Matching Items (5)
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- All Subjects: Mathematics Education
- Creators: Van de Sande, Carla
- Status: Published
Description
Past research has shown that students have difficulty developing a robust conception of function. However, little prior research has been performed dealing with student knowledge of function composition, a potentially powerful mathematical concept. This dissertation reports the results of an investigation into student understanding and use of function composition, set against the backdrop of a precalculus class that emphasized quantification and covariational reasoning. The data were collected using task-based, semi-structured clinical interviews with individual students outside the classroom. Findings from this study revealed that factors such as the student's quantitative reasoning, covariational reasoning, problem solving behaviors, and view of function influence how a student understands and uses function composition. The results of the study characterize some of the subtle ways in which these factors impact students' ability to understand and use function composition to solve problems. Findings also revealed that other factors such as a students' persistence, disposition towards "meaning making" for the purpose of conceptualizing quantitative relationships, familiarity with the context of a problem, procedural fluency, and student knowledge of rules of "order of operations" impact a students' progress in advancing her/his solution approach.
ContributorsBowling, Stacey (Author) / Carlson, Marilyn P (Thesis advisor) / Thompson, Patrick W (Committee member) / Moore, Kevin C (Committee member) / Milner, Fabio (Committee member) / Van de Sande, Carla (Committee member) / Arizona State University (Publisher)
Created2014
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
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
This study investigates the impact and experiences of students designated as English Language Learners (ELLs) as they engage with student-centered worked example videos (WEVs). Students from two southwestern high schools collaborated and provided their experiences as they watched WEVs and worked through four slope calculation problems. Although high school ELLs are placed in appropriate mathematics classes, the WEVs they engage with, by design, do not consider their diverse educational needs, one of which is the amount of cognitive load experienced when watching the videos. Through this Multi-Phase Mixed Methods study, I begin to understand inclusive design practices for WEVs, in which ELLs will not experience cognitive over-load, and as a result, will receive the needed remediation and/or instruction and develop concept proficiency through active learning as they engage with the videos. The research finds that specific design principles, closed captioning, conversational narration, and music, reduce cognitive load and provide ELLs a familiar and safe space from which to engage with mathematical content.
ContributorsRobles Ramirez, Rolando (Author) / Lee, Mi Yeon (Thesis advisor) / Van de Sande, Carla (Committee member) / Jimenez-Silva, Margarita (Committee member) / Arizona State University (Publisher)
Created2023
Description
Learning loss occurs during academic breaks, and this can be detrimental to student success especially in sequential classes like Arizona State University’s Engineering Calculus sequence in which retention of the topics taught in a prior class is expected. The Keeping in School Shape Program (KiSS) is designed as a cost effective, efficient, and accessible way of addressing this problem. The KiSS program uses push technology to give students a way to regularly review material over academic breaks while also fostering a growth mindset.Every day, during an academic break, students are sent a link via text message or email to access a multiple-choice daily review problem which represents material from a previous course that is requisite for success in an upcoming course. Before solving the daily problem, students use a 5-point scale to indicate how confident they are that they can solve the problem. Students then complete the daily review problem and have a variety of resources to support them as they do so, as well as options after they complete it. Students are able to view a hint and try a problem again, view a solution, and attempt a challenge problem. On Tuesdays (aka 2’s-Days) students are given the opportunity to complete either an additional daily review problem or an additional challenge problem, and on Sundays (aka Trivia Days) students can decide between completing only a mathematics trivia question or trivia along with the daily review problem.
There is much to be learned from each individual student who participates in the KiSS program. Three surveys were conducted during the Winter Break 2020 KiSS program that gave insight into students’ experience in the KiSS program along with their personal background and mindset regarding mathematics. Ten students responded to all three of these surveys. This thesis will present a case study for each of these ten students based on their data from program participation and survey responses. Conclusions will be drawn regarding ways in which the KiSS program is helping students and ways in which it can be improved to help students be better prepared for their upcoming studies.
ContributorsVandenberg, Jana Elle (Author) / Van de Sande, Carla (Thesis advisor) / Jones, Donald (Committee member) / Milner, Fabio (Committee member) / Verdín, Dina (Committee member) / Arizona State University (Publisher)
Created2021