Science and Mathematics Education Commons^™

Can Addressing Language Skills For Fifth Grade Ells In A Multiplication Curriculum Help Address The Achievement Gap In Math? A Multiplication Workbook For Big Kids, Michelle Douglas

Master's Projects and Capstones

Currently, the state of California has 1,332,405 students from grades k-12 who speak a language other than English at home (Caledfacts, 2016). When I started my first year teaching fifth grade with 95% of my students being English language learners (ELLs), I was surprised to see an achievement gap of two to three years in my student’s reading and math skills. I found that my student’s developmental language and math skills contributed to a lack of engagement during math time. Upon further research, I found that these three factors play a role in the wide achievement gaps between ELLs and …

Improving The Problem With Problem Solving, Cole Thibert

Essential Studies UNDergraduate Showcase

As a prospective math educator who will be teaching in the near future, I was concerned with the idea of preparing my future students for college math courses. I decided to research the effects of teaching students how to appropriately use problem solving strategies in math. My research led me towards looking at the benefits of students becoming better problem solvers and how teachers can implement problem solving into their daily lessons.

When this implementation is successful, students can become more independent with their learning, they are able to work and persevere through challenging problems, and they have a greater …

The Calculus War: The Ultimate Clash Of Genius, Walker Briles Bussey-Spencer

Chancellor’s Honors Program Projects

No abstract provided.

Farlie-Gumbel-Morgenstern Family: Equivalence Of Uncorrelation And Independence, G. Barmalzan, F. Vali

Applications and Applied Mathematics: An International Journal (AAM)

Considering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this problem in other distributions. In other words, whether the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. In this paper, we answer to this question and establish generalized Farlie-Gumbel-Morgenstern (FGM) family is another family of distributions under which uncorrelation is equivalent to independence.

Apathy And Concern Over The Future Habitability Of Earth: An Introductory College Assignment Of Forecasting Co2 In The Earth’S Atmosphere, Benjamin J. Burger

Journal on Empowering Teaching Excellence

Non-science, first year regional undergraduate students from rural Utah communities participated in an online introductory geology course and were asked to forecast the rise of CO₂ in the Earth’s atmosphere. The majority of students predicted catastrophic rise to 5,000-ppm sometime over the next 3,100 years, resulting in an atmosphere nearly uninhabitable to human life. However, the level of concern the students exhibited in their answers was not directly proportional with their timing in their forecasted rise of CO₂. This study showcases the importance of presenting students with actual data and using data to develop student forecasted models. …

The Roots Of Early Group Theory In The Works Of Lagrange, Janet Heine Barnett

Abstract Algebra

No abstract provided.

The Pell Equation In India, Toke Knudsen, Keith Jones

Number Theory

No abstract provided.

Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett

Number Theory

No abstract provided.

Special Issue Call For Papers: Mathematics And Motherhood, Pamela E. Harris, Becky Hall, Carrie Diaz Eaton, Emille Davie Lawrence

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Mathematics and Motherhood. Please send your abstract submissions via email to the guest editors by October 1, 2017. Initial submission of complete manuscripts is due January 1, 2018. The issue is currently scheduled to appear in July 2018.

I Love You Fifty, Nat Banting

Journal of Humanistic Mathematics

This article chronicles the merging of my roles of teacher and learner of mathematics with that of a relatively new pursuit: parenthood. Amidst my attempts to dutifully provide opportunities for my son to interact with various mathematical ideas and artifacts, it was an unanticipated moment of epiphany that allowed me to enter into his emerging world of mathematical significance and rediscover what first drew me to the teaching and learning of mathematics. My son’s innocent, yet potent, understanding of number provides an image of the power of mathematics to organize experience, structure significance, and communicate meaning.

Inquiry Based Learning From The Learner’S Point Of View: A Teacher Candidate’S Success Story, Caroline Johnson Caswell, Derek J. Labrie

Journal of Humanistic Mathematics

The goal of this paper is to review current research on Inquiry Based Learning (IBL) and shed some light, from a student's perspective, on the challenges and rewards of this pedagogy. The first part of the article provides an extensive review of the literature on IBL. The second part focuses on one student's experiences in an IBL classroom.

In particular, a graduate secondary mathematics student reflects upon his experiences in a college mathematics class where the instructor implemented an Inquiry Based Learning model. His experience is validated by current research on IBL educational methodology which structures the classroom environment for …

Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton

Numeracy

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of the Multidisciplinary Sustainability Education (MSE) project at Ithaca College. In the first year of the project, students received basic technical report guidelines. In year two, the report guidelines changed to include explicit language on how to incorporate figures. In year three, a grading rubric was added …

The Definite Integrals Of Cauchy And Riemann, Dave Ruch

Analysis

Rigorous attempts to define the definite integral began in earnest in the early 1800's. One of the pioneers in this development was A. L. Cauchy (1789-1857). In this project, students will read from his 1823 study of the definite integral for continuous functions . Then students will read from Bernard Riemann's 1854 paper, in which he developed a more general concept of the definite integral that could be applied to functions with infinite discontinuities.

Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett

Analysis

No abstract provided.

A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville

Topology

In a short paper published just one year prior to his thesis, Maurice Frechet gives a simple generalization one what we might today call the Extreme value theorem. This generalization is a simple matter of coming up with ``the right" definitions in order to make this work. In this mini PSP, we work through Frechet's entire 1.5 page paper to give an extreme value theorem in more general topological spaces, ones which, to use Frechet's newly coined term, are compact.

The Closure Operation As The Foundation Of Topology, Nicholas A. Scoville

Topology

No abstract provided.

Construction Of The Figurate Numbers, Jerry Lodder

Number Theory

No abstract provided.

Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett

Number Theory

No abstract provided.

Pascal's Triangle And Mathematical Induction, Jerry Lodder

Number Theory

No abstract provided.

Babylonian Numeration, Dominic Klyve

Number Theory

No abstract provided.

Primes, Divisibility, And Factoring, Dominic Klyve

Number Theory

No abstract provided.

Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett

Number Theory

No abstract provided.

Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg

Linear Algebra

No abstract provided.

Prevalence Of Typical Images In High School Geometry Textbooks, Megan N. Cannon

USF Tampa Graduate Theses and Dissertations

Visualization in mathematics can be discussed in many ways; it is a broad term that references physical visualization objects as well as the process in which we picture images and manipulate them in our minds. Research suggests that visualization can be a powerful tool in mathematics for intuitive understanding, providing and/or supporting proof and reasoning, and assisting in comprehension. The literature also reveals some difficulties related to the use of visualization, particularly how illustrations can mislead students if they are not comfortable seeing concepts represented in varied ways. However, despite the extensive research on the benefits and challenges of visualization …

Discovery Learning Plus Direct Instruction Equals Success: Modifying American Math Education In The Algebra Classroom, Sean P. Ferrill Mr.

Honors Projects

In light of both high American failure rates in algebra courses and the significant proportion of innumerate American students, this thesis examines a variety of effective educational methods in mathematics. Constructivism, discovery learning, traditional instruction, and the Japanese primary education system are all analyzed to incorporate effective education techniques. Based on the meta-analysis of each of these methods, a hybrid method has been constructed to adapt in the American Common Core algebra classroom.

The Resolved And Unresolved Conjectures Of R.D. Carmichael, Brian D. Beasley

ACMS Conference Proceedings 2017

Even before heading to Princeton University to work on his doctoral degree, Robert Daniel Carmichael started influencing the path of number theory in the 20th century. From his study of Euler's totient function to his discovery of the first absolute pseudoprime, he set the stage for years of productive research. This talk will present a brief overview of Carmichael's life, including his breadth of mathematical interests and his service on behalf of the Mathematical Association of America. It will focus mainly on his two most famous conjectures- which one has been settled, and which one remains open to this day?

"Big Idea" Reflection Assignments For Learning And Valuing Mathematics, Jeremy Case, Mark Colgan

ACMS Conference Proceedings 2017

While participating in a Faculty Learning Community, we explored the "big questions" we wanted our students to take away from our mathematics courses. We called these questions the Big Ideas of the course and developed a Big Ideas Reflection Assignment, which we continue to assign at the end of each of our courses. Students are able to demonstrate understanding and application of their learning as well as their values and appreciation of mathematics. The assignment encourages students to move beyond a focus on technique and symbolic manipulations towards a broader and more holistic approach, including making connections between their learning …

Using Real-World Team Projects: A Pedagogical Framework, Mike Leih

ACMS Conference Proceedings 2017

The use of team projects in a program capstone course for computer science or information systems majors has been a popular method for reinforcing and assessing program learning objectives for students in their final semester. Using real-world group projects as a learning activity is an excellent pedagogical approach in helping students develop critical thinking, team work, real-world problem solving, and communication skills. However, real-world group projects also provide many challenges to both the instructor and students alike. Instructors or students must find real-world projects appropriate for the learning objectives in the course. Instructors must determine how to provide teams with …

Variations On The Calculus Sequence, Christopher Micklewright

ACMS Conference Proceedings 2017

Many institutions have embraced a standard format for the Calculus sequence, comprising three four-credit courses covering a fairly consistent set of topics. While there is much to recommend this approach, it still leaves some fantastic concepts rushed or untouched, and it can be argued that it demands too much of students with weaker backgrounds. As such, some schools have experimented with variations on the standard format. In this talk, I will present the model that my institution currently uses, exploring the strengths and weaknesses of our particular approach. I will also suggest ideas, developed in conversation with other ACMS members …

The Topology Of Harry Potter: Exploring Higher Dimensions In Young Adult Fantasy Literature, Sarah Klanderman, Alexa Schut, Dave Klanderman, William Boerman-Cornell

ACMS Conference Proceedings 2017

As one of the most beloved series in children’s literature today, the Harry Potter books excite students of all ages with the adventures of living in a magical world. Magical objects (e.g., bottom-less handbags, the Knight Bus, time turners, and moving portraits) can inspire generalizations to mathematical concepts that would be relevant in an undergraduate geometry or topology course. Intuitive explanations for some of the magical objects connect to abstract mathematical ideas. We
offer a typology with a total of five categories, including Three Dimensions in Two Dimensions, Higher Dimensions in Three Dimensions, Two and Three Dimensional Movement, Higher Dimensional …