Mathematics Commons^™

Using Geogebra To Explore Properties Of Circles In Euclidean Geometry, Erin Hanna

Masters Essays

No abstract provided.

An Introduction To Topology For The High School Student, Nathaniel Ferron

Masters Essays

No abstract provided.

Ready, Set, Learn, Michael G. Wright

Masters Essays

No abstract provided.

Mathematical Justice?, Valorie L. Zonnefeld

Faculty Work Comprehensive List

"I’d like to suggest the possibility of guiding students toward more just ways of seeing and being in the world in mathematics class."

Posting about human flourishing through mathematical study­­­­­­­­ from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation.

http://inallthings.org/mathematical-justice/

Domain Coloring And The Argument Principle, Frank A. Farris

Mathematics and Computer Science

The domain-coloring algorithm allows us to visualize complex-valued functions on the plane in a single image—an alternative to before-and-after mapping diagrams. It helps us see when a function is analytic and aids in understanding contour integrals. The culmination of this article is a visual discovery and subsequent proof of the Argument Principle, which relates the count of poles and zeros of a meromorphic function inside a contour to the accumulated change in argument of the function around the contour. Throughout, I offer connections to standard learning goals of courses in complex variables.

Teachers' Theories Of Teaching And Learning And The Use Of Math Interventions, Nicole P. Jones

Walden Dissertations and Doctoral Studies

Despite the academic gap between students with learning disabilities (LD) and their nondisabled peers, schools continue to educate students with LD in regular education classrooms. In secondary math classes, such as Algebra 1, students with LD have high percentages of failure. The purpose of this cross-sectional study was to examine the relationship between teachers' personal theories of teaching and learning and their use of math interventions. Fox's (1983) theoretical framework of teaching and learning was used as a conceptual lens. Surveys were administered to 20 high school math teachers in an urban Northeastern U.S. school district. An ordinal logistic regression …

Freedom Through Inquiry, Francis Su

All HMC Faculty Publications and Research

I delivered this speech at the Inquiry‐Based Learning Forum & 19th Annual Legacy of R.L. Moore Conference on August 4, 2016. It is partly an homage to an influential teacher, partly an excuse to articulate what makes some styles of teaching so effective, and partly an excuse to talk about difficult issues facing our nation and our classrooms today.

Teaching Differential Equations Through A Modeling First Approach, Brian Winkel

Journal of Humanistic Mathematics

No abstract provided.

Teachers' Perceptions Of Manipulatives During Middle School Math Instruction, Angela L. Vizzi

Walden Dissertations and Doctoral Studies

In a Colorado school district, school personnel and parents were concerned that middle school math proficiency levels were low for 2011-2014 and math teachers were not using manipulatives in their classes to increase math performance. The district's math coordinator did not foresee providing specific professional development (PD) for math manipulative use to address these concerns. Without this PD, math teachers may be ill-quipped to teach math concepts when using manipulatives, which, in turn, could lead to further poor math performance. The purpose of this qualitative bounded collective case study was to explore middle school teachers' perceptions of PD and perceived …

Critical Thinking And High-Level Discourse In A 1:1 Environment, Ryan G. Zonnefeld, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Learn about our experiences co-teaching a K–8 methods course using 1:1 tablets in a high-tech lab. This innovative course included a move away from a textbook to a dynamic research-based curriculum supported by NCTM resources and CCSSM as well as integral utilization of apps, web 2.0 tools, and professional learning networks.

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.

Mathematics Education In A Multilingual And Multicultural Environment, Anjum Halai, Richard Barwell

Book Chapters / Conference Papers

No abstract provided.

Teac 451p: Learning And Teaching Principles And Practices (Secondary Mathematics)—A Peer Review Of Teaching Project Benchmark Portfolio, Lorraine Males

UNL Faculty Course Portfolios

The goal of my peer review portfolio was to better understand how to improve students' learning of how to teach secondary mathematics in reform-oriented ways. Most students that pursue admission into the Secondary Mathematics Teacher Education Program have little to no experience learning mathematics in reform-oriented ways. These preservice teachers (PSTs) were “successful” in mathematics courses in middle and high school, most of them taking honors or accelerated courses. However, many of these PSTs did not have opportunities to engage as active participants in their own learning and develop complex cognitive skills and processes, the focus of reform-oriented instruction. This …

Traditional Lecture Versus An Activity Approach For Teaching Statistics: A Comparison Of Outcomes, Jennifer L. Loveland

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many educational researchers have proposed teaching statistics with less lecture and more active learning methods. However, there are only a few comparative studies that have taught one section of statistics with lectures and one section with activity-based methods; of those studies, the results are contradictory. To address the need for more research on the actual effectiveness of active learning methods in introductory statistics, this research study was undertaken.

An introductory, university level course was divided into two sections. One section was taught entirely with traditional lecture. The other section was taught using active learning methods and a minimal amount of …

Inclusion: Problems And Potential Solutions In Mathematics Instruction, Lynnea Marie Salscheider

Mathematics Graduate Theses

The purpose of this study was (1) to identify and describe the attitudes and beliefs of general and special education teachers about inclusion and (2) to identify significant recommendations based on teacher attitudes for improving the teaching of mathematics to special needs students using inclusion.

Differentiated Instruction In The High School Mathematics Classroom, Sherri Kruger

Mathematics Graduate Theses

The purpose of this research paper is to address the challenges of instruction within a classroom whose census is a diverse mixture of student mathematical abilities. The diverse ability of low and high achieving students all required to master the different strands of mathematics creates problems for instructors and students to stay engaged and actively moving forward deepening and widening their knowledge base. This paper will focus on differentiated lessons, assessments, and projects of a mathematics classroom in a public high school.

Improving Student Achievement Through Feedback, Jennifer L. Mchlachlan

Mathematics Graduate Theses

This paper reviews the current research that exists on feedback given to students in an educational setting. Questions examined were what characteristics make feedback effective, what are the effects on student achievement if feedback is available to students in a math classroom and does timing of the feedback given play a role in its effectiveness. Results showed that feedback is effective if it is descriptive, including both strengths and weaknesses. Feedback given in small doses throughout the learning process, so as not to overwhelm students, has also proven effective. The research shows that the effect of feedback on student achievement …

A Data Generating Review That Bops, Twists And Pulls At Misconceptions, Kimberly Gardner

Faculty Articles

Statistics is an integral part of the K-12 mathematics curriculum (age 5-18). Naturally, students construct misconceptions of what they learn. This article discusses The Bop It^© Challenge, a review activity assesses student understanding and reveals their misundertandings of statistical concepts.

The Lesson Of Grace In Teaching, Francis Su

All HMC Faculty Publications and Research

I want to talk about the biggest life lesson that I have learned, and that I continue to learn over and over again. It is deep and profound. It has changed the way I relate with people. It has reshaped my academic life. And it continually renovates the way I approach my students.

A Comparison Of Two Teaching Methods For Pediatric Medication Administration: Multimedia And Text-Based Modules, Renee Granados

Doctoral Dissertations

A Comparison of Two Teaching Methods for Pediatrics: Multimedia and Text-based Modules to Teach Pediatric Medication Administration

Nurse educators are in a position to design and develop effective methods that consider the cognitive structures and how the mind processes information to teach pediatric medication content to nursing students. The majority of methods teaching medication administration use only one mode: the visual mode. One mode to present leaning material does not take advantage of the additive effects of using two modes to present learning material.

The purpose of the study was to compare the effectiveness of two teaching methods to present …

How To Reach All Types Of Learners Through The Use Of Manupulatives In Grades Three, Four, And Five, Cadie Fairchild

Mathematics Graduate Theses

This paper is an examination of research concerning the use of manipulatives with third, fourth, and fifth grade mathematics instruction. The research discusses the power of child discovery, stages of representation, using manipulatives to support learning, eliminating manipulatives prematurely, and eliminating negative stereotypes linked to manipulative use. A major concern of teaching with manipulatives is the knowledge of the teacher. An educator’s role is to provide the best learning opportunities for students. Research reviewed for this paper indicates frequent hands on activities using manipulatives. They need to be aware of the many learning stages and how to address each individual …

Professional Learning Community Impacts On Student Achievement In Middle School Mathematics, Jessica Stuewe

Mathematics Graduate Theses

The development of professional learning communities in middle level education is a relatively new and trendy concept sweeping the nation. School professional development committees are training large numbers of teachers through conferences, book studies and online webinars on how to collaborate to improve student learning. This research will explore the impact of the first year of implementation of a departmental professional learning community (PLC) on student achievement at the middle school level in the content area of mathematics. Student standardized test scores from 2010 and 2011 will be compared as a measure of success of the PLC. Teacher surveys are …

Some Results On Cryptanalysis Of Rsa And Factorization., Santanu Sarkar Dr.

Doctoral Theses

In this thesis, we propose some new results in Cryptanalysis of RSA and related Factorization problems. Till date, the best known algorithm to solve the Integer Factorization problem is the Number Field Sieve, which has a runtime greater than exp(log1/3 N) for factoring an integer N. However, if one obtains certain information about the RSA parameters, there are algorithms which can factor the RSA modulus N = pq quite efficiently. The intention of this thesis is to identify such weaknesses of the RSA cryptosystem and its variants. Further we study results related to factorization.In Africacrypt 2008, Nitaj presented a class …

What Does It Take To Teach Nonmajors Effectively?, Feryal Alayont, Gizem Karaali, Lerna Pehlivan

Pomona Faculty Publications and Research

Most MAA members teach mathematics at the college level, and many often teach courses intended for nonmajors. Indeed this is one of the main responsibilities of a mathematics department: offering service courses for client departments and general education courses for nonmajors. The three of us have been thinking about the question of how to teach nonmajors successfully for a while now. Finally we decided on a time-tested method of figuring things out: if you don't know what to do, ask the experts. We organized a panel titled "Effective Strategies for Teaching Classes for Nonmajors" for MAA MathFest 2012 and invited …

Humanistic Mathematics: An Oxymoron?, Gizem Karaali

Pomona Faculty Publications and Research

Mathematics faculty are trained as mathematicians, first and foremost. If we did not experience the soul-expanding possibilities of liberal education during our own undergraduate years, we may hesitate to bridge disciplinary divides when pursuing our core human need to inquire and understand. Although most mathematicians I know are amazing teachers, communicators, and mentors, many still teach the same material that their professors and their professors’ professors taught. This time-tested approach can be powerful, fascinating, and even quite entertaining. But it can also seem far removed from the world we inhabit. Yes, we teach “real world applications” of mathematical concepts. Yet …

Adventures In Teaching: A Professor Goes To High School To Learn About Teaching Math, Darryl H. Yong

All HMC Faculty Publications and Research

During the 2009–2010 academic year I did something unusual for a university mathematician on sabbatical: I taught high school mathematics in a large urban school district. This might not be so strange except that my school does not have a teacher preparation program and only graduates a few students per year who intend to be teachers. Why did I do this? I, like many of you, am deeply concerned about mathematics education and I wanted to see what a typical high school in my city is like. Because I regularly work with high school mathematics teachers, I wanted to experience …

A Wealth Of Numbers: An Anthology Of 500 Years Of Popular Mathematics Writing, By Benjamin Wardhaugh. Princeton University Press: Princeton, 2012 (Book Review), John A. Adam

Mathematics & Statistics Faculty Publications

(First paragraph) To describe the landscape encompassed by this book I can do no better than to quote the dust jacket: "A Wealth of Numbers includes recreational, classroom, and work mathematics; mathematical histories and biographies; accounts of higher mathematics; explanations of mathematical instruments; discussions of how math should be taught and learned; reflections on the place of math in the world; and math in fiction and humor." More such details can be found on the Princeton University Press website. I shall use this as a point of departure to describe the highlights of my own trajectory through the book. Not …

Constructivist And Behaviorist Approaches: Development And Initial Evaluation Of A Teaching Practice Scale For Introductory Statistics At The College Level, Rossi A. Hassad

Numeracy

This study examined the teaching practices of 227 college instructors of introductory statistics from the health and behavioral sciences. Using primarily multidimensional scaling (MDS) techniques, a two-dimensional, 10-item teaching-practice scale, TISS (Teaching of Introductory Statistics Scale), was developed. The two dimensions (subscales) are characterized as constructivist and behaviorist; they are orthogonal. Criterion validity of the TISS was established in relation to instructors’ attitude toward teaching, and acceptable levels of reliability were obtained. A significantly higher level of behaviorist practice (less reform-oriented) was reported by instructors from the U.S., as well as instructors with academic degrees in mathematics and engineering, whereas …

Teaching Research: Encouraging Discoveries, Francis E. Su

All HMC Faculty Publications and Research

What does it take to turn a learner into a discoverer? Or to turn a teacher into a co-adventurer? A handful of experiences—from teaching a middle-school math class to doing research with undergraduates—have changed the way that I would answer these questions. Some of the lessons I’ve learned have surprised me.

Teaching Probability Through Use Of An Applet, Melissa Gregory Jackson

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

The use of technology in the classroom is an ongoing debate by educators. Many teachers consider it to be a valuable teaching tool. Despite the many advantages, there are also drawbacks in using technology. A Java applet is a particular kind of multimedia technology proven to be useful in education. Because of students' struggles with learning basic probability in Statistics 1040, I have created a probability applet to reinforce the concept of probability. The applet was tested with two Statistics 1040 classes. The majority of students agreed that they learned more about probability from using the applet. Several of the …