(TCPS 5) Inviting All Students to Do Mathematics – Engaging Courses, Projects, and Activities for Liberal Arts Students

Part A: Thursday, August 4, 8:30 AM – 10:05 AM, Hyatt Regency Columbus, Union B

Part B: Friday, August 5, 8:30 AM – 9:45 AM, Hyatt Regency Columbus, Union C

Part C: Friday, August 5, 1 PM – 6:15 PM, Hyatt Regency Columbus, Union C

All students should have the opportunity to do mathematics in a meaningful way for the sheer fun of it. Such experiences, if well designed, improve students’ effective thinking skills, increase their appreciation of the beauty and utility of mathematics, and prepare them to be mathematically-literate members of society. This session invites talks on how we can engage the liberal arts student through courses specifically designed for them. We welcome presentations on innovative course design, pedagogy, projects, or activities, as well as talks on tools used to assess such courses. Presentations should include a research basis for the design or pedagogical choices, a report on outcomes in student learning or attitude, or other evidence of success. Papers about programs demonstrating success engaging students who enter the course reluctant to engage in mathematics are especially encouraged. We also welcome talks on first year seminars or other experiences that engage first year students in doing mathematics as well as Honors courses in mathematics that incorporate the liberal arts.

Organizers:

Suzanne Doree, Augsburg College

Sarah Mabrouk, Framingham State University

Jennifer Nordstrom, Linfield College

Victor Piercey, Ferris State University

Curriculum Renewal Across the First Two Years (CRAFTY) Committee

Part A: Thursday, August 4, 8:30 AM – 10:05 AM, Hyatt Regency Columbus, Union B

8:30 AM – 8:45 AM	Pascal, Rascals and Inquiry Philip Hotchkiss, Westfield State University This year several of us from the Discovering the Art of Mathematics project have had some remarkable student results while exploring Pascal’s Triangle and the Rascal Triangle in our Mathematics for Liberal Arts (MLA) courses. Our students made several discoveries: a new number triangle related to both Pascal’s Triangle and the Rascal Triangle, a simpler rule, as well as some equivalent rules (all of which were heretofore unknown), for generating the Rascal Triangle as well as several patterns within the Rascal Triangle. This inquiry has resulted in a wonderful level of engagement and excitement in mathematics for these students, many of whom have been disenfranchised by their previous mathematical education. · Discovering the Art of Mathematics: Mathematical Inquiry in the Liberal Arts: Home Page · Julian Fleron's Blog (December 15, 2015): Tackling Rascals’ Triangle - How Inquiry Challenges What We Know and How We Know It
8:50 AM – 9:05 AM	Mathematics around Central Field-Trips Brandy Wiegers, Central Washington University Mathematics around Central is a new one hour weekly seminar that orchestrates weekly field-trips to locations around our university campus and reveals the mathematics hidden across campus. Some field-trip locations included campus exhibitions at the art gallery, cultural museum, and the green house. Other locations included existing campus projects such as walking the scaled solar-system model spanning across campus and visiting physic's Foucault pendulum. A combination of math and liberal art majors in the course provided the opportunity for engaged in-class discussion of the connections between the field-trips and mathematics. Some connections were obvious (the art gallery had an exhibit on quantitative painting) while other field-trips provided the opportunity to connect mathematical concepts of patterns, symmetry, and sequences. Students especially appreciated the opportunity to learn about geocaching and at the end of class the students created a photo book that talks about the math at each of these experiences to share with future students. This was shared in the new geocache which was created by the students to commemorate their seminar experience.
9:10 AM – 9:25 AM	How I Spent My Summer Vacation or How to Plan and Organize a Math Study Abroad Withdrawn, July 19, 2016 Pamela Peters, San Juan College Lisa Ruffier, San Juan College In the summer of 2015, we led a very successful study abroad trip to Italy for students at our two year college, with the title, “Da Vinci, Scientist and Mathematician”. We believe that Study Abroad is an excellent way for students to broaden their horizons and enhance their world view. It also makes them more competitive in the job market where companies are becoming increasingly more global. Unfortunately, when we started working on this project, we found that there are no commercially available study abroad trips with any kind of a math emphasis. So we jumped into the deep end of the pool to organize our own Study Abroad trip. We will share our challenges, insights and recommendations gained from this fun and interesting endeavor.
9:30 AM – 9:45 AM	Making Polynomials Fun for All via Polynomiography Bahman Kalantari, Rutgers University Supported by numerous experiences with Polynomiography, I believe there is convincing evidence that polynomials could be turned into fun objects for all: not only K-16 students and educators, but the general public, even children. Polynomiography stands for algorithmic visualization in solving polynomial equations. Its underlying concepts and techniques, together with its software and apps help associate a kind of visual beauty to polynomials that offers numerous applications in STEM, fine art and more. It gives rise to numerous colorful images, not just fractal ones. More importantly, not only Polynomiography inspires students into learning diverse mathematical and algorithmic concepts, it promotes creativity and innovative applications of polynomials, far beyond the ordinary and dry applications in math and science. At Rutgers I have taught Polynomiography through Honors courses, First-Year Seminars, and undergraduate research programs. I have also collaborated with middle and high schools in New Jersey and elsewhere in designing related activities. In this talk I will describe several related experiences and activities. I will also invite educators into collaborations that would help them and their students experience the power and beauty of Polynomiography.
9:50 AM – 10:05 AM	Puzzles + Games = Analytical Thinking Edmund Lamagna, University of Rhode Island Puzzles and games provide a rich environment for acquiring critical mathematical thinking skills through active learning. The presenter designed and teaches a liberal arts math course using puzzles and games. Most students enrolled are non-STEM majors using the class to fulfill a general education requirement. Puzzles and games provide a way to "level the playing field'' among students with vastly different mathematical backgrounds. Importantly, students enjoy mathematical puzzles, and will put more effort into them than routine exercises. The course is taught without lectures. Students spend most of a class period working in small groups (2-4 individuals) solving several related puzzles or playing a game with a mathematical theme. Toward the end of class, students present and discuss their solutions with guidance from the instructor. Students individually write solutions to selected problems, often including ones not solved in class. Good writing and careful presentations are expected. The solutions are revised based on feedback, and compiled into a solutions manual submitted at the end of the term. The in-class group work and presentations, and the writing assignments help students to sharpen their reasoning and develop an ability to communicate mathematical ideas. Topics studied include sequential movement puzzles, probability, mathematical logic and deduction, basic number theory, summation and proofs without words, algorithms, recursion and induction, and graphs. The talk includes examples of several class activities, and discusses the critical reasoning they cultivate. Top of Page

Part B: Friday, August 5, 8:30 AM - 9:45 AM, Hyatt Regency Columbus, Union C

8:30 AM – 8:45 AM	Bringing the Arts into a Liberal Arts Math Course Angela Brown, Sul Ross State University At Sul Ross State University, all Bachelor of Science Majors are required to take College Algebra, Statistics, or higher level courses to meet their math requirement. This leaves those getting a Bachelor of Art degree as the students in Contemporary Mathematics, our liberal arts mathematics course. This being said, we try to bring creative components into this course. For my sections, this includes hands on activities that build these students' critical thinking skills and final projects that bring their creativity into play. We will discuss some of the aspects of how this course is taught at Sul Ross and how students have reacted to mathematics that most of them have not seen before.
8:50 AM – 9:05 AM	Puzzles and Paradoxes: Engaging the Interests of Both the Willing and the Reluctant Douglas Shier, Clemson University Marilyn Reba, Clemson University We describe a course on puzzles and paradoxes created to entice students to an appreciation of unifying mathematical concepts. Originally taught for students in the Honors College at Clemson University in 2008, this course was successfully modified in 2014 as a special critical thinking section of our liberal arts mathematics course. Both courses present a progression of puzzling situations and illustrate how mathematical formulation can be used to aid comprehension and generalization. Moreover, this approach links together seemingly unrelated situations by use of a common set of representations and solution strategies. In this talk we specifically illustrate the power of mathematical representation with examples drawn from biology, sports, gambling, and voting.
9:10 AM – 9:25 AM	Mathematics Without Calculations – It’s a Beautiful Thing! Jason Molitierno, Sacred Heart University Presentation File "Mathematics Without Calculations - It's a Beautiful Thing!" is a first year seminar course for non-math majors which focuses on writing about various concepts in mathematics rather than on rigorous calculations. By writing about mathematics, the non-math oriented student gains an appreciation for what mathematics is really like, and at the same time, improves his/her writing and speaking skills. In this talk, several creative writing projects will be presented along with the overall structure of the class which also includes research presentations. Projects pertaining to the infinitude of prime numbers, different levels of infinity, three-dimensional solids, four-dimensionality, fractional dimensions, and graph theory will be discussed.
9:30 AM – 9:45 AM	Projects for Poets Margaret Boman, Harrisburg Area Community College – Lebanon Campus Engaging the diverse set of students come to a Liberal Arts Math course is a challenge. I will discuss the challenges and successes I have had integrating projects on geometry, set theory, voting and probability into a community college Liberal Arts Math course. Top of Page

Part C: Friday, August 5, 1 PM - 6:15 PM, Hyatt Regency Columbus, Union C

1 PM – 1:15 PM	Using the History of Mathematics to Invigorate Honors Calculus Dan Kemp, South Dakota State University To make Honors Calculus 'honorable' I attempted to follow Abel's advice "It appears to me that if one wishes to make progress in mathematics, one should study the masters and not the pupils." Our friends in the Humanities apparently have great success with this model, but I quickly discovered that our freshman don't even know mathematics has 'Masters'. Many claim never to have heard of Euclid! To get over this hurdle I began having my student read a very introductory mathematics history text, The Story of Mathematics by Richard Mankiewicz, and submit reflection papers over their reading. This turned out to be popular and I will discuss the reading of history of mathematics in more detail. Reading mathematics written by masters for beginning calculus students seemed too ambitious, but writing Projects for them based on the works of masters did work. These projects, over topics related to the subject currently being studied, were assigned to groups of three or four students to be done outside of class. The result is a word processed paper. Added benefits include socialization of the students and them beginning to learn how to write mathematics. Examples of Projects will be given along with some student responses. One of my favorite projects begins by discussing the history of the problem of determining sum of the reciprocals of the squares of all positive integers and one of Euler’s remarkable proofs that the sum equals pi squared divided by six. Then the students work through a modern elementary proof that uses integration by parts, partials sums of series, and the squeeze theorem, all topics that they are currently studying.
1:20 PM – 1:35 PM	A Course on the Mathematics of the Pre-Columbian Americas Ximena Catepillan, Millersville University of Pennsylvania This presentation addresses the need and rationale for the creation of a course for non-STEM students on the mathematics of pre-Columbian Americas. Sample lessons for in-class work and projects with exercises also are included.
1:40 PM – 1:55 PM	Grounding Calculus Learning in the History of Mathematics Aaron Trocki, Elon University The study of Mathematics is integral to a liberal arts education and often includes a first course in Calculus. A challenge facing Calculus I instructors is that of connecting the content of Calculus to other pillars of a liberal arts education such as history, writing, and communication. A typical Calculus I course is content heavy leaving little time for supplemental activities and projects. A need then exists for course designs and projects that connect Calculus to other aspects of liberal arts while simultaneously contributing to the achievement of content goals. This presentation delineates one project and implementation that may work to meet this need for all Calculus learners. The project is entitled Giving a Historical Context to Calculus, and its purpose is to provide students an opportunity to familiarize themselves with the origins and archetypal problems of Calculus that led to our current conception of the field. Berlinghoff and Gouvea explain, “Learning about math is like getting to know another person. The more you know of someone’s past, the better able you are to understand and interact with him or her now and in the future” (p. 1, 2002). The project takes the form of a short paper and brief presentation. Project details and implementation are shared along with student work samples and reactions to the experience. · Calculus I History of Math Paper Guidelines
2 PM – 2:15 PM	Integration of Faith and Learning in the Mathematics Curriculum Filippo Posta, Grand Canyon University Ben Vanderlinden, Grand Canyon University There are more than 1,000 religiously affiliated Colleges and Universities in the United States. These schools are chosen by learners not only for their academic standards, but also because of their focus on religious and spiritual values. The mission statements at these Academic Institutions include words regarding integration of faith and learning (IFL) in the curriculum. However, how to apply IFL in a Mathematics classroom can be a daunting and uncomfortable endeavor. We present different approaches that vary in nature and effort. From motivational speeches aimed at creating a positive classroom atmosphere, that promotes student tenacity and limits math anxiety. To synchronous and asynchronous activities, that help relate abstract and isolated mathematical procedure to spiritual and social contexts, that are dear to our (and your) learners. We will discuss the evidence that we gather. We will show what worked and what to avoid.
2:20 PM – 2:35 PM	Mathematics in Ministry Jacqueline Brannon Giles, HCC Central College/Texas Southern University/S.H.A.P.E. Community Center Presentation Transcript The presenter will discuss creative examples of the use of mathematics in many aspects of our daily activities. Two year college students suggested three focus areas: ministry, money, and movies. The Faith Equation will be discussed and examples from numismatics and movies will be shared. The expected outcome for students and participants will be to inspire students from all echelons of society to Do mathematics, and to see that mathematics is in everything.
2:40 PM – 2:55 PM	Divination: Using Excel to Explore Ethnomathematics Osman Yurekli, Ithaca College Cristina Gomez, Ithaca College This presentation will provide an outline of an introductory liberal arts mathematics course where students will develop different methods of understanding mathematics as a human creation through looking at the development of mathematical ideas in different cultures at different times. Students experience various social activities such as divination and marking time. They learn how to reflect on broader ideas about how we discover and create mathematical knowledge and understand the world around us. As a demonstration of our ideas, we will present a divination process that originated in Madagascar centuries ago and is still practiced there to this day. We will then discuss how to model this divination using a spreadsheet program (Microsoft Excel).
3 PM – 3:15 PM	Teaching Proofs to Gen Ed-Lib Arts Learners—Leapfrogging Basic Skills Deficits While Building Learner Self-Confidence G. Gerard Wojnar, Frostburg State University Sadly, many general education-liberal arts students are in college math-phobic and with horribly inadequate basic math skills. These students are intelligent but suffer from poor self-images when it comes to math. Nevertheless, their general intelligence equips them to grasp various basic proofs with a sense of mastery, providing positive and authentic experiences of mathematics. Two such proofs are the infinitude of the primes, and the infinitude of the harmonic series.
3:20 PM – 3:35 PM	Math as a Creative Art: Reflections on an Honors Proofs Class for Liberal Arts Majors Pat Devlin, Rutgers University Presentation File Nora Devlin, Rutgers University In the words of Paul Halmos, `it saddens me that educated people don't even know that my subject exists. There is something that they call mathematics, but they neither know how the professionals use that word, nor can they conceive why anybody should do it.' To this end, we designed an honors-level course geared towards liberal arts majors to provide a taste of (and ideally appreciation for) `math as a creative art' (i.e., proofs). The mathematical content spanned many topics including (as two examples) combinatorial game theory and Cantor's diagonalization argument. Students were also exposed to social aspects of the discipline including its history, culture, and modern-day issues (e.g., under-representation of certain demographic groups). In this talk, we discuss an implementation of this course giving an overview of the structure chosen and the progression of student opinions towards the subject as a whole. We pay special attention to which activities and other pedagogical choices were (and which weren't) particularly effective in engaging students to think mathematically. In all, we found that the chosen format worked quite well, and in fact many students were themselves surprised to realize how much they were getting out of it.
3:40 PM – 3:55 PM	Graph Theory: Non-Quantitative Mathematics for Liberal Arts Students Jonathan Hulgan, Oxford College of Emory University The 100-level course Graph Theory and Math Models was designed to give all interested students a glimpse of mathematical research without regard for each student's particular mathematical background. For the first two-thirds of the semester, students explored fundamental topics in graph theory through guided inquiry activities. The last segment of the course saw students working to understand a classic paper in the field as well as develop a list of questions or conjectures inspired by these results and proofs. I will share how this course seemed to have a positive impact on students’ attitudes towards mathematics, as evidenced through comments from regular student reflections as well as course evaluation data
4 PM – 4:15 PM	Quantitative Literacy at Michigan State University: Present Successes and Challenges Samuel Luke Tunstall, Michigan State University Presentation File Richard Edwards, Michigan State University Jeff Craig, Michigan State University Andy Krause, Michigan State University Vince Melfi, Michigan State University Effecting curricular change at a large public institution is a nontrivial endeavor. In this presentation we discuss the creation of Math 101 and 102--each entitled Quantitative Literacy--at Michigan State University. The course fulfills a component of the University's general education mathematics requirement; its curriculum is context-driven, and its assessment is non-traditional. All of this was done while keeping in mind that students in the course may have mathematics anxiety and have faced challenges in previous mathematics courses. We begin with a brief outline of the course's development, then the bulk of the presentation will focus on curriculum (including example content and assignments), pedagogy, and assessment (both short- and long-term).
4:20 PM – 4:35 PM	Building Quantitative Reasoning Through Interdisciplinary Theme-Based First-Year Courses Rebecca Walker, Guttman Community College At Guttman Community College, a new community college that is part of the City University of New York, the first-year experience for all students, the majority of whom are liberal arts intending and have not yet demonstrated basic algebra proficiency, includes a year-long exposure to quantitative reasoning as part of two interdisciplinary courses that explore contemporary urban issues. In these City Seminar courses, social science, English, and mathematics faculty work collaboratively to develop and implement integrated projects that the students complete over the course of the semester. Through these projects and related class activities, we are able to address a range of developmental mathematics topics and help students see how mathematics and quantitative reasoning can be used to explore critical issues such as gentrification and immigration and how they can help support a thesis. In this talk, I will share the skill spines that serve as the basis for the course and examples of student-centered class activities and integrated projects. The challenges of allowing flexibility of City Seminar topics depending on faculty interest and expertise while maintaining consistency of quantitative reasoning development from section to section will also be discussed.
4:40 PM – 4:55 PM	Introducing Fermi Problems and the Art of Reckoning to Liberal Arts Students Alexander Atwood, Suffolk County Community College The art of calculating informed estimates using minimal information, as done by the physicist Enrico Fermi, can be effectively taught in a Mathematics class for Liberal Arts Students. Although many students are initially hesitant in making back-of-the-envelope estimates and calculations, they can become progressively much stronger. I will share my experiences of what works and what doesn’t work in nurturing students’ powers of guesstimation, and I will share my Fermi Problems that I use in the classroom.
5 PM – 5:15 PM	Innovations in a Liberal Arts Probability Course Michael Weingart, Rutgers University This talk will discuss recent innovations in both the format and content of the undergraduate probability course at Rutgers taken by a general liberal arts audience, much of which is decidedly math-phobic. The format innovation is to teach in a hybrid, flipped classroom model. The results have been positive, especially for the substantial population of international students in the course; they have performed significantly better in the flipped version. The content innovations include teaching expected value in a new way, inspired by cognitive science research on understanding natural frequencies, and restructuring the course plan so that what had been isolated topics are now recurring themes throughout the course. A series of exercises ask students not only to solve problems, but also to make their own individual decisions informed by (but not determined by) expected value computations, and keep track of their total “score” as the course goes on.
5:20 PM – 5:35 PM	Introductory Statistics – Group Project in a Large Class Catherine A. Robinson, University of Rhode Island Many students are required to take a first course in introductory statistics, and many of them are fearful or apprehensive as they see statistics as a foreign language. Having a group project in an introductory statistics class that is discussed in the very first class of the semester and due near the end of the semester is one way to help engage students, foster collaborative student efforts, and promote active learning throughout the course. The lecture class provides the necessary basic statistical concepts and a (smaller) recitation class provides weekly opportunity for students to work on practice exercises to reinforce the material presented in lecture, as well as for student groups to discuss and work on project deadlines. The first project related recitation exercise is to divide into self-selected student groups of 2-4 and discuss ideas for a project topic based on the students’ interests. Information on existing data sets is provided, as well as ideas on data collection. The grading rubric is provided at the onset of the semester, as well as the guidelines on the final project report preparation. Each week there is time devoted in recitation to another aspect of the group project. A project proposal (template is provided to students) is submitted mid-semester including the group’s topic, objectives, and variables to be utilized, as well as information regarding the analyses the group anticipates will be performed. The instructor provides feedback and guidance for each group project. Recitation instruction includes usage of statistical software to run analyses and creation graphs, tables, and charts. The final project report is due late in the semester.
5:40 PM – 5:55 PM	The Impact of Academic Presentations on Students Understanding of Mathematical Concepts in General Education Mathematics Hope Essien, Malcolm X College (City Colleges of Chicago) Encouraging an active learning environment for any group of students may pose challenges, particularly in a mathematics classroom. Recent curriculum recommends cognitive mathematical learning tasks for all students to utilize multiple modes of communication. The goal of this project was to create a mathematics learning space that facilitates activities and foster connections that enhanced student learning through collaborative work. Within that context, we investigated the impact of academic presentations on students understanding of mathematical concepts in a general education mathematics classroom. According to Huddle (McNamara, et al., 2010). “Poster preparation allows students to become active learners and encourages deeper learning”. Additionally, posters can be defined as “multimodal communicative genre, with text, graphics, color, speck, and even gesture used to convey meaning” (Kress & van Leeuwen, 2001). Participants included sophomore students in a Midwest, urban, public two-year community college, consisting predominantly of students of color during a 16-week semester. Analysis of the result demonstrates that students effectively analyzed and solved complex mathematical problems and explained their procedures when responding to probing questions. This investigation concludes that there is a relationship between academic presentation (active learning) techniques and students understanding of mathematical concepts. It affirms that poster utilizes students centered learning style that permits students to be deeper learners, encouraging students to reflect on materials covered using active learning, research skills and numeracy which is demonstrated during presentation.
6 PM – 6:15 PM	Revitalizing College Algebra and Pre-Calculus through Curricular Collaboration and Team Teaching with Partner Disciplines in a Liberal Education Program Lorraine F. Dame, University of Minnesota Rochester Presentation File Aminul Huq, University of Minnesota Rochester Bijaya Aryal, University of Minnesota Rochester Xavier Prat-Resina, University of Minnesota Rochester In the Center for Learning Innovation at the University of Minnesota Rochester (UMR), mathematics and partner discipline faculty are collaboratively engaged in re-envisioning the pre-calculus curriculum and its delivery to addresses specific needs of students in a Liberal Education program. Our new pre-calculus curriculum consists of two integrated three-credit courses, College Algebra with Physical Concepts and Pre-calculus with Physical Concepts. At their core, each of these courses has assessable learning objectives from mathematics, biology, chemistry and physics in a ratio of approximately two parts math to one part physical concepts. We are modifying curriculum delivery to include multi-disciplinary team teaching in which faculty from partner disciplines introduce related foundational physical concepts at key points in the delivery of the math curriculum. Our goals in modifying the curriculum and its delivery include: increasing the efficacy of transfer of pre-calculus knowledge to partner discipline courses; addressing the needs of students identified as struggling with mathematics upon entry to a health sciences program; and increasing motivation for students to develop pre-calculus skills. Preliminary evidence collected includes qualitative student & faculty interview results, student grade information, and before/after assessment using the Basic Skills Diagnostic Test developed by Dr. Jerome Epstein. In this talk we will discuss the successes and struggles thus far in designing and implementing the new pre-calculus curriculum and its delivery. We will also discuss future curriculum development plans for pre-calculus at UMR by our highly collaborative faculty. Top of Page

This page was created and is maintained by S. L. Mabrouk, Framingham State University.

This page was last modified on Thursday, August 11, 2016.