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published_or_final_version / Education / Master / Master of Education

A key issue for the success of students entering a first year mathematics course at tertiary level is whether or not they have an integrated understanding and view of the mathematical concepts acquired at school. Various integrated applications from first year mathematics suggest that a compartmentalised view of mathematics would be detrimental to any student's chances of passing mathematics at this level. This study tried to assess whether learners do have an integrated understanding of mathematics at grade 12 level.

Li, Xiaoqing. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 161-179). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

This dissertation focuses on examining the use of mathematical cartoons as a teaching tool in middle school mathematics classroom. A mixed methods research design was used to answer how the use of cartoon activities affects teacher and student perceptions of teaching and learning and student intrinsic motivation, interest, and mathematics anxiety in middle school mathematics. 17 students in 7th grade pre-algebra class and one teacher participated in this study. Eight cartoon activities were provided over a 10-week period, but no more than one cartoon activity per class period was given to them. Student surveys were analyzed using quantitative method, such as mean score, frequency, and percentage, and student mathematics journal and teacher journal were analyzed using descriptive analysis. The results of this study revealed that both students and teacher reported positive results from using cartoons in the mathematics classroom. Students became more open as time went on and it was possible to see their mathematical insights as the study progressed. They did not enjoy easy cartoon activities, but relished challenging ones. Their frustration at difficult-to-understand activities shows the importance of carefully matching cartoon activities to student abilities. When cartoon activities have appropriate levels of difficulty and are clearly understandable, students' intrinsic motivation and interest increased, and mathematics anxiety decreased. The teacher reported that students gave up less easily, participated more readily, and were more focused in classes with cartoon activities. Mathematics instruction with cartoon activities has shown the students that they can enjoy learning mathematics, mathematics can be fun, and they do have the ability to be successful in mathematics. The use of cartoon activity proved to be a valuable instructional tool for improving the quality of mathematics instruction in a 7th grade classroom.

This dissertation traces the history of mathematics education in Palestine Hebrew secondary schools from the foundation of the first Hebrew secondary school in 1905 until the establishment of the State of Israel in 1948. The study draws on primary sources from archives in Israel and analyzes curricula, textbooks, student notebooks, and examinations from the first half of the 20th century as well as reviews in contemporary periodicals and secondary sources. Hebrew secondary mathematics education was developed as part of the establishment of a new nation with a new educational system and a new language. The Hebrew educational system was generated from scratch in the early 20th century; mathematical terms in Hebrew were invented at the time, the first Hebrew secondary schools were founded, and the first Hebrew mathematics textbooks were created. The newly created educational system encountered several dilemmas and obstacles: the struggle to maintain an independent yet acknowledged Hebrew educational system under the British Mandate; the difficulties of constructing the first Hebrew secondary school curriculum; the issue of graduation examinations; the fight to teach all subjects in the Hebrew language; and the struggle to teach without textbooks or sufficient Hebrew mathematical terms. This dissertation follows the path of the development of Hebrew mathematics education and the first Hebrew secondary schools in Palestine, providing insight into daily school life and the turbulent history of Hebrew mathematics education in Palestine.

The purpose of this study was to determine the extent to which the modeling of deductive reasoning and proof-type thinking occurs in a mathematics course in which students are not explicitly preparing to write formal mathematical proofs. Algebra was chosen because it is the course that typically directly precedes a student's first formal introduction to proof in geometry in the United States. The lens through which this study aimed to examine the intended curriculum was by identifying and reviewing the modeling of proof and deductive reasoning in the most popular and widely circulated algebra textbooks throughout the United States. Textbooks have a major impact on mathematics classrooms, playing a significant role in determining a teacher's classroom practices as well as student activities. A rubric was developed to analyze the presence of reasoning and proof in algebra textbooks, and an analysis of the coverage of various topics was performed. The findings indicate that, roughly speaking, students are only exposed to justification of mathematical claims and proof-type thinking in 38% of all sections analyzed. Furthermore, only 6% of coded sections contained an actual proof or justification that offered the same ideas or reasoning as a proof. It was found that when there was some justification or proof present, the most prevalent means of convincing the reader of the truth of a concept, theorem, or procedure was through the use of specific examples. Textbooks attempting to give a series of examples to justify or convince the reader of the truth of a concept, theorem, or procedure often fell short of offering a mathematical proof because they lacked generality and/or, in some cases, the inductive step. While many textbooks stated a general rule at some point, most only used deductive reasoning within a specific example if at all. Textbooks rarely expose students to the kinds of reasoning required by mathematical proof in that they rarely expose students to reasoning about mathematics with generality. This study found a lack of sufficient evidence of instruction or modeling of proof and reasoning in secondary school algebra textbooks. This could indicate that, overall, algebra textbooks may not fulfill the proof and reasoning guidelines set forth by the NCTM Principles and Standards and the Common Core State Standards. Thus, the enacted curriculum in mathematics classrooms may also fail to address the recommendations of these influential and policy defining organizations.

This study examines how mathematical modeling activities within a collaborative group impact students' `value creation' through mathematics. Creating `value' in this study means to apply one's knowledge in a way that benefits the individual and society, and the notion of `value' was adopted from Makiguchi's theory of `value creation' (1930/1989). With a unified framework of Makiguchi's theory of `value', mathematical disposition, and identity, the study identified three aspects of value-beauty, gains, and social good-using observable evidence of mathematical disposition, identity, and sense of community. Sixty students who enrolled in a college algebra course participated in the study. The results showed significant changes in students' mathematics dispositions after engaging in the modeling activities. Analyses of students' written responses and interview data demonstrated that the modeling tasks associated with students' personal data and social interactions within a group contributed to students' developing their identity as doers of mathematics and creating social value. The instructional model aimed to balance the cognitive aspect and the affective skills of learning mathematics in a way that would allow students to connect mathematical concepts to their personal lives and social lives. As a result of the analysis of this study, there emerged a holistic view of the classroom as it reflects the Makiguchi's educational philosophy. Lastly, implications of this study for research and teaching are discussed.