Matching Items (1,543)
Filtering by
- Creators: School of Life Sciences
- Member of: Theses and Dissertations
Description
Based on poor student performance in past studies, the incoherence present in the teaching of inverse functions, and teachers' own accounts of their struggles to teach this topic, it is apparent that the idea of function inverse deserves a closer look and an improved pedagogical approach. This improvement must enhance students' opportunity to construct a meaning for a function's inverse and, out of that meaning, produce ways to define a function's inverse without memorizing some procedure. This paper presents a proposed instructional sequence that promotes reflective abstraction in order to help students develop a process conception of function and further understand the meaning of a function inverse. The instructional sequence was used in a teaching experiment with three subjects and the results are presented here. The evidence presented in this paper supports the claim that the proposed instructional sequence has the potential to help students construct meanings needed for understanding function inverse. The results of this study revealed shifts in the understandings of all three subjects. I conjecture that these shifts were achieved by posing questions that promoted reflective abstraction. The questions and subsequent interactions appeared to result in all three students moving toward a process conception of function.
ContributorsFowler, Bethany (Author) / Carlson, Marilyn (Thesis advisor) / Roh, Kyeong (Committee member) / Zandieh, Michelle (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
There have been a number of studies that have examined students’ difficulties in understanding the idea of logarithm and the effectiveness of non-traditional interventions. However, there have been few studies that have examined the understandings students develop and need to develop when completing conceptually oriented logarithmic lessons. In this document, I present the three papers of my dissertation study. The first paper examines two students’ development of concepts foundational to the idea of logarithm. This paper discusses two essential understandings that were revealed to be problematic and essential for students’ development of productive meanings for exponents, logarithms and logarithmic properties. The findings of this study informed my later work to support students in understanding logarithms, their properties and logarithmic functions. The second paper examines two students’ development of the idea of logarithm. This paper describes the reasoning abilities two students exhibited as they engaged with tasks designed to foster their construction of more productive meanings for the idea of logarithm. The findings of this study provide novel insights for supporting students in understanding the idea of logarithm meaningfully. Finally, the third paper begins with an examination of the historical development of the idea of logarithm. I then leveraged the insights of this literature review and the first two papers to perform a conceptual analysis of what is involved in learning and understanding the idea of logarithm. The literature review and conceptual analysis contributes novel and useful information for curriculum developers, instructors, and other researchers studying student learning of this idea.
ContributorsKuper Flores, Emily Ginamarie (Author) / Carlson, Marilyn (Thesis advisor) / Thompson, Patrick (Committee member) / Milner, Fabio (Committee member) / Zazkis, Dov (Committee member) / Czocher, Jennifer (Committee member) / Arizona State University (Publisher)
Created2018
Description
The advancement of technology has substantively changed the practices of numerous professions, including teaching. When an instructor first adopts a new technology, established classroom practices are perturbed. These perturbations can have positive and negative, large or small, and long- or short-term effects on instructors’ abilities to teach mathematical concepts with the new technology. Therefore, in order to better understand teaching with technology, we need to take a closer look at the adoption of new technology in a mathematics classroom. Using interviews and classroom observations, I explored perturbations in mathematical classroom practices as an instructor implemented virtual manipulatives as novel didactic objects in rational function instruction. In particular, the instructor used didactic objects that were designed to lay the foundation for developing a conceptual understanding of rational functions through the coordination of relative size of the value of the numerator in terms of the value of the denominator. The results are organized according to a taxonomy that captures leader actions, communication, expectations of technology, roles, timing, student engagement, and mathematical conceptions.
ContributorsPampel, Krysten (Author) / Currin van de Sande, Carla (Thesis advisor) / Thompson, Patrick W (Committee member) / Carlson, Marilyn (Committee member) / Milner, Fabio (Committee member) / Strom, April (Committee member) / Arizona State University (Publisher)
Created2017
Description
Researchers have described two fundamental conceptualizations for division, known as partitive and quotitive division. Partitive division is the conceptualization of a÷b as the amount of something per copy such that b copies of this amount yield the amount a. Quotitive division is the conceptualization of a÷b as the number of copies of the amount b that yield the amount a. Researchers have identified many cognitive obstacles that have inhibited the development of robust meanings for division involving non-whole values, while other researchers have commented on the challenges related to such development. Regarding division with fractions, much research has been devoted to quotitive conceptualizations of division, or on symbolic manipulation of variables. Research and curricular activities have largely avoided the study and development of partitive conceptualizations involving fractions, as well as their connection to the invert-and-multiply algorithm. In this dissertation study, I investigated six middle school mathematics teachers’ meanings related to partitive conceptualizations of division over the positive rational numbers. I also investigated the impact of an intervention that I designed with the intent of advancing one of these teachers’ meanings. My findings suggested that the primary cognitive obstacles were difficulties with maintaining multiple levels of units, weak quantitative meanings for fractional multipliers, and an unawareness of (and confusion due to) the two quantitative conceptualizations of division. As a product of this study, I developed a framework for characterizing robust meanings for division, indicated directions for future research, and shared implications for curriculum and instruction.
ContributorsWeber, Matthew Barrett (Author) / Strom, April D (Thesis advisor) / Thompson, Patrick W (Thesis advisor) / Carlson, Marilyn (Committee member) / Middleton, James (Committee member) / Tzur, Ron (Committee member) / Arizona State University (Publisher)
Created2019
Description
The concept of distribution is one of the core ideas of probability theory and inferential statistics, if not the core idea. Many introductory statistics textbooks pay lip service to stochastic/random processes but how do students think about these processes? This study sought to explore what understandings of stochastic process students develop as they work through materials intended to support them in constructing the long-run behavior meaning for distribution.
I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I worked with Bonnie in an exploratory teaching setting through three sets of activities to see what meanings she would develop for randomness and stochastic process. The final phase consisted of me working with Danielle as she worked through the same activities as Bonnie but this time in teaching experiment setting where I used a series of interventions to test out how Danielle was thinking about stochastic processes.
My analysis shows that students can be aware that the word “random” lives in two worlds, thereby having conflicting meanings. Bonnie’s meaning for randomness evolved over the course of the study from an unproductive meaning centered on the emotions of the characters in the context to a meaning that randomness is the lack of a pattern. Bonnie’s lack of pattern meaning for randomness subsequently underpinned her image of stochastic/processes, leading her to engage in pattern-hunting behavior every time she needed to classify a process as stochastic or not. Danielle’s image of a stochastic process was grounded in whether she saw the repetition as being reproducible (process can be repeated, and outcomes are identical to prior time through the process) or replicable (process can be repeated but the outcomes aren’t in the same order as before). Danielle employed a strategy of carrying out several trials of the process, resetting the applet, and then carrying out the process again, making replicability central to her thinking.
I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I worked with Bonnie in an exploratory teaching setting through three sets of activities to see what meanings she would develop for randomness and stochastic process. The final phase consisted of me working with Danielle as she worked through the same activities as Bonnie but this time in teaching experiment setting where I used a series of interventions to test out how Danielle was thinking about stochastic processes.
My analysis shows that students can be aware that the word “random” lives in two worlds, thereby having conflicting meanings. Bonnie’s meaning for randomness evolved over the course of the study from an unproductive meaning centered on the emotions of the characters in the context to a meaning that randomness is the lack of a pattern. Bonnie’s lack of pattern meaning for randomness subsequently underpinned her image of stochastic/processes, leading her to engage in pattern-hunting behavior every time she needed to classify a process as stochastic or not. Danielle’s image of a stochastic process was grounded in whether she saw the repetition as being reproducible (process can be repeated, and outcomes are identical to prior time through the process) or replicable (process can be repeated but the outcomes aren’t in the same order as before). Danielle employed a strategy of carrying out several trials of the process, resetting the applet, and then carrying out the process again, making replicability central to her thinking.
ContributorsHatfield, Neil (Author) / Thompson, Patrick (Thesis advisor) / Carlson, Marilyn (Committee member) / Middleton, James (Committee member) / Lehrer, Richard (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2019
Description
The inherent risk in testing drugs has been hotly debated since the government first started regulating the drug industry in the early 1900s. Who can assume the risks associated with trying new pharmaceuticals is unclear when looked at through society's lens. In the mid twentieth century, the US Food and Drug Administration (FDA) published several guidance documents encouraging researchers to exclude women from early clinical drug research. The motivation to publish those documents and the subsequent guidance documents in which the FDA and other regulatory offices established their standpoints on women in drug research may have been connected to current events at the time. The problem of whether women should be involved in drug research is a question of who can assume risk and who is responsible for disseminating what specific kinds of information. The problem tends to be framed as one that juxtaposes the health of women and fetuses and sets their health as in opposition. That opposition, coupled with the inherent uncertainty in testing drugs, provides for a complex set of issues surrounding consent and access to information.
ContributorsMeek, Caroline Jane (Author) / Maienschein, Jane (Thesis director) / Brian, Jennifer (Committee member) / School of Life Sciences (Contributor) / Sanford School of Social and Family Dynamics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Social-emotional learning (SEL) methods are beginning to receive global attention in primary school education, yet the dominant emphasis on implementing these curricula is in high-income, urbanized areas. Consequently, the unique features of developing and integrating such methods in middle- or low-income rural areas are unclear. Past studies suggest that students exposed to SEL programs show an increase in academic performance, improved ability to cope with stress, and better attitudes about themselves, others, and school, but these curricula are designed with an urban focus. The purpose of this study was to conduct a needs-based analysis to investigate components specific to a SEL curriculum contextualized to rural primary schools. A promising organization committed to rural educational development is Barefoot College, located in Tilonia, Rajasthan, India. In partnership with Barefoot, we designed an ethnographic study to identify and describe what teachers and school leaders consider the highest needs related to their students' social and emotional education. To do so, we interviewed 14 teachers and school leaders individually or in a focus group to explore their present understanding of “social-emotional learning” and the perception of their students’ social and emotional intelligence. Analysis of this data uncovered common themes among classroom behaviors and prevalent opportunities to address social and emotional well-being among students. These themes translated into the three overarching topics and eight sub-topics explored throughout the curriculum, and these opportunities guided the creation of the 21 modules within it. Through a design-based research methodology, we developed a 40-hour curriculum by implementing its various modules within seven Barefoot classrooms alongside continuous reiteration based on teacher feedback and participant observation. Through this process, we found that student engagement increased during contextualized SEL lessons as opposed to traditional methods. In addition, we found that teachers and students preferred and performed better with an activities-based approach. These findings suggest that rural educators must employ particular teaching strategies when addressing SEL, including localized content and an experiential-learning approach. Teachers reported that as their approach to SEL shifted, they began to unlock the potential to build self-aware, globally-minded students. This study concludes that social and emotional education cannot be treated in a generalized manner, as curriculum development is central to the teaching-learning process.
ContributorsBucker, Delaney Sue (Author) / Carrese, Susan (Thesis director) / Barab, Sasha (Committee member) / School of Life Sciences (Contributor, Contributor) / School of Civic & Economic Thought and Leadership (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
As of 2019, 30 US states have adopted abortion-specific informed consent laws that require state health departments to develop and disseminate written informational materials to patients seeking an abortion. Abortion is the only medical procedure for which states dictate the content of informed consent counseling. State abortion counseling materials have been criticized for containing inaccurate and misleading information, but overall, informed consent laws for abortion do not often receive national attention. The objective of this project was to determine the importance of informed consent laws to achieving the larger goal of dismantling the right to abortion. I found that informed consent counseling materials in most states contain a full timeline of fetal development, along with information about the risks of abortion, the risks of childbirth, and alternatives to abortion. In addition, informed consent laws for abortion are based on model legislation called the “Women’s Right to Know Act” developed by Americans United for Life (AUL). AUL calls itself the legal architect of the pro-life movement and works to pass laws at the state level that incrementally restrict abortion access so that it gradually becomes more difficult to exercise the right to abortion established by Roe v. Wade. The “Women’s Right to Know Act” is part of a larger package of model legislation called the “Women’s Protection Project,” a cluster of laws that place restrictions on abortion providers, purportedly to protect women, but actually to decrease abortion access. “Women’s Right to Know” counseling laws do not directly deny access to abortion, but they do reinforce key ideas important to the anti-abortion movement, like the concept of fetal personhood, distrust in medical professionals, the belief that pregnant people cannot be fully autonomous individuals, and the belief that abortion is not an ordinary medical procedure and requires special government oversight. “Women’s Right to Know” laws use the language of informed consent and the purported goal of protecting women to legitimize those ideas, and in doing so, they significantly undermine the right to abortion. The threat to abortion rights posed by laws like the “Women’s Right to Know” laws indicates the need to reevaluate and strengthen our ethical defense of the right to abortion.
ContributorsVenkatraman, Richa (Author) / Maienschein, Jane (Thesis director) / Brian, Jennifer (Thesis director) / Abboud, Carolina (Committee member) / Historical, Philosophical & Religious Studies (Contributor) / School of Life Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Turbidity is a known problem for UV water treatment systems as suspended particles can shield contaminants from the UV radiation. UV systems that utilize a reflective radiation chamber may be able to decrease the impact of turbidity on the efficacy of the system. The purpose of this study was to determine how kaolin clay and gram flour turbidity affects inactivation of Escherichia coli (E. coli) when using a UV system with a reflective chamber. Both sources of turbidity were shown to reduce the inactivation of E. coli with increasing concentrations. Overall, it was shown that increasing kaolin clay turbidity had a consistent effect on reducing UV inactivation across UV doses. Log inactivation was reduced by 1.48 log for the low UV dose and it was reduced by at least 1.31 log for the low UV dose. Gram flour had a similar effect to the clay at the lower UV dose, reducing log inactivation by 1.58 log. At the high UV dose, there was no change in UV inactivation with an increase in turbidity. In conclusion, turbidity has a significant impact on the efficacy of UV disinfection. Therefore, removing turbidity from water is an essential process to enhance UV efficiency for the disinfection of microbial pathogens.
ContributorsMalladi, Rohith (Author) / Abbaszadegan, Morteza (Thesis director) / Alum, Absar (Committee member) / Fox, Peter (Committee member) / School of Human Evolution & Social Change (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05