Thesis advisor: Lillie Richardson Albert / The purpose of this research is to identify the categories of South Korean elementary teachers' knowledge for teaching mathematics. Operating under the assumption that elementary teachers' knowledge for teaching affects students' learning, eleven South Korean elementary teachers volunteered to participate in this study. Emerging from the data collected and the subsequent analysis are five categories of South Korean elementary teachers' knowledge for teaching mathematics: Mathematics Curriculum Knowledge, Mathematics Learner Knowledge, Fundamental Mathematics Conceptual Knowledge, Mathematics Pedagogical Content Knowledge, and Mathematics Pedagogical Procedural Knowledge. The first three categories of knowledge play a significant role in mathematics instruction as an integrated form within Mathematics Pedagogical Content Knowledge. A notable conclusion of this study is that Pedagogical Content Knowledge might not be the sum of the other categories of knowledge for teaching mathematics. These findings may be connected to results from relevant studies in terms of the significant role of teachers' knowledge in their mathematics instruction. This study contributes to the existing literature in that it provides empirical bases for understanding teachers' knowledge for teaching mathematics and reveals the relationship among categories of knowledge for teaching mathematics. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Lynch School of Education. / Discipline: Teacher Education, Special Education, Curriculum and Instruction.

The purpose of this study is twofold: (1) to examine the effects of knowledge on cognition and regulation of cognition on declarative knowledge, conditional knowledge, and procedural knowledge in geometry and (2) to examine the interrelationships among declarative knowledge, conditional knowledge, and procedural knowledge in geometry. The reciprocal relationships between metacognitive and knowledge factors were modeled by using data from tenth grade secondary school students. Structural equation modeling was used to test the hypothesized relationships of two metacognitive factors (knowledge of cognition, regulation of cognition) and three knowledge factors (declarative knowledge, conditional knowledge, procedural knowledge). The observed variables representing the latent variables were determined by carrying out exploratory factor analysis and confirmatory factor analysis for the metacognitive awareness inventory and geometry knowledge test separately. Major findings revealed: (1) Declarative knowledge significantly and positively influences conditional and procedural knowledge / (2) Procedural knowledge has a signitificant and positive direct effect on conditional knowledge / (3) Declarative knowledge has a positive indirect effect on conditional knowledge / (4) Knowledge of cognition significantly and positively influences procedural knowledge / (5) Regulation of cognition has a significant but negative direct effect on procedural knowledge / (6) Knowledge of cognition has positive indirect effects on conditional and procedural knowledge / (7) Regulation of cognition has negative indirect effects on conditional and procedural knowledge / (8) Knowledge of cognition and regulation of cognition have non-significant direct effect on declarative and conditional knowledge. The results showed that knowledge of cognition has the strongest direct effect on procedural knowledge and the direct effect of declarative knowledge on conditional knowledge is stronger than on procedural knowledge. In view of the findings considerable suggestions is provided for teachers, instructional designers, and mathematics education researchers.

This study compared the effect of the use of physical manipulative with self-metacognitive questioning versus manipulative without self-metacognitive questioning on the knowledge acquisition in polygons. Participants were 220 sixth grade students. A pretest, treatment and posttest two-group design was used. There were two treatment groups: manipulative with self-metacognitive questioning (MAN+META) and manipulative without self-metacognitive questioning (MAN) Three distinct knowledge tests were designed by the researcher: Declarative, conditional and procedural. Declarative knowledge test consisted of 18 multiple-choice questions. The conditional and procedural knowledge tests consisted of six and ten open-ended questions respectively. Mixed design analysis of variance results revealed that there is a significant effect for time but no group-by-time interaction effect suggesting that both groups responded equally well to treatment in the amount of change in their scores on the two outcome measures: pretests and posttests. A follow up analysis (paired t-test) was conducted to evaluate the impact of time on students&rsquo / pretest and posttest scores. The large effect size indicated that there was a statistically significant increase in scores of all three tests.

The purpose of this study was to investigate sixth grade students&rsquo / conceptual and procedural knowledge and word problem solving skills in the domain of length, area, and volume measurement with respect to gender, previous mathematics achievement, and use of materials. Through the Conceptual Knowledge test (CKT), the Procedural Knowledge Test (PKT), and the Word Problems test (WPT) and the Student Questionnaire, the data were collected from 445 sixth grade students attending public schools located in four different main districts of Ankara. Both descriptive and inferential statistics techniques (MANOVA) were used for the data analysis. The results indicated that the students performed relatively poor in each test. The lowest mean scores were observed in the WPT, then CKT, and PKT respectively. The questions involving length measurement had higher mean scores than area and volume measurement questions in all tests. Additionally, the results highlighted a significant relationship not only between the tests but also between the domains of measurement with a strong and positive correlation. According to the findings, whereas the overall performances of students on the tests significantly differed according to previous mathematics achievement level, gender did not affect the students&rsquo / performance on the tests. Moreover, a wide range of mistakes were found from students&rsquo / written responses to the length, area, and volume questions in the tests. Besides, the results indicated that use of materials in teaching and learning measurement was quite seldom and either low or non-significant relationship between the use of materials and the students&rsquo / performance was observed.

This thesis discuss how balance between declarative and procedural knowledge can be reached in music education. The purpose is to shine light on how balance between different kinds of knowledge shows itself in South African music teachers descriptions of their ways of teaching. The main focus lies in how non verbal and verbal knowledge present itself in the teacher's philosophies. The categorisation of different kinds of knowledge from the book Music Matters by David Elliott is used to distinguish the main question in the analysis. This categorisation suggests there are five categories of knowledge of where one is verbal and four non verbal. Seven teachers are included in the study and the results show that there are some difficulties in the process of balancing verbal and non verbal knowledges in their teaching situations. The difficulties is shown largely between the desire to teach through non verbal methods and the traditional way of teaching that is more directed towards verbal knowledge and the fact that it is the easiest and quickest way to use spontaneously in the teaching situations. The thesis concludes that despite the fact that there are areas of development in balancing knowledges in teaching situations, there is more elements of the philosophical theories discovered in reality than expected. The pattern show that the teacher's philosophical reflections present more gaps individually than put together which results in the reflection that if teachers use the knowledge and experience among each other in a larger extent, balance between different kinds of knowledge is more easily approached than when doing it on their own.

Several factors that are known to influence attitudes of students towards learning have been documented. Some of these factors have been found to affect the achievement of students. In this study the relationship of the attitudinal disposition of students to their learning outcomes were assessed. Chemistry attitude questionnaire was used to assess the attitude of students and a pen and paper examination comprising of questions requiring declarative and procedural knowledge were used to assess learning outcomes of students. Correlation analysis and multiple linear regression analysis were used to assess relationship between attitude of students and their learning outcomes. The results showed that attitude of students had a positive but moderate influence on their performance. The ANOVA results showed a statistical significant relationship between attitude of students and students’ learning outcomes (F= 38.383, p=0.000). / Institute of Science and Technology Education / M.Sc. (Mathematics, Science and Technology Education)

Recent trends show that learners’ enrolment and performance in science at secondary school level is dwindling. Some science topics including genetics in biology are said to be difficult for learners to learn and thus they perform poorly in examinations. Teacher knowledge base, particularly topic-specific pedagogical content knowledge (PCK), has been identified by many researchers as an important factor that is linked with learner understanding and achievement in science. This qualitative study was an attempt to explore the PCK of four successful biology teachers and how they developed it in the context of teaching genetics. The purposive sampling technique was employed to select the participating teachers based on their schools’ performance in biology public examinations and recommendations by science specialists and school principals. Pedagogical content knowledge was used as a theoretical framework for the study, which guided the inquiry in data collection, analysis and discussion of the research findings. The study adopted the case study method and various sources of evidence including concept maps, lesson plans, pre-lesson interviews, lesson observations, post-teaching teacher questionnaire, post-lesson interviews and document analysis were used to collect data on teachers’ PCK as well as how PCK was assumed to have developed. The data were analysed in an attempt to determine the individual teachers’ school genetics’ content knowledge, related knowledge of instructional strategies and knowledge of learners’ preconceptions and learning difficulties. The analysis involved an iterative process of coding data into PCK categories of content knowledge, pedagogical knowledge and knowledge of learners’ preconceptions and learning difficulties. The findings of the study indicate that the four successful biology teachers generally have the necessary content knowledge of school genetics, used certain topic-specific instructional strategies, but lacked knowledge of genetics-related learners’ preconceptions and learning difficulties despite having taught the topic for many years. There were some instructional deficits in their approaches and techniques in teaching genetics. The teachers failed to use physical models, teacher demonstration and/or learner experimentation in their lessons (or include them in their lesson plans) to assist learners in visualizing or internalizing the genetics concepts or processes located at the sub-microscopic level. The teachers’ PCK in genetics teaching was assumed to have developed mainly through formal university education programmes, classroom teaching experiences, peer support and participation in in-service workshops. The implications for biology teacher education are also discussed. / Thesis (PhD)--University of Pretoria, 2014. / lk2014 / Humanities Education / PhD / Unrestricted

Title: Using online tools to assigns and assess the work of secondary school pupils in mathematics Author: Jiří Vančura Department: Department of Mathematics Education Supervisor: doc. RNDr. Jarmila Robová, CSc., Department of Mathematics Education Abstract: Despite the long-term trend of technology implementation in mathematics education, there is not much research that would empirically and long-term monitor the impact of technology on pupils' knowledge. The presented three studies examine the potential benefits of using Khan Academy as a tool for assigning and assessing homework in mathematics at upper secondary schools. The studies deal with three groups of research questions. What is the attitude of pupils towards the Khan Academy implementation, and what benefit do they see in the online practice? Can pupils transfer acquired knowledge from Khan Academy to the school context? In addition to procedural knowledge, does Khan Academy develop a deeper understanding of the underlying concepts? At the time of the research, the author was the mathematics teacher of some of the participating pupils. Based on the results of these studies, the consequences and recommendations for teaching mathematics at upper secondary schools using online platforms are discussed at the end of the thesis. Keywords: Khan Academy,...

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I identify a recent trend in school mathematics as well as in some of the research literature in mathematics education: an emphasis on creative uses of mathematics and an increased emphasis on verbalizations, reasoning and conceptualization as opposed to numerical and computational skills. With tools provided by a qualitative textual analysis of several Swedish curricula from the past from which I trace a shift of focus from the classical towards the conceptual aspects of mathematical knowledge, I examine the common research framework for discussing mathematical knowledge in terms of the procedural and the conceptual. I investigate whether the shift towards a conceptual approach to mathematical knowledge has occurred and how this presumed shift reveals itself. A close reading and comparison of the historical guidance documents' purpose descriptions and grading criteria concerning the mathematics subject is carried out. Commentary materials for the various course plans are examined. Here I conclude that a shift has occurred during the last decades in the mathematics curricula that may have severely affected the mathematical education in schools. I argue that this shift needs to be acknowledged in order to halt a tendency that seems to gravitate towards a decreasing mathematical competency among the Swedish students.