Academic Commons Search Results
http://academiccommons.columbia.edu/catalog.rss?f%5Bsubject_facet%5D%5B%5D=Mathematics+education&q=&rows=500&sort=record_creation_date+desc
Academic Commons Search Resultsen-usMathematical Modeling in the People's Republic of China ---Indicators of Participation and Performance on COMAP's modeling contest
http://academiccommons.columbia.edu/catalog/ac:176110
Tian, Xiaoxihttp://dx.doi.org/10.7916/D8WQ01Z9Mon, 07 Jul 2014 00:00:00 +0000In recent years, Mainland Chinese teams have been the dominant participants in the two COMAP-sponsored mathematical modeling competitions: the Mathematical Contest in Modeling (MCM) and the Interdisciplinary Contest in Modeling (ICM). This study examines five factors that lead to the Chinese teams' dramatic increase in participation rate and performance in the MCM and ICM: the Chinese government's support, pertinent organizations' efforts, support from initiators of Chinese mathematical modeling education and local resources, Chinese teams' preferences in selecting competition problems to solve, and influence from the Chinese National College Entrance Examination (NCEE). The data made clear that (1) the policy support provided by the Chinese government laid a solid foundation in popularizing mathematical modeling activities in China, especially in initial stages of the development of mathematical modeling activities. (2) Relevant organizations have been the main driving force behind the development of mathematical modeling activities in China. (3) Initiators of mathematical modeling education were the masterminds of Chinese mathematical modeling development; support from other local resources served as the foundation of mathematical modeling popularity in China. (4) Chinese teams have revealed a preference for discrete over continuous mathematical problems in the Mathematical Contest in Modeling. However, in general, the winning rates of these two problem types have been shown to be inversely related to their popularity — while discrete problems have traditionally had higher attempt rates, continuous problems enjoyed higher winning rates. (5) The NCEE mathematics examination seems to include mathematical application problems rather than actual mathematical modeling problems. Although the extent of NCEE influence on students' mathematical modeling ability is unclear, the content coverage suggests that students completing a high school mathematics curriculum should be able to apply what they learned to simplified real-world situations, and pose solutions to the simple models built in these situations. This focus laid a solid mathematics foundation for students' future study and application of mathematics.Mathematics educationMathematics, Science, and Technology, Mathematics EducationDissertationsConceptions of Creativity in Elementary School Mathematical Problem Posing
http://academiccommons.columbia.edu/catalog/ac:176065
Dickman, Benjaminhttp://dx.doi.org/10.7916/D8MC8X69Mon, 07 Jul 2014 00:00:00 +0000Mathematical problem posing and creativity are important areas within mathematics education, and have been connected by mathematicians, mathematics educators, and creativity theorists. However, the relationship between the two remains unclear, which is complicated by the absence of a formal definition of creativity. For this study, the Consensual Assessment Technique (CAT) was used to investigate different raters' views of posed mathematical problems. The principal investigator recruited judges from three different groups: elementary school mathematics teachers, mathematicians who are professors or professors emeriti of mathematics, and psychologists who have conducted research in mathematics education. These judges were then asked to rate the creativity of mathematical problems posed by the principal investigator, all of which were based on the multiplication table. By using Cronbach's coefficient alpha and the intraclass correlation method, the investigator measured both within-group and among-group agreement for judges' ratings of creativity for the posed problems. Previous studies using CAT to measure judges' ratings of creativity in areas other than mathematics or mathematics education have generally found high levels of agreement; however, the main finding of this study is that agreement was high only when measured within-group for the psychologists. The study begins with a review of the literature on creativity and on mathematical problem posing, describes the procedure and results, provides points for further consideration, and concludes with implications of the study along with suggested avenues for future research.Mathematics educationbmd2118Human Development, Mathematics EducationDissertationsThe Effects of Number Theory Study on High School Students' Metacognition and Mathematics Attitudes
http://academiccommons.columbia.edu/catalog/ac:176092
Miele, Anthonyhttp://dx.doi.org/10.7916/D8XP733JMon, 07 Jul 2014 00:00:00 +0000The purpose of this study was to determine how the study of number theory might affect high school students' metacognitive functioning, mathematical curiosity, and/or attitudes towards mathematics. The study utilized questionnaire and/or interview responses of seven high school students from New York City and 33 high school students from Dalian, China. The questionnaire components served to measure and compare the students' metacognitive functioning, mathematical curiosity, and mathematics attitudes before and after they worked on a number theory problem set included with the questionnaire. Interviews with 13 of these students also helped to reveal any changes in their metacognitive tendencies and/or mathematics attitudes or curiosity levels after the students had worked on said number theory problems. The investigator sought to involve very motivated as well as less motivated mathematics students in the study. The participation of a large group of Chinese students enabled the investigator to obtain a diverse set of data elements, and also added an international flavor to the research. All but one of the 40 participating students described or presented some evidence of metacognitive enhancement, greater mathematical curiosity, and/or improved attitudes towards mathematics after the students had worked on the assigned number theory problems. The results of the study thus have important implications for the value of number theory coursework by high school students, with respect to the students' metacognitive processes as well as their feelings about mathematics as an academic discipline.Mathematics educationMathematics, Science, and Technology, Mathematics EducationDissertationsMotivation and Study Habits of College Calculus Students: Does Studying Calculus in High School Make a Difference?
http://academiccommons.columbia.edu/catalog/ac:172257
Gibson, Megan E.http://dx.doi.org/10.7916/D8W37TCNTue, 01 Apr 2014 00:00:00 +0000Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the examination. These students take Calculus I in college having already seen most or all of the material. Students at two colleges were surveyed to determine whether prior calculus experience has an effect on these students' effort levels or motivation. Students who took calculus in high school did not spend as much time on their calculus coursework as those who did not take calculus, but they were just as motivated to do well in the class and they did not miss class any more frequently. Prior calculus experience was not found to have a negative effect on student motivation or effort. Colleges should work to ensure that all students with prior calculus experience receive the best possible placement, and consider making a separate course for these students, if it is practical to do so.Mathematics educationmeg2154Mathematics, Science, and Technology, Mathematics EducationDissertationsA Pre-Programming Approach to Algorithmic Thinking in High School Mathematics
http://academiccommons.columbia.edu/catalog/ac:174473
Nasar, Audrey Augustahttp://dx.doi.org/10.7916/D8BG2M1MThu, 20 Mar 2014 00:00:00 +0000Given the impact of computers and computing on almost every aspect of society, the ability to develop, analyze, and implement algorithms is gaining more focus. Algorithms are increasingly important in theoretical mathematics, in applications of mathematics, in computer science, as well as in many areas outside of mathematics. In high school, however, algorithms are usually restricted to computer science courses and as a result, the important relationship between mathematics and computer science is often overlooked (Henderson, 1997). The mathematical ideas behind the design, construction and analysis of algorithms, are important for students' mathematical education. In addition, exploring algorithms can help students see mathematics as a meaningful and creative subject. This study provides a review of the history of algorithms and algorithmic complexity, as well as a technical monograph that illustrates the mathematical aspects of algorithmic complexity in a form that is accessible to mathematics instructors at the high school level. The historical component of this study is broken down into two parts. The first part covers the history of algorithms with an emphasis on how the concept has evolved from 3000 BC through the Middle Ages to the present day. The second part focuses on the history of algorithmic complexity, dating back to the text of Ibn al-majdi, a fourteenth century Egyptian astronomer, through the 20th century. In particular, it highlights the contributions of a group of mathematicians including Alan Turing, Michael Rabin, Juris Hartmanis, Richard Stearns and Alan Cobham, whose work in computability theory and complexity measures was critical to the development of the field of algorithmic complexity. The technical monograph which follows describes how the complexity of an algorithm can be measured and analyzes different types of algorithms. It includes divide-and-conquer algorithms, search and sort algorithms, greedy algorithms, algorithms for matching, and geometric algorithms. The methods used to analyze the complexity of these algorithms is done without the use of a programming language in order to focus on the mathematical aspects of the algorithms, and to provide knowledge and skills of value that are independent of specific computers or programming languages. In addition, the study assesses the appropriateness of these topics for use by high school teachers by submitting it for independent review to a panel of experts. The panel, which consists of mathematics and computer science faculty in high school and colleges around the United States, found the material to be interesting and felt that using a pre-programming approach to teaching algorithmic complexity has a great deal of merit. There was some concern, however, that portions of the material may be too advanced for high school mathematics instructors. Additionally, they thought that the material would only appeal to the strongest students. As per the reviewers' suggestions, the monograph was revised to its current form.Mathematics educationaan2112Mathematics, Science, and Technology, Mathematics EducationDissertationsCross National Comparisons of Excellence in University Mathematics Instructors - An Analysis of Key Characteristics of Excellent Mathematics Instructors based on Teacher Evaluation Forms
http://academiccommons.columbia.edu/catalog/ac:168517
Grant, Frida Kristinhttp://dx.doi.org/10.7916/D8DJ5CKBMon, 06 Jan 2014 00:00:00 +0000Mathematicians have, historically, not been overly successful in their approach to teaching and much research has looked in to why this is so. Teaching mathematics is based on a solid understanding of the subject; however, instructors also need to be able to efficiently communicate the subject to their students. The purpose of this study was to establish common characteristics of excellent university lecturers in mathematics by applying Marsh's ten evaluation categories. This thesis sought to identify which of these areas were most consistently demonstrated by those university lecturers receiving the highest student ratings and whether there are any areas in which excellent lecturers received inconsistent ratings. The dissertation further used these observations to provide evidence of particular characteristics that are more important than others in the development of excellent university mathematics instructors. This study collected quantitative data in the shape of teacher evaluation forms from both Swedish and US mathematics institutions. The data suggests that instructors acknowledged to be excellent receive high ratings in areas concerning subject matter knowledge, explanatory ability, the fairness of examinations, and enthusiasm and commitment to students. Overall, items that explain a lecturer's persona, character and personality are generally more highly correlated with ratings for the instructor himself whereas categories which describe the preparation, organization and structure of the course, are generally more highly correlated with a student's overall learning experience and Overall Course rating.Mathematics educationfka2107Mathematics EducationDissertationsWhich Approaches Do Students Prefer? Analyzing the Mathematical Problem Solving Behavior of Mathematically Gifted Students
http://academiccommons.columbia.edu/catalog/ac:161908
Tjoe, Hartono Hardihttp://hdl.handle.net/10022/AC:P:20598Thu, 06 Jun 2013 00:00:00 +0000This study analyzed the mathematical problem solving behavior of mathematically gifted students. It focused on a specific fourth step of Polya's (1945) problem solving process, namely, looking back to find alternative approaches to solve the same problem. Specifically, this study explored problem solving using many different approaches. It examined the relationships between students' past mathematical experiences and the number of approaches and the kind of mathematics topics they used to solve three non-standard mathematics problems. It also analyzed the aesthetic of students' approaches from the perspective of expert mathematicians and the aesthetic of these experts' preferred approaches from the perspective of the students. Fifty-four students from a specialized high school were selected to participate in this study that began with the analysis of their past mathematical experiences by means of a preliminary survey. Nine of the 54 students took a test requiring them to solve three non-standard mathematics problems using many different approaches. A panel of three research mathematicians was consulted to evaluate the mathematical aesthetic of those approaches. Then, these nine students were interviewed. Also, all 54 students took a second survey to support inferences made while observing the problem solving behavior of the nine students. This study showed that students generally were not familiar with the practice of looking back. Indeed, students generally chose to supply only one workable, yet mechanistic approach as long as they obtained a correct answer to the problem. The findings of this study suggested that, to some extent, students' past mathematical experiences were connected with the number of approaches they used when solving non-standard mathematics problems. In particular, the findings revealed that students' most recent exposure of their then-AP Calculus course played an important role in their decisions on selecting approaches for solution. In addition, the findings showed that students' problem solving approaches were considered to be the least "beautiful" by the panel of experts and were often associated with standard approaches taught by secondary school mathematics teachers. The findings confirmed the results of previous studies that there is no direct connection between the experts' and students' views of "beauty" in mathematics.Mathematics educationhht2105Mathematics, Science, and Technology, Mathematics EducationDissertationsTeachers' Conceptions of Mathematical Modeling
http://academiccommons.columbia.edu/catalog/ac:161497
Gould, Heather Tianahttp://hdl.handle.net/10022/AC:P:20442Thu, 23 May 2013 00:00:00 +0000The release of the Common Core State Standards for Mathematics in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by teachers about mathematical models and modeling in order to aid in the development of teacher education and professional development programs. The study used a mixed methods approach. Quantitative data were collected through an online survey of a large sample of practicing and prospective secondary teachers of mathematics in the United States. The purpose of this was to gain an understanding of the conceptions held by the general population of United States secondary mathematics teachers. In particular, basic concepts of mathematical models, mathematical modeling, and mathematical modeling in education were analyzed. Qualitative data were obtained from case studies of a small group of mathematics teachers who had enrolled in professional development which had mathematical models or modeling as a focus. The purpose of these case studies was to give an illustrative view of teachers regarding modeling, as well as to gain some understanding of how participating in professional development affects teachers' conceptions. The data showed that US secondary mathematics teachers hold several misconceptions about models and modeling, particularly regarding aspects of the mathematical modeling process. Specifically, the majority of teachers do not understand that the mathematical modeling process always requires making choices and assumptions, and that mathematical modeling situations must come from real-world scenarios. A large minority of teachers have misconceptions about various other characteristics of mathematical models and the mathematical modeling process.Mathematics educationhtg2103Mathematics, Science, and Technology, Mathematics EducationDissertationsReforming Mathematics Classroom Pedagogy: Evidence-Based Findings and Recommendations for the Developmental Math Classroom
http://academiccommons.columbia.edu/catalog/ac:146949
Hodara, Michellehttp://hdl.handle.net/10022/AC:P:13232Thu, 17 May 2012 00:00:00 +0000For developmental education students, rates of developmental math course completion and persistence into required college-level math courses are particularly low. This Brief examines the evidence base on reforming mathematics classroom pedagogy, which may be a potential means for improving the course completion and learning outcomes of developmental mathematics students. Each study examined was classified into one of six sets: student collaboration, metacognition, problem representation, application, understanding student thinking, and computer-based learning. Because most of the studies across the sets did not employ rigorous methods, the evidence regarding the impact of these instructional practices on student outcomes is inconclusive. Nevertheless, analysis of the studies that did employ rigorous designs suggests that structured forms of student collaboration and instructional approaches that focus on problem representation may improve math learning and understanding. This Brief concludes by making a number of methodological recommendations, proposing several needed areas of research, and suggesting instructional practices that may improve the outcomes of developmental math students.Mathematics educationmeh70Economics and Education, Institute on Education and the Economy, Community College Research CenterReportsReforming Mathematics Classroom Pedagogy: Evidence-Based Findings and Recommendations for the Developmental Math Classroom
http://academiccommons.columbia.edu/catalog/ac:146653
Hodara, Michellehttp://hdl.handle.net/10022/AC:P:13144Fri, 04 May 2012 00:00:00 +0000For developmental education students, rates of developmental math course completion and persistence into required college-level math courses are particularly low. This literature review examines the evidence base on reforming mathematics classroom pedagogy, which may be a potential means for improving the course completion and learning outcomes of developmental mathematics students. Each study examined for this review was classified into one of six sets: student collaboration, metacognition, problem representation, application, understanding student thinking, and computer-based learning. Because most of the studies across the sets did not employ rigorous methods, the evidence regarding the impact of these instructional practices on student outcomes is inconclusive. Nevertheless, analysis of the studies that did employ rigorous designs suggests that structured forms of student collaboration and instructional approaches that focus on problem representation may improve math learning and understanding. This paper concludes by making a number of methodological recommendations, proposing several needed areas of research, and suggesting instructional practices that may improve the outcomes of developmental math students.Mathematics educationmeh70Economics and Education, Institute on Education and the Economy, Community College Research CenterWorking papersAsian American college students' mathematics success and the model minority stereotype
http://academiccommons.columbia.edu/catalog/ac:146308
Jo, Lydia Hyeryunghttp://hdl.handle.net/10022/AC:P:13045Thu, 19 Apr 2012 00:00:00 +0000The often aggregated reports of academic excellence of Asian American students as a whole, compared to students from other ethnic groups offers compelling evidence that Asian Americans are more academically successful than their ethnic counterparts, particularly in the area of mathematics. These comparative data have generated many topics of discussion including the model minority stereotype: a misconception that all Asian Americans are high academic achievers. Research has shown that this seemingly positive stereotype produces negative effects in Asian students. The aim of this study is to examine differences in mathematics success levels and beliefs about the model minority stereotype among different generations of Asian American college students. This study focuses on comparing three different generations of Asian American students with respect to: (1) their success and confidence in mathematics, (2) their personal views on the factors that contribute to their success, (3) their perceptions of the model minority stereotype and (4) how they believe the stereotype affects them. In this mixed methods study, a sample of n = 117 Asian American college students participated in an online survey to collect quantitative data and a subsample of n = 9 students were able to participate in a semi-structured interview. The results of the study indicated that there were almost no differences in either the mathematics success and confidence level, or in the perceptions and perceived effects of the model minority stereotype across generations. Quantitative results showed that all generations of Asian Americans generally are confident in their mathematics abilities. Qualitative analysis showed that the students felt that there were three reasons for their level of success: parental influence, differences in the education system between the U.S. and their home country, and using mathematics and science to get ahead academically as their native English speaking peers tend to be ahead of them in the liberal arts due to language barriers. Though there were mixed feelings among the sample subjects about the validity of the model minority stereotype, all three generations of Asian American students felt peer pressure from the stereotype to excel in mathematics, more frequently in high school than in college.Mathematics educationlhj2107Mathematics, Science, and Technology, Mathematics EducationDissertationsKnowledge-as-Theory-and-Elements
http://academiccommons.columbia.edu/catalog/ac:174305
Munson, Alexander Anhttp://hdl.handle.net/10022/AC:P:12408Tue, 31 Jan 2012 00:00:00 +0000This dissertation will examine the Knowledge-as-Theory-and-Elements perspective on knowledge structure. The dissertation creates a set of theoretical criteria given within a template by which lesson plans can be designed to teach mathematics and the physical sciences. The dissertation also will test the Knowledge-as-Theory and-Elements theoretical perspective by designing lesson plans to teach a branch of mathematics, graph theory, by using the new template. The dissertation will include a comparative study investigating the effectiveness of the lesson plans conforming to the new template and the lesson plans designed by the traditional theoretical perspective Knowledge-as-Elements.Mathematics educationaam2173Mathematics, Science, and Technology, Mathematics EducationDissertationsDiagrammatic Reasoning Skills of Pre-Service Mathematics Teachers
http://academiccommons.columbia.edu/catalog/ac:143877
Karrass, Margarethttp://hdl.handle.net/10022/AC:P:12378Fri, 27 Jan 2012 00:00:00 +0000This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers' content knowledge for teaching. However, there is no course in the mathematics curriculum that systematically develops diagrammatic reasoning skills, except Geometry. In the course of this study, a group of volunteers in the last semester of their teacher preparation program were presented with "visual proofs" of certain theorems from high school mathematics curriculum and asked to prove/explain these theorems by reasoning from the diagrams. The results of the interviews were analyzed with respect to the participants' attained van Hiele levels. The study found that participants who attained higher van Hiele levels were more skilled at recognizing visual theorems and "proving" them. Moreover, the study found a correspondence between participants' diagrammatic reasoning skills and certain behaviors attributed to van Hiele levels. However, the van Hiele levels attained by the participants were consistently higher than their diagrammatic reasoning skills would indicate.Mathematics educationrp2141Mathematics, Science, and Technology, Mathematics EducationDissertationsDiagrammatic Reasoning Skills of Pre-Service Mathematics Teachers
http://academiccommons.columbia.edu/catalog/ac:143601
Karrass, Margarethttp://hdl.handle.net/10022/AC:P:12335Wed, 25 Jan 2012 00:00:00 +0000This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers’ content knowledge for teaching. However, there is no course in the mathematics curriculum that systematically develops diagrammatic reasoning skills, except Geometry. In the course of this study, a group of volunteers in the last semester of their teacher preparation program were presented with “visual proofs” of certain theorems from high school mathematics curriculum and asked to prove/explain these theorems by reasoning from the diagrams. The results of the interviews were analyzed with respect to the participants’ attained van Hiele levels. The study found that participants who attained higher van Hiele levels were more skilled at recognizing visual theorems and “proving” them. Moreover, the study found a correspondence between participants’ diagrammatic reasoning skills and certain behaviors attributed to van Hiele levels. However, the van Hiele levels attained by the participants were consistently higher than their diagrammatic reasoning skills would indicate.Mathematics educationrp2141Mathematics, Science, and Technology, Mathematics EducationDissertationsBeginning mathematics teachers from alternative certification programs : their success in the classroom and how they achieved it
http://academiccommons.columbia.edu/catalog/ac:129624
Ham, Edwardhttp://hdl.handle.net/10022/AC:P:9834Fri, 25 Feb 2011 00:00:00 +0000This dissertation focuses on beginning mathematics teachers from alternative certification programs and their perceptions of what is required to be successful. A mixed - methods research study was completed with several goals in mind: (1) identifying how beginning mathematics teachers define success in the classroom during their earliest years, (2) identifying what important factors, attributes, or experiences helped them achieve this success, and (3) determining where these beginning mathematics teachers learned the necessary attributes, or experiences to become successful in the classroom. A sample of beginning mathematics teachers (n = 28) was selected from an alternative certification program in California for a quantitative survey. A subsample of teachers (n = 7) was then selected to participate further in a qualitative semi-structured interview. The results of the study revealed that beginning teachers defined success in their beginning years by their classroom learning environment, creating and implementing engaging lessons, and a belief in their own ability to grow professionally as educators. Mathematics content knowledge, classroom management, collaboration with colleagues and coaches, reflection, a belief in one's ability to grow professionally as a teacher, a belief in the ability to have a positive impact on students, personality, and previous leadership experiences were several of the factors, attributes, or experiences identified as most important by the participating teachers. The participating teachers also felt that before and after, but not during, their teacher preparation program were the stages of teacher development that best instilled the necessary factors, attributes, or experiences to become successful in a mathematics classroom.Mathematics educationeh2351Mathematics, Science, and Technology, Mathematics EducationDissertations