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Full-Text Articles in Physical Sciences and Mathematics

Reorganizing School Mathematics For Quantitative Literacy, Rick Gillman Jul 2010

Reorganizing School Mathematics For Quantitative Literacy, Rick Gillman

Numeracy

This paper offers an alternative curriculum for high school mathematics. It proposes replacing the Algebra-Geometry-Algebra rush to calculus model with one which focuses on improving student problem-solving skills and general quantitative literacy skills while reinforcing basic manipulative skills. Most of these goals are gained by expanding the current single-year algebra-one course into two years. The model proposes moving “learning to write proofs” from the traditional geometry course into a separate discrete mathematics course. It requires statistics for every student, and requires a senior-level modeling course for every college-going student. In addition, the proposed model creates opportunities for students to move …

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Spreadsheets Across The Curriculum, 1: The Idea And The Resource, H L Vacher, Emily Lardner Jul 2010

Spreadsheets Across The Curriculum, 1: The Idea And The Resource, H L Vacher, Emily Lardner

Numeracy

This paper introduces Spreadsheets Across the Curriculum, a workshop-based educational materials development project to build a resource to facilitate connecting mathematics and context in undergraduate college courses where mathematical problem solving is relevant. The central idea is “spreadsheet modules,” which, in essence, are elaborate word problems in the form of short PowerPoint presentations with embedded Excel spreadsheets. Students work through the presentations on their own, making and/or completing the spreadsheets displayed on the slides in order to perform calculations or draw graphs that address the issue (context) posed in the word problem. The end result of the project is the …

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Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community, Bernard L. Madison, Shannon W. Dingman Jul 2010

Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community, Bernard L. Madison, Shannon W. Dingman

Numeracy

Numerous questions about student learning of quantitative reasoning arose as we developed, taught and assessed the Quantitative Reasoning in the Contemporary World course described in the companion paper in this issue of Numeracy. In this paper, we present some of those questions and describe the context in which they arose. They fall into eight general problem areas: learning that is context-bound and does not easily transfer (i.e., situated learning); the need for a productive disposition regarding mathematics; the connection between QL and mathematical proficiency; the persistence of students, despite our efforts, for using the wrong base for percents; the inconsistent …

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Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:, Shannon W. Dingman, Bernard L. Madison Jul 2010

Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:, Shannon W. Dingman, Bernard L. Madison

Numeracy

The authors describe successes and challenges in developing a QL-friendly course at the University of Arkansas. This work is part of a three-year NSF project Quantitative Reasoning in the Contemporary World (QRCW) that supported the expansion of the course. The course, MATH 2183, began experimentally in Fall 2004 as a section of finite mathematics known informally as “News Math” for 26 students from arts and humanities disciplines. Over the past six years, the course has evolved and now MATH 2183 is approved to satisfy the College of Arts and Sciences mathematics requirement for the Bachelor of Arts degree. In 2009-2010, …

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Quantitative Literacy: Does It Work? Evaluation Of Student Outcomes At Colby-Sawyer College, Benjamin Steele, Semra Kilic-Bahi Jul 2010

Quantitative Literacy: Does It Work? Evaluation Of Student Outcomes At Colby-Sawyer College, Benjamin Steele, Semra Kilic-Bahi

Numeracy

Colby-Sawyer College has adopted a mission for quantitative literacy (QL) to give students the “necessary skills to understand and use quantitative information in their personal and professional lives.” We have implemented an across-the-curriculum approach to develop these skills. As part of this QL program, we administer two assessment tests, one in basic mathematical skills and one that applies those skills, plus an attitude survey to both freshmen and seniors. Three years of data show that seniors score about 10 percentage points higher than freshmen on these tests. However, seniors still scored below 55 percent on both tests, and many cannot …

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Science Literacy: Hand In Glove With Numeracy, Gerry G. Meisels Jul 2010

Science Literacy: Hand In Glove With Numeracy, Gerry G. Meisels

Numeracy

Science Literacy requires numeracy as part of its foundation, and much of Numeracy draws on examples and applications from the sciences. They share the goal of creating a society that is mathematics numerate and science literate, and are interrelated. National priorities to strengthen both among all our students are driven by practical considerations of economic competitiveness that increasingly depend on technological innovation. It is also critical to each individual for long-term job opportunities and for informed citizenship. With up to 80% of 21st century jobs requiring mathematics and science skills, a large majority of the 2,900,000 students who graduate from …

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Advancing Assessment Of Quantitative And Scientific Reasoning, Donna L. Sundre, Amy D. Thelk Jul 2010

Advancing Assessment Of Quantitative And Scientific Reasoning, Donna L. Sundre, Amy D. Thelk

Numeracy

Advancing Assessment of Quantitative and Scientific Reasoning is a four-year NSF Project (DUE-0618599) in part designed to evaluate the generalizability of quantitative (QR) and scientific reasoning (SR) assessment instruments created at James Madison University to four other four-year institutions with very distinct missions and student demographics. This article describes the methods, results, and findings we obtained in our studies. More specifically, we describe how to conduct content-alignment exercises in which faculty members map each item from a prospective test to the student learning objectives taught at the institution. Our results indicated that 92-100% of the QR and SR items were …

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The History Of Mathematics As A Pedagogical Tool: Teaching The Integral Of The Secant Via Mercator’S Projection, Nick Haverhals, Matt Roscoe Jul 2010

The History Of Mathematics As A Pedagogical Tool: Teaching The Integral Of The Secant Via Mercator’S Projection, Nick Haverhals, Matt Roscoe

The Mathematics Enthusiast

This article explores the use of the history of mathematics as a pedagogical tool for the teaching and learning of mathematics. In particular, we draw on the mathematically pedigreed but misunderstood development of the Mercator projection and its connection to the integral of the secant function. We discuss the merits and the possible pitfalls of this approach based on a teaching module with undergraduate students. The appendices contain activities that can be implemented as an enrichment activity in a Calculus course.

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Guest Editorial: A Starting Point, Ke Wu Norman Jul 2010

Guest Editorial: A Starting Point, Ke Wu Norman

The Mathematics Enthusiast

As a new faculty member in the Department of Mathematical Sciences at the University since Fall 2008, I was eager to find possible research partners with whom to build a research network for long term collaboration and support. I wondered “Where shall I start?” and “Whom shall I invite?” After several conversations with my colleague, Dr. Bharath Sriraman, and many phone calls to my good friend, Dr. Anne Kern, a new faculty at the University of Idaho, we came up with the idea of forming a support group of female faculty in the fields of mathematics and science education in …

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Tme Volume 7, Numbers 2 And 3 Jul 2010

Tme Volume 7, Numbers 2 And 3

The Mathematics Enthusiast

No abstract provided.

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Population Models With Allee Effect: A New Model, Saber Elaydi, Robert J. Sacker Jul 2010

Population Models With Allee Effect: A New Model, Saber Elaydi, Robert J. Sacker

Mathematics Faculty Research

In this paper we develop several mathematical models of Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model that is our focus of study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.

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Extension Of Plurisubharmonic Functions With Growth Control, Dan Coman, Vincent Guedj, Ahmed Zeriahi Jul 2010

Extension Of Plurisubharmonic Functions With Growth Control, Dan Coman, Vincent Guedj, Ahmed Zeriahi

Mathematics - All Scholarship

Suppose that X is an analytic subvariety of a Stein manifold M and that varphi is a plurisubharmonic (psh) function on X which is dominated by a continuous psh exhaustion function u of M. Given any number c > 1, we show that varphi admits a psh extension to M which is dominated by cu on M. We use this result to prove that any omega-psh function on a subvariety of the complex projective space is the restriction of a global omega-psh function, where omega is the Fubini-Study Kahler form.

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The Sixth International Mathematics Education And Society Conference: Finding Freedom In A Mathematics Education Ghetto, David W. Stinson Jul 2010

The Sixth International Mathematics Education And Society Conference: Finding Freedom In A Mathematics Education Ghetto, David W. Stinson

Middle-Secondary Education and Instructional Technology Faculty Publications

In this editorial, the author relates his experiences at the Sixth International Mathematics Education and Society Conference, held March 2010 in Berlin, Germany, and explores whether urban mathematics educators can navigate historically marginalized racial, ethnic, religious, cultural, gendered, sexual, intellectual, and other communities to find freedom in a what he sees as a "mathematics education ghetto."

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The Nuts And Bolts: A Review Of Culturally Specific Pedagogy In The Mathematics Classroom: Strategies For Teachers And Students, Shonda Lemons-Smith Jul 2010

The Nuts And Bolts: A Review Of Culturally Specific Pedagogy In The Mathematics Classroom: Strategies For Teachers And Students, Shonda Lemons-Smith

Middle-Secondary Education and Instructional Technology Faculty Publications

The author reviews Jacqueline Leonard's Culturally Specific Pedagogy in the Mathematics Classroom: Strategies for Teachers and Students.

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Collaborative Evaluative Inquiry: A Model For Improving Mathematics Instruction In Urban Elementary Schools, Iman C. Chahine, Lesa M. Covington Clarkson Jul 2010

Collaborative Evaluative Inquiry: A Model For Improving Mathematics Instruction In Urban Elementary Schools, Iman C. Chahine, Lesa M. Covington Clarkson

Middle-Secondary Education and Instructional Technology Faculty Publications

In this article, the authors describe the cyclical process of a collaborative evaluative inquiry project and the data collected throughout the project—data that not only informed "next steps" during the project but also show promise in documenting the benefits of such projects. Over a period of 18 months, seven elementary teachers from a K–6 urban elementary school collaborated with university personnel using Parsons’s (2002) Evaluative Inquiry Model, a 5-stage, cyclical model that includes defining, planning, and investigating challenges; collecting, analyzing, and synthesizing data; and communicating findings that transpire through collaborative inquiry. Overall, the project focused on improving the elementary teachers’ …

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Some Reflections On Hernández And López’S Reflections On The Chain Rule, Michael N. Fried Jul 2010

Some Reflections On Hernández And López’S Reflections On The Chain Rule, Michael N. Fried

The Mathematics Enthusiast

To shed light on how history of mathematics can play a role in mathematics education, Hernández and López chose well in focusing on the chain rule as a case study. Generally speaking, it is, as they point out, a topic students find difficult to grasp: it is a rule involving a different order of complexity than, say, the rule for differentiating functions of the form f(x)=xn, and, although it can eventually become intuitive, it is far from intuitive at the start. Harel et al. (2009) have pointed out that students’ difficulties with the chain rule involve: “...coordinating three or more …

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Rules Without Reason: Allowing Students To Rethink Previous Conceptions, Mary Mueller, Dina Yankelewitz, Carolyn Maher Jul 2010

Rules Without Reason: Allowing Students To Rethink Previous Conceptions, Mary Mueller, Dina Yankelewitz, Carolyn Maher

The Mathematics Enthusiast

This paper reports on the strategies chosen by a group of sixth-grade students in an urban informal learning program as they worked to solve an open-ended, nonroutine task. In particular, the paper focuses on the ability of these students to rise above their previous, procedure-based misconceptions and arrive at a mathematically reasonable solution. Aspects of the problem task, the problem-solving environment, and, importantly, of the nature of the teacher’s interventions are analyzed to determine the conditions that encouraged students to approach mathematics as a logical, meaningful, sense-making activity.

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Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment, Anne Birgitte Fyhn Jul 2010

Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment, Anne Birgitte Fyhn

The Mathematics Enthusiast

In this innovative teaching experiment, the context of climbing is used to induce the teaching and learning of angle concepts. This article reports on the outcomes of a three day teaching and climbing experiment and the impact of this experience on the teacher’s understanding of meso and micro embodiments of mathematics, angle representations, as well as shifts in their attitudes about teaching/learning geometry.

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Polysemy Of Symbols: Signs Of Ambiguity, Ami Mamolo Jul 2010

Polysemy Of Symbols: Signs Of Ambiguity, Ami Mamolo

The Mathematics Enthusiast

This article explores instances of symbol polysemy within mathematics as it manifests in different areas within the mathematics register. In particular, it illustrates how even basic symbols, such as ‘+’ and ‘1’, may carry with them meaning in ‘new’ contexts that is inconsistent with their use in ‘familiar’ contexts. This article illustrates that knowledge of mathematics includes learning a meaning of a symbol, learning more than one meaning, and learning how to choose the contextually supported meaning of that symbol.

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A Semiotic Reflection On The Didactics Of The Chain Rule, Omar Hernandez Rodriguez, Jorge M. Lopez Fernandez Jul 2010

A Semiotic Reflection On The Didactics Of The Chain Rule, Omar Hernandez Rodriguez, Jorge M. Lopez Fernandez

The Mathematics Enthusiast

According to (Fried, 2008), there is an intrinsic tension in trying to apply the history of mathematics to its didactics. Besides the widespread feeling that the introduction of didactic elements taken from the history of mathematics can detract the pedagogy of mathematics from the attainment of important goals, (Fried, 2008, p. 193) describes a pair of specific pitfalls that can arise in implementing such historical applications in mathematics education. The description in (Fried, 2008), is presented in the parlance of Sausserian Semiotics and identifies two semiotic “deformations” that arise when one fails to observe that the pairing between signs and …

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Epilogue, Bharath Sriraman Jul 2010

Epilogue, Bharath Sriraman

The Mathematics Enthusiast

The table of contents of this double issue included the above quote from the historian Howard Zinn which might seem puzzling to the reader. Why was this quote included and what is it supposed to mean? In the opening editorial, I mused over the whole enterprise of scholarly publishing and what it amounts to in the grand scheme of things. Zinn’s quote reminds us that academia is a cloistered unit and many of the things we place importance on in the academic culture of publish or perish seem insignificant when viewed through the lens of real problems that occur outside …

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The Influence Of A Multidisciplinary Scientific Research Experience On Teachers Views Of Nature Of Science, Jerine Pegg, Edith Gummer Jul 2010

The Influence Of A Multidisciplinary Scientific Research Experience On Teachers Views Of Nature Of Science, Jerine Pegg, Edith Gummer

The Mathematics Enthusiast

This study examined a professional development project for K-12 science teachers that engaged participants in an authentic scientific investigation along with explicit-reflective attention to nature of science (NOS). The Views of Nature of Science (VNOS) and Views of Scientific Inquiry (VOSI) Questionnaires (Lederman, Abd-El-Khalick, Bell, & Schwartz, 2002; Schwartz, Lederman, & Thompson, 2001) were used to examine the relationship between teachers’ views of NOS and specific aspects of the professional development project. Results of the study show that teachers’ views of NOS were influenced by the multidisciplinary, primarily non-experimental research that they engaged in, the opportunity to observe interactions of …

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A Graduate Level In-Service Teacher Education Curriculum Integrating Engineering Into Science And Mathematics Contents, Ke Wu Norman, Tamara J. Moore, Anne L. Kern Jul 2010

A Graduate Level In-Service Teacher Education Curriculum Integrating Engineering Into Science And Mathematics Contents, Ke Wu Norman, Tamara J. Moore, Anne L. Kern

The Mathematics Enthusiast

This paper presents the curriculum of a master’s level in-service teacher education course that integrates engineering into mathematics and science for high school mathematics and science teachers. The curricular design of the course including learning goals, reading list, course assignment and grading rubric, and a sample of Model-Eliciting Activities (MEAs) are discussed. In addition preliminary research results on teachers’ perception of engineering show that prior to taking this course, teachers’ understanding of engineering mainly focused on the professions of the engineering discipline. After the participation in the course, teachers’ perceptions of engineering were broadened and included the design process of …

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Star Unfolding Convex Polyhedra Via Quasigeodesic Loops, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu Jul 2010

Star Unfolding Convex Polyhedra Via Quasigeodesic Loops, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu

Computer Science: Faculty Publications

We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron ℘ to a simple (nonoverlapping) planar polygon: cut along one shortest path from each vertex of ℘ toQ, and cut all but one segment of Q.

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Magic Circles In The Arbelos, Christer Bergsten Jul 2010

Magic Circles In The Arbelos, Christer Bergsten

The Mathematics Enthusiast

In the arbelos three simple circles are constructed on which the tangency points for three circle chains, all with Archimedes’ circle as a common starting point, are situated. In relation to this setting, some algebraic formulae and remarks are presented. The development of the ideas and the relations that were “discovered” were strongly mediated by the use of dynamic geometry software.

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Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers", Miriam Amit Jul 2010

Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers", Miriam Amit

The Mathematics Enthusiast

This paper describes a singular process that has been transforming mathematics education in Israel over the past 20 years, as a result of a massive influx of mathematics teachers from the former Soviet Union (FSU). It traces the key points of conflict that marked the initial contact between Israel's mathematical and educational culture and the codes and values brought with the immigrant teachers from the FSU. It then shows how this conflict is gradually becoming resolved, as the two disparate cultures merge into a single, new culture, based on 'the best of both worlds.' This case, we claim, can serve …

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Vectors In Climbing, Anne Birgitte Fyhn Jul 2010

Vectors In Climbing, Anne Birgitte Fyhn

The Mathematics Enthusiast

In this article, the work on mesospace embodiments of mathematics is further developed by exploring the teaching and learning of vector concepts through climbing activities. The relevance and connection between climbing and vector algebra notions is illustrated via embedded digital videos.

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So Many Journals, So Many Words... So What?, Bharath Sriraman Jul 2010

So Many Journals, So Many Words... So What?, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

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Pre-Service Teachers In Mathematics Lesson Study, Elizabeth A. Burroughs, Jennifer L. Luebeck Jul 2010

Pre-Service Teachers In Mathematics Lesson Study, Elizabeth A. Burroughs, Jennifer L. Luebeck

The Mathematics Enthusiast

This paper presents qualitative evidence to answer the questions, “What are the outcomes of engaging pre-service and in-service teachers in a collaborative lesson study experience” and “How can the outcomes of this experience inform future ways to include preservice teachers in lesson study?” The data gathered demonstrate that including pre-service teachers in lesson study can introduce them to lesson-building as a process and cross-grades teacher collaboration. It can give them opportunities to be critical thinkers in the context of mathematics education and encourages them to think as teachers. One weakness the pre-service teachers demonstrated was an incomplete understanding of the …

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Internal And External Comments On Course Evaluations And Their Relationship To Course Grades, Hilary Smith Risser Jul 2010

Internal And External Comments On Course Evaluations And Their Relationship To Course Grades, Hilary Smith Risser

The Mathematics Enthusiast

The validity of student evaluations of courses and the relationship between evaluations and course outcomes has frequently been examined. Since many course evaluations give students an opportunity to provide answers to open-ended questions in addition to giving Likert scale ratings, it is important to understand the relationship between these responses and course outcomes. This study examined the relationship between student responses to open ended questions (specifically whether they attributed their achievement to factors within their control or factors not within their control) and their outcomes in the course. The results of the study indicate that students that identified external factors …

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