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- Creators: Barrett, The Honors College
Description
Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study is to look at classrooms and educators across six high achieving countries to identify and compare teaching strategies being used. In Finland, Hong Kong, Japan, New Zealand, Singapore, and Switzerland, twenty educators were interviewed and fourteen educators were observed teaching. Themes were first identified by comparing individual teacher responses within each country. These themes were then grouped together across countries and eight emerging patterns were identified. These strategies include students active involvement in the classroom, students given written feedback on assessments, students involvement in thoughtful discussion about mathematical concepts, students solving and explaining mathematics problems at the board, students exploring mathematical concepts either before or after being taught the material, students engagement in practical applications, students making connections between concepts, and students having confidence in their ability to understand mathematics. The strategies identified across these six high achieving countries can inform educators in their efforts of increasing student understanding of mathematical concepts and lead to an improvement in mathematics performance.
ContributorsAnglin, Julia Mae (Author) / Middleton, James (Thesis director) / Vicich, James (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-12
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
Previous research has examined difficulties that students have with understanding and productively working with function notation. Function notation is very prevalent throughout mathematics education, helping students to better understand and more easily work with functions. The goal of my research was to investigate students' current ways of thinking about function notation to better assist teachers in helping their students develop deeper and more productive understandings. In this study, I conducted two separate interviews with two undergraduate students to explore their meanings for function notation. I developed and adapted tasks aimed at investigating different aspects and uses of function notation. In each interview, I asked the participants to attempt each of the tasks, explaining their thoughts as they worked. While they were working, I occasionally asked clarifying questions to better understand their thought processes. For the second interviews, I added tasks based on difficulties I found in the first interviews. I video recorded each interview for later analysis. Based on the data found in the interviews, I will discuss the seven prevalent ways of thinking that I found, how they hindered or facilitated working with function notation productively, and suggestions for instruction to better help students understand the concept.
ContributorsMckee, Natalie Christina (Author) / Thompson, Patrick (Thesis director) / Zazkis, Dov (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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
Previous research discusses students' difficulties in grasping an operational understanding of covariational reasoning. In this study, I interviewed four undergraduate students in calculus and pre-calculus classes to determine their ways of thinking when working on an animated covariation problem. With previous studies in mind and with the use of technology, I devised an interview method, which I structured using multiple phases of pre-planned support. With these interviews, I gathered information about two main aspects about students' thinking: how students think when attempting to reason covariationally and which of the identified ways of thinking are most propitious for the development of an understanding of covariational reasoning. I will discuss how, based on interview data, one of the five identified ways of thinking about covariational reasoning is highly propitious, while the other four are somewhat less propitious.
ContributorsWhitmire, Benjamin James (Author) / Thompson, Patrick (Thesis director) / Musgrave, Stacy (Committee member) / Moore, Kevin C. (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / T. Denny Sanford School of Social and Family Dynamics (Contributor)
Created2014-05
Description
Currently conventional Subtitle D landfills are the primary means of disposing of our waste in the United States. While this method of waste disposal aims at protecting the environment, it does so through the use of liners and caps that effectively freeze the breakdown of waste. Because this method can keep landfills active, and thus a potential groundwater threat for over a hundred years, I take an in depth look at the ability of bioreactor landfills to quickly stabilize waste. In the thesis I detail the current state of bioreactor landfill technologies, assessing the pros and cons of anaerobic and aerobic bioreactor technologies. Finally, with an industrial perspective, I conclude that moving on to bioreactor landfills as an alternative isn't as simple as it may first appear, and that it is a contextually specific solution that must be further refined before replacing current landfills.
ContributorsWhitten, George Avery (Author) / Kavazanjian, Edward (Thesis director) / Allenby, Braden (Committee member) / Houston, Sandra (Committee member) / Civil, Environmental and Sustainable Engineering Programs (Contributor) / Barrett, The Honors College (Contributor)
Created2013-05
Characterization and Manipulation of Microbiomes From Arid Landfills for Improved Methane Production
Description
Environmentally harmful byproducts from solid waste’s decomposition, including methane (CH4) emissions, are managed through standardized landfill engineering and gas-capture mechanisms. Yet only a limited number of studies have analyzed the development and composition of Bacteria and Archaea involved in CH4 production from landfills. The objectives of this research were to compare microbiomes and bioactivity from CH4-producing communities in contrasting spatial areas of arid landfills and to tests a new technology to biostimulate CH4 production (methanogenesis) from solid waste under dynamic environmental conditions controlled in the laboratory. My hypothesis was that the diversity and abundance of methanogenic Archaea in municipal solid waste (MSW), or its leachate, play an important role on CH4 production partially attributed to the group’s wide hydrogen (H2) consumption capabilities. I tested this hypothesis by conducting complementary field observations and laboratory experiments. I describe niches of methanogenic Archaea in MSW leachate across defined areas within a single landfill, while demonstrating functional H2-dependent activity. To alleviate limited H2 bioavailability encountered in-situ, I present biostimulant feasibility and proof-of-concepts studies through the amendment of zero valent metals (ZVMs). My results demonstrate that older-aged MSW was minimally biostimulated for greater CH4 production relative to a control when exposed to iron (Fe0) or manganese (Mn0), due to highly discernable traits of soluble carbon, nitrogen, and unidentified fluorophores found in water extracts between young and old aged, starting MSW. Acetate and inhibitory H2 partial pressures accumulated in microcosms containing old-aged MSW. In a final experiment, repeated amendments of ZVMs to MSW in a 600 day mesocosm experiment mediated significantly higher CH4 concentrations and yields during the first of three ZVM injections. Fe0 and Mn0 experimental treatments at mesocosm-scale also highlighted accelerated development of seemingly important, but elusive Archaea including Methanobacteriaceae, a methane-producing family that is found in diverse environments. Also, prokaryotic classes including Candidatus Bathyarchaeota, an uncultured group commonly found in carbon-rich ecosystems, and Clostridia; All three taxa I identified as highly predictive in the time-dependent progression of MSW decomposition. Altogether, my experiments demonstrate the importance of H2 bioavailability on CH4 production and the consistent development of Methanobacteriaceae in productive MSW microbiomes.
ContributorsReynolds, Mark Christian (Author) / Cadillo-Quiroz, Hinsby (Thesis advisor) / Krajmalnik-Brown, Rosa (Thesis advisor) / Wang, Xuan (Committee member) / Kavazanjian, Edward (Committee member) / Arizona State University (Publisher)
Created2022
Description
Zero-Valent Metals (ZVM) are highly reactive materials and have been proved to be effective in contaminant reduction in soils and groundwater remediation. In fact, zero-Valent Iron (ZVI) has proven to be very effective in removing, particularly chlorinated organics, heavy metals, and odorous sulfides. Addition of ZVI has also been proved in enhancing the methane gas generation in anaerobic digestion of activated sludge. However, no studies have been conducted regarding the effect of ZVM stimulation to Municipal Solid Waste (MSW) degradation. Therefore, a collaborative study was developed to manipulate microbial activity in the landfill bioreactors to favor methane production by adding ZVMs. This study focuses on evaluating the effects of added ZVM on the leachate generated from replicated lab scale landfill bioreactors. The specific objective was to investigate the effects of ZVMs addition on the organic and inorganic pollutants in leachate. The hypothesis here evaluated was that adding ZVM including ZVI and Zero Valent Manganese (ZVMn) will enhance the removal rates of the organic pollutants present in the leachate, likely by a putative higher rate of microbial metabolism. Test with six (4.23 gallons) bioreactors assembled with MSW collected from the Salt River Landfill and Southwest Regional Landfill showed that under 5 grams /liter of ZVI and 0.625 grams/liter of ZVMn additions, no significant difference was observed in the pH and temperature data of the leachate generated from these reactors. The conductivity data suggested the steady rise across all reactors over the period of time. The removal efficiency of sCOD was highest (27.112 mg/lit/day) for the reactors added with ZVMn at the end of 150 days for bottom layer, however the removal rate was highest (16.955 mg/lit/day) for ZVI after the end of 150 days of the middle layer. Similar trends in the results was observed in TC analysis. HPLC study indicated the dominance of the concentration of heptanoate and isovalerate were leachate generated from the bottom layer across all reactors. Heptanoate continued to dominate in the ZVMn added leachate even after middle layer injection. IC analysis concluded the chloride was dominant in the leachate generated from all the reactors and there was a steady increase in the chloride content over the period of time. Along with chloride, fluoride, bromide, nitrate, nitrite, phosphate and sulfate were also detected in considerable concentrations. In the summary, the addition of the zero valent metals has proved to be efficient in removal of the organics present in the leachate.
ContributorsPandit, Gandhar Abhay (Author) / Cadillo – Quiroz, Hinsby (Thesis advisor) / Olson, Larry (Thesis advisor) / Boyer, Treavor (Committee member) / Arizona State University (Publisher)
Created2019