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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
The purpose of this study is to impact the teaching and learning of math of 2nd through 4th grade math students at Porfirio H. Gonzales Elementary School. The Cognitively Guided Instruction (CGI) model serves as the independent variable for this study. Its intent is to promote math instruction that emphasizes problem-solving to a greater degree and facilitates higher level questioning of teachers during their instructional dialogue with students. A mixed methods approach is being employed to see how the use of the CGI model of instruction impacts the math achievement of 2nd through 4th grade students on quarterly benchmark assessments administered at this school, to see how students problem-solving abilities progress over the duration of the study, and to see how teacher practices in questioning progress. Quantitative methods are used to answer the first of these research questions using archival time series (Amrein & Berliner, 2002) to view trends in achievement before and after the implementation of the CGI model. Qualitative methods are being used to answer questions around students' progression in their problem-solving abilities and teacher questioning to get richer descriptions of how these constructs evolve over the course of the study.
ContributorsMedrano Cotito, Juan (Author) / Ann, Keith (Thesis advisor) / David, Carlson L (Committee member) / Thomas, Heck (Committee member) / Reynaldo, Rivera (Committee member) / Arizona State University (Publisher)
Created2012
Description
The focus of this study was to examine how a student's understanding of function notation impacted their approaches to problem solving. Before this question could be answered, students' understandings about function notation had to be determined. The goal of the first part of the data was to determine the norm of understanding for function notation for students after taking a college level pre-calculus class. From the data collected, several ideas about student understanding of notation emerged. The goal of the second data set was to determine if student understanding of notation impacted their reasoning while problem solving, and if so, how it impacted their reasoning. Collected data suggests that much of what students "understand" about function notation comes from memorized procedures and that the notation may have little or no meaning for students in context. Evidence from this study indicates that this lack of understanding of function notation does negatively impact student's ability to solve context based problems. In order to build a strong foundation of function, a well-developed understanding of function notation is necessary. Because function notation is a widely accepted way of communicating information about function relationships, understanding its uses and meanings in context is imperative for developing a strong foundation that will allow individuals to approach functions in a meaningful and productive manner.
ContributorsLe, Lesley Kim (Author) / Carlson, Marilyn (Thesis director) / Greenes, Carole (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2015-05
Description
The focus of the study was to identify secondary school students' difficulties with aspects of linearity and linear functions, and to assess their teachers' understanding of the nature of the difficulties experienced by their students. A cross-sectional study with 1561 Grades 8-10 students enrolled in mathematics courses from Pre-Algebra to Algebra II, and their 26 mathematics teachers was employed. All participants completed the Mini-Diagnostic Test (MDT) on aspects of linearity and linear functions, ranked the MDT problems by perceived difficulty, and commented on the nature of the difficulties. Interviews were conducted with 40 students and 20 teachers. A cluster analysis revealed the existence of two groups of students, Group 0 enrolled in courses below or at their grade level, and Group 1 enrolled in courses above their grade level. A factor analysis confirmed the importance of slope and the Cartesian connection for student understanding of linearity and linear functions. There was little variation in student performance on the MDT across grades. Student performance on the MDT increased with more advanced courses, mainly due to Group 1 student performance. The most difficult problems were those requiring identification of slope from the graph of a line. That difficulty persisted across grades, mathematics courses, and performance groups (Group 0, and 1). A comparison of student ranking of MDT problems by difficulty and their performance on the MDT, showed that students correctly identified the problems with the highest MDT mean scores as being least difficult for them. Only Group 1 students could identify some of the problems with lower MDT mean scores as being difficult. Teachers did not identify MDT problems that posed the greatest difficulty for their students. Student interviews confirmed difficulties with slope and the Cartesian connection. Teachers' descriptions of problem difficulty identified factors such as lack of familiarity with problem content or context, problem format and length. Teachers did not identify student difficulties with slope in a geometric context.
ContributorsPostelnicu, Valentina (Author) / Greenes, Carole (Thesis advisor) / Pambuccian, Victor (Committee member) / Sloane, Finbarr (Committee member) / Arizona State University (Publisher)
Created2011