements for showing validity of the construct measured by the instrument. The Topic Specific PCK tool is validated with a group of 20 practicing teachers. The tool is scored, using a rubric corresponding to the five components with each being rated on a four point scale, from 1 (Limited) to 4 (Exemplary). The analysis of the generated scores is done using the Rasch statistical model (Winstep, version 3.72.3). The reliability indices as indicated by person reliability and item reliability are found to be high at 0.86 at 0.91, respectively. The persons and item scores reflect measures well inside the conventionally acceptable range of -2 and +2. A further indicator of validity of the tool is the empirically calculated hierarchy of test items’ order of difficulty, found similar to the theoretically predicted pattern for the teacher group. Based on the above analysis and findings, I regard the tool as valid and reliable. My research design is based on mixed-methods research (MM). The research strategy takes the form of a case study. The study is located in a methodology class for final year physical science pre-service teachers. They formed an experimental group (N=16) for this study. I delivered an intervention, targeting understanding of transformation of Chemical Equilibrium concepts, using the above listed five knowledge components. I collected data through a combination of tools, including the newly designed Topic Specific PCK tool in Chemical Equilibrium, an Achievement tool and a science teacher Belief tool. Both the Achievement and the Belief tools were adapted from existing tools, and were thus considered tried and validated. The findings suggest that the quality of Topic Specific PCK in chemical equilibrium may be improved in pre-service teachers by the explicit discussion of the knowledge enabling its transformation. They also suggest that, in the process of discussing aspects of subject matter knowledge related to its transformation, pre-service teachers improve their conceptual understanding of chemical equilibrium. Both these improvements were not affected by the shift or lack of shift in teacher beliefs from teacher-centred towards student-centred practices. I acknowledge the small size of the sample as a practical limitation to the generalization of the statistical findings in this study. I suggest that emphasis be placed on the trends displayed, as they are similar to those obtained from the multiple sources of the qualitative component of the study. Finally, I recommend that the development of PCK in pre-service teachers be considered in a topic by topic manner. I urge that the teaching of chemistry topics be explicitly organized in a format in which pre-service teachers would be expected to reason about them, and particularly transform them for teaching.

ABSTRACT This study investigates what and how mathematics (for teaching) is constituted in classroom practice. Specifically mathematical knowledge for teaching fractions in Grade 7. One teacher was studied to gain insight into the mathematical problemsolving the teacher does and the dilemmas he faces as he goes about his work. The analysis of the data show that the mathematical problem-solving that this particular teacher engaged in can be classified as demonstrating, encouraging and working with learner ideas. He appealed to mathematics (rules & empirical), experience (everyday) and the curriculum (tests and exams) to fix meaning. The mathematical problem solving and appeals he made threw up dilemmas of representing the content, competing goals and student thinking. This aided in providing a description of what mathematics for teaching is in this practice. The report concludes with a discussion of what teachers need to know or study in order to become better mathematics teachers and where do they find these courses to accommodate their need to improve as mathematics teachers.