Matching Items (4)
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- All Subjects: Algebra
- Creators: Buss, Ray
- Creators: Castillo-Chavez, Carlos
- Member of: Theses and Dissertations
- Status: Published
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
The purpose of this study was to identify the algebraic reasoning abilities of young students prior to instruction. The goals of the study were to determine the influence of problem, problem type, question, grade level, and gender on: (a) young children’s abilities to predict the number of shapes in near and far positions in a “growing” pattern without assistance; (b) the nature and amount of assistance needed to solve the problems; and (c) reasoning methods employed by children.
The 8-problem Growing Patterns and Functions Assessment (GPFA), with an accompanying interview protocol, were developed to respond to these goals. Each problem presents sequences of figures of geometric shapes that differ in complexity and can be represented by the function, y = mf +b: in Type 1 problems (1 - 4), m = 1, and in Type 2 problems (5 - 8), m = 2. The two questions in each problem require participants to first, name the number of shapes in the pattern in a near position, and then to identify the number of shapes in a far position. To clarify reasoning methods, participants were asked how they solved the problems.
The GPFA was administered, one-on-one, to 60 students in Grades 1, 2, and 3 with an equal number of males and females from the same elementary school. Problem solution scores without and with assistance, along with reasoning method(s) employed, were tabulated.
Results of data analyses showed that when no assistance was required, scores varied significantly by problem, problem type, and question, but not grade level or gender. With assistance, problem scores varied significantly by problem, problem type, question, and grade level, but not gender.
The 8-problem Growing Patterns and Functions Assessment (GPFA), with an accompanying interview protocol, were developed to respond to these goals. Each problem presents sequences of figures of geometric shapes that differ in complexity and can be represented by the function, y = mf +b: in Type 1 problems (1 - 4), m = 1, and in Type 2 problems (5 - 8), m = 2. The two questions in each problem require participants to first, name the number of shapes in the pattern in a near position, and then to identify the number of shapes in a far position. To clarify reasoning methods, participants were asked how they solved the problems.
The GPFA was administered, one-on-one, to 60 students in Grades 1, 2, and 3 with an equal number of males and females from the same elementary school. Problem solution scores without and with assistance, along with reasoning method(s) employed, were tabulated.
Results of data analyses showed that when no assistance was required, scores varied significantly by problem, problem type, and question, but not grade level or gender. With assistance, problem scores varied significantly by problem, problem type, question, and grade level, but not gender.
ContributorsCavanagh, Mary Clare (Author) / Greenes, Carole E. (Thesis advisor) / Buss, Ray (Committee member) / Surbeck, Elaine (Committee member) / Arizona State University (Publisher)
Created2016
Description
Over the past 25 years, efforts have been made to integrate technology into teaching and learning. In particular, the personalized learning approach has sought to leverage technology to deliver instruction that is adaptive to the learner and personalized learning environments were used as tools in tailoring instruction to match learner needs. Typically, personalized instruction has been delivered using technology, such as the computer. However, little research has focused on using personalized learning as a tool for remediation. The goal of this study was to empirically investigate the efficacy of personalized learning in Algebra as a remediation tool. This study used a mixed-methods approach to analyze satisfaction with the learning environment, perception of and attitudes toward the content being delivered, and the reported overall experience and the personalized experience in the context of two versions of a computer-based multimedia Algebra learning environment. A total of 117 high school students in grades 10 through 12 participated on a voluntary basis. They had previously taken an introductory Algebra course and were now enrolled in a different math course. The students were assigned to one of two conditions: (a) the computer-based multimedia learning environment on the personalized learning platform known as Personalized Learning and (b) the same learning environment without the Personalized Learning platform. In addition to completing a pre- and post-test, participants were administered attitudinal surveys. Results indicated no knowledge gains in either group at the post-test assessment. Further, analyses by gender and race also did not reveal any significant differences among the groups. However, survey results indicated one significant finding: the students exposed to the personalized learning environment had more positive perceptions towards personalized learning than towards the overall experience with the learning environment.
Implications for these results and further goals for this line of research are discussed in greater detail within the context of personalized learning, user experience, and social aspects of learning. This work also provides opportunities in helping educators choose adequate tools for teaching and delivering instruction tailored to learners’ needs.
Implications for these results and further goals for this line of research are discussed in greater detail within the context of personalized learning, user experience, and social aspects of learning. This work also provides opportunities in helping educators choose adequate tools for teaching and delivering instruction tailored to learners’ needs.
ContributorsSavio-Ramos, Caroline Andrea (Author) / Bitter, Gary G. (Thesis advisor) / Buss, Ray (Committee member) / Legacy, Jane (Committee member) / Arizona State University (Publisher)
Created2015
Description
The purpose of this action research study was to implement and analyze an intervention designed to improve perceptions of working with others as well as practice and improve emotional tools related to such interactions through the systematic development of ability emotional intelligence (EI) related skills. The present study sought to: (1) explore high school students’ perceptions of their role as part of a team during teamwork; (1a) investigate how perceptions differed by EI level; (2) examine how students’ perceptions of their role in teamwork were influenced by being paired with more advanced (ability EI) peers or less advanced peers, based on ability emotional intelligence test scores; (3) determine if ability emotional intelligence related skills could be developed over the course of a 7-week intervention.
The intervention took place in a 12th grade US Government & Economics classroom with 34 participants for examination of general trends, and 11 focal participants for focused and in-depth analysis. Students were taught about emotion theory and engaged in two weeks of ability emotional intelligence skills training, followed by a five-week project cycle in which students were required to work together to achieve a common goal. The research design was mixed methods convergent parallel. Quantitative data were collected from post- and retrospective pre-intervention surveys regarding student perceptions about working with others and their ability EI related skills. Qualitative data were collected through on-going student reflective journal entries, observational field notes, and interviews with the focal group of participants.
Results suggested the intervention had a significant effect on students’ perceptions of working with others and perceived ability emotional intelligence related skills. Significant positive change was found through quantitative data analysis, revealing students’ perceptions about working with others in teams had improved as a result of the intervention as had their perceptions about their ability EI related skills. Qualitative analysis revealed rich, thick descriptions exploring this shift in perception among the 11 focal students, providing the evidence necessary to support the effectiveness of the intervention. Results suggested the possibilities for improved teamwork in the classroom.
The intervention took place in a 12th grade US Government & Economics classroom with 34 participants for examination of general trends, and 11 focal participants for focused and in-depth analysis. Students were taught about emotion theory and engaged in two weeks of ability emotional intelligence skills training, followed by a five-week project cycle in which students were required to work together to achieve a common goal. The research design was mixed methods convergent parallel. Quantitative data were collected from post- and retrospective pre-intervention surveys regarding student perceptions about working with others and their ability EI related skills. Qualitative data were collected through on-going student reflective journal entries, observational field notes, and interviews with the focal group of participants.
Results suggested the intervention had a significant effect on students’ perceptions of working with others and perceived ability emotional intelligence related skills. Significant positive change was found through quantitative data analysis, revealing students’ perceptions about working with others in teams had improved as a result of the intervention as had their perceptions about their ability EI related skills. Qualitative analysis revealed rich, thick descriptions exploring this shift in perception among the 11 focal students, providing the evidence necessary to support the effectiveness of the intervention. Results suggested the possibilities for improved teamwork in the classroom.
ContributorsZuniga, Alison Kara (Author) / Bertrand, Melanie (Thesis advisor) / Buss, Ray (Committee member) / Caruso, David (Committee member) / Arizona State University (Publisher)
Created2019