Matching Items (13)
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- All Subjects: Mathematics Education
- All Subjects: Social networks
- Genre: Academic theses
- Creators: Castillo-Chavez, Carlos
- Creators: Saldanha, Luis
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
I compare the effect of anonymous social network ratings (Yelp.com) and peer group recommendations on restaurant demand. I conduct a two-stage choice experiment in which restaurant visits in the first stage are informed by online social network reviews from Yelp.com, and visits in the second stage by peer network reviews. I find that anonymous reviewers have a stronger effect on restaurant preference than peers. I also compare the power of negative reviews with that of positive reviews. I found that negative reviews are more powerful compared to the positive reviews on restaurant preference. More generally, I find that in an environment of high attribute uncertainty, information gained from anonymous experts through social media is likely to be more influential than information obtained from peers.
ContributorsTiwari, Ashutosh (Author) / Richards, Timothy J. (Thesis advisor) / Qiu, Yueming (Committee member) / Grebitus, Carola (Committee member) / Arizona State University (Publisher)
Created2013
Description
Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative combinatorics problems and how students conceptualize the set of elements being counted in such problems, called the solution set. In particular, the focus was on the stable patterns of reasoning, known as ways of thinking, which students applied in a variety of combinatorial situations and tasks. This study catalogued students' ways of thinking about solution sets as they progressed through an instructional sequence. In addition, the relationships between the catalogued ways of thinking were explored. Further, the study investigated the challenges students experienced as they interacted with the tasks and instructional interventions, and how students' ways of thinking evolved as these challenges were overcome. Finally, it examined the role of instruction in guiding students to develop and extend their ways of thinking. Two pairs of undergraduate students with no formal experience with combinatorics participated in one of the two consecutive teaching experiments conducted in Spring 2012. Many ways of thinking emerged through the grounded theory analysis of the data, but only eight were identified as robust. These robust ways of thinking were classified into three categories: Subsets, Odometer, and Problem Posing. The Subsets category encompasses two ways of thinking, both of which ultimately involve envisioning the solution set as the union of subsets. The three ways of thinking in Odometer category involve holding an item or a set of items constant and systematically varying the other items involved in the counting process. The ways of thinking belonging to Problem Posing category involve spontaneously posing new, related combinatorics problems and finding relationships between the solution sets of the original and the new problem. The evolution of students' ways of thinking in the Problem Posing category was analyzed. This entailed examining the perturbation experienced by students and the resulting accommodation of their thinking. It was found that such perturbation and its resolution was often the result of an instructional intervention. Implications for teaching practice are discussed.
ContributorsHalani, Aviva (Author) / Roh, Kyeong Hah (Thesis advisor) / Fishel, Susanna (Committee member) / Saldanha, Luis (Committee member) / Thompson, Patrick (Committee member) / Zandieh, Michelle (Committee member) / Arizona State University (Publisher)
Created2013
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
Research shows that the subject of mathematics, although revered, remains a source of trepidation for many individuals, as they find it difficult to form a connection between the work they do on paper and their work's practical applications. This research study describes the impact of teaching a challenging introductive applied mathematics course on high school students' skills and attitudes towards mathematics in a college Summer Program. In the analysis of my research data, I identified several emerging changes in skills and attitudes towards mathematics, skills that high-school students needed or developed when taking the mathematical modeling course. Results indicated that the applied mathematics course had a positive impact on several students' attitudes, in general, such as, self-confidence, meanings of what mathematics is, and their perceptions of what solutions are. It also had a positive impact on several skills, such as translating real-life situations to mathematics via flow diagrams, translating the models' solutions back from mathematics to the real world, and interpreting graphs. Students showed positive results when the context of their problems was applied or graphical, and fewer improvement on problems that were not. Research also indicated some negatives outcomes, a decrease in confidence for certain students, and persistent negative ways of thinking about graphs. Based on these findings, I make recommendations for teaching similar mathematical modeling at the pre-university level, to encourage the development of young students through educational, research and similar mentorship activities, to increase their inspiration and interest in mathematics, and possibly consider a variety of sciences, technology, engineering and mathematics-related (STEM) fields and careers.
Contributorsagoune, linda (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Castillo-Garsow, Carlos W (Thesis advisor) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2020
Description
Understanding the consequences of changes in social networks is an important an-
thropological research goal. This dissertation looks at the role of data-driven social
networks on infectious disease transmission and evolution. The dissertation has two
projects. The first project is an examination of the effects of the superspreading
phenomenon, wherein a relatively few individuals are responsible for a dispropor-
tionate number of secondary cases, on the patterns of an infectious disease. The
second project examines the timing of the initial introduction of tuberculosis (TB) to
the human population. The results suggest that TB has a long evolutionary history
with hunter-gatherers. Both of these projects demonstrate the consequences of social
networks for infectious disease transmission and evolution.
The introductory chapter provides a review of social network-based studies in an-
thropology and epidemiology. Particular emphasis is paid to the concept and models
of superspreading and why to consider it, as this is central to the discussion in chapter
2. The introductory chapter also reviews relevant epidemic mathematical modeling
studies.
In chapter 2, social networks are connected with superspreading events, followed
by an investigation of how social networks can provide greater understanding of in-
fectious disease transmission through mathematical models. Using the example of
SARS, the research shows how heterogeneity in transmission rate impacts super-
spreading which, in turn, can change epidemiological inference on model parameters
for an epidemic.
Chapter 3 uses a different mathematical model to investigate the evolution of TB
in hunter-gatherers. The underlying question is the timing of the introduction of TB
to the human population. Chapter 3 finds that TB’s long latent period is consistent
with the evolutionary pressure which would be exerted by transmission on a hunter-
igatherer social network. Evidence of a long coevolution with humans indicates an
early introduction of TB to the human population.
Both of the projects in this dissertation are demonstrations of the impact of var-
ious characteristics and types of social networks on infectious disease transmission
dynamics. The projects together force epidemiologists to think about networks and
their context in nontraditional ways.
thropological research goal. This dissertation looks at the role of data-driven social
networks on infectious disease transmission and evolution. The dissertation has two
projects. The first project is an examination of the effects of the superspreading
phenomenon, wherein a relatively few individuals are responsible for a dispropor-
tionate number of secondary cases, on the patterns of an infectious disease. The
second project examines the timing of the initial introduction of tuberculosis (TB) to
the human population. The results suggest that TB has a long evolutionary history
with hunter-gatherers. Both of these projects demonstrate the consequences of social
networks for infectious disease transmission and evolution.
The introductory chapter provides a review of social network-based studies in an-
thropology and epidemiology. Particular emphasis is paid to the concept and models
of superspreading and why to consider it, as this is central to the discussion in chapter
2. The introductory chapter also reviews relevant epidemic mathematical modeling
studies.
In chapter 2, social networks are connected with superspreading events, followed
by an investigation of how social networks can provide greater understanding of in-
fectious disease transmission through mathematical models. Using the example of
SARS, the research shows how heterogeneity in transmission rate impacts super-
spreading which, in turn, can change epidemiological inference on model parameters
for an epidemic.
Chapter 3 uses a different mathematical model to investigate the evolution of TB
in hunter-gatherers. The underlying question is the timing of the introduction of TB
to the human population. Chapter 3 finds that TB’s long latent period is consistent
with the evolutionary pressure which would be exerted by transmission on a hunter-
igatherer social network. Evidence of a long coevolution with humans indicates an
early introduction of TB to the human population.
Both of the projects in this dissertation are demonstrations of the impact of var-
ious characteristics and types of social networks on infectious disease transmission
dynamics. The projects together force epidemiologists to think about networks and
their context in nontraditional ways.
ContributorsNesse, Hans P (Author) / Hurtado, Ana Magdalena (Thesis advisor) / Castillo-Chavez, Carlos (Committee member) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2019
Description
The popularity of social media has generated abundant large-scale social networks, which advances research on network analytics. Good representations of nodes in a network can facilitate many network mining tasks. The goal of network representation learning (network embedding) is to learn low-dimensional vector representations of social network nodes that capture certain properties of the networks. With the learned node representations, machine learning and data mining algorithms can be applied for network mining tasks such as link prediction and node classification. Because of its ability to learn good node representations, network representation learning is attracting increasing attention and various network embedding algorithms are proposed.
Despite the success of these network embedding methods, the majority of them are dedicated to static plain networks, i.e., networks with fixed nodes and links only; while in social media, networks can present in various formats, such as attributed networks, signed networks, dynamic networks and heterogeneous networks. These social networks contain abundant rich information to alleviate the network sparsity problem and can help learn a better network representation; while plain network embedding approaches cannot tackle such networks. For example, signed social networks can have both positive and negative links. Recent study on signed networks shows that negative links have added value in addition to positive links for many tasks such as link prediction and node classification. However, the existence of negative links challenges the principles used for plain network embedding. Thus, it is important to study signed network embedding. Furthermore, social networks can be dynamic, where new nodes and links can be introduced anytime. Dynamic networks can reveal the concept drift of a user and require efficiently updating the representation when new links or users are introduced. However, static network embedding algorithms cannot deal with dynamic networks. Therefore, it is important and challenging to propose novel algorithms for tackling different types of social networks.
In this dissertation, we investigate network representation learning in social media. In particular, we study representative social networks, which includes attributed network, signed networks, dynamic networks and document networks. We propose novel frameworks to tackle the challenges of these networks and learn representations that not only capture the network structure but also the unique properties of these social networks.
Despite the success of these network embedding methods, the majority of them are dedicated to static plain networks, i.e., networks with fixed nodes and links only; while in social media, networks can present in various formats, such as attributed networks, signed networks, dynamic networks and heterogeneous networks. These social networks contain abundant rich information to alleviate the network sparsity problem and can help learn a better network representation; while plain network embedding approaches cannot tackle such networks. For example, signed social networks can have both positive and negative links. Recent study on signed networks shows that negative links have added value in addition to positive links for many tasks such as link prediction and node classification. However, the existence of negative links challenges the principles used for plain network embedding. Thus, it is important to study signed network embedding. Furthermore, social networks can be dynamic, where new nodes and links can be introduced anytime. Dynamic networks can reveal the concept drift of a user and require efficiently updating the representation when new links or users are introduced. However, static network embedding algorithms cannot deal with dynamic networks. Therefore, it is important and challenging to propose novel algorithms for tackling different types of social networks.
In this dissertation, we investigate network representation learning in social media. In particular, we study representative social networks, which includes attributed network, signed networks, dynamic networks and document networks. We propose novel frameworks to tackle the challenges of these networks and learn representations that not only capture the network structure but also the unique properties of these social networks.
ContributorsWang, Suhang (Author) / Liu, Huan (Thesis advisor) / Aggarwal, Charu (Committee member) / Sen, Arunabha (Committee member) / Tong, Hanghang (Committee member) / Arizona State University (Publisher)
Created2018
Description
Teachers must recognize the knowledge they possess as appropriate to employ in the process of achieving their goals and objectives in the context of practice. Such recognition is subject to a host of cognitive and affective processes that have thus far not been a central focus of research on teacher knowledge in mathematics education. To address this need, this dissertation study examined the role of a secondary mathematics teacher’s image of instructional constraints on his enacted subject matter knowledge. I collected data in three phases. First, I conducted a series of task-based clinical interviews that allowed me to construct a model of David’s mathematical knowledge of sine and cosine functions. Second, I conducted pre-lesson interviews, collected journal entries, and examined David’s instruction to characterize the mathematical knowledge he utilized in the context of designing and implementing lessons. Third, I conducted a series of semi-structured clinical interviews to identify the circumstances David appraised as constraints on his practice and to ascertain the role of these constraints on the quality of David’s enacted subject matter knowledge. My analysis revealed that although David possessed many productive ways of understanding that allowed him to engage students in meaningful learning experiences, I observed discrepancies between and within David’s mathematical knowledge and his enacted mathematical knowledge. These discrepancies were not occasioned by David’s active compensation for the circumstances and events he appraised as instructional constraints, but instead resulted from David possessing multiple schemes for particular ideas related to trigonometric functions, as well as from his unawareness of the mental actions and operations that comprised these often powerful but uncoordinated cognitive schemes. This lack of conscious awareness made David ill-equipped to define his instructional goals in terms of the mental activity in which he intended his students to engage, which further conditioned the circumstances and events he appraised as constraints on his practice. David’s image of instructional constraints therefore did not affect his enacted subject matter knowledge. Rather, characteristics of David’s subject matter knowledge, namely his uncoordinated cognitive schemes and his unawareness of the mental actions and operations that comprise them, affected his image of instructional constraints.
ContributorsTallman, Michael Anthony (Author) / Carlson, Marilyn P (Thesis advisor) / Thompson, Patrick W (Committee member) / Saldanha, Luis (Committee member) / Middleton, James (Committee member) / Harel, Guershon (Committee member) / Arizona State University (Publisher)
Created2015
Description
The Mathematical and Theoretical Biology Institute (MTBI) is a summer research program for undergraduate students, largely from underrepresented minority groups. Founded in 1996, it serves as a 'life-long' mentorship program, providing continuous support for its students and alumni. This study investigates how MTBI supports student development in applied mathematical research. This includes identifying of motivational factors to pursue and develop capacity to complete higher education.
The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to the collaborative and creative way students co-create the process of becoming scientists. This results in building a continuing network of academic and professional relationships among peers and mentors, in which around three quarters of MTBI PhD graduates come from underrepresented groups.
The extent to which MTBI creates a Vygotskian learning environment is explored from the perspectives of participants who earned doctoral degrees. Previously hypothesized factors (Castillo-Garsow, Castillo-Chavez and Woodley, 2013) that affect participants’ educational and professional development are expanded on.
Factors identified by participants are a passion for the mathematical sciences; desire to grow; enriching collaborative and peer-like interactions; and discovering career options. The self-recognition that they had the ability to be successful, key element of the Vygotskian-Holzman theoretical framework, was a commonly identified theme for their educational development and professional growth.
Participants characterize the collaborative and creative aspects of MTBI. They reported that collaborative dynamics with peers were strengthened as they co-created a learning environment that facilitated and accelerated their understanding of the mathematics needed to address their research. The dynamics of collaboration allowed them to complete complex homework assignments, and helped them formulate and complete their projects. Participants identified the creative environments of their research projects as where creativity emerged in the dynamics of the program.
These data-driven findings characterize for the first time a summer program in the mathematical sciences as a Vygotskian-Holzman environment, that is, a `place’ where participants are seen as capable applied mathematicians, where the dynamics of collaboration and creativity are fundamental components.
The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to the collaborative and creative way students co-create the process of becoming scientists. This results in building a continuing network of academic and professional relationships among peers and mentors, in which around three quarters of MTBI PhD graduates come from underrepresented groups.
The extent to which MTBI creates a Vygotskian learning environment is explored from the perspectives of participants who earned doctoral degrees. Previously hypothesized factors (Castillo-Garsow, Castillo-Chavez and Woodley, 2013) that affect participants’ educational and professional development are expanded on.
Factors identified by participants are a passion for the mathematical sciences; desire to grow; enriching collaborative and peer-like interactions; and discovering career options. The self-recognition that they had the ability to be successful, key element of the Vygotskian-Holzman theoretical framework, was a commonly identified theme for their educational development and professional growth.
Participants characterize the collaborative and creative aspects of MTBI. They reported that collaborative dynamics with peers were strengthened as they co-created a learning environment that facilitated and accelerated their understanding of the mathematics needed to address their research. The dynamics of collaboration allowed them to complete complex homework assignments, and helped them formulate and complete their projects. Participants identified the creative environments of their research projects as where creativity emerged in the dynamics of the program.
These data-driven findings characterize for the first time a summer program in the mathematical sciences as a Vygotskian-Holzman environment, that is, a `place’ where participants are seen as capable applied mathematicians, where the dynamics of collaboration and creativity are fundamental components.
ContributorsEvangelista, Arlene Morales (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Holmes, Raquell M. (Committee member) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2015
Description
This dissertation reports three studies of students’ and teachers’ meanings for quotient, fraction, measure, rate, and rate of change functions. Each study investigated individual’s schemes (or meanings) for foundational mathematical ideas. Conceptual analysis of what constitutes strong meanings for fraction, measure, and rate of change is critical for each study. In particular, each study distinguishes additive and multiplicative meanings for fraction and rate of change.
The first paper reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on written items. Few teachers conveyed that a rate of change compares the relative sizes of changes in two quantities. Teachers’ weak measurement schemes were associated with limited meanings for rate of change. Overall, the data suggests that rate of change should be a topics of targeted professional development.
The second paper reports the quantitative part of a mixed method study of 153 calculus students at a large public university. The majority of calculus students not only have weak meanings for fraction, measure, and constant rates but that having weak meanings is predictive of lower scores on a test about rate of change functions. Regression is used to determine the variation in student success on questions about rate of change functions (derivatives) associated with variation in success on fraction, measure, rate, and covariation items.
The third paper investigates the implications of two students’ fraction schemes for their understanding of rate of change functions. Students’ weak measurement schemes obstructed their ability to construct a rate of change function given the graph of an original function. The two students did not coordinate three levels of units, and struggled to relate partitioning and iterating in a way that would help them reason about fractions, rate of change, and rate of change functions.
Taken as a whole the studies show that the majority of secondary teachers and calculus students studied have weak meanings for foundational ideas and that these weaknesses cause them problems in making sense of more applications of rate of change.
The first paper reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on written items. Few teachers conveyed that a rate of change compares the relative sizes of changes in two quantities. Teachers’ weak measurement schemes were associated with limited meanings for rate of change. Overall, the data suggests that rate of change should be a topics of targeted professional development.
The second paper reports the quantitative part of a mixed method study of 153 calculus students at a large public university. The majority of calculus students not only have weak meanings for fraction, measure, and constant rates but that having weak meanings is predictive of lower scores on a test about rate of change functions. Regression is used to determine the variation in student success on questions about rate of change functions (derivatives) associated with variation in success on fraction, measure, rate, and covariation items.
The third paper investigates the implications of two students’ fraction schemes for their understanding of rate of change functions. Students’ weak measurement schemes obstructed their ability to construct a rate of change function given the graph of an original function. The two students did not coordinate three levels of units, and struggled to relate partitioning and iterating in a way that would help them reason about fractions, rate of change, and rate of change functions.
Taken as a whole the studies show that the majority of secondary teachers and calculus students studied have weak meanings for foundational ideas and that these weaknesses cause them problems in making sense of more applications of rate of change.
ContributorsByerley, Cameron (Author) / Thompson, Patrick W (Thesis advisor) / Carlson, Marilyn P (Committee member) / Middleton, James A. (Committee member) / Saldanha, Luis (Committee member) / Mcnamara, Allen (Committee member) / Arizona State University (Publisher)
Created2016