Education Commons^™

Some Observations On Scientific Epistemology With Applications To Conflict Resolution And Constructive Controversy, Judith Puncochar, Don Faust

Other Presentations

An overview, by Judy and Don (published in 2013 in the BULLETIN OF SYMBOLIC LOGIC):

Explorationism is a perspective wherein all of our knowledge is (so far) less than certain, and naturally would come equipped with a base logic entailing machinery for representing and processing evidential knowledge. One such base logic is Evidence Logic, which strives to deal with the phenomenon of the gradational presence of both confirmatory and refutatory evidence. From this perspective, we will address questions surrounding sociological problem areas that we see as deeply infused with substantial epistemological factors. By defining a framework as any theory, …

Motivation For Achievement And Attitudes Toward Mathematics Instruction In A Required Calculus Course At The Norwegian University Of Science And Technology, Donna Sundre, Carol Barry, Vidar Gynnild, Erin Tangen Ostgard

Donna L. Sundre

This study from the Norwegian University of Science and Technology (NTNU) examines students’ learning goals and attitudes toward mathematics in a first-year calculus course in undergraduate engineering education. Achievement motivation research using the Achievement Goal Questionnaire (AGQ) is advanced from current literature with two additions: (1) a course specific context using introductory college calculus students, and (2) participation of Norwegian students. Pre- and posttest measures of attitudes indicate that students do change learning goals over time, unfortunately opposite to the instructors’ aspirations. A significant increase in “Mastery Avoidance” and “Work Avoidance” was accompanied with a drop in “Mastery Approach” and …

A Statistical Analysis Of The Role Of Critical-Thinking Games In College Students' Quantitative Reasoning, Melissa Radevicz

Honors Program Theses and Projects

Improving college students' quantitative reasoning is crucial to increase STEM-field retention rates. The National Survey of Student Engagement (NSSE), results indicate that "college students don't always get exposure to activities that develop [quantitative reasoning]" (Berrett & Sander, 2013). This study aimed to engage college students in quantitative reasoning through critical-thinking games. Phase 1, conducted in summer 2014 with a university research grant, involved a correlation analysis of the work of 133 college students enrolled in Elementary Statistics I, Chemical Principles II, Elements of Calculus, Pre-Calculus with Trigonometry, Multivariable Calculus, and Differential Equations. Participants held a variety of 39 different majors, …

Analyzing State Attempts At Implementing The Common Core State Standards For High School Geometry: Case Studies Of Utah And New York, Edward Steltenpohl

Theses and Dissertations

This study analyzes two state attempts at aligning curricula to the Common Core State Standards (CCSS) in secondary school geometry. The education departments of Utah and New York have approved curricula aimed at aligning to the Common Core State Standards: the Mathematics Vision Project (MVP) and EngageNY (ENY) respectively. This study measures the extent to which those curricula align with the content demands of the relevant Common Core Standards. The results indicate that, while the two curricula vary in structure and assumptions about learners, each one aligns well with the Common Core State Standards in secondary school geometry. We conclude …

Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang

Department of Mathematical Sciences Faculty Publications

In this note we consider a discrete symmetric function f(x, y) where f(x; a) + f(y, b) ≥ f(y, a) + f(x, b) for any x ≥ y and a ≥ b, associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as Σ _uv∈E(T) f(deg(u), deg(v)), are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randić index follow as corollaries. The extremal structures for …

Symplectic Mackey Theory, Francois Ziegler

Department of Mathematical Sciences Faculty Publications

Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup. In this paper, we develop the attendant imprimitivity theorem and Mackey analysis in the full generality needed to deal with arbitrary closed normal subgroups.

Online Resource Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen Mageean

Conference papers

Engineering education is facing many challenges: a decline in core mathematical skills; lowering entry requirements; and the diversity of the student cohort. One approach to confronting these challenges is to make subject content appropriate to the communication styles of today’s student. To achieve this, a pedagogical shift from the traditional hierarchical approach to learning to one that embraces the use of technology as a tool to enhance the student learning experience is required. By including the student as co-creator of course content, a greater sense of engagement is achieved and a change to one where students become agents of their …

A Case Study Of How Ninth Grade Mathematics Students Construct Knowledge During A Productive Failure Model, Amy F. Westbrook Dr.

Georgia Educational Research Association Conference

The purpose of this qualitative study was to explain how ninth grade mathematics students at a rural high school in Georgia constructed knowledge through student talk when problem solving using Kapur’s (2012) productive failure design. An embedded case study design was used to understand how a group of students constructed knowledge through their use of talk, persistence during the task, and use of prior knowledge while working on a productive failure modeled task. Triangulation resulted from the collected data from multiple sources, which included videotaping, interviewing, and analyzing student artifacts. Utilization of the constructivist perspectives of Vygotsky (1934/1962), Piaget (1971), …

Exploring The Relationship Between K-8 Prospective Teachers’ Algebraic Thinking Proficiency And The Questions They Pose During Diagnostic Algebraic Thinking Interviews, Leigh A. Van Den Kieboom, Marta T. Magiera, John C. Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. …

Synthetic Lethality As A Promising Approach For Targeted Cancer Prevention, Wei Tu, Hua Wang, Guang Peng

Department of Mathematical Sciences Faculty Publications

Carcinogenesis is recognized as a multistep process. It occurs over a relative long span of time, which offers intervention opportunities for cancer prevention [1] . Using drugs to prevent cancer rather than treat cancer is the major research goal in the field of ‘chemoprevention’. Tremendous research efforts have been devoted toward using natural, synthetic or biological agents to prevent, suppress or delay the initiation and or the progression of premalignant cells to cancer [1] . However a big challenge for effective cancer prevention is to identify chemoprevention agents with demonstrable efficacy and safety for healthy general …

Fast Inverse Distance Weighting-Based Spatiotemporal Interpolation: A Web-Based Application Of Interpolating Daily Fine Particulate Matter Pm2.5 In The Contiguous U.S. Using Parallel Programming And K-D Tree, Lixin Li, Travis Losser, Charles Yorke, Reinhard E. Piltner

Department of Mathematical Sciences Faculty Publications

Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. …

Op-Ed: Solve This Math Problem: The Gender Gap, Francis Su

All HMC Faculty Publications and Research

Women may not face such blatant impediments to doing math and science today. But Mirzakhani's achievement aside, we are still a long way from adequately recognizing the outstanding work of women.

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva, James P. Braselton

Department of Mathematical Sciences Faculty Publications

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator-prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

Math Talk: Preparing Your Conference Presentation, Gizem Karaali

Pomona Faculty Publications and Research

If you are a typical reader of this blog, then you recently wrapped up your finals week and then dutifully made a summer plan. And then came the summer. Your plan may have involved working on a manuscript, preparing for a qualifying exam or a new course coming up in the fall, drafting a grant proposal, learning a new language (human or machine), eating kale in four different forms, and perhaps some fun times under the sun. Some, like me, also made plans to travel to conferences and give talks. Gearing up to get ready for my first conference of …

Living At The Friendship House: Findings From Thetransition Planning Inventory, Jane E. Finn, Vicky-Lynn Holmes, Rebecca Johnson

Faculty Publications

A residential initiative, named the Friendship House, was created through advocates focused on helping people with intellectual disabilities live independently in affordable and safe housing on a university campus. The Friendship House is a small residence hall where individuals with intellectual disabilities live side-by-side with similarly aged and same gendered university students. Qualitative finding as in resident reports and observational data provides support that the Friendship House experience has been successful. However, to better equip these residents with intellectual disabilities, it is important to assess the program in terms of post school transition acquisition skills. This study focuses on whether …

Fejér And Suffridge Polynomials In The Delayed Feedback Control Theory, Dmitriy Dmitrishin, Anna Khamitova, Anatolii Korenovskyi, Alexander M. Stokolos

Department of Mathematical Sciences Faculty Publications

A remarkable connection between optimal delayed feedback control (DFC) and complex polynomial mappings of the unit disc is established. The explicit form of extremal polynomials turns out to be related with the Fejer polynomials. The constructed DFC can be used to stabilize cycles of one-dimensional non-linear discrete systems.

Examining The Process Of Identification In The Mathematics Classroom And The Role Of Students’ Academic Communities, Richard J. Robinson

Doctoral Dissertations

The primary purpose of this research was to provide insight into the identities students develop as they interact in a high school mathematics classroom. A normative divide developed which eventually split the classroom into two distinct academic factions: those who resisted the emerging local definition of what it meant to do mathematics and those who did not resist (i.e. complied or identified). A secondary purpose of this research was to understand the role of students’ academic communities in mathematics identity development. Student narratives helped uncover mathematical spaces outside the classroom that each developed their own unique definition of what it …

Reasoning & Proof In The Hs Common Core, Laurie O. Cavey

Laurie O. Cavey

No abstract provided.

Hoijer '15 Studies Correlations Between Mathematics And Music, Danielle Kamp

News and Events

No abstract provided.

Simmons' Research Aims To Improve Function For Online Security, Danielle Kamp

News and Events

No abstract provided.

The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried

Journal of Humanistic Mathematics

Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of …

How Do They Know It Is A Parallelogram? Analysing Geometric Discourse At Van Hiele Level 3, Sasha Wang, Margaret Kinzel

Mathematics Faculty Publications and Presentations

In this article, we introduce Sfard's discursive framework and use it to investigate prospective teachers' geometric discourse in the context of quadrilaterals. In particular, we focus on describing and analysing two participants' use of mathematical words and substantiation routines related to parallelograms and their properties at van Hiele level 3 thinking. Our findings suggest that a single van Hiele level of thinking encompasses a range of complexity of reasoning and differences in discourse and thus a deeper investigation of students' mathematical thinking within assigned van Hiele levels is warranted.

How Does One Design Or Evaluate A Course In Quantitative Reasoning?, Bernard L. Madison

Numeracy

In the absence of generally accepted content standards and with little evidence on the learning for long-term retrieval and transfer, how does one design or evaluate a course in quantitative reasoning (QR)? This is a report on one way to do so. The subject QR course, which has college algebra as a prerequisite and has been taught for 8 years, is being modified slightly to be offered as an alternative to college algebra. One modification is adding a significant formal writing component. As the modification occurs, the current course and the modified one are judged according to six sets of …

What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, John Tabak

Journal of Interpretation

Courses and seminars in higher mathematics are some of the most challenging assignments faced by academic interpreters. Difficulties interpreting higher mathematics can adversely impact the academic and professional aspirations of deaf mathematics students and professionals. This paper discusses the nature of higher mathematics with the goal of identifying what distinguishes higher mathematics from other subjects; it then reviews the history of attempts to sign/interpret higher mathematics with particular attention to current challenges associated with expressing higher mathematics in sign. The final part of the paper discusses strategies for more effectively expressing higher mathematics in American Sign Language.

Existence Of Positive Solutions For P(X)-Laplacian Equations With A Singular Nonlinear Term, Jingjing Liu, Qihu Zhang, Chunshan Zhao

Department of Mathematical Sciences Faculty Publications

In this article, we study the existence of positive solutions for the p(x)-Laplacian Dirichlet problem −∆_p(x)u = λf(x, u) in a bounded domain Ω ⊂ R^N. The singular nonlinearity term f is allowed to be either f(x, s) → +∞, or f(x, s) → +∞ as s → 0+ for each x ∈ Ω. Our main results generalize the results in [15] from constant exponents to variable exponents. In particular, we give the asymptotic behavior of solutions of a simpler equation which is useful for finding supersolutions of differential equations with variable exponents, which is of independent …

Work In Progress: Online Resource Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen Mageean

Conference papers

Mathematics is intrinsic to engineering and as such plays an integral role in the education of engineers. New challenges are being faced in higher education particularly in the areas of student motivation, engagement and attainment. As a result mathematics is often the focus of engineering education research. Traditional methods of delivery such as lectures and tutorials need to evolve to counter these challenges with new pedagogical approaches explored including the use of new technologies. Today’s students are immersed in an increasingly technological world and are willing to adapt to new technological advances. This paper describes a study being undertaken in …

Why You Need A Summer Plan, Gizem Karaali

Pomona Faculty Publications and Research

In the last decade, for many times, I have tasted first-hand the end-of-summer blues I described above. I have spent many early spring months dreaming of all that I would be doing when the summer arrives, only to realize that it was already September and I had not much to show for for the months in between. I have also observed many of my peers going through similar things, and I just assumed for years that this was how it had to be. But then some time in the middle of the tenure track, I decided to try approaching my …

An Analysis And Comparison Of The Common Core State Standards For Mathematics And The Singapore Mathematics Curriculum Framework, Heidi Ann Ertl

Theses and Dissertations

In this analysis and comparison we look at the Common Core State Standards for Mathematics and the Singapore Mathematics Curriculum Framework, standards documents that guide primary and secondary mathematics education in the United States and Singapore respectively. The official Common Core State Standards for Mathematics website claims that the standards have been developed to be "internationally benchmarked, so that all students are prepared for the 21st century". Singapore has recently been recognized as a world leader in mathematics education. We investigate the claim that the Common Core State Standards for Mathematics are internationally benchmarked by comparing the Common Core State …

Teachers' Beliefs And Practices Regarding Homework: An Examination Of The Cognitive Domain Embedded In Third Grade Mathematics Homework, Pandora Dell Bedford

Theses and Dissertations

The purpose of this phenomenological study was to gain a better understanding of third grade math teachers''beliefs and practices regarding homework, to explain how teachers''beliefs and practices regarding homework aligned to the framework of the Revised Bloom's'Taxonomy Cognitive Domain, and to determine the administrative influences on homework practices. The data were collected during October and November 2013. Six third grade math teachers (primary unit of analysis) and four principals (secondary unit of analysis) were interviewed from Dell School District. Each participant (teacher and principal) was interviewed for approximately one hour. A second meeting was set at a later time with …

High Cognitive Test Item Development And Implementation, Ashley Salisbury

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In secondary math classrooms there has been a movement toward discovery and problem solving based instruction. This type of instruction requires teachers to teach on what is often considered a higher level of cognition and allows students to discover more ideas and concepts on their own as opposed to traditional lecture style. Teachers with well thought-out examples, questions, and activities provide students with tools to solve problems on their own requiring students to make mathematical discoveries and connections. These skills not only benefit students in their math class but are analytical skills students can use throughout their lives.

With this …