Science and Mathematics Education Commons^™

Paper Abstracts (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

19th Conference Of The Associations Of Christians In The Mathematical Sciences, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Association of Christians in the Mathematical Sciences 19th Biennial Conference Proceedings, May 29 - June 1, 2011, Bethel University.

Mathematical Knowledge For Teaching And Visualizing Differential Geometry, Nathan Pinsky

HMC Senior Theses

In recent decades, education researchers have recognized the need for teachers to have a nuanced content knowledge in addition to pedagogical knowledge, but very little research was conducted into what this knowledge would entail. Beginning in 2008, math education researchers began to develop a theoretical framework for the mathematical knowledge needed for teaching, but their work focused primarily on elementary schools. I will present an analysis of the mathematical knowledge needed for teaching about the regular curves and surfaces, two important concepts in differential geometry which generalize to the advanced notion of a manifold, both in a college classroom 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.

Comparing The Impact Of Traditional And Modeling College Algebra Courses On Student Performance In Survey Of Calculus, Jerry West

Graduate Theses and Dissertations

Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to maximize students' potential in utilizing mathematics and gaining skills required in subsequent math-based courses when necessary. The Committee for Undergraduate Programs in Mathematics has gone through extensive work to help mathematics departments reform their college algebra courses in order to help students gain interest in the utilization of mathematics …

Mapcores 2012-2013 Assessment Report, Kristen Nairn, Pamela L. Bacon, Jim Crumley, Lynn Ziegler

MapCores Faculty Publications

This is a report showing the assessment results for the MapCores (MAthematics, Physics, COmputer science REsearch Scholars) program at the College of Saint Benedict. Started in 2009, MapCores is a cohort-based program designed to increase women's interest and achievement in mathematics, physics, computer science and engineering. The report was submitted for the National Science Foundation grant number 0965705.

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 …

Measuring A Circle: A Math Lesson For Grades 5-10, Robert C. Moore

Faculty Publications

This article is designed to promote teaching methods that engage students in active learning and result in deep conceptual understanding by offering a sample lesson to help students (grades 5-10, ages 10-15) answer questions about and gain a deeper understanding of how to measure the circumference and area of a circle.

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.

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 …

Developing A Stem Teacher Recruitment Pipeline, Kimberly Shaw, Cindy Ticknor, Tim Howard

Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)

The Columbus Region Academy of Future Teachers of STEM (CRAFT-STEM), a Phase I Robert Noyce Teacher Scholarship Program, combines internships and scholarships, an exciting summer STEM Honors Camp, a new Teaching Connections Seminar, and an impressive array of existing resources to recruit, prepare, and graduate an increasing number of STEM teachers committed to serving high need high schools.

Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn

Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)

The aim of this session is to demonstrate the tools used to help reinforce and recreate students’ conceptual knowledge of fractions, specifically targeting the unit of reference. These manipulatives will provide teachers with instructional support for Common Core Standards, which emphasize critical thinking skills and various representations of knowledge, specifically with fractions. Participants will become actively engaged in learning about these tools, including jumping on a number line floor mat, working with circular fraction pieces and placing fractions on a number line rope. By representing knowledge through circular and linear methods, students will use critical thinking skills and support will …

Trig-Star, James M. Anderson

Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)

A TRIG-STAR is a mathematics student who has demonstrated in competition that he or she is the most skilled among classmates in the practical application of trigonometry. The competition for the honor is a timed exercise which is the solving of a trigonometry problem that incorporates the use of right triangle formulas, circle formulas, the law of sines, and the law of cosines. The contest helps to promote careers in surveying and mapping to students at the High Schools across the country. The award is sponsored by the National Society of Professional Surveyors and cosponsored locally. State winners also have …

Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn

Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)

Many students are overwhelmed by mathematics because the language is too difficult, the teaching strategies are insufficient or they have lost motivation. With a recent emphasis on meeting the Common Core expectations, using manipulatives to eliminate misconceptions in the mathematical classroom has become even more prevalent. I explored the misconceptions that many students struggle with and provided possible methods of eliminating them at all levels for learning. During this investigation, I studied the effect of manipulatives on students’ understanding of fraction concepts and the students’ conceptions of the unit of reference when working with fraction word problems. I learned that …

Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

Journal of Humanistic Mathematics

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …

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.

Student Success In Subsequent Mathematics Courses After Taking Ma 004, Andrea Winchester

Summer Community of Scholars Posters (RCEU and HCR Combined Programs)

No abstract provided.

Math Department Newsletter, 2012-2013 (Year In Review), Mathematics Department

Mathematics Newsletter

No abstract provided.

Horizon Content Knowledge In The Work Of Teaching: A Focus On Planning, Nick Wasserman, Julianna Connelly Stockton

Mathematics Faculty Publications

Horizon content knowledge, one component of Ball et al.’s mathematical knowledge for teaching framework (e.g., Ball, Thames, & Phelps, 2008), has yet to reach adequate clarity and consensus in the field. Recently, various scholars have worked to further conceptualize and describe the mathematical horizon (e.g., Jakobsen, Thames & Ribeiro, 2013; Figueiras et al., 2011; Zazkis & Mamolo, 2011). In this communication, we identify some limitations in the ways such knowledge has thus far been described and offer an additional form of potential impact of horizon content knowledge on the work of teaching.

Investigating The Validity Of A Survey Intended To Gauge Mathematics Problem-Solving Disposition Along The Impulsive-Analytic Dimension, Miguel Mendoza

Open Access Theses & Dissertations

This study investigates the validity of the Likelihood-to-Act (LtA) survey developed to assess respondents' problem-solving disposition along the impulsive-analytic dimension. Sixteen pre-service teachers were strategically selected from a pool of 495 LtA survey respondents to participate in a semi-structured task-based interview approximately one hour in length. The interview consisted of three main parts: a problem solving section, a consistency section, and a classification section.

* Part 1 of the interview was developed to get interviewees to solve five open-response problems meant to elicit an impulsive response. Interviewees were also asked to verbalize their thought process in order for the researchers …

Increasing Automaticity, Sara Burns

Online Theses and Dissertations

Automaticity is defined as the process of developing fluency in mathematics and the ability to answer a basic math problem routinely. Automaticity is one of the most important skills that a student can possess in mathematics. While there are many ways that an educator can implement strategies to increase automaticity in the classroom, the purpose of this study was to determine which of these methods of implementation is more effective: requiring students to practice automaticity three times per week or requiring students to practice automaticity five times per week.

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 …

Color Models As Tools In Teaching Mathematics, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

In this paper we discuss various situations how color models and patterns can be used to simplify the study of abstract mathematics and serve as tools in understanding mathematical ideas. We illustrate the realization of such models through the development of advanced computer technology. In particular, we present how a computer algebra software such as Mathematica, or a dynamic geometry environment, can be utilized to facilitate the study of transformation geometry and group theory.

Using The Taylor Center To Teach Odes, Alexander Gofen

CODEE Journal

This article introduces a powerful ODE solver called the Taylor Center for PCs (http://taylorcenter.org/Gofen/) as a tool for teaching and performing numeric experiments with ODEs. The Taylor Center is an All-in-One GUI-style application for integrating ODEs by applying the modern Taylor Method (Automatic Differentiation). The Taylor Center also offers dynamic graphics (including 3D stereo vision). After a brief review of the features of the Taylor Center, we consider instructive examples of ODEs in various applications and also several particular examples illustrating intricacies of numeric integration. The article therefore continues the thesis of Borrelli and Coleman (CODEE Journal, http://www.codee.org/ref/CJ09-0157) that awareness …

The Awards Project: Promoting Good Practices In Award Selection, Betty Mayfield, Francis Su

All HMC Faculty Publications and Research

Every year the MAA honors many members of our community with a wide variety of prizes, awards, and certificates for excellence in teaching, writing, scholarship, and service (see maa.org/awards). The winners exemplify our ideals as an association; consequently, they are often viewed as role models and leaders. So it is important to ask: Do these awards, as a whole, reflect the outstanding contributions of the breadth of association membership?

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 …

Commutative Rings Graded By Abelian Groups, Brian P. Johnson

Department of Mathematics: Dissertations, Theses, and Student Research

Rings graded by Z and Z^d play a central role in algebraic geometry and commutative algebra, and the purpose of this thesis is to consider rings graded by any abelian group. A commutative ring is graded by an abelian group if the ring has a direct sum decomposition by additive subgroups of the ring indexed over the group, with the additional condition that multiplication in the ring is compatible with the group operation. In this thesis, we develop a theory of graded rings by defining analogues of familiar properties---such as chain conditions, dimension, and Cohen-Macaulayness. We then study the …