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- Creators: Arizona State University
- Creators: Savenye, Wilhelmina
- Creators: Atkinson, Robert K
Description
This study contributes to the ongoing discussion of Mathematical Knowledge for Teaching (MKT). It investigates the case of Rico, a high school mathematics teacher who had become known to his colleagues and his students as a superbly effective mathematics teacher. His students not only developed excellent mathematical skills, they also developed deep understanding of the mathematics they learned. Moreover, Rico redesigned his curricula and instruction completely so that they provided a means of support for his students to learn mathematics the way he intended. The purpose of this study was to understand the sources of Rico's effectiveness. The data for this study was generated in three phases. Phase I included videos of Rico's lessons during one semester of an Algebra II course, post-lesson reflections, and Rico's self-constructed instructional materials. An analysis of Phase I data led to Phase II, which consisted of eight extensive stimulated-reflection interviews with Rico. Phase III consisted of a conceptual analysis of the prior phases with the aim of creating models of Rico's mathematical conceptions, his conceptions of his students' mathematical understandings, and his images of instruction and instructional design. Findings revealed that Rico had developed profound personal understandings, grounded in quantitative reasoning, of the mathematics that he taught, and profound pedagogical understandings that supported these very same ways of thinking in his students. Rico's redesign was driven by three factors: (1) the particular way in which Rico himself understood the mathematics he taught, (2) his reflective awareness of those ways of thinking, and (3) his ability to envision what students might learn from different instructional approaches. Rico always considered what someone might already need to understand in order to understand "this" in the way he was thinking of it, and how understanding "this" might help students understand related ideas or methods. Rico's continual reflection on the mathematics he knew so as to make it more coherent, and his continual orientation to imagining how these meanings might work for students' learning, made Rico's mathematics become a mathematics of students--impacting how he assessed his practice and engaging him in a continual process of developing MKT.
ContributorsLage Ramírez, Ana Elisa (Author) / Thompson, Patrick W. (Thesis advisor) / Carlson, Marilyn P. (Committee member) / Castillo-Chavez, Carlos (Committee member) / Saldanha, Luis (Committee member) / Middleton, James A. (Committee member) / Arizona State University (Publisher)
Created2011
Description
This study empirically evaluated the effectiveness of the instructional design, learning tools, and role of the teacher in three versions of a semester-long, high-school remedial Algebra I course to determine what impact self-regulated learning skills and learning pattern training have on students' self-regulation, math achievement, and motivation. The 1st version was a business-as-usual traditional classroom teaching mathematics with direct instruction. The 2rd version of the course provided students with self-paced, individualized Algebra instruction with a web-based, intelligent tutor. The 3rd version of the course coupled self-paced, individualized instruction on the web-based, intelligent Algebra tutor coupled with a series of e-learning modules on self-regulated learning knowledge and skills that were distributed throughout the semester. A quasi-experimental, mixed methods evaluation design was used by assigning pre-registered, high-school remedial Algebra I class periods made up of an approximately equal number of students to one of the three study conditions or course versions: (a) the control course design, (b) web-based, intelligent tutor only course design, and (c) web-based, intelligent tutor + SRL e-learning modules course design. While no statistically significant differences on SRL skills, math achievement or motivation were found between the three conditions, effect-size estimates provide suggestive evidence that using the SRL e-learning modules based on ARCS motivation model (Keller, 2010) and Let Me Learn learning pattern instruction (Dawkins, Kottkamp, & Johnston, 2010) may help students regulate their learning and improve their study skills while using a web-based, intelligent Algebra tutor as evidenced by positive impacts on math achievement, motivation, and self-regulated learning skills. The study also explored predictive analyses using multiple regression and found that predictive models based on independent variables aligned to student demographics, learning mastery skills, and ARCS motivational factors are helpful in defining how to further refine course design and design learning evaluations that measure achievement, motivation, and self-regulated learning in web-based learning environments, including intelligent tutoring systems.
ContributorsBarrus, Angela (Author) / Atkinson, Robert K (Thesis advisor) / Van de Sande, Carla (Committee member) / Savenye, Wilhelmina (Committee member) / Arizona State University (Publisher)
Created2013
Description
This action research study, set in a community college in the southwestern United States, was designed to investigate the effects of implementing cooperative learning strategies in a developmental mathematics course. Introductory algebra was formerly taught in a lecture based format, and as such regularly had a low course completion rate. To create a more engaging learning environment, formal and informal cooperative learning activities were integrated into the curriculum. Bandura's self-efficacy theory, Vygotsky's constructivist theory, and Deutsch's social interdependence theory guided this study. Qualitative and quantitative data were collected through pre and post self-efficacy surveys, semi-structured student interviews, student journal entries, class observations, focus groups, and pre and post mathematics assessments. Data were analyzed using a mixed methods approach. As a result of implementing cooperative learning practices as a part of my teaching, there was an increase in student attendance as well as a decrease in student withdrawal rates. Students were also more motivated to work with each other on mathematics homework outside of class sessions. There was a strong sense of community that I had not witnessed in previous courses that I have taught. Use of cooperative learning practices served as a vehicle to motivate students to work on their mathematics coursework with their peers. Keywords: cooperative learning, developmental mathematics, constructivism, social interdependence theory, self-efficacy, community college
ContributorsRivera, Natalie (Author) / Zambo, Ron (Thesis advisor) / Jiménez, Rosa (Committee member) / Rivera, Reynaldo (Committee member) / Arizona State University (Publisher)
Created2013
Description
Many students in the United States are graduating from high school without the math skills they need to be considered college ready. For many of these graduates, who find themselves starting their higher education at a community college, remedial math can become an insurmountable barrier that ends their aspirations for a degree or certificate. Some students must take as many as four remedial courses before they are considered college ready. Studies report that between 60% and 70% of students placed into remedial math classes either do not successfully complete the sequence of required courses or avoid taking math altogether and therefore never graduate (Bailey, Jeong, & Cho, 2010). This study compared three low-level freshman math classes in one Arizona high school. The purpose of this study was to implement an innovative learning intervention to find out if there was a causal relationship between the addition of technology with instruction in a blended learning environment and performance in math. The intervention measured growth (pre- and posttest) and grade-level achievement (district-provided benchmark test) in three Foundations of Algebra classes. The three classes ranged on a continuum with the use of technology and personalized instruction. Additionally, focus groups were conducted to better understand the challenges this population of students face when learning math. The changes in classroom practices showed no statistical significance on the student outcomes achieved. Students in a blended online environment learned the Foundations of Algebra concepts similarly to their counterparts in a traditional, face-to-face learning environment.
ContributorsBolley, Staci (Author) / Schugurensky, Daniel, 1958- (Thesis advisor) / Cruz, Heather (Committee member) / Barnett, Joshua (Committee member) / Arizona State University (Publisher)
Created2013
Description
In any instructional situation, the instructor's goal is to maximize the learning attained by students. Drawing on the adage, 'we learn best what we have taught,' this action research project was conducted to examine whether students, in fact, learned college algebra material better if they taught it to their peers. The teaching-to-learn process was conducted in the following way. The instructor-researcher met with individual students and taught a college algebra topic to a student who served as the leader of a group of four students. At the next step, the student who originally learned the material from the instructor met with three other students in a small group session and taught the material to them to prepare an in-class presentation. Students in these small group sessions discussed how best to present the material, anticipated questions, and prepared a presentation to be shared with their classmates. The small group then taught the material to classmates during an in-class review session prior to unit examinations. Quantitative and qualitative data were gathered. Quantitative data consisted of pre- and post-test scores on four college algebra unit examinations. In addition, scores from Likert-scale items on an end-of-semester questionnaire that assessed the effectiveness of the teaching-to-learn process and attitudes toward the process were obtained. Qualitative data consisted of field notes from observations of selected small group sessions and in-class presentations. Additional qualitative data included responses to open-ended questions on the end-of-semester questionnaire and responses to interview items posed to groups of students. Results showed the quantitative data did not support the hypothesis that material, which was taught, was better learned than other material. Nevertheless, qualitative data indicated students were engaged in the material, had a deeper understanding of the material, and were more confident about it as a result of their participation in the teaching-to-learn process. Students also viewed the teaching-to-learn process as being effective and they had positive attitudes toward the teaching-to-learn process. Discussion focused on how engagement, deeper understanding and confidence interacted with one another to increase student learning. Lessons learned, implications for practice, and implications for further action research were also discussed.
ContributorsNicoloff, Stephen J (Author) / Buss, Ray R (Thesis advisor) / Zambo, Ronald (Committee member) / Shaw, Phyllis J (Committee member) / Arizona State University (Publisher)
Created2011
Description
The mathematics test is the most difficult test in the GED (General Education Development) Test battery, largely due to the presence of story problems. Raising performance levels of story problem-solving would have a significant effect on GED Test passage rates. The subject of this formative research study is Ms. Stephens’ Categorization Practice Utility (MS-CPU), an example-tracing intelligent tutoring system that serves as practice for the first step (problem categorization) in a larger comprehensive story problem-solving pedagogy that purports to raise the level of story problem-solving performance. During the analysis phase of this project, knowledge components and particular competencies that enable learning (schema building) were identified. During the development phase, a tutoring system was designed and implemented that algorithmically teaches these competencies to the student with graphical, interactive, and animated utilities. Because the tutoring system provides a much more concrete rather than conceptual, learning environment, it should foster a much greater apprehension of a story problem-solving process. With this experience, the student should begin to recognize the generalizability of concrete operations that accomplish particular story problem-solving goals and begin to build conceptual knowledge and a more conceptual approach to the task. During the formative evaluation phase, qualitative methods were used to identify obstacles in the MS-CPU user interface and disconnections in the pedagogy that impede learning story problem categorization and solution preparation. The study was conducted over two iterations where identification of obstacles and change plans (mitigations) produced a qualitative data table used to modify the first version systems (MS-CPU 1.1). Mitigation corrections produced the second version of the MS-CPU 1.2, and the next iteration of the study was conducted producing a second set of obstacle/mitigation tables. Pre-posttests were conducted in each iteration to provide corroboration for the effectiveness of the mitigations that were performed. The study resulted in the identification of a number of learning obstacles in the first version of the MS-CPU 1.1. Their mitigation produced a second version of the MS-CPU 1.2 whose identified obstacles were much less than the first version. It was determined that an additional iteration is needed before more quantitative research is conducted.
ContributorsRitchey, ChristiAnne (Author) / VanLehn, Kurt (Thesis advisor) / Savenye, Wilhelmina (Committee member) / Hong, Yi-Chun (Committee member) / Arizona State University (Publisher)
Created2018
Description
Over the past 25 years, efforts have been made to integrate technology into teaching and learning. In particular, the personalized learning approach has sought to leverage technology to deliver instruction that is adaptive to the learner and personalized learning environments were used as tools in tailoring instruction to match learner needs. Typically, personalized instruction has been delivered using technology, such as the computer. However, little research has focused on using personalized learning as a tool for remediation. The goal of this study was to empirically investigate the efficacy of personalized learning in Algebra as a remediation tool. This study used a mixed-methods approach to analyze satisfaction with the learning environment, perception of and attitudes toward the content being delivered, and the reported overall experience and the personalized experience in the context of two versions of a computer-based multimedia Algebra learning environment. A total of 117 high school students in grades 10 through 12 participated on a voluntary basis. They had previously taken an introductory Algebra course and were now enrolled in a different math course. The students were assigned to one of two conditions: (a) the computer-based multimedia learning environment on the personalized learning platform known as Personalized Learning and (b) the same learning environment without the Personalized Learning platform. In addition to completing a pre- and post-test, participants were administered attitudinal surveys. Results indicated no knowledge gains in either group at the post-test assessment. Further, analyses by gender and race also did not reveal any significant differences among the groups. However, survey results indicated one significant finding: the students exposed to the personalized learning environment had more positive perceptions towards personalized learning than towards the overall experience with the learning environment.
Implications for these results and further goals for this line of research are discussed in greater detail within the context of personalized learning, user experience, and social aspects of learning. This work also provides opportunities in helping educators choose adequate tools for teaching and delivering instruction tailored to learners’ needs.
Implications for these results and further goals for this line of research are discussed in greater detail within the context of personalized learning, user experience, and social aspects of learning. This work also provides opportunities in helping educators choose adequate tools for teaching and delivering instruction tailored to learners’ needs.
ContributorsSavio-Ramos, Caroline Andrea (Author) / Bitter, Gary G. (Thesis advisor) / Buss, Ray (Committee member) / Legacy, Jane (Committee member) / Arizona State University (Publisher)
Created2015
Description
This dissertation contains three main results. First, a generalization of Ionescu's theorem is proven. Ionescu's theorem describes an unexpected connection between graph C*-algebras and fractal geometry. In this work, this theorem is extended from ordinary directed graphs to higher-rank graphs. Second, a characterization is given of the Cuntz-Pimsner algebra associated to a tensor product of C*-correspondences. This is a generalization of a result by Kumjian about graphs algebras. This second result is applied to several important special cases of Cuntz-Pimsner algebras including topological graph algebras, crossed products by the integers and crossed products by completely positive maps. The result has meaningful interpretations in each context. The third result is an extension of the second result from an ordinary tensor product to a special case of Woronowicz's twisted tensor product. This result simultaneously characterizes Cuntz-Pimsner algebras of ordinary and graded tensor products and Cuntz-Pimsner algebras of crossed products by actions and coactions of discrete groups, the latter partially recovering earlier results of Hao and Ng and of Kaliszewski, Quigg and Robertson.
ContributorsMorgan, Adam (Author) / Kaliszewski, Steven (Thesis advisor) / Quigg, John (Thesis advisor) / Spielberg, Jack (Committee member) / Kawski, Matthias (Committee member) / Kotschwar, Brett (Committee member) / Arizona State University (Publisher)
Created2016
Description
A new algebraic system, Test Algebra (TA), is proposed for identifying faults in combinatorial testing for SaaS (Software-as-a-Service) applications. In the context of cloud computing, SaaS is a new software delivery model, in which mission-critical applications are composed, deployed, and executed on cloud platforms. Testing SaaS applications is challenging because new applications need to be tested once they are composed, and prior to their deployment. A composition of components providing services yields a configuration providing a SaaS application. While individual components
in the configuration may have been thoroughly tested, faults still arise due to interactions among the components composed, making the configuration faulty. When there are k components, combinatorial testing algorithms can be used to identify faulty interactions for t or fewer components, for some threshold 2 <= t <= k on the size of interactions considered. In general these methods do not identify specific faults, but rather indicate the presence or absence of some fault. To identify specific faults, an adaptive testing regime repeatedly constructs and tests configurations in order to determine, for each interaction of interest, whether it is faulty or not. In order to perform such testing in a loosely coupled distributed environment such as
the cloud, it is imperative that testing results can be combined from many different servers. The TA defines rules to permit results to be combined, and to identify the faulty interactions. Using the TA, configurations can be tested concurrently on different servers and in any order. The results, using the TA, remain the same.
in the configuration may have been thoroughly tested, faults still arise due to interactions among the components composed, making the configuration faulty. When there are k components, combinatorial testing algorithms can be used to identify faulty interactions for t or fewer components, for some threshold 2 <= t <= k on the size of interactions considered. In general these methods do not identify specific faults, but rather indicate the presence or absence of some fault. To identify specific faults, an adaptive testing regime repeatedly constructs and tests configurations in order to determine, for each interaction of interest, whether it is faulty or not. In order to perform such testing in a loosely coupled distributed environment such as
the cloud, it is imperative that testing results can be combined from many different servers. The TA defines rules to permit results to be combined, and to identify the faulty interactions. Using the TA, configurations can be tested concurrently on different servers and in any order. The results, using the TA, remain the same.
ContributorsQi, Guanqiu (Author) / Tsai, Wei-Tek (Thesis advisor) / Davulcu, Hasan (Committee member) / Sarjoughian, Hessam S. (Committee member) / Yu, Hongyu (Committee member) / Arizona State University (Publisher)
Created2014
Description
The purpose of this study was to identify the algebraic reasoning abilities of young students prior to instruction. The goals of the study were to determine the influence of problem, problem type, question, grade level, and gender on: (a) young children’s abilities to predict the number of shapes in near and far positions in a “growing” pattern without assistance; (b) the nature and amount of assistance needed to solve the problems; and (c) reasoning methods employed by children.
The 8-problem Growing Patterns and Functions Assessment (GPFA), with an accompanying interview protocol, were developed to respond to these goals. Each problem presents sequences of figures of geometric shapes that differ in complexity and can be represented by the function, y = mf +b: in Type 1 problems (1 - 4), m = 1, and in Type 2 problems (5 - 8), m = 2. The two questions in each problem require participants to first, name the number of shapes in the pattern in a near position, and then to identify the number of shapes in a far position. To clarify reasoning methods, participants were asked how they solved the problems.
The GPFA was administered, one-on-one, to 60 students in Grades 1, 2, and 3 with an equal number of males and females from the same elementary school. Problem solution scores without and with assistance, along with reasoning method(s) employed, were tabulated.
Results of data analyses showed that when no assistance was required, scores varied significantly by problem, problem type, and question, but not grade level or gender. With assistance, problem scores varied significantly by problem, problem type, question, and grade level, but not gender.
The 8-problem Growing Patterns and Functions Assessment (GPFA), with an accompanying interview protocol, were developed to respond to these goals. Each problem presents sequences of figures of geometric shapes that differ in complexity and can be represented by the function, y = mf +b: in Type 1 problems (1 - 4), m = 1, and in Type 2 problems (5 - 8), m = 2. The two questions in each problem require participants to first, name the number of shapes in the pattern in a near position, and then to identify the number of shapes in a far position. To clarify reasoning methods, participants were asked how they solved the problems.
The GPFA was administered, one-on-one, to 60 students in Grades 1, 2, and 3 with an equal number of males and females from the same elementary school. Problem solution scores without and with assistance, along with reasoning method(s) employed, were tabulated.
Results of data analyses showed that when no assistance was required, scores varied significantly by problem, problem type, and question, but not grade level or gender. With assistance, problem scores varied significantly by problem, problem type, question, and grade level, but not gender.
ContributorsCavanagh, Mary Clare (Author) / Greenes, Carole E. (Thesis advisor) / Buss, Ray (Committee member) / Surbeck, Elaine (Committee member) / Arizona State University (Publisher)
Created2016