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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
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
During the downswing all golfers must roll their forearms and twist the club handle in order to square the club face into impact. Anecdotally some instructors say that rapidly twisting the handle and quickly closing the club face is the best technique while others disagree and suggest the opposite. World class golfers have swings with a range of club handle twist velocities (HTV) from very slow to very fast and either method appears to create a successful swing. The purpose of this research was to discover the relationship between HTV at impact and selected body and club biomechanical characteristics during a driver swing. Three-dimensional motion analysis methods were used to capture the swings of 94 tour professionals. Pearson product-moment correlation was used to determine if a correlation existed between HTV and selected biomechanical characteristics. The total group was also divided into two sub-groups of 32, one group with the fastest HTV (Hi-HTV) and the other with the slowest HTV (Lo-HTV). Single factor ANOVAs were completed for HTV and each selected biomechanical parameter. No significant differences were found between the Hi-HTV and Lo-HTV groups for both clubhead speed and driving accuracy. Lead forearm supination velocity at impact was found to be significantly different between groups with the Hi-HTV group having a higher velocity. Lead wrist extension velocity at impact, while not being significantly different between groups was found to be positive in both groups, meaning that the lead wrist is extending at impact. Lead wrist ulnar deviation, lead wrist release and trail elbow extension velocities at maximum were not significantly different between groups. Pelvis rotation, thorax rotation, pelvis side bend and pelvis rotation at impact were all significantly different between groups, with the Lo-HTV group being more side bent tor the trail side and more open at impact. These results suggest that world class golfers can successfully use either the low or high HTV technique for a successful swing. From an instructional perspective it is important to be aware of the body posture and wrist/forearm motion differences between the two techniques so as to be consistent when teaching either method.
ContributorsCheetham, Phillip (Author) / Hinrichs, Richard (Thesis advisor) / Ringenbach, Shannon (Committee member) / Dounskaia, Natalia (Committee member) / Crews, Debra (Committee member) / Arizona State University (Publisher)
Created2014
Description
Skeletal muscle injury may occur from repetitive short bursts of biomechanical strain that impair muscle function. Alternatively, variations of biomechanical strain such as those held for long-duration are used by clinicians to repair muscle and restore its function. Fibroblasts embedded within the unifying connective tissue of skeletal muscle experience these multiple and diverse mechanical stimuli and respond by secreting cytokines. Cytokines direct all stages of muscle regeneration including myoblasts differentiation, fusion to form myotubes, and myotube functionality. To examine how fibroblasts respond to variations in mechanical strain that may affect juxtapose muscle, a myofascial junction was bioengineered that examined the interaction between the two cell types. Fibroblasts were experimentally shown to increase myoblast differentiation, and fibroblast biomechanical strain mediated the extent to which differentiation occurred. Intereleukin-6 is a strain-regulated cytokine secreted by fibroblasts was determined to be necessary for fibroblast-mediated myoblast differentiation. Myotubes differentiated in the presence of strained fibroblasts express greater number of acetylcholine receptors, greater acetylcholine receptor sizes, and modified to be more or less sensitive to acetylcholine-induced contraction. This study provides direct evidence that strained and non-strained fibroblasts can serve as a vehicle to modify myoblast differentiation and myotube functionality. Further understanding the mechanisms regulating these processes may lead to clinical interventions that include strain-activated cellular therapies and bioengineered cell engraftment for mediating the regeneration and function of muscle in vivo.
ContributorsHicks, Michael (Author) / Standley, Paul R (Thesis advisor) / Rawls, Jeffrey (Committee member) / Lake, Douglas (Committee member) / Hinrichs, Richard (Committee member) / Arizona State University (Publisher)
Created2014
Description
Industry, academia, and government have spent tremendous amounts of money over several decades trying to improve the mathematical abilities of students. They have hoped that improvements in students' abilities will have an impact on adults' mathematical abilities in an increasingly technology-based workplace. This study was conducted to begin checking for these impacts. It examined how nine adults in their workplace solved problems that purportedly entailed proportional reasoning and supporting rational number concepts (cognates).
The research focused on four questions: a) in what ways do workers encounter and utilize the cognates while on the job; b) do workers engage cognate problems they encounter at work differently from similar cognate problems found in a textbook; c) what mathematical difficulties involving the cognates do workers experience while on the job, and; d) what tools, techniques, and social supports do workers use to augment or supplant their own abilities when confronted with difficulties involving the cognates.
Noteworthy findings included: a) individual workers encountered cognate problems at a rate of nearly four times per hour; b) all of the workers engaged the cognates primarily via discourse with others and not by written or electronic means; c) generally, workers had difficulty with units and solving problems involving intensive ratios; d) many workers regularly used a novel form of guess & check to produce a loose estimate as an answer; and e) workers relied on the social structure of the store to mitigate the impact and defuse the responsibility for any errors they made.
Based on the totality of the evidence, three hypotheses were discussed: a) the binomial aspect of a conjecture that stated employees were hired either with sufficient mathematical skills or with deficient skills was rejected; b) heuristics, tables, and stand-ins were maximally effective only if workers individually developed them after a need was recognized; and c) distributed cognition was rejected as an explanatory framework by arguing that the studied workers and their environment formed a system that was itself a heuristic on a grand scale.
The research focused on four questions: a) in what ways do workers encounter and utilize the cognates while on the job; b) do workers engage cognate problems they encounter at work differently from similar cognate problems found in a textbook; c) what mathematical difficulties involving the cognates do workers experience while on the job, and; d) what tools, techniques, and social supports do workers use to augment or supplant their own abilities when confronted with difficulties involving the cognates.
Noteworthy findings included: a) individual workers encountered cognate problems at a rate of nearly four times per hour; b) all of the workers engaged the cognates primarily via discourse with others and not by written or electronic means; c) generally, workers had difficulty with units and solving problems involving intensive ratios; d) many workers regularly used a novel form of guess & check to produce a loose estimate as an answer; and e) workers relied on the social structure of the store to mitigate the impact and defuse the responsibility for any errors they made.
Based on the totality of the evidence, three hypotheses were discussed: a) the binomial aspect of a conjecture that stated employees were hired either with sufficient mathematical skills or with deficient skills was rejected; b) heuristics, tables, and stand-ins were maximally effective only if workers individually developed them after a need was recognized; and c) distributed cognition was rejected as an explanatory framework by arguing that the studied workers and their environment formed a system that was itself a heuristic on a grand scale.
ContributorsOrletsky, Darryl William (Author) / Middleton, James (Thesis advisor) / Greenes, Carole (Committee member) / Judson, Eugene (Committee member) / Arizona State University (Publisher)
Created2015
Description
This study explores teacher educators' personal theories about the instructional practices central to preparing future teachers, how they enact those personal theories in the classroom, how they represent the relationship between content, pedagogy, and technology, and the function of technology in teacher educators' personal theories about the teaching of mathematics and their practices as enacted in the classroom. The conceptual frameworks of knowledge as situated and technology as situated provide a theoretical and analytical lens for examining individual instructor's conceptions and classroom activity as situated in the context of experiences and relationships in the social world. The research design employs a mixed method design to examine data collected from a representative sample of three full-time faculty members teaching methods of teaching mathematics in elementary education at the undergraduate level. Three primary types of data were collected and analyzed:
a) structured interviews using the repertory grid technique to model the mathematics education instructors' schemata regarding the teaching of mathematics methods; b) content analysis of classroom observations to develop models that represent the relationship of pedagogy, content, and technology as enacted in the classrooms; and c) brief retrospective protocols after each observed class session to explore the reasoning and individual choices made by an instructor that underlie their teaching decisions in the classroom. Findings reveal that although digital technology may not appear to be an essential component of an instructor's toolkit, technology can still play an integral role in teaching. This study puts forward the idea of repurposing as technology -- the ability to repurpose items as models, tools, and visual representations and integrate them into the curriculum. The instructors themselves became the technology, or the mediational tool, and introduced students to new meanings for "old" cultural artifacts in the classroom. Knowledge about the relationships between pedagogy, content, and technology and the function of technology in the classroom can be used to inform professional development for teacher educators with the goal of improving teacher preparation in mathematics education.
a) structured interviews using the repertory grid technique to model the mathematics education instructors' schemata regarding the teaching of mathematics methods; b) content analysis of classroom observations to develop models that represent the relationship of pedagogy, content, and technology as enacted in the classrooms; and c) brief retrospective protocols after each observed class session to explore the reasoning and individual choices made by an instructor that underlie their teaching decisions in the classroom. Findings reveal that although digital technology may not appear to be an essential component of an instructor's toolkit, technology can still play an integral role in teaching. This study puts forward the idea of repurposing as technology -- the ability to repurpose items as models, tools, and visual representations and integrate them into the curriculum. The instructors themselves became the technology, or the mediational tool, and introduced students to new meanings for "old" cultural artifacts in the classroom. Knowledge about the relationships between pedagogy, content, and technology and the function of technology in the classroom can be used to inform professional development for teacher educators with the goal of improving teacher preparation in mathematics education.
ContributorsToth, Meredith Jean (Author) / Middleton, James (Thesis advisor) / Sloane, Finbarr (Committee member) / Buss, Ray (Committee member) / Atkinson, Robert (Committee member) / Arizona State University (Publisher)
Created2014
Description
Conceptual change has been a large part of science education research for several decades due to the fact that it allows teachers to think about what students' preconceptions are and how to change these to the correct scientific conceptions. To have students change their preconceptions teachers need to allow students to confront what they think they know in the presence of the phenomena. Students then collect and analyze evidence pertaining to the phenomena. The goal in the end is for students to reorganize their concepts and change or correct their preconceptions, so that they hold more accurate scientific conceptions. The purpose of this study was to investigate how students' conceptions of the Earth's surface, specifically weathering and erosion, change using the conceptual change framework to guide the instructional decisions. The subjects of the study were a class of 25 seventh grade students. This class received a three-week unit on weathering and erosion that was structured using the conceptual change framework set by Posner, Strike, Hewson, and Gertzog (1982). This framework starts by looking at students' misconceptions, then uses scientific data that students collect to confront their misconceptions. The changes in students' conceptions were measured by a pre concept sketch and post concept sketch. The results of this study showed that the conceptual change framework can modify students' preconceptions of weathering and erosion to correct scientific conceptions. There was statistical significant difference between students' pre concept sketches and post concept sketches scores. After examining the concept sketches, differences were found in how students' concepts had changed from pre to post concept sketch. Further research needs to be done with conceptual change and the geosciences to see if conceptual change is an effective method to use to teach students about the geosciences.
ContributorsTillman, Ashley (Author) / Luft, Julie (Thesis advisor) / Middleton, James (Committee member) / Semken, Steven (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
Writing scientific explanations is increasingly important, and today's students must have the ability to navigate the writing process to create a persuasive scientific explanation. One aspect of the writing process is receiving feedback before submitting a final draft. This study examined whether middle school students benefit more in the writing process from receiving peer feedback or teacher feedback on rough drafts of scientific explanations. The study also looked at whether males and females reacted differently to the treatment groups. And it examined if content knowledge and the written scientific explanations were correlated. The study looked at 38 sixth and seventh-grade students throughout a 7-week earth science unit on earth systems. The unit had six lessons. One lesson introduced the students to writing scientific explanations, and the other five were inquiry-based content lessons. They wrote four scientific explanations throughout the unit of study and received feedback on all four rough drafts. The sixth-graders received teacher feedback on each explanation and the seventh-graders received peer-feedback after learning how to give constructive feedback. The students also took a multiple-choice pretest/posttest to evaluate content knowledge. The analyses showed that there was no significant difference between the group receiving peer feedback and the group receiving teacher feedback on the final drafts of the scientific explanations. There was, however, a significant effect of practice on the scores of the scientific explanations. Students wrote significantly better with each subsequent scientific explanation. There was no significant difference between males and females based on the treatment they received. There was a significant correlation between the gain in pretest to posttest scores and the scientific explanations and a significant correlation between the posttest scores and the scientific explanations. Content knowledge and written scientific explanations are related. Students who wrote scientific explanations had significant gains in content knowledge.
ContributorsLange, Katie (Author) / Baker, Dale (Thesis advisor) / Megowan, Colleen (Committee member) / Middleton, James (Committee member) / Arizona State University (Publisher)
Created2011
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