Matching Items (21)
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- All Subjects: Mathematics Education
- All Subjects: Efficacy
- Creators: Roh, Kyeong Hah
- Creators: Zambo, Ronald
- Creators: Saldanha, Luis
Description
This study contributes to the ongoing discussion of Mathematical Knowledge for Teaching (MKT). It investigates the case of Rico, a high school mathematics teacher who had become known to his colleagues and his students as a superbly effective mathematics teacher. His students not only developed excellent mathematical skills, they also developed deep understanding of the mathematics they learned. Moreover, Rico redesigned his curricula and instruction completely so that they provided a means of support for his students to learn mathematics the way he intended. The purpose of this study was to understand the sources of Rico's effectiveness. The data for this study was generated in three phases. Phase I included videos of Rico's lessons during one semester of an Algebra II course, post-lesson reflections, and Rico's self-constructed instructional materials. An analysis of Phase I data led to Phase II, which consisted of eight extensive stimulated-reflection interviews with Rico. Phase III consisted of a conceptual analysis of the prior phases with the aim of creating models of Rico's mathematical conceptions, his conceptions of his students' mathematical understandings, and his images of instruction and instructional design. Findings revealed that Rico had developed profound personal understandings, grounded in quantitative reasoning, of the mathematics that he taught, and profound pedagogical understandings that supported these very same ways of thinking in his students. Rico's redesign was driven by three factors: (1) the particular way in which Rico himself understood the mathematics he taught, (2) his reflective awareness of those ways of thinking, and (3) his ability to envision what students might learn from different instructional approaches. Rico always considered what someone might already need to understand in order to understand "this" in the way he was thinking of it, and how understanding "this" might help students understand related ideas or methods. Rico's continual reflection on the mathematics he knew so as to make it more coherent, and his continual orientation to imagining how these meanings might work for students' learning, made Rico's mathematics become a mathematics of students--impacting how he assessed his practice and engaging him in a continual process of developing MKT.
ContributorsLage Ramírez, Ana Elisa (Author) / Thompson, Patrick W. (Thesis advisor) / Carlson, Marilyn P. (Committee member) / Castillo-Chavez, Carlos (Committee member) / Saldanha, Luis (Committee member) / Middleton, James A. (Committee member) / Arizona State University (Publisher)
Created2011
Description
Teacher attrition and the migration between schools and districts can have a negative impact on quality of education and teacher performance. Novice teachers leave the profession because they are overwhelmed by the workload and responsibilities of the job. In a previous action research cycle, I found that novice teachers' perceptions of isolation and lack of opportunities to share experiences had a negative effect on teacher perceptions of efficacy. This action research project examines the effect of leveraging social media and professional learning communities to provide opportunities for a group of novice teachers to share experiences and seek advice. By addressing the challenges that novice teachers face and providing solutions for common problems, it is the hope of this researcher that highly effective teachers will remain in the classroom. The results of the study indicate that the combined use of Twitter and YouTube in collaboration with professional learning communities will improve teacher perceptions of efficacy. Teachers who participated in the social media based professional learning communities are also more likely to remain in the classroom.
ContributorsBostick, Bradley Alan (Author) / Zambo, Ronald (Thesis advisor) / Heck, Thomas (Committee member) / Isai, Shelley (Committee member) / Arizona State University (Publisher)
Created2013
Description
The need for improved mathematics education in many of America's schools that serve students from low income households has been extensively documented. This practical action research study, set in a suburban Title I school with a primarily Hispanic, non-native English speaking population, is designed to explore the effects of the progression through a set of problem solving solution strategies on the mathematics problem solving abilities of 2nd grade students. Students worked in class with partners to complete a Cognitively Guided Instruction-style (CGI) mathematics word problem using a dictated solution strategy five days a week for twelve weeks, three or four weeks for each of four solution strategies. The phases included acting out the problem using realia, representing the problem using standard mathematics manipulatives, modeling the problem using a schematic representation, and solving the problem using a number sentence. Data were collected using a five question problem solving pre- and post-assessment, video recorded observations, and Daily Answer Recording Slips or Mathematics Problem Solving Journals. Findings showed that this problem solving innovation was effective in increasing the problem solving abilities of all participants in this study, with an average increase of 63% in the number of pre-assessment to post-assessment questions answered correctly. Additionally, students increased the complexity of solutions used to solve problems and decreased the rate of guessing at answers to word problems. Further rounds of research looking into the direct effects of the MKO are suggested as next steps of research.
ContributorsSpilde, Amy (Author) / Zambo, Ronald (Thesis advisor) / Heck, Thomas (Committee member) / Nicoloff, Stephen J. (Committee member) / Arizona State University (Publisher)
Created2013
Description
ABSTRACT There is a continuing emphasis in the United States to improve student's mathematical abilities and one approach is to better prepare teachers. This study investigated the effects of using lesson study with preservice secondary mathematics teachers to improve their proficiency at planning and implementing instruction. The participants were students (preservice teachers) in an undergraduate teacher preparation program at a private university who were enrolled in a mathematics methods course for secondary math teachers. This project used lesson study to engage preservice teachers in collaboratively creating lessons, field testing them, using feedback to revise the lessons, and re-teaching the revised lesson. The preservice teachers worked through multiple cycles of the process in their secondary math methods class receiving feedback from their peers and instructor prior to teaching the lessons in their field experience (practicum). A mixed methods approach was implemented to investigate the preservice teacher's abilities to plan and implement instruction as well as their efficacy for teaching. Data were collected from surveys, video analysis, student reflections, and semi-structured interviews. The findings from this study indicate that lesson study for preservice teachers was an effective means of teacher education. Lesson study positively impacted the preservice teachers' ability to plan and teach mathematical lessons more effectively. The preservice teachers successfully transitioned from teaching in the methods classroom to their field experience classroom during this innovation. Further, the efficacy of the preservice teachers to teach secondary mathematics increased based on this innovation. Further action research cycles of lesson study with preservice teachers are recommended.
ContributorsMostofo, Jameel (Author) / Zambo, Ronald (Thesis advisor) / Elliott, Sherman (Committee member) / Heck, Thomas (Committee member) / Arizona State University (Publisher)
Created2013
Description
Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative combinatorics problems and how students conceptualize the set of elements being counted in such problems, called the solution set. In particular, the focus was on the stable patterns of reasoning, known as ways of thinking, which students applied in a variety of combinatorial situations and tasks. This study catalogued students' ways of thinking about solution sets as they progressed through an instructional sequence. In addition, the relationships between the catalogued ways of thinking were explored. Further, the study investigated the challenges students experienced as they interacted with the tasks and instructional interventions, and how students' ways of thinking evolved as these challenges were overcome. Finally, it examined the role of instruction in guiding students to develop and extend their ways of thinking. Two pairs of undergraduate students with no formal experience with combinatorics participated in one of the two consecutive teaching experiments conducted in Spring 2012. Many ways of thinking emerged through the grounded theory analysis of the data, but only eight were identified as robust. These robust ways of thinking were classified into three categories: Subsets, Odometer, and Problem Posing. The Subsets category encompasses two ways of thinking, both of which ultimately involve envisioning the solution set as the union of subsets. The three ways of thinking in Odometer category involve holding an item or a set of items constant and systematically varying the other items involved in the counting process. The ways of thinking belonging to Problem Posing category involve spontaneously posing new, related combinatorics problems and finding relationships between the solution sets of the original and the new problem. The evolution of students' ways of thinking in the Problem Posing category was analyzed. This entailed examining the perturbation experienced by students and the resulting accommodation of their thinking. It was found that such perturbation and its resolution was often the result of an instructional intervention. Implications for teaching practice are discussed.
ContributorsHalani, Aviva (Author) / Roh, Kyeong Hah (Thesis advisor) / Fishel, Susanna (Committee member) / Saldanha, Luis (Committee member) / Thompson, Patrick (Committee member) / Zandieh, Michelle (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation describes an investigation of four students' ways of thinking about functions of two variables and rate of change of those two-variable functions. Most secondary, introductory algebra, pre-calculus, and first and second semester calculus courses do not require students to think about functions of more than one variable. Yet vector calculus, calculus on manifolds, linear algebra, and differential equations all rest upon the idea of functions of two (or more) variables. This dissertation contributes to understanding productive ways of thinking that can support students in thinking about functions of two or more variables as they describe complex systems with multiple variables interacting. This dissertation focuses on modeling the way of thinking of four students who participated in a specific instructional sequence designed to explore the limits of their ways of thinking and in turn, develop a robust model that could explain, describe, and predict students' actions relative to specific tasks. The data was collected using a teaching experiment methodology, and the tasks within the teaching experiment leveraged quantitative reasoning and covariation as foundations of students developing a coherent understanding of two-variable functions and their rates of change. The findings of this study indicated that I could characterize students' ways of thinking about two-variable functions by focusing on their use of novice and/or expert shape thinking, and the students' ways of thinking about rate of change by focusing on their quantitative reasoning. The findings suggested that quantitative and covariational reasoning were foundational to a student's ability to generalize their understanding of a single-variable function to two or more variables, and their conception of rate of change to rate of change at a point in space. These results created a need to better understand how experts in the field, such as mathematicians and mathematics educators, thinking about multivariable functions and their rates of change.
ContributorsWeber, Eric David (Author) / Thompson, Patrick (Thesis advisor) / Middleton, James (Committee member) / Carlson, Marilyn (Committee member) / Saldanha, Luis (Committee member) / Milner, Fabio (Committee member) / Van de Sande, Carla (Committee member) / Arizona State University (Publisher)
Created2012
Description
In any instructional situation, the instructor's goal is to maximize the learning attained by students. Drawing on the adage, 'we learn best what we have taught,' this action research project was conducted to examine whether students, in fact, learned college algebra material better if they taught it to their peers. The teaching-to-learn process was conducted in the following way. The instructor-researcher met with individual students and taught a college algebra topic to a student who served as the leader of a group of four students. At the next step, the student who originally learned the material from the instructor met with three other students in a small group session and taught the material to them to prepare an in-class presentation. Students in these small group sessions discussed how best to present the material, anticipated questions, and prepared a presentation to be shared with their classmates. The small group then taught the material to classmates during an in-class review session prior to unit examinations. Quantitative and qualitative data were gathered. Quantitative data consisted of pre- and post-test scores on four college algebra unit examinations. In addition, scores from Likert-scale items on an end-of-semester questionnaire that assessed the effectiveness of the teaching-to-learn process and attitudes toward the process were obtained. Qualitative data consisted of field notes from observations of selected small group sessions and in-class presentations. Additional qualitative data included responses to open-ended questions on the end-of-semester questionnaire and responses to interview items posed to groups of students. Results showed the quantitative data did not support the hypothesis that material, which was taught, was better learned than other material. Nevertheless, qualitative data indicated students were engaged in the material, had a deeper understanding of the material, and were more confident about it as a result of their participation in the teaching-to-learn process. Students also viewed the teaching-to-learn process as being effective and they had positive attitudes toward the teaching-to-learn process. Discussion focused on how engagement, deeper understanding and confidence interacted with one another to increase student learning. Lessons learned, implications for practice, and implications for further action research were also discussed.
ContributorsNicoloff, Stephen J (Author) / Buss, Ray R (Thesis advisor) / Zambo, Ronald (Committee member) / Shaw, Phyllis J (Committee member) / Arizona State University (Publisher)
Created2011
Description
ABSTRACT The integration of technology into content area teaching while taking into account state standards is a continuing challenge for secondary teachers. To address this challenge, six high school teachers participated in one-on-one tutoring sessions conducted by the researcher. The Technological Pedagogical Content Knowledge (TPACK), which posits that teachers add technology into their practice by blending it with content and pedagogy, served as the theoretical framework and guided implementation of the project. During the one-on-one tutoring sessions, which occurred weekly in hour-long sessions for a five- to eight-week period, teachers selected the focus of the training sessions. To assess teacher perceptions of efficacy quantitative data were gathered prior to and following the intervention using an on-line survey tool. Although pre- to post-intervention scores on the survey increased, the difference was not significant. With respect to the qualitative data four themes emerged. First, there were specific processes and patterns that emerged within the sessions related to the TPACK framework. Teachers selected either technology or content to initiate sessions. Teachers did not begin sessions with high yield pedagogical strategies as a focus. Second, one-on-one tutoring fostered an initial sense of community, and as the project progressed, a community of practice emerged. Third, challenges emerged related to technology and high yield pedagogical strategies. At times technology did not work or teachers expressed there was too much to grasp and apply to their practice. Additionally, the appropriate applications of high yield instructional strategies also presented challenges to participants. Fourth, based on their participation in the project, teachers expressed an increased sense of efficacy with respect to conducting their work. The discussion was focused on how teachers created a community of practice to support their professional growth, which influenced efficacy for teaching as they became increasingly effective in blending technology, pedagogy and content.
ContributorsWilson, Michele (Michelle Jo) (Author) / Buss, Ray R. (Thesis advisor) / Zambo, Ronald (Committee member) / Thomason, Mickael (Committee member) / Arizona State University (Publisher)
Created2011
Description
This dissertation reports three studies about what it means for teachers and students to reason with frames of reference: to conceptualize a reference frame, to coordinate multiple frames of reference, and to combine multiple frames of reference. Each paper expands on the previous one to illustrate and utilize the construct of frame of reference. The first paper is a theory paper that introduces the mental actions involved in reasoning with frames of reference. The concept of frames of reference, though commonly used in mathematics and physics, is not described cognitively in any literature. The paper offers a theoretical model of mental actions involved in conceptualizing a frame of reference. Additionally, it posits mental actions that are necessary for a student to reason with multiple frames of reference. It also extends the theory of quantitative reasoning with the construct of a ‘framed quantity’. The second paper investigates how two introductory calculus students who participated in teaching experiments reasoned about changes (variations). The data was analyzed to see to what extent each student conceptualized the variations within a conceptualized frame of reference as described in the first paper. The study found that the extent to which each student conceptualized, coordinated, and combined reference frames significantly affected his ability to reason productively about variations and to make sense of his own answers. The paper ends by analyzing 123 calculus students’ written responses to one of the tasks to build hypotheses about how calculus students reason about variations within frames of reference. The third paper reports how U.S. and Korean secondary mathematics teachers reason with frame of reference on open-response items. An assessment with five frame of reference tasks was given to 539 teachers in the US and Korea, and the responses were coded with rubrics intended to categorize responses by the extent to which they demonstrated conceptualized and coordinated frames of reference. The results show that the theory in the first study is useful in analyzing teachers’ reasoning with frames of reference, and that the items and rubrics function as useful tools in investigating teachers’ meanings for quantities within a frame of reference.
ContributorsJoshua, Surani Ashanthi (Author) / Thompson, Patrick W (Thesis advisor) / Carlson, Marilyn (Committee member) / Roh, Kyeong Hah (Committee member) / Middleton, James (Committee member) / Culbertson, Robert (Committee member) / Arizona State University (Publisher)
Created2019
Description
This study investigated two undergraduate mathematics students’ meanings for derivatives of univariable and multivariable functions when creating linear approximations. Both participants completed multivariable calculus at least two semesters prior to participating in a sequence of four to five exploratory teaching interviews. One purpose of the interviews was to understand the students’ meaning of the idea of rate of change and its role in their understanding ideas of derivative, partial derivative, and directional derivative. A second purpose was to understand and advance the ways in which each student used the idea of rate of change to make linear approximations. My analysis of the data revealed (i) how a student’s understanding of constant rate of change impacted their conception of derivatives, partial derivatives, and directional derivatives, and (ii) how each student used these ideas to make linear approximations. My results revealed that conceptualizing a rate of change as the ratio of two quantities’ values as they vary together was critical for their conceptualizing partial and directional derivatives quantitatively as directional rates of change, and in particular, how they visualized these ideas graphically and constructed symbols to represent the quantities and the relationships between their values. Further, my results revealed the importance of distinguishing between conceptualizing an instantaneous rate of change assuming a constant rate of change over any amount of change in the independent quantity(s) and using this rate of change to generate an approximate amount of change in the value of the dependent quantity. Alonzo initially conceptualized rate of change and derivative as the slantiness of a line that intersected a function’s curve. John also referred to the derivative at a point as the slope of the line tangent to the curve at that point, but he appeared to conceptualize the derivative as a ratio of the changes in two quantities values and imagined (represented graphically) two changes while discussing how to make this ratio more precise and use its value to make linear projections of future function values and amounts of accumulation. John also conceptualized the derivative as the best local, linear approximation for a function.
ContributorsBettersworth, Zachary S (Author) / Carlson, Marilyn (Thesis advisor) / Harel, Guershon (Committee member) / Roh, Kyeong Hah (Committee member) / Thompson, Patrick W. (Committee member) / Zandieh, Michelle (Committee member) / Arizona State University (Publisher)
Created2023