Mathematics Commons^™

Session B-1: Geometry In Art & Architecture, Julie Dowling

Professional Learning Day

Math is all around us! Discover how to implement geometry lessons using art and architecture that the students see around them every day.

Session A-2: Cycloids!, Ruth Dover

Professional Learning Day

This session includes a hands-on exploration to see graphs of different types of cycloids. Participants will use trigonometry to create the parametric equations for the graphs. This topic lends itself nicely to projects for pre-calculus students. Software will be shown to help see more examples and patterns.

The Impact And Effectiveness Of Student-Centered Classroom Structure, Amie P. Westberg

Mathematics Graduate Theses

The purpose of this paper is to explore the effectiveness of student-centered learning as an alternative classroom structure. It is important that we continually reflect on our teaching methods and explore alternatives that can help give our students the best chance to succeed. While the literature is mixed with regard to which classroom style is best, there are many sources showing the benefits of student-centered instruction over a strictly teacher- centered classroom. Sources also showed that teachers do not need to choose exclusively one style of teaching, and that a blended classroom using a variety of teaching styles can be …

Culturally Relevant Pedagogy: Secondary Mathematics In An Urban Classroom, Julia Glissmann North

Honors Program Theses

Research and test scores have shown that African-American, Latino, Native American, and other minority students are underachieving in secondary mathematics. This is concerning not only to school personnel – who are under pressure to have students perform well on standardized tests – but also to the future of the country. When teachers adopt a culturally relevant pedagogy, diverse students will have a better opportunity to learn and retain mathematical content. When academic content is taught in a culturally relevant way, students are able to retain the information, improve their performance in school, and become more informed participants in society. Through …

Using Topology To Explore Mathematics Education Reform, Carling Sugarman

HMC Senior Theses

Mathematics education is a constant topic of conversation in the United States. Many attempts have been made historically to reform teaching methods and improve student results. Particularly, past ideas have emphasized problem-solving to make math feel more applicable and enjoyable. Many have additionally tackled the widespread problem of “math anxiety” by creating lessons that are more discussion-based than drill-based to shift focus from speed and accuracy. In my project, I explored past reform goals and some added goals concerning students' perceptions of mathematics. To do so, I created and tested a pilot workshop in topology, a creative and intuitive field, …

A Primer For Mathematical Modeling, Marla A. Sole

Publications and Research

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school with the mathematics they will use outside of school. Instructors have found mathematical modeling difficult to teach. To successfully incorporate modeling activities I believe that curricular changes should be accompanied by professional development for curriculum developers, classroom teachers, and higher education professionals. This article serves as an introduction to modeling by …

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.

Can The Differentiated Math Classroom Be A Reality?, Carl Jeff Morris

Mathematics Graduate Theses

Imagine a math classroom that looked more like a Google workplace where collaboration, teamwork, and innovation are the centerpieces. Instead of just students sitting in rows passively learning about the nature of mathematics, picture a classroom of students in small circle discussing mathematics. This could range from groups working together on a problem solving strategy for a newly learned concept, students helping students using technology as an aid, another small group receiving intervention from the teacher, or individual students making or viewing instructional math videos. All of this according to research focused on classroom differentiation; specifically in middle school and …

Common Misconceptions And Instructional Best Practices For Teaching Fractions To Students In Grades Three, Four, And Five, Dan Fairchild

Mathematics Graduate Theses

This research paper will identify common misconceptions related to the teaching and learning fractions for students in grades three, four, and five. Different fraction subconstructs will be identified and instructional best practices will be identified for the teaching and learning of comparing fractions, ordering fractions, adding fractions, and subtracting fractions.

Finances & Algebra Too!, Anne J. Catlla, Jonathan Foster, Charlene Frazier

Arthur Vining Davis High Impact Fellows Projects

The focus of this project is to provide an application-based approach to teaching algebra 2. Students will study algebraic concepts and functions through the lens of personal finance. After each unit of study, students will complete a financial application project that will go into each student’s “financial” portfolio.

Student Centered Mathematics In An Isolated Skill Environment-Constructivist Methods In Mathematics, Amy Katherine Sorenson

Mathematics Graduate Theses

"A research paper submitted to the Faculty of the Department of Mathematics in partial fulfillment of the requirements for the degree of Master of Science in Elementary and Middle Mathematics Education"

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 …

Variation Of Instructor-Student Interactions In An Introductory Interactive Physics Course, Emily West, Cassandra Paul, David Webb, Wendell Potter

Faculty Publications

The physics instruction at UC Davis for life science majors takes place in a long-standing reformed large-enrollment physics course in which the discussion or laboratory instructors (primarily graduate student teaching assistants) implement the interactive-engagement (IE) elements of the course. Because so many different instructors participate in disseminating the IE course elements, we find it essential to the instructors’ professional development to observe and document the student-instructor interactions within the classroom. Out of this effort, we have developed a computerized real-time instructor observation tool (RIOT) to take data of student-instructor interactions. We use the RIOT to observe 29 different instructors for …

Creating An Interdisciplinary Research Course In Mathematical Ecology, Glenn Ledder, Brigitte Tenhumberg

School of Biological Sciences: Faculty Publications

An integrated interdisciplinary research course in biology and mathematics is useful for recruiting students to interdisciplinary research careers, but there are difficulties involved in creating and implementing it. We describe the genesis, objectives, design policies, and structure of the Research Skills in Theoretical Ecology course at the University of Nebraska–Lincoln and discuss the difficulties that can arise in designing and implementing interdisciplinary courses.

An Interdisciplinary Research Course In Theoretical Ecology For Young Undergraduates, Glenn Ledder, Brigitte Tenhumberg, G. Travis Adams

School of Biological Sciences: Faculty Publications

As part of an interdepartmental effort to attract promising young students to research at the interface between mathematics and biology, we created a course in which groups of recent high school graduates and first-year college students conducted a research project in insect population dynamics. The students set up experiments, collected data, used the data to develop mathematical models, tested their models against further experiments, and prepared their results for dissemination. The course was self-contained in that the lecture portion developed the mathematical, statistical, and biological background needed for the research. A special writing component helped students learn the principles of …

Effects Of Tracking Students In A Secondary Mathematics Classroom, Nicole Seyfried

Mathematics Graduate Theses

This paper evaluates current research on the effect of grouping students of comparable abilities, a process known as tracking, in a secondary mathematics classroom. The research explores questions regarding the advantages and the disadvantages of tracking students by ability; the manner in which tracking affects the achievement of students in homogeneous and heterogeneous settings, and the ways tracking affects the achievement gap. In addition, this paper answers the question of how tracking affects students’ self- concept and self-esteem. Lastly, it examines changes in teacher attitude with respect to each track level and the impact of ability grouping on classroom structure …

Cognitively Guided Instruction (Cgi): Whats The Point? A Look Into Cgi And Cgi’S Potential Role In An 8th Grade Mathematics Class, Bryan C. Anderson

Mathematics Graduate Theses

This study examined the current research that exists on Cognitively Guided Instruction (CGI) and how it would look when implemented into an 8th grade mathematics classroom. Additional questions examined are if CGI would develop strong student understanding between mathematical concepts and their real world applications; if CGI techniques and questioning impact the interest level of mathematics students; and what type of extra resources would be needed by teachers to implement Cognitively Guided Instruction into their curriculum. Although much of the CGI research has been done on elementary students, by also examining key algebra practices the author was able to synthesize …

How Ipads Can Be Used In The Math Classroom To Improve Student Learning, Katie Ann Garrity Smieja

Mathematics Graduate Theses

This study explores how iPads can be used to enhance student learning in the math classroom. The author reviews current literature to determine how iPads are being used to facilitate communication, formative assessment, and promising practices in math education such as discovery learning and use of spreadsheets, graphing calculators, and manipulatives. Additionally, challenges and drawbacks to using iPads in the classroom are examined. Research supports the use of iPads to provide students access to digital content including online discussion boards and practice activities with instant feedback. iPads can also be used as student response systems to engage students in instruction …

Mathematics Classrooms At The Middle School Level: Does Grouping Make A Difference In Achievement, Adam Smieja

Mathematics Graduate Theses

This paper reviewed related research on student achievement based on how students were grouped, homogeneously or heterogeneously. Questions examined were whether students performed better in heterogeneous or homogenous groupings and to what extent did high-, average-, and low-ability students perform better in a particular group. Results showed that high-ability students in homogeneous groupings had higher gains in achievement when compared to their counterparts in heterogeneous groupings. However, gains for these high-ability students were not statistically significant. On the contrary, average-, and low-ability students did show statistically significant gains in achievement in the heterogeneous groupings. Yet, despite their effectiveness, implementation of …

The Mathematics Portfolio: An Alternative Tool To Evaluate Students’ Progress, Marla A. Sole

Publications and Research

This article describes the need for more thorough and varied forms of assessment to evaluate students’ level of understanding in mathematics. Portfolios are one type of assessment tool that, when added to a teacher’s repertoire can improve students’ comprehension and retention and enable students to monitor their own progress and to take more responsibility for their own learning. Portfolio assignments can also help students and teachers to detect and remedy weaknesses and misunderstandings and can increase students’ self-confidence in mathematics. This article discusses what a portfolio is, gives an example of a unit portfolio used in an undergraduate Finite Mathematics …

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 …

Session D-3: Discrete Mathematics: A Great Curriculum Connector, Donald Porzio

Professional Learning Day

Many topics that fall under the umbrella of Discrete Mathematics cut across the traditional high school curriculum areas of algebra, geometry, and pre-calculus. Come try some classroom-ready hands-on Discrete Mathematics activities that illustrate the true interconnectedness of mathematics.

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 …

Extreme Math Makeover: Mathematics Assessment And Reporting In The Era Of The Common Core Standards, Glenn W. "Max" Mcgee

Publications & Research

This presentation discusses the need to develop high quality performance based assessments of the Common Core Mathematical Standards and Mathematical Practices. Several examples of performance assessments from high achieving countries as well as from the 2009 PISA test are included.

The Impact Of Manipulatives On Learning In The Elementary And Middle School Mathematics Classroom, Laura Dahl

Mathematics Graduate Theses

This paper is a review of research pertaining to the use of manipulatives in the elementary and middle school mathematics classrooms. It embodies the logic behind using manipulative materials in the classroom setting and the impact their use will have on student understanding and enjoyment for learning mathematical concepts. This research paper will identify the struggles and concerns of manipulative use along with the need of increased professional development and training for teachers to be better prepared for the daunting, yet rewarding challenges of successfully teaching mathematics.

2011-2012 Unlv Mcnair Journal, Cyndy Anang, Sajar Camara, Pamela Cornejo, Carla Antonieta Farcello, Ilse Anahi Garcia, Natiera Magnuson, William L. Mccurdy, Lorena Munoz, Maxym V. Myroshnychenko, Ricardo Rios, Theodore Waldeck, Barbara Wallen, Ana Zuniga, Brenda M. Aguilar, Tiffany Alexandra Alvarez, Daniel N. Erosa, Paige C. Espinosa, Carla Antonieta Farcello, Julienne Jochel Paraiso, Nathaniel Derek Phillipps, Carmen Vallin, Jacent N. Wamala, Ernesto Zamora-Ramos

McNair Journal

Journal articles based on research conducted by undergraduate students in the McNair Scholars Program

Table of Contents

Biography of Dr. Ronald E. McNair

Statements:

Dr. Neal J. Smatresk, UNLV President

Dr. Juanita P. Fain, Vice President of Student Affairs

Dr. William W. Sullivan, Associate Vice President for Retention and Outreach

Mr. Keith Rogers, Deputy Executive Director of the Center for Academic Enrichment and Outreach

McNair Scholars Institute Staff

Enhancing The Teaching And Learning Of Computational Estimation In Year 6, Paula Mildenhall

Theses: Doctorates and Masters

There have been repeated calls for computational estimation to have a more prominent position in mathematics teaching and learning but there is still little evidence that quality time is being spent on this topic. Estimating numerical quantities is a useful skill for people to be able to use in their everyday lives in order to meet their personal needs. It is also accepted that number sense is an important component of mathematics learning (McIntosh, Reys, Reys, Bana, & Farrell, 1997; Paterson, 2004) and that computational estimation is an important part of number sense (Edwards, 1984; Markovits & Sowder, 1988; Schoen, …

Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan

Department of Math & Statistics Faculty Publications

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …

Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan

Biology Faculty Publications

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …