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- All Subjects: curriculum development
- Creators: Middleton, James
- Member of: Theses and Dissertations
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
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
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
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
A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance with AP style Related Rate questions and changes in conceptions, beliefs, and influences. The research design followed a treatment-control multiple post-assessment model with three periods of data collection. Four high school calculus classes were selected for the study, with one class designated as the treatment and three as the controls. Measures for this study include a skills assessment, Related Rate word problem assessments, and a motivation problem solving survey. Data analysis utilized a mixed methods approach. Quantitative analysis consisted of descriptive and inferential methods utilizing nonparametric statistics for performance comparisons and structural equation modeling to determine the underlying structure of the problem solving motivation survey. Statistical results indicate that time on task was a major factor in enhanced performance between measurement time points 1 and 2. In the experimental classroom, the engineering design process as a problem solving strategy emerged as an important factor in demonstrating sustained achievement across the measurement time series when solving volumetric rates of change as compared to traditional problem solving strategies. In the control classrooms, where traditional problem solving strategies were emphasized, a greater percentage of students than in the experimental classroom demonstrated enhanced achievement from point 1 to 2, but showed decrease in achievement from point 2 to 3 in the measurement time series. Results from the problem solving motivation survey demonstrated that neither time on task nor instruction strategy produced any effect on student beliefs about and perceptions of problem solving. Qualitative error analysis showed that type of instruction had little effect on the type and number of errors committed, with the exception of procedural errors from performing a derivative and errors decoding the problem statement. Results demonstrated that students who engaged in the engineering design-based committed a larger number of decoding errors specific to Pythagorean type Related Rate problems; while students who engaged in routine problem solving did not sustain their ability to correctly differentiate a volume equation over time. As a whole, students committed a larger number of misused data errors than other types of errors. Where, misused data errors are the discrepancy between the data as given in a problem and how the student used the data in problem solving.
ContributorsThieken, John (Author) / Ganesh, Tirupalavanam G. (Thesis advisor) / Sloane, Finbarr (Committee member) / Middleton, James (Committee member) / Arizona State University (Publisher)
Created2012
Description
Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study is to look at classrooms and educators across six high achieving countries to identify and compare teaching strategies being used. In Finland, Hong Kong, Japan, New Zealand, Singapore, and Switzerland, twenty educators were interviewed and fourteen educators were observed teaching. Themes were first identified by comparing individual teacher responses within each country. These themes were then grouped together across countries and eight emerging patterns were identified. These strategies include students active involvement in the classroom, students given written feedback on assessments, students involvement in thoughtful discussion about mathematical concepts, students solving and explaining mathematics problems at the board, students exploring mathematical concepts either before or after being taught the material, students engagement in practical applications, students making connections between concepts, and students having confidence in their ability to understand mathematics. The strategies identified across these six high achieving countries can inform educators in their efforts of increasing student understanding of mathematical concepts and lead to an improvement in mathematics performance.
ContributorsAnglin, Julia Mae (Author) / Middleton, James (Thesis director) / Vicich, James (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-12