Academic Commons Search Results
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Academic Commons Search Resultsen-usWhat Makes a Good Problem? Perspectives of Students, Teachers, and Mathematicians
http://academiccommons.columbia.edu/catalog/ac:188061
DeGraaf, Elizabeth Brennanhttp://dx.doi.org/10.7916/D8NV9HC3Thu, 04 Jun 2015 00:00:00 +0000While mathematical problem solving and problem posing are central to good mathematics teaching and mathematical learning, no criteria exist for what makes a good mathematics problem. This grounded theory study focused on defining attributes of good mathematics problems as determined by students, teachers, and mathematicians. The research questions explored the similarities and differences of the responses of these three populations. The data were analyzed using the grounded theory approach of the constant comparative method. Fifty eight students from an urban private school, 15 teachers of mathematics, and 7 mathematicians were given two sets of problems, one with 10 algebra problems and one with 10 number theory problems, and were asked choose which problems they felt were the “best” and the “least best”. Once their choices were made, they were asked to list the attributes of the problems that lead to their choices. Responses were coded and the results were compared within each population between the two different problem sets and between populations. The results of the study show that while teachers and mathematicians agree, for the most part, about what attributes make a good mathematics problem, neither of those populations agreed with the students. The results from this study may be useful for teachers as they write or evaluate problems to use in their classes.Mathematics educationecb2154Mathematics, Science, and Technology, Mathematics EducationDissertationsQuaternions: A History of Complex Noncommutative Rotation Groups in Theoretical Physics
http://academiccommons.columbia.edu/catalog/ac:187914
Familton, Johannes C.http://dx.doi.org/10.7916/D8FB521PTue, 12 May 2015 00:00:00 +0000The purpose of this dissertation is to clarify the emergence of quaternions in order to make the history of quaternions less opaque to teachers and students in mathematics and physics. ‘Quaternion type Rotation Groups’ are important in modern physics. They are usually encountered by students in the form of: Pauli matrices, and SU(2) & SO(4) rotation groups. These objects did not originally appear in the neat form presented to students in modern mathematics or physics courses. What is presented to students by instructors is usually polished and complete due to many years of reworking. Often neither students of physics, mathematics or their instructors have an understanding about how these objects came into existence, or became incorporated into their respected subject in the first place. This study was done to bridge the gaps between the history of quaternions and their associated rotation groups, and the subject matter that students encounter in their course work.Mathematics educationMathematics, Science, and Technology, Mathematics EducationDissertationsMathematics Identities of Non-STEM Major Female Students
http://academiccommons.columbia.edu/catalog/ac:186989
Guzman, Anahuhttp://dx.doi.org/10.7916/D8NS0SZXThu, 07 May 2015 00:22:16 +0000The mathematics education literature has documented gender differences in the learning of mathematics, interventions that promote female and minority students to pursue STEM majors, and the persistence of the gender, achievement, and opportunity gaps. However, there is a significantly lower number of studies that address the mathematics identities of students not majoring in science, technology, engineering, and mathematics (STEM). Even more elusive or non-existent are studies that focus on the factors that shaped the mathematics identities of female students not pursuing STEM majors (non-STEM female students). Because the literature has shown the importance of understanding students' mathematics identities given its correlation with student achievement, motivation, engagement, and attitudes toward mathematics, it is vital to understand the factors that influence the construction of mathematics identities in particular of those students that have been historically marginalized.
To address this issue, I explored the mathematics identities held by 12 non-STEM major students (six taking a remedial mathematics course and six others taking a non-remedial mathematics course) in one urban business college in a metropolitan area of the Northeastern United States. This study used Martin's (2000) definition of mathematics identity as the framework to explore the factors that have influenced the mathematics identities of non-STEM female students. The data for this qualitative study were drawn from mathematics autobiographies, one questionnaire, two interviews, and three class observations.
I found that the mathematics identities of non-STEM major female students' in remedial and non-remedial mathematics courses were influenced by the same factors but in different ways. Significant differences indicated how successful and non-successful students perceive, interpret, and react to those factors. One of those factors was non-successful students believe some people are born with the ability to do mathematics; consequently, they attributed their lack of success to not having this natural ability. Most of the successful students in remedial mathematics attribute their success to effort and most successful students in non-remedial mathematics attribute their success to having a natural ability to do mathematics. Another factor was successful students expressed having an emotional connection to mathematics. This was evident in cases where mathematics was an emotional bond between father and daughter and those in which mathematics was a family trait.
Moreover, the mathematics activities in both classrooms were scripted and orchestrated with limited room for improvisation. However, the non-remedial students experienced moments in which their academic curiosity contributed to opportunities to exercise conceptual agency and author some of their mathematics knowledge. Further, successful students in remedial mathematics did not have the ability to continue the development of positive mathematics identities given rigid classroom activities that contributed to a limited sense of community to support mathematics learning.Mathematics educationMathematics Education, Mathematics, Science, and TechnologyDissertationsOn the Consideration of Adoption and Implementation of The Next Generation Science Standards in a Local-Control Context: Supporting the Epistemology of Science through Education Policy
http://academiccommons.columbia.edu/catalog/ac:184049
Lazzaro, Christopher C.http://dx.doi.org/10.7916/D8WH2NTNWed, 18 Feb 2015 00:00:00 +0000On the Consideration of Adoption and Implementation of The Next Generation Science Standards in a Local-Control Context: Supporting the Epistemology of Science through Education Policy Christopher C Lazzaro The primary purpose of this research is to understand how and why members at each of the three levels of the education system within a local-control state made the decisions they did in supporting or hindering the adoption and implementation of the Next Generation Science Standards. This research concentrates on three levels of the education system in a local-control state; 1) the state level 2) the district level, and 3) the school/teacher level, while investigating the following questions: 1. To what extent, and in what ways, do members in each of the three levels of the state education system advocate for adoption and implementation of the Next Generation Science Standards? 2. Are the members in each of the three levels motivated or compelled to consider adoption and implementation of the Next Generation Science Standards, why or why not? 3. To what extent, and in what ways, do the members in each of the three levels take into account science epistemology in their overall consideration of adoption/implementation of the NGSS? The data drew from a series of interviews from a prior study, "Challenges of Implementing the Next Generation Science Standards in Local-Control States in the U.S." (Sevian, Foster, and Scheff, 2012). After these data were coded and analyzed around the three research questions, this phenomenographic research study identified four key findings: Key Finding 1 - As the District Coordinators are uniquely situated within the state education system to be able to see both the on-the-ground practical implications and the high-level policy pressures of adopting and implementing the NGSS, they reflect the deepest level of awareness of how to best advocate for adoption and implementation of the NGSS. Key Finding 2 - Motivation to adopt and implement the NGSS is highly nuanced. The most significant factor influencing motivation to adopt or implement the NGSS at each level is related to assessment. The reasons assessment affects motivation is different at each level. Key Finding 3 - Each interviewee at each level demonstrated awareness that the NGSS are significantly different from prior standards in some way. While teachers and SSCs sometimes cited the science practices as the critical difference, they were not able to meaningfully elaborate on what "science practices" are. Conversely, the District Coordinators demonstrated a deeper level of awareness and were able to comment more specifically on the practices and how they would affect science education in their state. Key Finding 4 - Regardless of level, the better a participant reflected an awareness of epistemology, the more likely they were to advocate for adoption and implementation of the NGSS. Similarly, the better a participant reflected an awareness of epistemology, the more likely they were motivated to consider adoption and implementation of the NGSS. The implications of the findings in this current study can; inform the supplemental materials and dissemination of information by standards writers, help policy makers engage stakeholders appropriately at each level by illustrating how national reform efforts play out in local-control states, and aid school based employees by identifying how and where they can participate in state level policy discussion and where their input could be valuable.Science educationScience Education, Mathematics, Science, and TechnologyDissertationsPlaying Prejudice: The Impact of Game-Play on Attributions of Racial and Gender Bias
http://academiccommons.columbia.edu/catalog/ac:175406
Hammer, Jessicahttp://dx.doi.org/10.7916/D8BP00ZKMon, 07 Jul 2014 00:00:00 +0000This dissertation explores new possibilities for changing Americans' theories about racism and sexism. Popular American rhetorics of discrimination, and learners' naïve models, are focused on individual agents' role in creating bias. These theories do not encompass the systemic and structural aspects of discrimination in American society. When learners can think systemically as well as agentically about bias, they become more likely to support systemic as well as individual remedies. However, shifting from an agentic to a systemic model of discrimination is both cognitively and emotionally challenging. To tackle this difficult task, this dissertation brings together the literature on prejudice reduction and conceptual change to propose using games as an entertainment-based intervention to change players' attribution styles around sexism and racism, as well as their attitudes about the same issues. "Playable model— anomalous data" theory proposes that games can model complex systems of bias, while instantiating learning mechanics that help players confront the limits of their existing models. The web-based game Advance was designed using playable model — anomalous data theory, and was used to investigate three questions. First, can a playable model — anomalous data game change players' likelihood of using systemic explanations for bias, and how does it compare to the effectiveness of a control text? Second, how does the game change players' attitudes as compared to a control text? Finally, are there differences between three different versions of the game that offer players different rewards for investigating the bias in the game system? Advance did not outperform the control text at changing players' likelihood of using systemic attributions for racism and sexism, nor did it outperform the control text in changing players' attitudes. However, significant differences were found between White and non-White player populations in their sensitivity to the different game conditions. White players were unaffected by differences between versions of the game, while non-White players showed differences in play behaviors, in systemic attribution likelihood, and in attitude. Given that White Americans may have more entrenched ideas about discrimination in America, we consider the impacts of the game on non-White player populations as an indicator of what future development of playable model — anomalous data games may be able to achieve.Educational psychology, Communication, Social psychologyCognitive Studies in Education, Mathematics, Science, and TechnologyDissertationsRelationships between Conceptual Knowledge and Reasoning about Systems: Implications for Fostering Systems Thinking in Secondary Science
http://academiccommons.columbia.edu/catalog/ac:175489
Lyons, Cherylhttp://dx.doi.org/10.7916/D8G73BTTMon, 07 Jul 2014 00:00:00 +0000Reasoning about systems is necessary for understanding many modern issues that face society and is important for future scientists and all citizens. Systems thinking may allow students to make connections and identify common themes between seemingly different situations and phenomena, and is relevant to the focus on cross-cutting concepts in science emphasized in the Framework for K-12 Science Education Standards (NRC, 2011) and Next Generation Science Standards (Achieve, 2013). At the same time, there is emerging empirical and theoretical support in science education for fostering the development of science reasoning alongside content understanding, as opposed to the perspective that reasoning occurs after a certain threshold of content mastery has been achieved. However, existing research on systems thinking has treated this reasoning as a set of universal skills and neglected the role of content, or has conceptualized a progression in which content mastery precedes systems reasoning without consideration of rudimentary forms of reasoning. This study focused on describing individual variations in the ways that 8th and 9th grade students reason about changes in a system over time to identify characteristics of systems and pre-systems thinking and to investigate the relationship between this reasoning and the students' application of content. This study found a generally linear relationship between content and reasoning, with interesting deviations from this trend among students who demonstrated at least a moderate level of content understanding but had not yet achieved mastery. Four profiles of this relationship emerged which warrant different instructional support. Implications are presented for science educators and developers of curricula and assessments. This includes recommendations for learning objectives, the design of written curriculum materials, and the development of assessments that aim to promote and measure reasoning about systems in science.Science educationcal2154Science Education, Mathematics, Science, and TechnologyDissertationsThe Effects Of Elementary Departmentalization On Mathematics Proficiency
http://academiccommons.columbia.edu/catalog/ac:175720
Taylor-Buckner, Nicolehttp://dx.doi.org/10.7916/D8D50K49Mon, 07 Jul 2014 00:00:00 +0000Mathematics education in the elementary schools has experienced many changes in recent decades. With the curriculum becoming more complex as a result of each modification, immense pressure has been put on schools to increase student proficiency. The Common Core State Standards is the latest example of this. These revisions to the mathematics curriculum require a comprehensive understanding of mathematics that the typical elementary teacher lacks. Some elementary schools have begun changing the organization of their classrooms from self-contained to departmentalized as a possible solution to this problem. The purpose of this quantitative study was to examine the effects of elementary departmentalization on student mathematics proficiency. This was done by exploring and comparing the background and educational characteristics, teaching practices, assessment methods, beliefs, and influence of departmentalized elementary mathematics teachers. The study also investigated the circumstances under which there are significant differences in mathematics proficiency between departmentalized and non-departmentalized elementary students, and examined if these differences continued into students' eighth-grade years and/or led to higher level eighth-grade mathematics course attainment. Additionally, the study aimed to determine if there was a relationship between elementary departmentalization and mathematics proficiency and also to identify additional factors that could lead to mathematics proficiency. Data came from the U.S. Department of Education's Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 (ECLS-K) data set. The ECLS-K is a national data set that followed the same children from kindergarten to eighth grade focusing on their school experiences from 1998 to 2007. Numerous statistical analyses were conducted on this rich data set, utilizing the statistical software Stata 13 and R. The results of this study indicate that there is a significant difference in the mathematics proficiency of departmentalized and non-departmentalized students when teachers have below-average mathematics backgrounds. The students of the mathematically below-average departmentalized teachers displayed the highest mathematics proficiency as well as the biggest gain in mathematics proficiency, and these higher proficiencies and gains continued into later grade levels. However, when exploring differences in mathematics proficiency among all students, there were no conclusive differences between departmentalized and non-departmentalized students. Regression models yielded inconclusive results as well, even after controlling for factors pertaining to classroom size, student demographics and socioeconomic status, student confidence, parental background, teacher knowledge and instructional practices, and prior student mathematical proficiency. Other findings include self-contained and departmentalized third-grade teachers being very similar in their educational backgrounds and teaching practices, whereas departmentalized and non-departmentalized fifth-grade teachers were found to be fairly different in their educational backgrounds and instructional practices. However, in both grade levels, self-contained teachers appeared to be more reliant on printed materials than departmentalized teachers.Mathematics education, Education policy, Elementary educationMathematics, Science, and Technology, Mathematics EducationDissertationsProfessional Learning Communities (PLCs) as a Means for School-Based Science Curriculum change
http://academiccommons.columbia.edu/catalog/ac:175723
Browne, Christihttp://dx.doi.org/10.7916/D88C9TD1Mon, 07 Jul 2014 00:00:00 +0000The challenge of school-based science curriculum change and educational reform is often presented to science teachers and departments who are not necessarily prepared for the complexity of considerations that change movements require. The development of a Professional Learning Community (PLC) focused on a science department's curriculum change efforts, may provide the necessary tools to foster sustainable school-based curriculum science changes. This research presents a case study of an evolving science department PLC consisting of 10 middle school science teachers from the same middle school and their efforts of school-based science curriculum change. A transformative mixed model case study with qualitative data and deepened by quantitative analysis, was chosen to guide the investigation. Collected data worked to document the essential developmental steps, the occurrence and frequency of the five essential dimensions of successful PLCs, and the influences the science department PLC had on the middle school science department's progression through school-based science curriculum change, and the barriers, struggles and inhibiting actions of the science department PLC. Findings indicated that a science department PLC was unique in that it allowed for a focal science departmental lens of science curriculum change to be applied to the structure and function of the PLC and therefore the process, proceedings, and results were directly aligned to and driven by the science department. The science PLC, while logically difficult to set-up and maintain, became a professional science forum where the middle school science teachers were exposed to new science teaching and learning knowledge, explored new science standards, discussed effects on student science learning, designed and critically analyzed science curriculum change application. Conclusions resulted in the science department PLC as an identified tool providing the ability for science departmental actions to lead to outcomes of science curriculum change improvements with the consideration but not the dictation of the larger school community and state agendas. Thus, the study's results work to fuse previously separated research on general PLCs and curriculum change efforts into a cohesive understanding of the unexplored potential of a science PLC and school-based science curriculum change.Science education, Teacher educationScience Education, Mathematics, Science, and TechnologyDissertationsExploring the Development of Classroom Group Identities in an Urban High School Chemistry Class
http://academiccommons.columbia.edu/catalog/ac:175708
Macaluso, Stefaniahttp://dx.doi.org/10.7916/D8F47M9KMon, 07 Jul 2014 00:00:00 +0000A key to achieving academic success in science is providing students with meaningful experiences and skills to negotiate how these experiences affect them and the society in which they live. Although students strive for academic success, a challenge that faces many urban science students and their teachers is finding ways to promote student engagement in the science classroom. In order to support students in urban settings and to better identify the ways in which students may better learn science concepts and develop a sense of belonging or affiliation to science, this qualitative research study explores the development of a classroom group identity (CGI) based on the frameworks of social identity theory, interaction ritual chain theory, and communities of practice. The interactions and experiences of eighteen student participants in a Bronx high school chemistry class were studied over the course of a full school year. Using a conceptual lens of classroom group identity, a model construct and definition were built identifying four stages of CGI development. At the culmination of the study, a positive change in perceptions, attitudes, leadership skills, and classroom behaviors in learning science was primarily observed by two students developing a CGI. The study has implications for the teaching and learning of high school sciences.Science education, Secondary education, Teacher educationsm3068Science Education, Mathematics, Science, and TechnologyDissertationsMathematical 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 EducationDissertationsUncovering Black/African American and Latina/o Students' Motivation to Learn Science: Affordances to Science Identity Development
http://academiccommons.columbia.edu/catalog/ac:176621
Mahfood, Denisehttp://dx.doi.org/10.7916/D8WH2N54Mon, 07 Jul 2014 00:00:00 +0000The following dissertation reports on a qualitative exploration that serves two main goals: (1) to qualitatively define and highlight science motivation development of Black/African American and Latina/o students as they learn science in middle school, high school, and in college and (2) to reveal through personal narratives how successful entry and persistence in science by this particular group is linked to the development of their science identities. The targeted population for this study is undergraduate students of color in science fields at a college or university. The theoretical frameworks for this study are constructivist theory, motivation theory, critical theory, and identity theories. The methodological approach is narrative which includes students' science learning experiences throughout the course of their academic lives. I use The Science Motivation Questionnaire II to obtain baseline data to quantitatively assess for motivation to learn science. Data from semi-structured interviews from selected participants were collected, coded, and configured into a story, and emergent themes reveal the important role of science learning in both informal and formal settings, but especially in informal settings that contribute to better understandings of science and the development of science identities for these undergraduate students of color. The findings have implications for science teaching in schools and teacher professional development in science learning.Science education, Educationdm2564Science Education, Mathematics, Science, and TechnologyDissertationsSounding Out Science: Incorporating Audio Technology to Assist Students with Learning Differences in Science Education
http://academiccommons.columbia.edu/catalog/ac:176062
Gomes, Clementhttp://dx.doi.org/10.7916/D8R49NZ2Mon, 07 Jul 2014 00:00:00 +0000With the current focus to have all students reach scientific literacy in the U.S, there exists a need to support marginalized students, such as those with Learning Disabilities/Differences (LD), to reach the same educational goals as their mainstream counterparts. This dissertation examines the benefits of using audio assistive technology on the iPad to support LD students to achieve comprehension of science vocabulary and semantics. This dissertation is composed of two papers, both of which include qualitative information supported by quantified data. The first paper, titled Using Technology to Overcome Fundamental Literacy Constraints for Students with Learning Differences to Achieve Scientific Literacy, provides quantified evidence from pretest and posttest analysis that audio technology can be beneficial for seventh grade LD students when learning new and unfamiliar science content. Analysis of observations and student interviews support the findings. The second paper, titled Time, Energy, and Motivation: Utilizing Technology to Ease Science Understanding for Students with Learning Differences, supports the importance of creating technology that is clear, audible, and easy for students to use so they benefit and desire to utilize the learning tool. Multiple correlation of Likert Survey analysis was used to identify four major items and was supported with analysis from observations of and interviews with students, parents, and educators. This study provides useful information to support the rising number of identified LD students and their parents and teachers by presenting the benefits of using audio assistive technology to learn science.Science education, Special education, Educational technologycvg2101Science Education, Mathematics, Science, and TechnologyDissertationsThe 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 EducationDissertationsScience Specialists in Urban Elementary Schools: An Ethnography Examining Science Teaching Identity, Motivation and Hierarchy in a High-Stakes Testing Climate
http://academiccommons.columbia.edu/catalog/ac:176821
Ronan, Darcyhttp://dx.doi.org/10.7916/D86T0JS3Mon, 07 Jul 2014 00:00:00 +0000There are few studies exploring the impact and effectiveness of the science specialist model or its implementation specifically in urban schools. This ethnography explores the roles and responsibilities of science specialists in urban elementary schools, drawing upon interviews with the science specialists, classroom teachers, and building administrators to portray the science-teaching identity and characteristics of the science specialists according to Social Identity Theory (Gee, 2000-2001) as well as classroom teacher science-teaching motivation, according to Expectancy Theory (Vroom, 1964). In this role, specialists provide science instruction, curriculum coordination and communication, and support of classroom teachers. The expectations and limits of leadership from the science specialist are also discussed. The use of science specialists to provide pull-out instruction, wherein a classroom teacher drops off her class for instruction by the specialist, results in a decreased sense of classroom teacher instrumentality. This model of science specialist instruction can also undercut other science-teaching motivation components like expectancy of success, science-teaching identity, self-efficacy and valence for science teaching. Science specialist instruction in a pull-out model can result in teacher disengagement from science instruction. Additionally, hierarchies flowing from school and district-level policy and practice are described and analyzed according to how they mediate and are mediated by a science specialist model.Science educationScience Education, Mathematics, Science, and TechnologyDissertations'Value Creation' Through Mathematical Modeling: Students' Mathematics Dispositions and Identities Developed in a Learning Community
http://academiccommons.columbia.edu/catalog/ac:176803
Park, Joo younghttp://dx.doi.org/10.7916/D87S7KXXMon, 07 Jul 2014 00:00:00 +0000This 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.Mathematics education, MathematicsMathematics, 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 EducationDissertationsExploring Algebra-based Problem Solving and Strategies of Spanish-speaking High School Students
http://academiccommons.columbia.edu/catalog/ac:165177
Hernandez-Duhon, Andreahttp://hdl.handle.net/10022/AC:P:21628Fri, 13 Sep 2013 00:00:00 +0000This dissertation analyzes differences found in Spanish-speaking middle school and high school students in algebra-based problem solving. It identifies the accuracy differences between word problems presented in English, Spanish and numerically based problems. The study also explores accuracy differences between each subgroup of Spanish-speaking students in each category. It identifies specific strategies used by successful students when solving algebra problems. The study also sought to identify factors that could serve to predict Spanish-speaking students' ability to accurately solve algebra word problems presented in English and Spanish. A heterogeneous urban sample composed of one hundred and fifty two middle school and high school students were given an assessment composed of pre-approved algebra-based problems and a biographical information sheet. Specific students were then chosen for individual interviews in which researcher sought to gain more in depth information about student's reaction to assessment. The study found that the average accuracy rate for Hispanics non-ELL and non-Hispanic students was significantly higher for numerically based problems than Spanish word problems. Similarly, the average accuracy rate for Hispanics non-ELL and non-Hispanic students was significantly higher in English word problems that in Spanish word problems. Results showed that there was a significant difference in the overall performance of the assessment between Hispanic ELL and Hispanic non-ELL students. On one particular set, set C (Spanish word problems), findings showed that Hispanic ELL students performed better than Hispanic non-ELL students and non-Hispanic students. All other subgroup comparisons did not show a significant difference. The study found that students who were most successful in the assessment: (a) used previous linguistics knowledge and memory of previously seen mathematical problems properly; (b) highlighted the question being asked; (c) used key words to identify mathematical principles and to aid in the translation process; (d) used diagrams, tables and graphs to organize data; (e) showed work and had all processes laid out clearly; and (f) displayed a clear verification process for their answer as strategies for successfully answering the problems. As it was evident through the study, the diversity in the Spanish speaking population and their needs exposes the need for teaching methods, which are inclusive of all populations. Schools must be sensitive to the diversity in which students learn and aim to individualize the teaching for every student. As Hispanics become the largest minority in the United States, understanding the diverse needs of Spanish speaking students in the classroom will be necessary for the development of a better educated society.Mathematics education, Hispanic American studiesach2125Mathematics, Science, and Technology, Mathematics EducationDissertationsIncreasing Diversity: Modeling of Social Capital for Navigating the Science and Health Professions Pipeline
http://academiccommons.columbia.edu/catalog/ac:174347
Rumala, Bernice B.http://hdl.handle.net/10022/AC:P:20860Fri, 28 Jun 2013 00:00:00 +0000Social capital theory states that resources, both actual and prospective, are inherently linked to networks and relationships that can be used as opportunities. Therefore, a basic tenet of social capital theory is that "relationships matter." In the science and health profession pipeline, strong mentoring relationships and collaborative research networks are critical elements in developing an individual's capacity for navigating the pipeline and for success and advancement in these fields. However, underrepresented minorities are often bereft of social capital because they lack proper mentorships and are often not part of "inner" circles for networking. Additionally, social capital can be leveraged to develop organizational capacity that supports diversity. In this dissertation, social capital theory is examined through the lens of three pipeline initiatives targeting pre-high school, high school, undergraduate, and graduate-level populations. The three initiatives (E-matching, achieving Successful Productive Academic Research Careers, and Mentoring in Medicine) were evaluated and the results are presented here as three related but unique manuscripts. The particular forms of social capital examined are knowledge, mentorship, and networks needed to navigate the pipeline for science and health professions careers. All three initiatives had significant impact on increasing social capital via the social capital indicators of increased knowledge, mentorship, networks, information and resources. Study results suggest that it would be useful to replicate these initiatives on a larger scale to build social capital at earlier levels of the pipeline to enhance diversity in the science and health professions. Additionally, study results suggest that the social capital obtained from brief interactions in short duration initiatives is valuable as a factor in assisting students to navigate the pipeline; therefore this should not be underestimated. Lastly, a logic model framework is provided for measuring social capital for navigating the STEM and health professions pipeline.Applied mathematics, Science education, Health sciencesbr2111Science Education, Mathematics, Science, and TechnologyDissertationsExploring the Impact of the Implementation of Reality Pedagogy: Self-efficacy, Social Capital, and Distributed Cognition
http://academiccommons.columbia.edu/catalog/ac:174519
Taher, Tanzinahttp://hdl.handle.net/10022/AC:P:20861Fri, 28 Jun 2013 00:00:00 +0000As our current society becomes more and more dependent on science and technology, it calls for our students to be more science-oriented and involved in science. However, as statistics show, our urban students are not as engaged in science classes, resulting in poor performance in science. With this fact in mind, this study explores a recently developed pedagogic approach called reality pedagogy. In this qualitative ethnographic case study, the yearlong experience of six urban students enrolled in a science class of an urban public secondary school where the pedagogic tools of reality pedagogy were being implemented is examined. The study examines reality pedagogy via the lens of self-efficacy, social capital, and distributed cognition frames in order to understand the contribution the tools of reality pedagogy offer. Participants in this study included immigrant and non-immigrant urban science students as well as students with learning disabilities (LD) and students with no learning disabilities (NLD). Findings of this study revealed that participating in reality pedagogy facilitated the development of self-efficacy in science of three of the four students, where one was an LD student and two were NLD students. The experiences of all four of these students are discussed in detail. The study also revealed that the two immigrant participants of reality pedagogy were positively impacted, in that both students' shared social capital was positively impacted and the frame of distributed cognition played a role in their science classroom participation.Science educationtt2137Science Education, Mathematics, Science, and TechnologyDissertationsState Policies to Achieve the Dream in Five States: An Audit of State Policies to Aid Student Access to and Success in Community Colleges in the First Five Achieving the Dream States
http://academiccommons.columbia.edu/catalog/ac:162392
Dougherty, Kevin J.; Kerrigan, Monica Reid; Nienhusser, Helmut Kennyhttp://hdl.handle.net/10022/AC:P:20762Fri, 14 Jun 2013 00:00:00 +0000This report presents the findings of an audit of state policies affecting access to, and success in, community colleges in five states—Florida, New Mexico, North Carolina, Texas, and Virginia. Given recent local and state initiatives to implement programs to improve student access and success, this report explores the existence of key policies relating to tuition, student aid, open door admissions, remedial (or developmental education), transfer, performance accountability, and a number of other key areas. Recommendations for future state policy are also discussed.Education policy, Community college educationkd109, hkn2001Mathematics, Science, and Technology, Higher and Postsecondary Education, Community College Research CenterReportsWhich 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 EducationDissertationsThe Mathematical Content Knowledge of Prospective Teachers in Iceland
http://academiccommons.columbia.edu/catalog/ac:161616
Johannsdottir, Bjorghttp://hdl.handle.net/10022/AC:P:20479Thu, 30 May 2013 00:00:00 +0000This study focused on the mathematical content knowledge of prospective teachers in Iceland. The sample was 38 students in the School of Education at the University of Iceland, both graduate and undergraduate students. All of the participants in the study completed a questionnaire survey and 10 were interviewed. The choice of ways to measure the mathematical content knowledge of prospective teachers was grounded in the work of Ball and the research team at the University of Michigan (Delaney, Ball, Hill, Schilling, and Zopf, 2008; Hill, Ball, and Schilling, 2008; Hill, Schilling, and Ball, 2004), and their definition of common content knowledge (knowledge held by people outside the teaching profession) and specialized content knowledge (knowledge used in teaching) (Ball, Thames, and Phelps, 2008). This study employed a mixed methods approach, including both a questionnaire survey and interviews to assess prospective teachers' mathematical knowledge on the mathematical topics numbers and operations and patterns, functions, and algebra. Findings, both from the questionnaire survey and the interviews, indicated that prospective teachers' knowledge was procedural and related to the "standard algorithms" they had learned in elementary school. Also, findings indicated that prospective teachers had difficulties evaluating alternative solution methods, and a common denominator for a difficult topic within both knowledge domains, common content knowledge and specialized content knowledge, was fractions. During the interviews, the most common answer for why a certain way was chosen to solve a problem or a certain step was taken in the solution process, was "because that is the way I learned to do it." Prospective teachers' age did neither significantly influence their test scores, nor their approach to solving problems during the interviews. Supplementary analysis revealed that number of mathematics courses completed prior to entering the teacher education program significantly predicted prospective teachers' outcome on the questionnaire survey.Comparison of the findings from this study to findings from similar studies carried out in the US indicated that there was a wide gap in prospective teachers' ability in mathematics in both countries, and that they struggled with similar topics within mathematics. In general, the results from this study were in line with prior findings, showing, that prospective elementary teachers relied on memory for particular rules in mathematics, their knowledge was procedural and they did not have an underlying understanding of mathematical concepts or procedures (Ball, 1990; Tirosh and Graeber, 1989; Tirosh and Graeber, 1990; Simon, 1993; Mewborn, 2003; Hill, Sleep, Lewis, and Ball, 2007). The findings of this study highlight the need for a more in-depth mathematics education for prospective teachers in the School of Education at the University of Iceland. It is not enough to offer a variety of courses to those specializing in the field of mathematics education. It is also important to offer in-depth mathematics education for those prospective teachers focusing on general education. If those prospective teachers teach mathematics, they will do so in elementary school where students are forming their identity as mathematics students.Mathematics education, Teacher educationbj2231Mathematics, Science, and Technology, Mathematics EducationDissertationsSocial Capital and Adolescents Mathematics Achievement: A Comparative Analysis of Eight European Cities
http://academiccommons.columbia.edu/catalog/ac:161622
Gisladottir, Berglindhttp://hdl.handle.net/10022/AC:P:20481Thu, 30 May 2013 00:00:00 +0000This study examines the impact of social capital on mathematics achievement in eight European cities. The study draws on data from the 2008 Youth in Europe survey, carried out by the Icelandic Center for Social Research and Analysis. The sample contains responses from 17,312 students in 9th and 10th grade of local secondary schools in the following cities: Bucharest in Romania, Kaunas, Klaípéda and Vilnius in Lithuania, Reykjavík in Iceland, Riga and Jurmala in Latvia and Sofia in Bulgaria. The study builds on social capital theory presented in 1988 by the American sociologist James Coleman. He argued that social capital in both family and community is a key factor in the creation of human capital, meaning that children that possess more social capital in their lives will do better in school. Several prior studies have empirically supported the theory, although most of those studies were carried out in the United States. The current study tests whether the theory of social capital holds across different cultures. The findings partly support the theory, showing that the key measures of social capital are positively correlated with mathematics achievement in all of the cities. The impact however was less in many of the cities than expected. Additionally, Coleman's key social capital variable did not positively associate with mathematics achievement in cities around Europe. The implications of that finding are discussed in the thesis.Mathematics education, Sociologybg2347Mathematics, 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 EducationDissertationsExamining the Effects of Gender, Poverty, Attendance, and Ethnicity on Algebra, Geometry, and Trigonometry Performance in a Public High School
http://academiccommons.columbia.edu/catalog/ac:160486
Shafiq, Hasanhttp://hdl.handle.net/10022/AC:P:20075Wed, 01 May 2013 00:00:00 +0000Over the last few decades school accountability for student performance has become an issue at the forefront of education. The federal No Child Left Behind Act of 2001 (NCLB) and various regulations by individual states have set standards for student performance at both the district and individual public and charter school levels, and certain consequences apply if the performance of students in an institution is deemed unsatisfactory. Conversely, rewards come to districts or schools that perform especially well or make a certain degree of improvement over their earlier results. Albeit with certain conditions, the federal government makes additional education money available to the states under NCLB. While testing is nothing new in American public education, the concept of district/school accountability for performance is at least relatively so. In New York City, where New York State Regents Examinations (NYSRE) have been a measure of student performance for many years, scores on these tests are low, often preventing students from receiving course credit, which in turn results in failure to graduate on schedule. In addition, rates of graduation from public high schools are low. The city and state have kept data on student performance broken out by a number of factors including socioeconomic status, ethnicity, attendance, and gender which point to an achievement gap among different groups. This study investigates a series of those factors associated with the mastery of high school Algebra, Geometry, and Trigonometry. This study concerns itself specifically with the effect that gender, socioeconomic status, attendance, and ethnicity may have on student achievement in a mathematics course and on standardized tests, specifically the NYSRE, an annual rite of passage for students in grades 9 through 11. This research considered and ran tests on data gathered from a single large New York City high school. In this study, a 12 two-way (between-groups) univariate analyses of variance (ANOVAs) were conducted to assess whether there were differences in students' mathematics achievement scores by gender, ethnicity, attendance, and family socio-economic status (SES). In addition, three Pearson correlation analyses were conducted to determine whether there was a correlation among Integrated Algebra, Geometry, and Algebra II/Trigonometry unit examination scores and Regents scores. Nine Pearson correlation analyses were conducted to determine whether there was a correlation between Regents scores and mathematics achievement unit examination scores. A correlation was run between each mathematics achievement score with the Regents score from each subject. Six two-way (between-groups) ANOVA were also conducted to assess whether there were difference in students' mathematics achievement among Black males, Black females, Hispanic males, and Hispanic females. Data were gathered, merged, and transferred into a Statistical Package for the Social Sciences (SPSS) 19.0 (IBM, 2010) for analysis. The findings indicate that attendance and family SES have a meaningful relationship to mathematics achievement in the New York City public high school which was the subject of this investigation. On the other hand, gender and ethnicity showed no relationship to students' mathematics achievement. As an implication of this research, school policies must focus more on the achievement gap of students from low-SES families and must encourage students to maintain good attendance. Students should have access to different forms of academic interventions that go beyond after-school or Saturday tutoring; academic intervention services; community counseling or mediation; or peer intervention or peer counseling through which students learn basic mathematics skills from each other to achieve college readiness.Mathematics education, Mathematicsmhs2143Mathematics, Science, and Technology, Mathematics EducationDissertationsAn Analysis of Interactions and Outcomes Associated with an Online Professional Development Course for Science Teachers
http://academiccommons.columbia.edu/catalog/ac:160552
Randle, David E.http://hdl.handle.net/10022/AC:P:20146Wed, 01 May 2013 00:00:00 +0000This mixed-methods study examined the interactions and learning outcomes of science teachers in an online graduate-level course on evolutionary biology intended to improve their content knowledge and science lesson planning. Discussion posts made by the teachers in this seven-week course were analyzed for cognitive presence using the Community of Inquiry framework. Compared to other studies examining cognitive presence, high levels of Integration level cognitive activity were observed (47% of total posts). This was most likely due to the design of the discussion prompts and expectations used to frame student participation. The questions were open-ended, and students were expected to use reference materials to construct their responses. During the course, 395 student posts contained statements that could be coded for scientific accuracy. Of these, 85% were coded as scientifically accurate. This reinforces reports from previous literature that the online environment is conducive to reflective and careful contributions by participants.As the course progressed, the number of faculty posts per discussion declined, while the number of student posts remained relatively constant. Student-to-student posts increased in frequency as faculty participation dropped. The number of student posts increased towards the end of each two-week discussion period, however the frequencies of posts with scientifically accurate statements and Integration level cognitive activity remained relatively constant over this same period. The increase in total posts was due to the increase in other types of communication in the discussions. Case study analysis was used to examine patterns of online behavior in three participants who achieved different course grades. A low-performing student had a pattern of intermittent activity, made low numbers of posts in each discussion, and had low percentages of posts that contained scientific statements or indicators of Integration level cognitive activity compared to classmates. A medium-performing learner posted infrequently but was efficient in making scientifically accurate posts that demonstrated Integration. Both the medium and low performer made most of their posts near the end of each two-week discussion period and had limited interaction with other learners. The high-performing learner demonstrated high levels of engagement with the course material. She posted frequently, introduced new resources to the other learners, and had high numbers of scientifically accurate and Integration level posts. An examination of teachers' views of the Nature of Science (NOS) using a pre- and post course Views of Nature of Science - C survey indicated that this group of teachers began the course with relatively informed views of many of the nature of science aspects. An exception was views about the nature of scientific theories and laws. At the start of the course 10 of 18 participants had naive views, five had partially informed views, and three had informed views. While scientific definitions of theories and laws were addressed in the course, there was no task that asked teachers to apply their understanding of this topic. When the course finished, six participants still had naive views, six held partially informed views, and six had informed views. Participants used course content to create teaching unit plans that indicated how they might use the course outcomes in their practice. Most of the learning objectives stated in the unit plans were grade-level appropriate when referenced to the Benchmarks for Science Literacy. The exception was the inclusion by some middle school teachers of detailed analyses of evolutionary relationships using genetic data. Although there was alignment of stated objectives to content from the online course and lesson activities, some of the teachers did not fully align assessments with their objectives.Based on these findings, it is suggested that designers of online instruction be mindful in the framing of learning tasks and use open-ended discussion prompts that require the use of reference materials if Integration level cognitive activity is the goal. The teachers in this course were generally able to utilize content from the course to create teaching applications, but more support for pedagogical applications could be an important addition for teachers who struggled with this task. This study reinforces previous research that indicates that online asynchronous discussions encourage reflection by learners. However, analysis of individuals who struggled in the course indicates that the online format may not suit all learners since consistent effort and the ability to communicate effectively in writing are important for success.Science education, Teacher educationder54Science Education, Mathematics, Science, and TechnologyDissertationsLearning the Rules of the Game: The Nature of Game and Classroom Supports When Using a Concept-Integrated Digital Physics Game in the Middle School Science Classroom
http://academiccommons.columbia.edu/catalog/ac:160791
Stewart Jr., Philliphttp://hdl.handle.net/10022/AC:P:20088Wed, 01 May 2013 00:00:00 +0000Games in science education is emerging as a popular topic of scholarly inquiry. The National Research Council recently published a report detailing a research agenda for games and science education entitled Learning Science Through Computer Games and Simulations (2011). The report recommends moving beyond typical proof-of-concept studies into more exploratory and theoretically-based work to determine how best to integrate games into K-12 classrooms for learning , as well as how scaffolds from within the game and from outside the game (from peers and teachers) support the learning of applicable science. This study uses a mixed-methods, quasi-experimental design with an 8th grade class at an independent school in southern Connecticut to answer the following questions: 1. What is the nature of the supports for science content learning provided by the game, the peer, and the teacher, when the game is used in a classroom setting? 2. How do the learning gains in the peer support condition compare to the solo play condition, both qualitatively and quantitatively? The concept-integrated physics game SURGE (Scaffolding Understanding through Redesigning Games for Education) was selected for this study, as it was developed with an ear towards specific learning theories and prior work on student understandings of impulse, force, and vectors. Stimulated recall interviews and video observations served as the primary sources and major patterns emerged through the triangulation of data sources and qualitative analysis in the software QSR NVivo 9. The first pattern which emerged indicated that scaffolding from within the game and outside the game requires a pause in game action to be effective, unless that scaffolding is directly useful to the player in the moment of action. The second major pattern indicated that both amount and type of prior gaming experience has somewhat complex effects on both the uses of supports and learning outcomes. In general, a high correlation was found between students who were more successful navigating supports from the game, the teacher, and the peer and higher gain scores from pre- to posttest. However, students with a lot of prior game experience that found the game to be easy without much assistance did not do as well from pre- to posttest as they did not need as much assistance from the game to do well and therefore missed out on important physics connections to impulse, force, and vectors. However, those students with little prior game experience did not find game scaffolds as useful and did not do as well from pre- to posttest without significant teacher and peer support to bolster or supplant the game's intended scaffolding. Implications for educators, educational game designers, and games in science education researchers are presented. It is argued that teachers must find ways to extract those scaffolds from the game which are easy to miss or require failure to activate so that all students, even those who find the game easy, are exposed to the intended learning in the game. Ideally, game designers are encouraged to find new ways to present scaffolds such that players of any ability can benefit from the connections from the game to physics.Science education, Physicspms2127Science Education, Mathematics, Science, and TechnologyDissertationsTetrahedra and Their Nets: Mathematical and Pedagogical Implications
http://academiccommons.columbia.edu/catalog/ac:160274
Mussa, Deregehttp://hdl.handle.net/10022/AC:P:20037Tue, 30 Apr 2013 00:00:00 +0000If one has three sticks (lengths), when can you make a triangle with the sticks? As long as any two of the lengths sum to a value strictly larger than the third length one can make a triangle. Perhaps surprisingly, if one is given 6 sticks (lengths) there is no simple way of telling if one can build a tetrahedron with the sticks. In fact, even though one can make a triangle with any triple of three lengths selected from the six, one still may not be able to build a tetrahedron. At the other extreme, if one can make a tetrahedron with the six lengths, there may be as many 30 different (incongruent) tetrahedra with the six lengths. Although tetrahedra have been studied in many cultures (Greece, India, China, etc.) Over thousands of years, there are surprisingly many simple questions about them that still have not been answered. This thesis answers some new questions about tetrahedra, as well raising many more new questions for researchers, teachers, and students. It also shows in an appendix how tetrahedra can be used to illustrate ideas about arithmetic, algebra, number theory, geometry, and combinatorics that appear in the Common Cores State Standards for Mathematics (CCSS -M). In particular it addresses representing three-dimensional polyhedra in the plane. Specific topics addressed are a new classification system for tetrahedra based on partitions of an integer n, existence of tetrahedra with different edge lengths, unfolding tetrahedra by cutting edges of tetrahedra, and other combinatorial aspects of tetrahedra.Mathematics education, Mathematicsdhm2114Mathematics, Science, and Technology, Mathematics EducationDissertationsMathematics Self-Efficacy and Its Relation to Profiency-Promoting Behavior and Performance
http://academiccommons.columbia.edu/catalog/ac:160627
Causapin, Mark Gabrielhttp://hdl.handle.net/10022/AC:P:19428Mon, 25 Mar 2013 00:00:00 +0000The purpose of this study was to verify Bandura's theory on the relationship of self-efficacy and performance particularly in mathematics among high school students. A rural school in the Philippines was selected for its homogenous student population, effectively reducing the effects of confounding variables such as race, ethnic and cultural backgrounds, socioeconomic status, and language. It was shown that self-efficacy was a positive but minor predictor of future performance only for male students who previously had higher mathematics grades. The effects were different between genders. It was not a strong predictor for women regardless of previous grades, and men with weaker mathematics skills. On the other hand, mathematics self-efficacy was predicted by previous mathematics achievement for women; and also the number of siblings and parental education for the higher performing women. The use of a second language in the mathematics classroom negatively affected confidence and performance. It was also found that there were differences in terms of academic behavior, peers, and family life between students with high and low self-efficacy. Positive behaviors were found for all female students regardless of self-efficacy levels and fewer were found among men. Negative behaviors were only found among low self-efficacy students. No differences were found in terms of the lives and families of the participants, but the interviews revealed that family members and their experiences of poverty affected educational goals and ambitions. In terms of other dispositional factors, students expressed classroom and test anxieties, concerns of being embarrassed in front of their classmates, and beliefs that mathematics was naturally difficult and not enjoyable. The students who did not talk about any of these themes were better performing and had higher self-efficacy scores.Mathematics education, Educational psychologyMathematics, Science, and Technology, Mathematics EducationDissertationsThe role of Bacterial-based Protist Communities in Aquatic and Soil Ecosystems and the Carbon Biogeochemical Cycle, with Emphasis on Naked Amoebae
http://academiccommons.columbia.edu/catalog/ac:157530
Anderson, O. Rogerhttp://hdl.handle.net/10022/AC:P:19334Wed, 13 Mar 2013 00:00:00 +0000Current research is reviewed on aquatic and soil microbial ecology with attention to the fate of organic carbon in bacterial-based protist food webs, including some new data. Particular attention is given to the effects of pulsed sources of low-molecular weight organic sources of carbon on soil respiration, changes in bacterial, nanoflagellate, and naked amoeba C-biomass, and evidence for throughput of carbon in microbial food webs in Arctic and some low-latitude, temperate soil environments. The proportion of pulsed sources of glucose-C that is sequestered in microbial biomass relative to loss as CO2 is examined in laboratory experimental studies, and implications of the research for microbial community dynamics and global warming due to terrestrial sources of respiratory CO2 are discussed.Biogeochemistry, Microbiology, Ecologyora1Lamont-Doherty Earth Observatory, Mathematics, Science, and TechnologyArticlesGood Mathematics Teaching: Perspectives of Beginning Secondary Teachers
http://academiccommons.columbia.edu/catalog/ac:159494
Leong, Kwan Euhttp://hdl.handle.net/10022/AC:P:19322Mon, 11 Mar 2013 00:00:00 +0000What is good mathematics teaching? The answer depends on whom you are asking. Teachers, researchers, policymakers, administrators, and parents usually provide their own view on what they consider is good mathematics teaching and what is not. The purpose of this study was to determine how beginning teachers define good mathematics teaching and what they report as being the most important attributes at the secondary level. This research explored whether there was a relationship between the demographics of the participants and the attributes of good teaching. In addition, factors that influence the understanding of good mathematics teaching were explored. A mixed methodology was used to gather information from the research participants regarding their beliefs and classroom practices of good mathematics teaching. The two research instruments used in this study were the survey questionnaire and a semi-structured interview. Thirty-three respondents who had one to two years of classroom experience comprised the study sample. They had graduated from a school of education in an eastern state and had obtained their teacher certification upon completing their studies. The beginning mathematics teachers selected these four definitions of good teaching as their top choices: 1) have High Expectations that all students are capable of learning; 2) have strong content knowledge (Subject Matter Knowledge); 3) create a Learning Environment that fosters the development of mathematical power; and 4) bring Enthusiasm and excitement to classroom. The three most important attributes in good teaching were: Classroom Management, Motivation, and Strong in Content Knowledge. One interesting finding was the discovery of four groups of beginning teachers and how they were associated with specific attributes of good mathematics teaching according to their demographics. Beginning teachers selected Immediate Classroom Situation, Mathematical Beliefs, Pedagogical Content Knowledge, and Colleagues as the top four factors from the survey analysis that influenced their understanding of good mathematics teaching. The study's results have implications for informing the types of mathematical knowledge required for pre-service teachers that can be incorporated into teacher education programs and define important attributes of good mathematics teaching during practicum.Mathematics education, Mathematics, Teacher educationMathematics, Science, and Technology, Mathematics EducationDissertationsWhen beginning mathematics teachers report acquiring successful attributes: Reflections on teacher education
http://academiccommons.columbia.edu/catalog/ac:157016
Wasserman, Nicholashttp://hdl.handle.net/10022/AC:P:19103Mon, 18 Feb 2013 00:00:00 +0000Education plays a vital role in any society; so much so, that countries strive to have not only adequate, but excellent educators in their classrooms. The aim of this study was to understand how beginning secondary mathematics teachers define success and to what experiences they attribute that success. Specifically, the central research question addressed was, "To what degree were significant attributes or experiences, important to the success of the first year teaching, learned pre-teacher education program, during a program, or post-program?" The practical goal of filling classrooms with great educators needs to be informed by research on how best to recruit highly qualified candidates into the field of mathematics education and how best to facilitate the teacher preparation process. This study employed a mixed methodology, using a sample of beginning secondary mathematics teachers to gather both quantitative and qualitative data on when they reported gaining influential knowledge or experiences. In particular, input from those who have had some success as beginning mathematics teachers was desired. The interview protocol designed for these participants added depth to the survey responses. Emphasis was placed on the relative importance of the three stages, pre-, during, and post-program, in developing common attributes associated with good teaching. Two characteristics were generally discussed as developing pre-program: being a self-starting and hard-working individual, and holding a belief that every student can learn. Beginning teachers viewed these traits as important for their success. Participants also felt that they acquired both practical classroom tools and educational theory from their teacher education program; having program instructors model pedagogy and mathematical instruction, and having opportunities to practice incorporating theory into their teaching were also seen as important. These aspects distinguished particularly prominent roles that the teacher education program played in shaping its graduates. Classroom management and being flexible and adaptive to different contexts were the most notable qualities frequently reported as being learned post-program. The study's results have implications for informing the types of students a mathematics education program should try to attract or recruit and defining areas where practicum or internship components might be incorporated into the teacher education process.Mathematics education, Teacher education, Secondary educationMathematics, Science, and Technology, Mathematics EducationDissertationsProof and Reasoning in Secondary School Algebra Textbooks
http://academiccommons.columbia.edu/catalog/ac:156775
Dituri, Philip Charleshttp://hdl.handle.net/10022/AC:P:19092Fri, 15 Feb 2013 00:00:00 +0000The 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.Mathematics education, Mathematics, Educationpcd2102Mathematics, Science, and Technology, Mathematics EducationDissertationsGender, Ethnicity, and Physics Education: Understanding How Black Women Build Their Identities as Scientists
http://academiccommons.columbia.edu/catalog/ac:155693
Rosa, Katemarihttp://hdl.handle.net/10022/AC:P:18782Wed, 23 Jan 2013 00:00:00 +0000This research focuses on the underrepresentation of minoritized groups in scientific careers. The study is an analysis of the relationships between race, gender, and those with careers in the sciences, focusing on the lived experiences of Black women physicists, as viewed through the lens of women scientists in the United States. Although the research is geographically localized, the base-line question is clear and mirrors in the researcher's own intellectual development: "How do Black women physicists describe their experiences towards the construction of a scientific identity and the pursuit of a career in physics?" Grounded on a critical race theory perspective, the study uses storytelling to analyze how these women build their identities as scientists and how they have negotiate their multiple identities within different communities in society. Findings show that social integration is a key element for Black women physicists to enter study groups, which enables access to important resources for academic success in STEM. The study has implications for physics education and policymakers. The study reveals the role of the different communities that these women are part of, and the importance of public policies targeted to increase the participation of underrepresented groups in science, especially through after-school programs and financial support through higher education.Science education, Gender studies, Black studieskdr2109Science Education, Mathematics, Science, and TechnologyDissertationsAnalysis of Mathematical Fiction with Geometric Themes
http://academiccommons.columbia.edu/catalog/ac:153198
Shloming, Jennifer Rebeccahttp://hdl.handle.net/10022/AC:P:14870Wed, 10 Oct 2012 00:00:00 +0000Analysis of mathematical fiction with geometric themes is a study that connects the genre of mathematical fiction with informal learning. This study provides an analysis of 26 sources that include novels and short stories of mathematical fiction with regard to plot, geometric theme, cultural theme, and presentation. The authors' mathematical backgrounds are presented as they relate to both geometric and cultural themes. These backgrounds range from having little mathematical training to advance graduate work culminating in a Ph.D. in mathematics. This thesis demonstrated that regardless of background, the authors could write a mathematical fiction novel or short story with a dominant geometric theme. The authors' pedagogical approaches to delivering the geometric themes are also discussed. Applications from this study involve a pedagogical component that can be used in a classroom setting. All the sources analyzed in this study are fictional, but the geometric content is factual. Six categories of geometric topics were analyzed: plane geometry, solid geometry, projective geometry, axiomatics, topology, and the historical foundations of geometry. Geometry textbooks aligned with these categories were discussed with regard to mathematical fiction and formal learning. Cultural patterns were also analyzed for each source of mathematical fiction. There were also an analysis of the integration of cultural and geometric themes in the 26 sources of mathematical fiction; some of the cultural patterns discussed are gender bias, art, music, academia, mysticism, and social issues. On the basis of this discussion, recommendations for future studies involving the use of mathematical fiction were made.Mathematics education, Mathematicsjrs2137Mathematics, Science, and Technology, Mathematics EducationDissertationsModern incursions of tropical Radiolaria into the Arctic Ocean
http://academiccommons.columbia.edu/catalog/ac:151921
Bjørklund, Kjell R.; Kruglikova, Svetlana B.; Anderson, O. Rogerhttp://hdl.handle.net/10022/AC:P:14474Tue, 21 Aug 2012 00:00:00 +0000Plankton samples obtained by the Norwegian Polar Institute (August, 2010) in an area north of Svalbard contained an unusual abundance of tropical and subtropical radiolarian taxa (98 in 145 total observed taxa), not typically found at these high latitudes. A detailed analysis of the composition and abundance of these Radiolaria suggests that a pulse of warm Atlantic water entered the Norwegian Sea and finally entered into the Arctic Ocean, where evidence of both juvenile and adult forms suggests they may have established viable populations. Among radiolarians in general, this may be a good example of ecotypic plasticity. Radiolaria, with their high species number and characteristic morphology, can serve as a useful monitoring tool for pulses of warm water into the Arctic Ocean. Further analyses should be followed up in future years to monitor the fate of these unique plankton assemblages and to determine variation in northward distribution and possible penetration into the polar basin. The fate of this tropical fauna (persistence, disappearance, or genetic intermingling with existing taxa) is presently unknown. The current event may not be unique, nor a consequence of global warming, because analyses of sediment samples suggest that several natural pulses of warm water of this kind occurred in the prior century and, indeed, there may be more in years to come.Biological oceanographyLamont-Doherty Earth Observatory, Mathematics, Science, and TechnologyArticlesThe Use of Cartoons as Teaching a Tool in Middle School Mathematics
http://academiccommons.columbia.edu/catalog/ac:149393
Cho, Hoyunhttp://hdl.handle.net/10022/AC:P:13930Mon, 09 Jul 2012 00:00:00 +0000This 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.Mathematics education, Teacher education, Educationhc2483Mathematics, Science, and Technology, Mathematics EducationDissertationsVisual thinking networking promotes long-term meaningful learning and achievement for 9th grade earth science students
http://academiccommons.columbia.edu/catalog/ac:149291
Longo, Palma Jonihttp://hdl.handle.net/10022/AC:P:13894Fri, 06 Jul 2012 00:00:00 +0000An experimental and interview-based design was used to test the efficacy of visual thinking networking (VTN), a new generation of metacognitive learning strategies. Students constructed network diagrams using semantic and figural elements to represent knowledge relationships. The findings indicated the importance of using color in VTN strategies. The use of color promoted the encoding and reconstruction of earth science knowledge in memory and enhanced higher order thinking skills of problem solving. Fifty-six ninth grade earth science students (13-15 years of age) in a suburban school district outside New York City were randomly assigned to three classes with the same instructor. Five major positive findings emerged in the areas of problem solving achievement, organization of knowledge in memory, problem solving strategy dimensionality, conceptual understanding, and gender differences. A multi-covariate analysis was conducted on the pre-post gain scores of the AGI/NSTA Earth Science Examination (Part 1). Students who used the color VTN strategies had a significantly higher mean gain score on the problem solving criterion test items than students who used the black/white VTN (p = .003) and the writing strategies for learning science (p < .001). During a think-out-loud problem solving interview, students who used the color VTN strategies: (1) significantly recalled more earth science knowledge than students who used the black/white VTN (p = .021) and the writing strategies (p < .001); (2) significantly recalled more interrelated earth science knowledge than students who used black/white VTN strategies (p = .048) and the writing strategy (p < .001); (3) significantly used a greater number of action verbs than students who used the writing strategy (p = .033). a significantly higher mean number of conceptually accurate propositions than students who used the black/white VTN (p = .018) and the writing strategies (p = .010). Gender influenced the choice of VTN strategy. Females used significantly more color VTN strategies, while males used predominately black/white VTN strategies (p = .01). A neurocognitive model, the encoding activation theory of the anterior cingulate (ENACT-AC), is proposed as an explanation for these findings.Science education, Secondary educationScience Education, Lamont-Doherty Earth Observatory, Mathematics, Science, and TechnologyDissertationsDe-Marginalizing Science in the Early Elementary Classroom: Fostering Reform-Based Teacher Change through Professional Development, Accountability, and Addressing Teachers' Dilemmas
http://academiccommons.columbia.edu/catalog/ac:147638
Berg, Alissa Bethanyhttp://hdl.handle.net/10022/AC:P:13422Wed, 06 Jun 2012 00:00:00 +0000To develop a scientifically literate populace, students must acquire the motivation and foundational skills for success in science beginning at an early age. Unfortunately, science instruction is often marginalized in elementary schools for reasons including teachers' lack of confidence in teaching science and an overemphasis on literacy and mathematics. This study employed a case study design to examine the impact of teachers' dilemmas, career stage, coaching, and other forms of support on elementary teachers' abilities to teach science more often and in more reform-based ways. The conceptual lenses used to guide this dissertation include the theory related to teacher change, dilemmas, reform-oriented science teaching, and the professional learning continuum. Findings suggest that teachers' dilemmas must be addressed in order for them to move toward more reform-based science teaching practices. It was found that how teachers reconcile their dilemmas is due in part to their career stage, level of readiness, and access to a more knowledgeable other who can assist them in learning and enacting reform-based instruction. Moreover, the likelihood and extent of teacher change appears to be related to teachers recognizing a need to change their practice, developing the capacity to change, feeling accountable to change, and possessing the motivation to change. Implications for teacher educators, professional development providers, and curriculum developers are presented. It is argued that teachers require support the length of their career and, to be effective, this support must be personalized to their diverse and changing needs and responsive to the context in which they teach.Science education, Elementary education, Adult educationabb2142Science Education, Mathematics, Science, and TechnologyDissertationsDeveloping Computational Thinking Through Grounded Embodied Cognition
http://academiccommons.columbia.edu/catalog/ac:146732
Fadjo, Cameron Lawrencehttp://hdl.handle.net/10022/AC:P:13168Mon, 07 May 2012 00:00:00 +0000Two studies were conducted to examine the use of grounded embodied pedagogy, construction of Imaginary Worlds (Study 1), and context of instructional materials (Study 2) for developing learners' Computational Thinking (CT) Skills and Concept knowledge during the construction of digital artifacts using Scratch, a block-based programming language. Utilizing a conceptual framework for grounded embodied pedagogy called Instructional Embodiment, learners physically enacted (Direct Embodiment) and mentally simulated (Imagined Embodiment) the actions and events as presented within pre-defined Scripts. Instructional Embodiment utilizes action, perception, and environment to create a dynamic, interactive teaching and learning scenario that builds upon previous research in embodied teaching and learning. The two studies described herein examined the effects of Instructional Embodiment, Imaginary World Construction, and Context on the development of specific Computational Thinking Concepts and Skills. In particular, certain CT Concepts, such as Conditionals, Variables, Thread Synchronization, Collision Detection, and Events, and CT Skills, such as abstraction and pattern recognition, were identified and measured within the learners' individual digital artifacts. Presence and/or frequency of these Concepts and Skills were used to determine the extent of Computational Thinking development. In Study 1, fifty-six sixth- and seventh-grade students participated in a fifteen-session curricular program during the academic school day. This study examined the type of instruction and continuity of Imaginary World Construction on the development of certain CT Skills and Concepts used in a visual novel created in Scratch. Main effects were found for learners who physically embodied the pre-defined instructional materials: embodying the pre-defined Scripts led to the learners using significantly more 'speech' Blocks in their projects and more Absolute Positioning Blocks for 'motion' than those who did not physically embody the same Scripts. Significant main effects were also found for continuity of Imaginary World Construction: learners who were instructed to continue the premise of the first digital artifact (Instructional Artifact) implemented significantly more computational structures in their second digital artifact (Unique Artifact) than those who were instructed to create a Unique Artifact with a premise of their own design. In Study 2, seventy-eight sixth- and seventh-grade students participated in a seventeen-session curricular program during the academic school day. This study examined the type of instruction and context of instructional materials on the development of CT Skills and Concepts during the construction of a video game using Scratch. Similar to Study 1, findings suggest that physically embodying the actions presented within the pre-defined instructional materials leads to greater implementation of many of these same structures during individual artifact construction. The study also showed that as the pre-defined Scripts become more complex (e.g. single-threaded to multi-threaded), the effect of physical embodiment on the development of CT Skills and complex CT Concept structures becomes less pronounced. Findings from this study also suggest that Context has a significant effect on identifying and implementing the CT Skill pattern recognition: learning CT Concepts from an Unfamiliar Context had a significant positive effect on the implementation of both Broadcast/Receive couplings and Conditional Logic and Operator patterns. In sum, the findings suggest that the type of instruction, the continuity of the Imaginary World being constructed, and the context of the instructional materials all play a significant role in the learners' ability to develop certain Computational Thinking Skills and Concept knowledge. The findings also suggest that a physically embodied approach to teaching abstract concepts that is grounded in an unfamiliar context is the most effective way to integrate a grounded embodied approach to pedagogy within a formal instructional setting.Cognitive psychology, Educational psychology, Educational technologyclf2110Cognitive Studies in Education, Human Development, Mathematics, Science, and TechnologyDissertationsA Cabinet of Mathematical Curiosities at Teachers College: David Eugene Smith's Collection
http://academiccommons.columbia.edu/catalog/ac:185885
Murray, Diane Rosehttp://dx.doi.org/10.7916/D8RV0MPWMon, 30 Apr 2012 00:00:00 +0000This dissertation is a history of David Eugene Smith's collection of historical books, manuscripts, portraits, and instruments related to mathematics. The study analyzes surviving documents, images, objects, college announcements and catalogs, and secondary sources related to Smith's collection. David Eugene Smith (1860 - 1944) travelled the world in search of rare and interesting pieces of mathematics history. He enjoyed sharing these experiences and objects with his family, friends, colleagues, and students. Smith's collection had a remarkable journey itself. It was once part of the Educational Museum of Teachers College. This museum existed from 1899 - 1914 and was quite popular among educators and students. Smith was director of the museum beginning in 1909, although, he had a major influence on the museum from the moment he began his professorship at Teachers College in 1901. After the Educational Museum of Teachers College disbanded, the collection was exhibited in numerous venues. George A. Plimpton (1855 - 1936) created the Permanent Educational Exhibit that housed both modern educational items, as well as, historical pieces for display. Since Smith and Plimpton were great friends and fellow collectors, Smith's collection was included in the historical section of Plimpton's establishment. Unfortunately, due to the hard times of the world at this moment, the Permanent Educational Exhibit closed in 1917. Smith continued to exhibit his collection of mathematical artifacts through the Museums of the Peaceful Arts, founded by George F. Kunz (1856 - 1932), the New York Museum of Science and Industry, Teachers College, and Columbia University. Smith's research, teaching, and publications were directly influenced by his collection. Throughout most of his published works are images and photographs of items in his collection. He also believed in the importance of having primary sources included in mathematics education. This view he followed in his own teaching, which included research in his collection. David Eugene Smith's collection could never be replicated and thus is quite unique and valuable. Smith donated his collection to Columbia University's Libraries in the 1930s. Various exhibits of his collection have occurred since then, the most recent concluded in 2003. The history of Smith's mathematical collection is important to the history of mathematics education as it displays the importance of preserving mathematical books, manuscripts, portraits, and instruments for future generations to research.Mathematics education, History of education, Museum studiesdrm2132Mathematics, Science, and Technology, Mathematics EducationDissertationsAsian 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 EducationDissertationsStatistics for Learning Genetics
http://academiccommons.columbia.edu/catalog/ac:146201
Charles, Abigail Sheenahttp://hdl.handle.net/10022/AC:P:13015Tue, 17 Apr 2012 00:00:00 +0000This study investigated the knowledge and skills that biology students may need to help them understand statistics/mathematics as it applies to genetics. The data are based on analyses of current representative genetics texts, practicing genetics professors' perspectives, and more directly, students' perceptions of, and performance in, doing statistically-based genetics problems. This issue is at the emerging edge of modern college-level genetics instruction, and this study attempts to identify key theoretical components for creating a specialized biological statistics curriculum. The goal of this curriculum will be to prepare biology students with the skills for assimilating quantitatively-based genetic processes, increasingly at the forefront of modern genetics. To fulfill this, two college level classes at two universities were surveyed. One university was located in the northeastern US and the other in the West Indies. There was a sample size of 42 students and a supplementary interview was administered to a select 9 students. Interviews were also administered to professors in the field in order to gain insight into the teaching of statistics in genetics. Key findings indicated that students had very little to no background in statistics (55%). Although students did perform well on exams with 60% of the population receiving an A or B grade, 77% of them did not offer good explanations on a probability question associated with the normal distribution provided in the survey. The scope and presentation of the applicable statistics/mathematics in some of the most used textbooks in genetics teaching, as well as genetics syllabi used by instructors do not help the issue. It was found that the text books, often times, either did not give effective explanations for students, or completely left out certain topics. The omission of certain statistical/mathematical oriented topics was seen to be also true with the genetics syllabi reviewed for this study. Nonetheless, although the necessity for infusing these quantitative subjects with genetics and, overall, the biological sciences is growing (topics including synthetic biology, molecular systems biology and phylogenetics) there remains little time in the semester to be dedicated to the consolidation of learning and understanding.Mathematics education, Statistics, Geneticsasc2119Mathematics, 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 EducationDissertationsSoil Respiration, Climate Change and the Role of Microbial Communities
http://academiccommons.columbia.edu/catalog/ac:141222
Anderson, O. Rogerhttp://hdl.handle.net/10022/AC:P:11729Mon, 07 Nov 2011 00:00:00 +0000Although this contribution is not intended to be a comprehensive perspective on current knowledge of soil respiration, a brief overview of some pertinent research on global patterns of soil respiration is presented first to establish a context for the subsequent more focused discussion of the role of microbial communities in soil carbon budgets and net respiratory CO2 flux to the atmosphere. Major reviews, and relevant broad research studies of current knowledge about regional and global respiratory flux patterns, are available from other sources. These include reviews of terrestrial respiration in broad geographical regions (e.g. [Luo and Zhou, 2006] , [Peng and Apps, 2000] , [Raich and Schlesinger, 1992] , [Schimel, 1995] and [Schlesinger, 1997] ); in particular geographic regimes and biomes (e.g. [Anderson, 2010a] , [Bekku et al., 2003] , [Bond-Lamberty and Thomson, 2010] and [Townsend et al., 1992] ); and in relation to soil decomposition processes (e.g. [Adl, 2003] and [Tate, 1995] ). Calculated on a global scale, soil respiration releases carbon at a rate that is more than one order of magnitude larger than anthropogenic emissions (Luo and Zhou 2006, p. 24). With increasing evidence of global climate change, including increasing global temperature and likely major changes in patterns of precipitation, effects on soil microbial communities are likely to be significant, especially at higher latitudes where thawing of the permafrost may release substantial quantities of stored-up carbon compounds, thus increasing microbial respiration and efflux of CO2 to the atmosphere. In the final sections, discussion focuses on emerging evidence of the effects of climate change, especially changing precipitation patterns and soil moisture, on the dynamics of microbial communities and respiratory CO2 emissions. Some of the prospects and challenges for future inquiry on the role of soil microbial communities in terrestrial carbon budgets and CO2 efflux are discussed in relation to emerging research themes and new methodological approaches.Environmental science, Climate changeora1Lamont-Doherty Earth Observatory, Mathematics, Science, and TechnologyArticlesA History of Trigonometry Education in the United States: 1776-1900
http://academiccommons.columbia.edu/catalog/ac:132221
Van Sickle, Jennahttp://hdl.handle.net/10022/AC:P:10377Mon, 16 May 2011 00:00:00 +0000This dissertation traces the history of the teaching of elementary trigonometry in United States colleges and universities from 1776 to 1900. This study analyzes textbooks from the eighteenth and nineteenth centuries, reviews in contemporary periodicals, course catalogs, and secondary sources. Elementary trigonometry was a topic of study in colleges throughout this time period, but the way in which trigonometry was taught and defined changed drastically, as did the scope and focus of the subject. Because of advances in analytic trigonometry by Leonhard Euler and others in the seventeenth and eighteenth centuries, the trigonometric functions came to be defined as ratios, rather than as line segments. This change came to elementary trigonometry textbooks beginning in antebellum America and the ratios came to define trigonometric functions in elementary trigonometry textbooks by the end of the nineteenth century. During this time period, elementary trigonometry textbooks grew to have a much more comprehensive treatment of the subject and considered trigonometric functions in many different ways. In the late eighteenth century, trigonometry was taught as a topic in a larger mathematics course and was used only to solve triangles for applications in surveying and navigation. Textbooks contained few pedagogical tools and only the most basic of trigonometric formulas. By the end of the nineteenth century, trigonometry was taught as its own course that covered the topic extensively with many applications to real life. Textbooks were full of pedagogical tools. The path that the teaching of trigonometry took through the late eighteenth and nineteenth centuries did not always move in a linear fashion. Sometimes trigonometry education stayed the same for a long time and then was suddenly changed, but other times changes happened more gradually. There were many international influences, and there were many influential Americans and influential American institutions that changed the course of trigonometry instruction in this country. This dissertation follows the path of those changes from 1776 to 1900. After 1900, trigonometry instruction became a topic of secondary education rather than higher education.Mathematics education, Higher education, History of educationjrv2107Mathematics, 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 EducationDissertationsFinal Report: Video Interactions for Teaching and Learning (VITAL): A Learning Environment for Courses in Early Childhood Mathematics Education
http://academiccommons.columbia.edu/catalog/ac:125650
Moretti, Frank A.; Ginsburg, Herbert P.http://hdl.handle.net/10022/AC:P:8678Fri, 02 Apr 2010 00:00:00 +0000The VITAL Early Childhood Mathematics Education Project final report summarizes a five-year endeavor funded by the National Science Foundation to support the development of and research on Video Interactions for Teaching and Learning (VITAL), a web-based platform for the dissemination of courses on early childhood mathematics education and tools for video analysis. Developed by the Columbia Center for New Media Teaching and Learning (CCNMTL) and Jacob H. Schiff Foundations Professor of Psychology and Education Herbert P. Ginsburg of Teachers College, VITAL helps education students learn more about the teaching and assessment of children by viewing, clipping, and annotating videos of children engaged in mathematical activities, and using their selected clips as evidence to support arguments in a multimedia essay space, thereby encouraging the development of formative assessment skills and better-informed practice as teachers. The VITAL report details the products created throughout the grant period, including the open-source VITAL software—tools for viewing and editing videos and a multimedia essay space—the VITAL early childhood mathematics curriculum, video library, model courses for use at other institutions, faculty guide, and numerous publications, as well as results of research performed by the VITAL assessment team. The Java-based iteration of the VITAL codebase has been released under the Educational Community License, Version 2.0. http://code.google.com/p/vital-video/Library sciencefam21, hpg4Human Development, Mathematics, Science, and Technology, Libraries and Information Services, Columbia Center for New Media Teaching and LearningReports