Matching Items (9)
Filtering by
- All Subjects: Mathematics Education
- All Subjects: Professional Development
- Creators: Judson, Eugene
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
To develop critical reasoning skills potentially advances students' ability to critically consume information, make informed decisions, and actively participate in a democracy. An inquiry-based pedagogical approach to science teaching remains an effective means to develop critical reasoning skills. Participating in scientific inquiry requires students to generate arguments and test alternative hypotheses using experimental evidence. Scientific inquiry demands that students use their critical reasoning skills. Unfortunately, many teachers fail to allocate an adequate amount of time for genuine experimentation in science classes. As a result, science classes often leave students unprepared to think critically and apply their knowledge in a practical manner.
The focus of this study was to investigate the extent to which an inquiry-based professional development experience, including a two-day summer workshop and 18 weeks of follow up Professional Learning Community (PLC) support, affected the attitudes and pedagogical skills regarding scientific inquiry among six high school biology teachers. A concurrent mixed methods, action research design was used to measure changes in teachers' attitudes, perceptions, and skills regarding inquiry-based pedagogy was measured throughout the 22 weeks of the study. A survey instrument, card sorting activity, classroom observations using the Reformed Teacher Observation Protocol (RTOP), individual interviews, and PLC observations were used to gather data. Results indicated the professional development was effective in transforming the participating teachers' attitudes, perceptions, and skills regarding inquiry-based pedagogy.
The focus of this study was to investigate the extent to which an inquiry-based professional development experience, including a two-day summer workshop and 18 weeks of follow up Professional Learning Community (PLC) support, affected the attitudes and pedagogical skills regarding scientific inquiry among six high school biology teachers. A concurrent mixed methods, action research design was used to measure changes in teachers' attitudes, perceptions, and skills regarding inquiry-based pedagogy was measured throughout the 22 weeks of the study. A survey instrument, card sorting activity, classroom observations using the Reformed Teacher Observation Protocol (RTOP), individual interviews, and PLC observations were used to gather data. Results indicated the professional development was effective in transforming the participating teachers' attitudes, perceptions, and skills regarding inquiry-based pedagogy.
ContributorsBlechacz, Sarah (Author) / Hermanns, Carl (Thesis advisor) / Judson, Eugene (Committee member) / Bostick, Bradley (Committee member) / Arizona State University (Publisher)
Created2018
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
This is a report of a study that investigated the thinking of a high-achieving precalculus student when responding to tasks that required him to define linear formulas to relate covarying quantities. Two interviews were conducted for analysis. A team of us in the mathematics education department at Arizona State University initially identified mental actions that we conjectured were needed for constructing meaningful linear formulas. This guided the development of tasks for the sequence of clinical interviews with one high-performing precalculus student. Analysis of the interview data revealed that in instances when the subject engaged in meaning making that led to him imagining and identifying the relevant quantities and how they change together, he was able to give accurate definitions of variables and was usually able to define a formula to relate the two quantities of interest. However, we found that the student sometimes had difficulty imagining how the two quantities of interest were changing together. At other times he exhibited a weak understanding of the operation of subtraction and the idea of constant rate of change. He did not appear to conceptualize subtraction as a quantitative comparison. His inability to conceptualize a constant rate of change as a proportional relationship between the changes in two quantities also presented an obstacle in his developing a meaningful formula that relied on this understanding. The results further stress the need to develop a student's ability to engage in mental operations that involve covarying quantities and a more robust understanding of constant rate of change since these abilities and understanding are critical for student success in future courses in mathematics.
ContributorsKlinger, Tana Paige (Author) / Carlson, Marilyn (Thesis director) / Thompson, Pat (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
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
Description
Studies of discourse are prevalent in mathematics education, as are investigations on facilitating change in instructional practices that impact student attitudes toward mathematics. However, the literature has not sufficiently addressed the operationalization of the commognitive framework in the context of Calculus I, nor considered the inevitable impact on students’ attitudes of persistence, confidence, and enjoyment of mathematics. This study presents an innovation, founded, designed, and implemented, utilizing four frameworks. The overarching theory pivots to commognition, a theory that asserts communication is tantamount to thinking. Students experienced a Calculus I class grounded on four frames: a theoretical, a conceptual, a design pattern, and an analytical framework, which combined, engaged students in discursive practices. Multiple activities invited specific student actions: uncover, play, apply, connect, question, and realize, prompting calculus discourse. The study exploited a mixed-methods action research design that aimed to explore how discursive activities impact students’ understanding of the derivative and how and to what extent instructional practices, which prompt mathematical discourse, impact students’ persistence, confidence, and enjoyment of calculus.
This study offers a potential solution to a problem of practice that has long challenged practitioners and researchers—the persistence of Calculus I as a gatekeeper for Science, Technology, Engineering, and Mathematics (STEM). In this investigation it is suggested that Good and Ambitious Teaching practices, including asking students to explain their thinking and assigning group projects, positively impact students’ persistence, confidence, and enjoyment. Common calculus discourse among the experimental students, particularly discursive activities engaging word use and visual representations of the derivative, warrants further research for the pragmatic utility of the fine grain of a commognitive framework. For researchers the work provides a lens through which they can examine data resulting from the operationalization of multiple frameworks working in tandem. For practitioners, mathematical objects as discursive objects, allow for classrooms with readily observable outcomes.
ContributorsChowdhury, Madeleine Perez (Author) / Judson, Eugene (Thesis advisor) / Buss, Ray (Committee member) / Reinholz, Daniel (Committee member) / Arizona State University (Publisher)
Created2022
Description
The purpose of this quantitative action research study was to evaluate the effectiveness of an organization-wide book study in the K-12 environment. A growing charter school network was working towards an improved organizational culture to meet its mission. This study examined whether an organization-wide book study can make a difference in workplace belongingness, one of the core beliefs of the network. Bloom's Revised Taxonomy shaped the design of three distinct format options for the book study: facilitated, book club, and asynchronous. The study compared participants and non-participants in workplace belonging. Workplace belonging was measured using the Jena and Pradhan Workplace Belongingness Scale. Additionally, the study analyzed how the three different formats are more or less effective according to the Kirkpatrick Four-Level Model of Evaluation. The book study format effectiveness was measured using a modified version of the Lau, Henry, and Ebekozien training survey. Results were mixed. There was no significant difference found in workplace belonging among the three formats, and there was no significant difference found between the control group and experimental group. Significant difference was found in the facilitated format’s overviews and discussions when compared to the asynchronous group. Significant difference was also found in the book club’s discussions when compared to the asynchronous group.
ContributorsFowler, Betsy (Author) / Judson, Eugene (Thesis advisor) / Maddin, Brent (Committee member) / Assisi, Nicole (Committee member) / Arizona State University (Publisher)
Created2024
Description
The problem of practice addressed in this mixed-methods research study is assessing whether participating in professional development workshops helped community college instructors improve their pedagogical practices, leading to improved student success and achievement rates. In this study, I explore the effects of an intervention I designed to help English 101 instructors teach a new, direct-placement composition class, which was created to comply with the mandates of AB-705, an educational reform bill in California. I used three guiding theories to undergird and evaluate the intervention: Darling-Hammond et al.'s Accountability Approach (2014), Freire's Critical Pedagogy (1970), and Kirkpatrick and Kayser-Kirkpatrick’s Model of Training Effectiveness (2009). To address the research questions of this study, I analyzed pre- and post-surveys, faculty interviews, and student success and retention data. The results from the data were mixed. While the quantitative survey data did not support the claim that the College of the Canyons (COC) SkillShare Workshops affected instructors’ attitudes about teaching and their teaching behaviors, the qualitative interview data showed that the workshops did improve instructors’ professional capacities and were a valuable professional development resource. Additionally, the quantitative institutional data demonstrated that workshop participation significantly increased instructors’ student success and retention rates.
ContributorsTerzian-Zeitounian, Alene (Author) / Judson, Eugene (Thesis advisor) / Ross, Lydia (Committee member) / Meuschke, Daylene (Committee member) / Arizona State University (Publisher)
Created2022
Description
Efforts to improve student learning in K-12 education in the US are not new; however, educational research has traditionally focused on individual components of schools (e.g., teacher professional development, leadership, social relationships, programs, curricula) targeting teachers to improve student learning. While these innovations provide hope for change, they are limited in their focus and application to other school settings in that school contexts are unique to the individuals making them up and the collaborative missions and goals they pursue. To foster capacity for teachers to implement instructional reforms (i.e., how teachers teach), research must be focused on a holistic interpretation of the school as an organization. This study developed and validated a survey to examine elementary teachers’ science and mathematics instructional practice use as well as their perceptions of instructional reform capacity within their school environment from an ecological organization perspective. Over 300 elementary teachers from a large urban district participated in the survey over the course of four weeks. Findings indicated elementary teachers utilized teacher-centered instructional practices more frequently than reform-oriented (i.e., student-centered) instructional practices. However, teachers reported more frequent use of instructional practices in their mathematics lessons compared to science lessons. Furthermore, data was used to investigate the underlying dimensions of instructional reform capacity and examine the relationship between those dimensions and instructional practice use both within and between subjects (i.e., science and mathematics). Results revealed dimensions underlying instructional reform capacity as well as correlations with instructional practice use are not the same for elementary science and mathematics. Dimensions of professional learning, structure, and policy were more strongly correlated with reform-oriented (i.e., student-centered) instructional practices. Implications from these findings suggest the necessity of a more holistic perspective of instructional reform capacity to better support instructional reforms across subject areas in schools, on both the local level and within research.
ContributorsGlassmeyer, Kristi (Author) / Judson, Eugene (Thesis advisor) / Hayes, Kathryn (Committee member) / Kim, Jeongeun (Committee member) / Arizona State University (Publisher)
Created2022