Science and Mathematics Education Commons^™

Technology Use In The Middle School Mathematics Classroom, Heather Prestegord

Mathematics Graduate Theses

This paper will examine the outcomes of using technology in middle school mathematics. The author will find research on how implementing technology affects students’ ability to learn mathematics. The author will also analyze if teachers are incorporating technology effectively and how teachers can be better equipped to successfully use technology in the middle school mathematics classroom.

Factors That Contribute To Persistence And Retention Of Underrepresented Minority Undergraduate Students In Science, Technology, Engineering, And Mathematics (Stem), Sidney Kirk Mitchell

Dissertations

The objective of this research was to identify specific factors that contribute to underrepresented minority (African American, Hispanic, Native American) undergraduate students‟ success in STEM disciplines at a regional university during the 2007-2010 timeframe. As more underrepresented minority (URM) students complete STEM degrees, many will possess the skills to become part of the domestic human capital needed to meet U. S. workforce demands and enhance the nation‟s STEM innovation. According to Burke and Mattis (2007), the lack of URM students in STEM education and in the workforce is one of the major contributors to STEM shortages in the United States. …

Investigating Macroscopic, Submicroscopic, And Symbolic Connections In A College-Level General Chemistry Laboratory, Felicia Culver Thadison

Dissertations

Explanations of chemical phenomena rely on understanding the behavior of submicroscopic particles. Because this level is “invisible,” it is described using symbols such as models, diagrams and equations. For this reason, students often view chemistry as a “difficult” subject. The laboratory offers a unique opportunity for the students to experience chemistry macroscopically as well as symbolically. The purpose of this investigation was to determine how chemistry lab students explained chemical phenomenon on the macroscopic, submicroscopic, and representational/symbolic level. The participants were undergraduate students enrolled in an introductory level general chemistry lab course. Students’ background information (gender, the number of previous …

Investigating The Effects Of Addition With Regrouping Strategy Instruction Among Elementary Students With Learning Disabilities, Christi Miller Carmack

UNLV Theses, Dissertations, Professional Papers, and Capstones

Many students, specifically those with learning disabilities, struggle to master foundational computation skills such as addition with regrouping. With this in mind, the purpose of this research was to examine the effects of strategy instruction that involved the use of the concrete-representational-abstract teaching sequence on the addition with regrouping computation and word problem-solving skills of students with learning disabilities. This study involved the use of a multiple probe across participants design with two replications. The participants included nine second through sixth graders who had been identified as having a learning disability and were demonstrating mathematics difficulties. There were three females …

Incorporating Case Studies Into An Undergraduate Genetics Course, Marlene Murray

Faculty Publications

Genetics is considered one of the most challenging courses in the biology curricula at both the secondary and post secondary levels. Case based teaching has been shown to improve student perception and performance outcomes in both non-science and science courses. Thus in an effort to improve outcomes, case studies were integrated into an undergraduate genetics course as a supplement to lecture and replacement to recitation. Student perception and performance when case studies were used was compared to two previous years before the incorporation of case studies. Student course evaluations, pre and post surveys of student knowledge, and exam scores indicated …

A Mathematician Weighs In On The Evolution Debate, Kris H. Green

Journal of Humanistic Mathematics

There are a variety of reasons underlying the lack of public acceptance for the theory of evolution in the United States. An overlooked cause is related to problems with the mathematics curriculum in the K-12 setting. In this essay, we examine this relationship and propose changes to the mathematics curriculum that could improve mathematical thinking while also providing a basis for understanding theories, like evolution, that are poorly understood.

On Doing Mathematics, Sue Vanhattum

Journal of Humanistic Mathematics

Who is a mathematician? What does it mean to do mathematics? I discuss my process in solving a math problem, and what it meant to me.

Covariant Representations Of C*-Dynamical Systems Involving Compact Groups, Firuz Kamalov

Department of Mathematics: Dissertations, Theses, and Student Research

Given a C*-dynamical system (A, G, σ) the crossed product C*-algebra A x _σG encodes the action of G on A. By the universal property of A x _σG there exists a one to one correspondence between the set all covariant representations of the system (A, G, σ) and the set of all *-representations of A x _σG. Therefore, the study of representations of A x _σG is equivalent to that of covariant representations of (A, G, σ).

We study induced covariant representations of systems involving compact groups. We prove that every irreducible (resp. factor) covariant …

Computational Insight With Monte Carlo Simulations, Boyan Kostadinov

Publications and Research

We introduce Monte Carlo simulations for estimating areas by playing a game of "darts". We also introduce simulations of random walks. We use compact, vectorized programming, based on the R language, for all computer simulations and visualizations, aimed at high school students. This presentation is based on the Invited, prime time lecture given at the summer camp for gifted high school students at City College of New York, July 13, 2011.

How Student Positioning Can Lead To Failure In Inquiry-Based Classrooms, Kelly Beatrice Campbell

Theses and Dissertations

In an effort to improve mathematics instruction, I studied how the positions students choose or are pressed to take on can lead to failure in an inquiry-based classroom. Positioning refers to the temporary roles that a student or a teacher can place each other in or take on in a given classroom environment. Since positions are constructed and maintained by language use, I drew from positioning theory and discourse theory for my theoretical framework. From analyzing transcripts of classroom episodes and interviews with the teacher and a student, I identified common positions that the teacher and the student took on. …

Parts Of The Whole: An Algebra Lesson, Dorothy Wallace

Numeracy

This column draws on research of Eon Harper to demonstrate how an understanding of his proposed stages of algebra acquisition would inform a systemic overhaul of algebra education. Harper's stages also explain why students may pass a series of algebra courses yet still be unable to make sense of calculus, as well as offering insight on what aspects of algebra support quantitative literacy.

Reducing Math Anxiety: Findings From Incorporating Service Learning Into A Quantitative Reasoning Course At Seattle University, Allison Henrich, Kristi Lee

Numeracy

How might one teach mathematics to math-anxious students and at the same time reduce their math anxiety? This paper describes what we found when we incorporated a service learning component into a quantitative reasoning course at Seattle University in Fall 2010 (20 students) and Spring 2011 (28 students). The course is taken primarily by humanities majors, many of whom would not take a course in math if they didn’t need to satisfy the university’s core requirement. For the service learning component, each student met with and tutored children at local schools for 1-2 hours per week (total about 15 service …

Quantitative Reasoning In The Contemporary World, 3: Assessing Student Learning, Stuart Boersma, Caren Diefenderfer, Shannon W. Dingman, Bernard L. Madison

Numeracy

In this third paper in a series describing the Quantitative Reasoning in the Contemporary World course, the authors provide an adaptation of the Association of American Colleges and Universities quantitative literacy VALUE rubric. Describing achievement levels in six core competencies (interpretation, representation, calculation, analysis/synthesis, and communication), the resulting Quantitative Literacy Assessment Rubric (QLAR) is applicable to grading student work and has exhibited a high degree of reliability in two separate scoring tests (97% and 88% respectively). The distribution of the six core competencies across the 24 case studies in the authors’ quantitative reasoning casebook shows that interpretation, calculation, and analysis/synthesis …

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 …

Quantitative Literacy At Michigan State University, 2: Connection To Financial Literacy, Dennis Gilliland, Vince Melfi, Alla Sikorskii, Edward Corcoran, Eleanor Melfi

Numeracy

The lack of capability of making financial decisions has been recently described for the adult United States population. A concerted effort to increase awareness of this crisis, to improve education in quantitative and financial literacy, and to simplify financial decision-making processes is critical to the solution. This paper describes a study that was undertaken to explore the relationship between quantitative literacy and financial literacy for entering college freshmen. In summer 2010, incoming freshmen to Michigan State University were assessed. Well-tested financial literacy items and validated quantitative literacy assessment instruments were administered to 531 subjects. Logistic regression models were used to …

Quantitative Literacy At Michigan State University, 1: Development And Initial Evaluation Of The Assessment, Alla Sikorskii, Vince Melfi, Dennis Gilliland, Jennifer Kaplan, Suzie Ahn

Numeracy

Development, psychometric testing, and the results of the administration of a quantitative literacy (QL) assessment to undergraduate students are described. Three forms were developed covering a wide range of skills, contexts, and quantitative information presentation formats. Following item generation and revision based on preliminary testing and cognitive interviewing, a total of 3,701 consented undergraduate students at Michigan State University completed one of the three forms. Two of the forms contained 14 multiple-choice items, and one form contained 17 multiple-choice items. All forms were completed by students in less than 30 minutes. Evidence of validity and reliability were obtained for the …

Development Of An Assessment Of Quantitative Literacy For Miami University, Rose Marie Ward, Monica C. Schneider, James D. Kiper

Numeracy

Quantitative Literacy is a competence as important as general literacy; yet, while writing requirements are seemingly ubiquitous across the college curriculum, quantitative literacy requirements are not. The current project provides preliminary evidence of the reliability and validity of a quantitative literacy measure suitable for delivery online. A sample of 188 undergraduate students from Miami University, a midsize university in the midwestern U.S., participated in the current study. Scores on the measure, were inversely related to statistical/mathematical anxiety measures, directly related to subjective assessment of numeracy, and did not differ across gender or year in school. The resulting measure provides a …

Communicating Quantitative Literacy: An Examination Of Open-Ended Assessment Items In Timss, Nals, Ials, And Pisa, Karl W. Kosko, Jesse L. M. Wilkins

Numeracy

Quantitative Literacy (QL) has been described as the skill set an individual uses when interacting with the world in a quantitative manner. A necessary component of this interaction is communication. To this end, assessments of QL have included open-ended items as a means of including communicative aspects of QL. The present study sought to examine whether such open-ended items typically measured aspects of quantitative communication, as compared to mathematical communication, or mathematical skills. We focused on public-released items and rubrics from four of the most widely referenced assessments: the Third International Mathematics and Science Study (TIMSS-95): the National Adult Literacy …

A Quantitative Literacy View Of Natural Disasters And Nuclear Facilities, C. B. Connor

Numeracy

The March 11, 2011 earthquake, tsunami, and nuclear disaster in Tohoku, Japan, highlights the need to improve quantitative literacy (QL) in natural hazard assessment. A critical understanding of natural hazard assessments requires a sophisticated perspective on the mathematical and statistical tools used to estimate the odds of disaster, and the roles of data quality, model development, and subjective probability in estimation of uncertainty. Thus, improved QL is a basic requirement for improved decision-making about the safety of critical infrastructure, such as nuclear facilities.

A Leap Forward For Quantitative Literacy, H. L. Vacher

Numeracy

The Association of American College and Universities’ Learning Education and America’s Promise (LEAP) initiative has identified quantitative literacy (QL) as one of its Essential Learning Outcomes and classified it amongst five other Intellectual and Practical Skills such as inquiry and analysis, critical and creative thinking, and written and oral communication. This brings to mind a spreadsheet in which these transdisciplinary intellectual and practical skills are rows and academic disciplines are columns. With the view that the learning outcome QL is a row crossing mathematics and other disciplinary columns, this editorial considers how the papers in this and previous issues of …