Education Commons^™

Student Understanding Of The Boltzmann Factor, Trevor I. Smith, Donald B. Mountcastle, John R. Thompson

Physics and Astronomy Faculty Scholarship

We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us …

Identifying Student Difficulties With Heat Engines, Entropy, And The Carnot Cycle, Trevor I. Smith, Warren M. Christensen, Donald B. Mountcastle, John R. Thompson

Physics and Astronomy Faculty Scholarship

We report on several specific student difficulties regarding the second law of thermodynamics in the context of heat engines within upper-division undergraduate thermal physics courses. Data come from ungraded written surveys, graded homework assignments, and videotaped classroom observations of tutorial activities. Written data show that students in these courses do not clearly articulate the connection between the Carnot cycle and the second law after lecture instruction. This result is consistent both within and across student populations. Observation data provide evidence for myriad difficulties related to entropy and heat engines, including students’ struggles in reasoning about situations that are physically impossible …

Learning Of Business Processes & Application: An Industry-Ready Approach, Yi Meng Lau, Yu Yee Poon, Mike Wee

Research Collection School Of Computing and Information Systems

The Learning Framework for Business Processes was developed by lectures from School of InfoComm Technology (ICT)to support their students’ learning in the Diploma of Financial Informatics. This framework leverage on the use of learning approaches such as Inquiry based learning to create opportunities for students to be engaged, explore, explain and apply their learning. This framework was presented at International Symposium on Advances in Technology Education (ISATE) 2015 in Nagaoka, Japan.

Contracting Endomorphisms And Dualizing Complexes, Saeed Nasseh, Sean Sather-Wagstaff

Department of Mathematical Sciences Faculty Publications

We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring R. Our focus is on homological properties of contracting endomorphisms of R, e.g., the Frobenius endomorphism when R contains a field of positive characteristic. For instance, in this case, when R is F-finite and C is a semidualizing R-complex, we prove that the following conditions are equivalent: (i) C is a dualizing R-complex; (ii) C ∼RHomR(nR,C) for some n > 0; (iii) GC-dimnR < ∞ and C is derived …

Gaise Into The Future: Updating A Landmark Report For An Increasingly Data-Centric World, Michelle Everson, Paul Velleman, Beverly Wood, John Gabrosek, Megan Mocko, Robert Carver

Publications

Ever since its official endorsement by the American Statistical Association in 2005, the Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report has had a profound impact on the teaching of statistics. Now, a decade later, it is important to recognize the changing nature in what and how we teach our introductory statistics students. Changes in technology and assessment practices, just over the past 10 years, have made it possible to do new and exciting things in our courses, in very different ways than were envisioned by the authors of the original GAISE College Report. Further, our world …

A Survey Of Mathematical Models Of Dengue Fever, James P. Braselton, Iurii Bakach

Department of Mathematical Sciences Faculty Publications

In this paper, we compare and contrast five models of dengue fever, a serious illness that affects tropical and subtropical areas around the world. We evaluate each model using different scenarios and identify the strengths and weakness of each of the models. The goal of our analysis is to indicate the strengths and weaknesses of current mathematical models of dengue fever that should assist future researchers in forming models that accurately measure the variables they are studying that affect the spread and progression of the disease.

Homology Over Trivial Extensions Of Commutative Dg Algebras, Luchezar L. Avramov, Srikanth B. Iyengar, Saeed Nasseh, Sean Sather-Wagstaff

Department of Mathematical Sciences Faculty Publications

Conditions on the Koszul complex of a noetherian local ring R guarantee that TorRi(M,N) is non-zero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.

Guidelines For Good Mathematical Writing, Francis Su

All HMC Faculty Publications and Research

Communicating mathematics well is an important part of doing mathematics. Many of us know from writing papers or giving talks that communicating effectively not only serves our audience but also clarifies and structures our own thinking. There is an art and elegance to good writing that every writer should strive for. And writing, as a work of art, can bring a person great personal satisfaction.

Within the MAA, we value exposition and mathematical communication. In this column, I’m sharing the advice I give my students to help them write well. There are more extensive treatments (e.g., see Paul Halmos’s How …

Extended Book Review: Really Big Numbers, By Richard Evan Schwartz; The Boy Who Loved Math: The Improbable Life Of Paul Erdös, By Deborah Heiligman; The Short Seller, By Elissa Brent Weissman, Gizem Karaali

Pomona Faculty Publications and Research

The genre of math lit for children is not huge, but it is growing. My kid loves the early reader books by my friend and colleague Julie Glass (A Dollar for Penny (1998), The Fly On the Ceiling (2000)). I found Izolda Fotiyeva’s Math with Mom (2003) too late for my daughter but will definitely read it with my son. For a neat twist on the traditional alphabet book, I recommend The Technical Alphabet (2014) by the engineer sisters Lavanya and Melissa Jawaharlal. More recently a colleague introduced me to Laura Overdeck’s Bedtime Math series; these will soon join …

The Impact Of Meaningful High School Computer Science Experiences In The Chicago Public Schools, Lucia Dettori, Ronald I. Greenberg, Steven Mcgee, Dale Reed

Computer Science: Faculty Publications and Other Works

We report on initial outcomes of the Taste of Computing project, under which a meaningful computer science course has been initiated in many high schools of the Chicago Public Schools system. Surveys of students have shown that they attribute high value to the course and have experienced increases in their understanding and interest regarding the computing field. Data was also collected from teachers participating in professional development regarding their preparation and confidence in teaching the new course. We report on the strengths of various survey responses and their relationships, and we compare student responses by race and gender. The data …

A Toast! To The International Year Of Light, Michael Bass

UCF Forum

December 2013, at the United Nations’ 68th General Assembly meeting, the assembled countries could not as usual solve the problems of world conflicts, human slavery, wide-spread famine and the Israeli-Palestinian question. So, it decided to do something it could: It declared that 2015 would be the International Year of Light.

Meander Graphs And Frobenius Seaweed Lie Algebras Ii, Vincent Coll, Matthew Hyatt, Colton Magnant, Hua Wang

Department of Mathematical Sciences Faculty Publications

We provide a recursive classification of meander graphs, showing that each meander is identified by a unique sequence of fundamental graph theoretic moves. This sequence is called the meander’s signature and can be used to construct arbitrarily large sets of meanders, Frobenius or otherwise, of any size and configuration. In certain special cases, the signature is used to produce an explicit formula for the index of seaweed Lie subalgebra of sl(n) in terms of elementary functions.

How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’, Don Faust, Judith Puncochar

Conference Presentations

Collaboration, if to occur successfully at all, needs to be based on careful representation and communication of each stakeholder’s knowledge. In this paper, we investigate, from a foundational logical and epistemological point of view, how such representation and communication can be accomplished. What we tentatively conclude, based on a careful delineation of the logical technicalities necessarily involved in such representation and communication, is that a complete representation is not possible. This inference, if correct, is of course rather discouraging with regard to what we can hope to achieve in the knowledge representations that we bring to our collaborations. We suggest …

Mathematician's Apology, Tom Clark

Faculty Work Comprehensive List

"Better standards may help all math teachers to shape our classes to better reflect the creativity and play at the heart of mathematics."

Posting about ways to improve math's negative image­­­­­­­­ from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/a-mathematicians-apology/

On The Generalized Linear And Non-Linear Dfc In Non-Linear Dynamics, Dmitriy Dmitrishin, Anna Khamitova, Alexander M. Stokolos

Department of Mathematical Sciences Faculty Publications

The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization of the equilibrium of the system are provided. Surprisingly enough it turns out that the generalized linear delayed feedback control has same limitation as the classical Pyragas DFC. This generalized Ushio 1996 DFC limitation statement. Note that in scalar case a generalized non-linear control can robustly stabilize an equilibrium for any admissible range of multipliers. In the current article similar result is obtained in the …

Enhanced Presentation Of Tomographic Data, Carmen Watts Clayton, Bernice Mills, George Beffleben, Thien Vu-Nguyen

STAR Program Research Presentations

X-ray tomography yields a very large amount of data in three dimensions. Effectively displaying this data to a broad audience is a challenge. Techniques are discussed to improve presentation of movies of both 2D and 3D tomographic data using commercially available softwares.

Enriching Gender In Per: A Binary Past And A Complex Future, Adrienne L. Traxler, Ximena C. Cid, Jennifer Blue, Ramón Barthelemy

Physics Faculty Publications

In this article, we draw on previous reports from physics, science education, and women's studies to propose a more nuanced treatment of gender in physics education research (PER). A growing body of PER examines gender differences in participation, performance, and attitudes toward physics. We have three critiques of this work: (1) it does not question whether the achievements of men are the most appropriate standard, (2) individual experiences and student identities are undervalued, and (3) the binary model of gender is not questioned. Driven by these critiques, we propose a conception of gender that is more up-to-date with other fields …

Tools For Outreach Presentations, Ronald I. Greenberg, Dale Reed

Computer Science: Faculty Publications and Other Works

We present resources we have constructed and culled from the internet that can be used in computing outreach visits in K–12 classrooms, especially high schools. We have used such tools at about 100 schools, reaching several thousand students, and achieving positive attitudinal responses in surveys of several hundred of these students.

Investigating The Efficacy Of Algorithmic Student Modelling In Predicting Students At Risk Of Failing In The Early Stages Of Tertiary Education: Case Study Of Experience Based On First Year Students At An Institute Of Technology In Ireland., Geraldine Gray

Doctoral

The application of data analytics to educational settings is an emerging and growing research area. Much of the published works to-date are based on ever-increasing volumes of log data that are systematically gathered in virtual learning environments as part of module delivery. This thesis took a unique approach to modelling academic performance; it is a first study to model indicators of students at risk of failing in first year of tertiary education, based on data gathered prior to commencement of first year, facilitating early engagement with at-risk students.

The study was conducted over three years, in 2010 through 2012, and …

Consciousness-Raising, Error Correction And Proofreading., Josephine O'Brien

All Works

The paper discusses the impact of developing a consciousness-raising approach in error correction at the sentence level to improve students' proofreading ability. Learners of English in a foreign language environment often rely on translation as a composing tool and while this may act as a scaffold and provide some support, it frequently leads to predictable and persistent errors. Such fossilization can cause inaccuracies that detract from student composition and that require instruction and repeated practice in order to eradicate the errors. The current paper reports on an experiment in consciousness-raising about specific categories of errors with a group of 30 …

Developing A Physics Expert Identity In A Biophysics Research Group, Idaykis Rodriguez, Michelle Goertzen, Eric Brewe, Laird H. Kramer

Stem Transformation Institute

We investigate the development of expert identities through the use of the sociocultural perspective of learning as participating in a community of practice. An ethnographic case study of biophysics graduate students focuses on the experiences the students have in their research group meetings. The analysis illustrates how the communities of practice-based identity constructs of competencies characterize student expert membership. A microanalysis of speech, sound, tones, and gestures in video data characterize students’ social competencies in the physics community of practice. Results provide evidence that students at different stages of their individual projects have opportunities to develop social competencies such as …

How To Take Into Account A Student's Degree Of Certainty When Evaluating The Test Results, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To more adequately gauge the student's knowledge, it is desirable to take into account not only whether the student's answers on the test are correct or nor, but also how confident the students are in their answers. For example, a situation when a student gives a wrong answer, but understands his/her lack of knowledge on this topic, is not as harmful as the situation when the student is absolutely confident in his/her wrong answer. In this paper, we use the general decision making theory to describe the best way to take into account the student's degree of certainty when evaluating …

Math Department Newsletter, 2014-2015, Mathematics Department

Mathematics Newsletter

No abstract provided.

Work Integrated Learning In Stem In Australian Universities: Final Report: Submitted To The Office Of The Chief Scientist, Daniel Edwards, Kate Perkins, Jacob Pearce, Jennifer Hong

Higher education research

The Australian Council for Educational Research (ACER) undertook this study for the Office of the Chief Scientist (OCS). It explores the practice and application of Work Integrated Learning (WIL) in STEM, with a particular focus on natural and physical sciences, information technology, and agriculture departments in Australian universities. The project involved a detailed ‘stocktake’ of WIL in practice in these disciplines, with collection of information by interview, survey instruments, consultation with stakeholders and literature reviews. Every university in Australia was visited as part of this project, with interviews and consultation sessions gathering insight from more than 120 academics and support …

To The Mathematical Beach, Francis Su

All HMC Faculty Publications and Research

What context am I missing that hinders my connection with my students? How often do I take the time to get to know their backgrounds? What are the primary experiences that shaped them, and do those present obstacles or opportunities for learning? And in what ways does the mathematical beach say “open to all” but still feel restricted?

These questions appear unrelated to mathematics, but if we ignore their effects, some of our students will not flourish.

Practical Applications Of An Integrally Christian Approach To Teaching Mathematics, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Descriptions of various frameworks and approaches to integrating Christian faith in the mathematics classroom are explored, as well as examples and techniques. In particular, a subject-centered approach is advocated in contrast to the traditional teacher-centered approach or, more recently, the student-centered approach.

God: One, Daniel Kiteck

ACMS Conference Proceedings 2015

I see the most mathematically significant verse as Deut. 6:4 where God says He is ONE. (And I don’t believe that it is an accident that the greatest commandment to love God with all we are immediately follows.) What is the concept of “one” in relationship to God? Is God dependent on the concept of “one?” What if “one” is ultimately always a comparison going back to God? God is also commonly viewed as infinite. How is this connected to our understanding of the mathematical continuum? Could this help us see how God is foundational both to discrete and continuous …

Software Engineering I: Teaching Challenges, Paul C. Grabow

ACMS Conference Proceedings 2015

The term software engineering can be traced to the late 1960s in response to large-scale, software development problems. Since then it has evolved as a discipline, both within industry and the academy. There have been distinct educational successes: “Standard practice” has matured (and found its way into more textbooks),the ACM and IEEE Computer Society have published curriculum guidelines, computer science programs commonly offer at least one software engineering course, and software engineering degrees (undergraduate or graduate) are more common. However, software engineering still presents a challenge. The term itself has become contorted by companies (and society in general); software has …

Designing For Mistrust, Eric Gossett

ACMS Conference Proceedings 2015

The 2014 ACM North Central Region programming contest contained a problem about a group of v bandits who want to use multiple locks to seal their treasure and distribute keys in such a way that no group of less than m bandits can open all the locks. The problem asks for an algorithm that will determine the number of locks needed for any set of parameters (v, m). I will present an analytic solution that produces a minimum number of locks, a recurrence relation solution, and a constructive algorithm that can print out a table showing the …

Parables To A Mathematician, Melvin Royer

ACMS Conference Proceedings 2015

Jesus frequently used parables in His ministry, usually short narratives illustrating the outcomes of people’s choices. In John 3:12 and Matthew 13:10-15, He explained that one reason was to be sure that people who genuinely wanted to understand His message would be able to do so. Since most of His audience was familiar with an agrarian economy, Jesus spoke extensively of wheat, fish, trees, wine, debt, tenants, lamps, etc. Many people have speculated on parables Jesus might have used had He lived in a different society. This non-scholarly (but hopefully thought-provoking) talk will propose parables targeted toward groups of mathematicians …