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- Creators: Arizona State University
- Creators: Carlson, Marilyn P
- Creators: School of Mathematical and Statistical Sciences
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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 examine the impact of individualized afterschool tutoring, under federal Supplemental Educational Services (SES), on mathematical and general academic intrinsic motivation and mathematical achievement of at-risk students. The population of this study consisted of two third graders and five fourth graders from an elementary school in the Reynolds School District in Portland, Oregon. One participant was male. The other six were female. Six of the students were Hispanic, and one student was multiethnic. Students' parents enrolled their children in free afterschool tutoring with Mobile Minds Tutoring, an SES provider in the state of Oregon. The participants were given pre- and post-assessments to measure their intrinsic motivation and achievement. The third graders took the Young Children's Academic Intrinsic Motivation Inventory (Y-CAIMI) and the fourth graders took the Children's Academic Intrinsic Motivation Inventory (CAIMI). All students took the Group Mathematics Assessment and Diagnostic Evaluation (GMADE) according to their grade level. The findings from this study are consistent with the literature review, in that individualized tutoring can help increase student motivation and achievement. Six out of the seven students who participated in this study showed an increase in mathematical achievement, and four out of the seven showed an increase in intrinsic motivation.
ContributorsBallou, Cherise (Author) / Middleton, James (Thesis advisor) / Kinach, Barbara (Committee member) / Bitter, Gary (Committee member) / Arizona State University (Publisher)
Created2011
Description
A fundamental motivation for this study was the underrepresentation of women in Science, Technology, Engineering and Mathematics careers. There is no doubt women and men can achieve at the same level in Mathematics, yet it is not clear why women are opting out. Adding race to the equation makes the underrepresentation more dramatic. Considering the important number of Latinos in the United States, especially in school age, it is relevant to find what reasons could be preventing them from participating in the careers mentioned. This study highlight the experiences young successful Latinas have in school Mathematics and how they shape their identities, to uncover potential conflicts that could later affect their participation in the field. In order to do so the author utilizes feminist approaches, Latino Critical Theory and Critical Race Theory to analyze the stories compiled. The participants were five successful Latinas in Mathematics, part of the honors track in a school in the Southwest of the United States. The theoretical lenses chosen allowed women of color to tell their story, highlighting the intersection of race, gender and socio-economical status as a factor shaping different schooling experiences. The author found that the participants distanced themselves from their home culture and from other girls at times to allow themselves to develop and maintain a successful identity as a Mathematics student. When talking about Latinos and their culture, the participants shared a view of themselves as proud Latinas who would prove others what Latinas can do. During other times while discussing the success of Latinos in Mathematics, they manifested Latinos were lazy and distance themselves from that stereotype. Similar examples about gender and Mathematics can be found in the study. The importance of the family as a motivator for their success was clear, despite the participants' concern that parents cannot offer certain types of help they feel they need. This was manifest in a tension regarding who owns the "right" Mathematics at home. Results showed that successful Latinas in the US may undergo a constant negotiation of conflicting discourses that force them to distance themselves from certain aspects of their culture, gender, and even their families, to maintain an identity of success in mathematics.
ContributorsGuerra Lombardi, Paula Patricia (Author) / Middleton, James (Thesis advisor) / Battey, Daniel (Committee member) / Koblitz, Ann (Committee member) / Flores, Alfinio (Committee member) / Arizona State University (Publisher)
Created2011
Description
In 2007, Arizona voters passed House Bill (HB) 2064, a law that fundamentally restructured the Structured English Immersion (SEI) program, putting into place a 4-hour English language development (ELD) block for educating English language learners (ELLs). Under this new language policy, ELL students are segregated from their English-speaking peers to receive a minimum of four hours of instruction in discrete language skills with no contextual or native language support. Furthermore, ELD is separate from content-area instruction, meaning that language and mathematics are taught as two separate entities. While educators and researchers have begun to examine the organizational structure of the 4-hour block curriculum and implications for student learning, there is much to be understood about the extent to which this policy impacts ELLs opportunities to learn mathematics. Using ethnographic methods, this dissertation documents the beliefs and practices of four Arizona teachers in an effort to understand the relationship between language policy and teacher beliefs and practice and how together they coalesce to form learning environments for their ELL students, particularly in mathematics. The findings suggest that the 4-hour block created disparities in opportunities to learn mathematics for students in one Arizona district, depending on teachers' beliefs and the manner in which the policy was enacted, which was, in part, influenced by the State, district, and school. The contrast in cases exemplified the ways in which policy, which was enacted differently in the various classes, restricted teachers' practices, and in some cases resulted in inequitable opportunities to learn mathematics for ELLs.
ContributorsLlamas-Flores, Silvia (Author) / Middleton, James (Thesis advisor) / Battey, Daniel (Committee member) / Sloane, Finbarr (Committee member) / Macswan, Jeffrey (Committee member) / Arizona State University (Publisher)
Created2013
Description
This action research study, set in a community college in the southwestern United States, was designed to investigate the effects of implementing cooperative learning strategies in a developmental mathematics course. Introductory algebra was formerly taught in a lecture based format, and as such regularly had a low course completion rate. To create a more engaging learning environment, formal and informal cooperative learning activities were integrated into the curriculum. Bandura's self-efficacy theory, Vygotsky's constructivist theory, and Deutsch's social interdependence theory guided this study. Qualitative and quantitative data were collected through pre and post self-efficacy surveys, semi-structured student interviews, student journal entries, class observations, focus groups, and pre and post mathematics assessments. Data were analyzed using a mixed methods approach. As a result of implementing cooperative learning practices as a part of my teaching, there was an increase in student attendance as well as a decrease in student withdrawal rates. Students were also more motivated to work with each other on mathematics homework outside of class sessions. There was a strong sense of community that I had not witnessed in previous courses that I have taught. Use of cooperative learning practices served as a vehicle to motivate students to work on their mathematics coursework with their peers. Keywords: cooperative learning, developmental mathematics, constructivism, social interdependence theory, self-efficacy, community college
ContributorsRivera, Natalie (Author) / Zambo, Ron (Thesis advisor) / Jiménez, Rosa (Committee member) / Rivera, Reynaldo (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
In this mixed-methods study, I examined the relationship between professional development based on the Common Core State Standards for Mathematics and teacher knowledge, classroom practice, and student learning. Participants were randomly assigned to experimental and control groups. The 50-hour professional development treatment was administered to the treatment group during one semester, and then a follow-up replication treatment was administered to the control group during the subsequent semester. Results revealed significant differences in teacher knowledge as a result of the treatment using two instruments. The Learning Mathematics for Teaching scales were used to detect changes in mathematical knowledge for teaching, and an online sorting task was used to detect changes in teachers' knowledge of their standards. Results also indicated differences in classroom practice between pairs of matched teachers selected to participate in classroom observations and interviews. No statistical difference was detected between the groups' student assessment scores using the district's benchmark assessment system. This efficacy study contributes to the literature in two ways. First, it provides an evidence base for a professional development model designed to promote effective implementation of the Common Core State Standards for Mathematics. Second, it addresses ways to impact and measure teachers' knowledge of curriculum in addition to their mathematical content knowledge. The treatment was designed to focus on knowledge of curriculum, but it also successfully impacted teachers' specialized content knowledge, knowledge of content and students, and knowledge of content and teaching.
ContributorsRimbey, Kimberly A (Author) / Middleton, James A. (Thesis advisor) / Sloane, Finbarr (Committee member) / Atkinson, Robert K (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
Recently there has been an increase in the number of people calling for the incorporation of relevant mathematics in the mathematics classroom. Unfortunately, various researchers define the term relevant mathematics differently, establishing several ideas of how relevancy can be incorporated into the classroom. The differences between mathematics education researchers' definitions of relevant and the way they believe relevant math should be implemented in the classroom, leads one to conclude that a similarly varied set of perspectives probably exists between teachers and students as well. The purpose of this exploratory study focuses on how the student and teacher perspectives on relevant mathematics in the classroom converge or diverge. Specifically, do teachers and students see the same lessons, materials, content, and approach as relevant? A survey was conducted with mathematics teachers at a suburban high school and their algebra 1 and geometry students to provide a general idea of their views on relevant mathematics. An analysis of the findings revealed three major differences: the discrepancy between frequency ratings of teachers and students, the differences between how teachers and students defined the term relevance and how the students' highest rated definitions were the least accounted for among the teacher generated questions, and finally the impact of differing attitudes towards mathematics on students' feelings towards its relevance.
ContributorsRedman, Alexandra P (Author) / Middleton, James (Thesis advisor) / Sloane, Finbarr (Committee member) / Blumenfeld-Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2012
Description
The research indicated effective mathematics teaching to be more complex than assuming the best predictor of student achievement in mathematics is the mathematical content knowledge of a teacher. This dissertation took a novel approach to addressing the idea of what it means to examine how a teacher's knowledge of mathematics impacts student achievement in elementary schools. Using a multiple case study design, the researcher investigated teacher knowledge as a function of the Mathematics Teaching Cycle (NCTM, 2007). Three cases (of two teachers each) were selected using a compilation of Learning Mathematics for Teaching (LMT) measures (LMT, 2006) and Developing Mathematical Ideas (DMI) measures (Higgins, Bell, Wilson, McCoach, & Oh, 2007; Bell, Wilson, Higgins, & McCoach, 2010) and student scores on the Arizona Assessment Collaborative (AzAC). The cases included teachers with: a) high knowledge & low student achievement v low knowledge & high student achievement, b) high knowledge & average achievement v low knowledge & average achievement, c) average knowledge & high achievement v average knowledge & low achievement, d) two teachers with average achievement & very high student achievement. In the end, my data suggested that MKT was only partially utilized across the contrasting teacher cases during the planning process, the delivery of mathematics instruction, and subsequent reflection. Mathematical Knowledge for Teaching was utilized differently by teachers with high student gains than those with low student gains. Because of this insight, I also found that MKT was not uniformly predictive of student gains across my cases, nor was it predictive of the quality of instruction provided to students in these classrooms.
ContributorsBurke, Margaret Kathleen (Author) / Middleton, James A. (Thesis advisor) / Sloane, Finbarr (Thesis advisor) / Battey, Daniel S (Committee member) / Arizona State University (Publisher)
Created2013