Science and Mathematics Education Commons^™

Making Mathematics Memorable, Meaningful, And Fun: Activities To Enhance Precalculus, Nat White

Theses and Dissertations

To master material, students need to make it their own. As teachers, we should structure their interactions with mathematics in ways that are memorable, meaningful, and fun. One way to do this is to provide activities that stretch beyond the textbook and lead students to think and talk to one another about mathematics. This thesis contains a set of activities designed to enhance a precalculus course, along with solutions and feedback on each activity.

On The Stability Of A Pexiderized Functional Equation In Intuitionistic Fuzzy Banach Spaces, Nabin C. Kayal, Pratap Mondal, T. K. Samanta

Applications and Applied Mathematics: An International Journal (AAM)

During the last few decades several researchers have been devoted to establishing stability of different kinds of functional equations, differential equations, functional differential equations, fractional differential equations, etc. under different sufficient conditions in different spaces like Banach spaces, Banach modules, fuzzy Banach spaces etc. In this paper, we remain confined in the discussion of stability of functional equations in intuitionistic fuzzy Banach spaces. Ulam was the first person who introduced an open question concerning the stability of a group homomorphism in an international conference. Thereafter several researchers have replied and are still replying to this open question in different contexts. …

Flipped Calculus: A Study Of Student Performance And Perceptions, Lori Beth Ziegelmeier, Chad M. Topaz

Lori Beth Ziegelmeier

No abstract provided.

Flipped Calculus: A Study Of Student Performance And Perceptions, Lori Beth Ziegelmeier, Chad M. Topaz

Chad M. Topaz

No abstract provided.

Art, Math, And Physics; All About For, Chris Brownell, Steve Pauls

The STEAM Journal

Anish Kapoor’s public sculpture “Cloud Gate” and Frame of Reference.

Ambiguity In Speaking Chemistry And Other Stem Content: Educational Implications, Mick D. Isaacson, Michelle Michaels

Journal of Science Education for Students with Disabilities

Ambiguity in speech is a possible barrier to the acquisition of knowledge for students who have print disabilities (such as blindness, visual impairments, and some specific learning disabilities) and rely on auditory input for learning. Chemistry appears to have considerable potential for being spoken ambiguously and may be a barrier to accessing knowledge and to learning. Educators in chemistry may be unaware of, or have limited awareness of, potential ambiguity in speaking chemistry and may speak chemistry ambiguously to their students. One purpose of this paper is to increase awareness of potential ambiguity in speaking chemistry and other STEM fields …

The Design And Validation Of A Group Theory Concept Inventory, Kathleen Mary Melhuish

Dissertations and Theses

Within undergraduate mathematics education, there are few validated instruments designed for large-scale usage. The Group Concept Inventory (GCI) was created as an instrument to evaluate student conceptions related to introductory group theory topics. The inventory was created in three phases: domain analysis, question creation, and field-testing. The domain analysis phase included using an expert consensus protocol to arrive at the topics to be assessed, analyzing curriculum, and reviewing literature. From this analysis, items were created, evaluated, and field-tested. First, 383 students answered open-ended versions of the question set. The questions were converted to multiple-choice format from these responses and disseminated …

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 Integration Of Kinesthetic Learning Through The Math & Movement Program: Pilot Study 2015, Benjamin Ferder

Master's Theses

Purpose: The primary purpose of this pilot study was to verify that the use of kinesthetic learning (Math & Movement Program) in the classroom increases retention of multiplication facts at a greater rate than traditional drill and practice. The Math & Movement Program uses a kinesthetic learning-based approach for practicing, learning, and memorizing mathematics through the incorporation of bodily movement(s). Participants: The directors of the research project for the participating school district selected the sample of convenience. The population size of this study included 213 third and fourth grade students during the second half of the 2011-2012 school years. Data …

On Similarities And Differences Between Proving And Problem Solving, Milos Savic

Journal of Humanistic Mathematics

A link between proving and problem solving has been established in the literature [5, 21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribepen data from a previous study [13]. I focus on two participants’ proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the …

The Math You Need, When You Need It (Tmyn): Leveling The Playing Field, Jennifer M. Wenner, Eric M. D. Baer

Numeracy

The Math You Need, When You Need It (TMYN) is a set of online tutorials designed to help students develop and review mathematical skills that are applied in undergraduate geoscience courses. We present results of a three-year study of more than 4000 students in 106 geoscience courses at a variety of post-secondary schools who were assigned TMYN tutorials as supplemental mathematics instruction. Changes in student scores from pre- to post-test suggest that the support provided by programs such as TMYN can begin to reduce the gap between mathematically well-prepared and underprepared students; in essence, TMYN levels the quantitative playing field …

High Impact Strategies And The Effect It Has On Students’ Mathematics Attitudes, Lauren A. Ryba

All Student Theses

This study was designed to determine if innovative strategies such as the use of technology and Supplemental Instruction (SI) could have an impact on students in an introductory statistics course. The study describes the use of a reliable instrument to measure students’ attitudes and beliefs about mathematics. Martha Tapia developed the Attitudes Toward Mathematics Inventory (ATMI) instrument in 1996 and later Lim and Chapman further refined a short form in 2012. The purpose of the ATMI was to measure mathematics attitudes in four ways: (1) enjoyment of mathematics, (2) motivation to do mathematics, (3) self confidence in mathematics, and (4) …

Math Department Newsletter, 2014-2015, Mathematics Department

Mathematics Newsletter

No abstract provided.

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.

Algebra 1 Students’ Ability To Relate The Definition Of A Function To Its Representations, Sarah A. Thomson

Electronic Theses, Projects, and Dissertations

One hundred high school Algebra students from a southern California school participated in this study to provide information on students’ ability to relate the definition of function to its representations. The goals of the study were (1) to explore the extent to which students are able to distinguish between representations of functions/non-functions; (2) to compare students’ ability to distinguish between familiar/unfamiliar representations of functions/non-functions; (3) to explore the extent to which students are able to apply the definition of function to verify function representations; and (4) to explore the extent to which students are able to provide an adequate definition …

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 …

Physical Activity In A Theory Of Computing Class, Nancy Lynn Tinkham

ACMS Conference Proceedings 2015

Physical activity breaks, sometimes called brain breaks, are beginning to gain attention among K-12 teachers as a way to keep their students alert and engaged in the classroom. In the Fall 2014 semester, faced with the task of teaching an introductory course in Theory of Computing in a once-a-week, 2 1/2-hour format, I decided to try incorporating physical activity into my own classroom. Time is precious in the college classroom, so any physical activities have to be directly related to the course material. I will describe some physically active exercises that I used in the classroom to teach students about …

Preparing Students To Read A Calculus Textbook, Douglas Phillippy

ACMS Conference Proceedings 2015

Consider the exercise of reading the textbook before class. While most educators agree that this practice leads to better learning, too often students enrolled in a calculus class do not find pre-class reading a valuable use of their time, and their commitment to doing so fades. Why is this? As instructors, we hope that these students will be well-versed in the fundamental concepts of the subject by the time they prepare for their final exam, but as they progress through the course and encounter new concepts, they may not be ready for the technical language of the standard calculus textbook. …

The Best Religious Calendar, Andrew Simoson

ACMS Conference Proceedings 2015

Many religions have deep roots in the rhythms of the moon. And ever since at least the fifth century BC man has known that the moon repeats itself every n = 19 years. Is this integer valuen the best of all choices?Easter follows such a calendar. We briefly show that 19 is second best. And then we run time backwards, and give a rationale as to why a certain species of cicada has a life cycle of 17 years. The answer involves the moon, the Farey series, and Kepler’s laws of motion.

Home Primes And Foreign Primes, Nicholas Zoller

ACMS Conference Proceedings 2015

Home primes and foreign primes are produced by a simple recipe that blends prime factorizations with recursion. The home prime of a positive integer n is formed by concatenating the prime factors of n in non-decreasing order. If the resulting integer is prime, then we have found the home prime of n. If not, then we repeat the process as many times as needed to obtain a prime. For instance, 35 = 5·7. After concatenation, we have 57 = 3·19, which is followed by 319 = 11·29, which is followed by 1129, which is prime. Thus, the home prime …

A Triune Philosophy Of Mathematics, Dusty Wilson

ACMS Conference Proceedings 2015

What is mathematics and is it discovered or invented? The Humanist, Platonist, and Foundationalist each provide answers. But are the options within the philosophy of mathematics so limited? Rather than viewing and describing mathematics in a mutually exclusive manner, each of these approaches includes components of truth from a greater triune philosophy of mathematics. This talk will introduce this inclusive triune paradigm through which to explore fundamental questions about mathematics.

The Remarkable Mrs. Somerville, Richard Stout

ACMS Conference Proceedings 2015

As a woman growing up in the late eighteenth century, Mary Somerville (1780-1872) was denied access to most formal education and getting a university education was completely out of the question. Yet her interests in nature, science, and mathematics, coupled with an intense curiosity and tenacious desire to learn led her to eventually be known and respected by scientists, mathematicians, and intellectuals in both Britain and France. She is one of the important woman in the history of mathematics, even though she did not publish original work. However, she was a talented writer, producing several significant works, including Mechanism of …

Pressure And Impulse In Student Learning: What I Learned From Teaching Physics, Kim Jongerius

ACMS Conference Proceedings 2015

In the fall of 2014, a one-semester gap between the departure of one physics professor and the arrival of the next afforded me the opportunity(?) to teach a first-semester, calculus-based physics class. The thirty-year gap between the last (of three) physics courses I had taken myself and this course I was to teach, combined with a two-week notice prior to the start of the semester, placed me in the interesting position of learning alongside my students. Wading through an unfamiliar text, trying to understand publisher-produced lecture slides, learning from and getting frustrated with online homework, entering review sessions fearful of …

On Random Numbers And God’S Nature, James Bradley

ACMS Conference Proceedings 2015

I start with mathematical Platonism, an ancient stream of thought that views numbers as transcending physical reality. I join this to recent insights into mathematical randomness from theoretical computer science. Joining these streams – one ancient, one recent – yields the surprising conclusion that randomness, defined in a particular way, is part of the nature of God. I then explore some of the implications of this conclusion for our understanding of the doctrine of God’s infinitude.

Experiencing A Paradigm Shift: Teaching Statistics Through Simulation-Based Inference, Dave Klanderman, Mandi Maxwell, Nathan Tintle

ACMS Conference Proceedings 2015

For decades, statistics has been taught as an application of formulas, making use of normal and other distributions, and relying heavily on algebraic skills of students, in short, emphasizing mathematical thinking. More recently, several textbook author teams have published statistics books that place an increased emphasis on simulation and randomization methods, and a corresponding decreased emphasis on the algebraic manipulation in formulas (e.g., Lock et al., 2012; Tintle et al., 2015) as a way to encourage better statistical thinking.This session describes simulation-based inference curricula more fully, reports on the necessary steps towards implementation of such an approach, and provides both …

Math, God And Politics—A Fight Over Geometry In 19th Century Italy, Donna Pierce

ACMS Conference Proceedings 2015

In 1839 a polemic, reminiscent of the Renaissance public challenges over mathematical problems, was issued by the leader of the synthetic school of geometry, Vincent Flauti, to the analytical school, headed by Fortunato Padula. Three geometric problems were proposed, all carefully chosen to guarantee a victory for the synthetic school. The judges were from the Royal Academy of Sciences, men also favorable to the synthetic method. Why then did the analytics take up this challenge, and who were the real victors? This was not just a fight over the ‘correct’ way to do geometry, it was a fight over politics, …