Mathematics Commons^™

About Furuta's Inequality And Aluthge Transform On Pseudo-Hilbert Spaces, Loredana Ciudariu

ACMS Conference Proceedings 2009

No abstract provided.

Paper Abstracts (2009), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2009

Seventeenth Conference of the Association of Christians in the Mathematical Sciences

Introduction (2009), Terry Perciante

ACMS Conference Proceedings 2009

Seventeenth Conference of the Association of Christians in the Mathematical Sciences

The Heavens And The Scriptures In The Eyes Of Johannes Kepler, Dale L. Mcintyre

ACMS Conference Proceedings 2009

The heavens declare the glory of God… Ps. 19:1 Acclaimed as one of the most accomplished and influential scientists of his time, the subject of this paper was also a passionate defender of the Christian faith who believed he had been called by God to glorify Him in the study of His Creation. We see a man who was so immersed in both the Scriptures and his exploration of the heavens that his scholarly writings often burst forth with biblical quotations and songs of praise for God the Creator. Though always magnanimous and tolerant of others, he suffered persecution from …

Table Of Contents (2009), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2009

Seventeenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2009), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2009

Seventeenth Conference of the Association of Christians in the Mathematical Sciences

Combinatorial And Commutative Manipulations In Feynman's Operational Calculi For Noncommuting Operators, Duane Einfeld

Department of Mathematics: Dissertations, Theses, and Student Research

In Feynman's Operational Calculi, a function of indeterminates in a commutative space is mapped to an operator expression in a space of (generally) noncommuting operators; the image of the map is determined by a choice of measures associated with the operators, by which the operators are 'disentangled.' Results in this area of research include formulas for disentangling in particular cases of operators and measures. We consider two ways in which this process might be facilitated. First, we develop a set of notations and operations for handling the combinatorial arguments that tend to arise. Second, we develop an intermediate space for …

Parts Of The Whole: Is Everything Equally Important?, Dorothy Wallace

Numeracy

Two strategies are proposed for sorting out priorities and goals in education. At the college level the column argues that goals, and therefore requirements, should be set based on the desired knowledge base of the entire population rather than the individual. At the scale of a single K-12 classroom the column argues that priority be given to content requiring most instructor intervention, describing how the structure of class time and school activities would change as a result. Implementation of these strategies would lead to more efficient use of teacher’s time and effort, better allocation of systemic resources, and clarity of …

Review Of The Chicago Guide To Writing About Numbers By Jane E. Miller, Neil Lutsky

Numeracy

Miller, J. E. 2004. The Chicago Guide to Writing about Numbers. Chicago, IL: University of Chicago Press. 304 pp. Cloth $45 ISBN: 9780226526300, Softcover $17. ISBN: 9780226526317.

The Chicago Guide to Writing about Numbers is a reference work suitable for anyone interested in understanding, using, or promoting quantitative thinking. Its primary aim is to identify and illustrate ways in which information associated with numbers can be conveyed most effectively given a particular communication purpose and context. The book is directed at writers who incorporate numbers in verbal or visual displays in documents, in oral presentations, or on the Web. The …

Quantitative Literacy On The Web Of Science, 2 – Mining The Health Numeracy Literature For Assessment Items, H L. Vacher, Todd Chavez

Numeracy

A topic search of the Web of Science (WoS) database using the term “numeracy” produced a bibliography of 293 articles, reviews and editorial commentaries (Oct 2008). The citation graph of the bibliography clearly identifies five benchmark papers (1995-2001), four of which developed numeracy assessment instruments. Starting with the 80 papers that cite these benchmarks, we identified a set of 25 papers (1995-2008) in which the medical research community reports the development and/or application of health-numeracy assessments. In all we found 10 assessment instruments from which we have compiled a total of 48 assessment items. There are both general and context-specific …

The Case For Infusing Quantitative Literacy Into Introductory Geoscience Courses, Jennifer M. Wenner, Eric M. Baer, Cathryn A. Manduca, R. Heather Macdonald, Samuel Patterson, Mary Savina

Numeracy

We present the case for introductory geoscience courses as model venues for increasing the quantitative literacy (QL) of large numbers of the college-educated population. The geosciences provide meaningful context for a number of fundamental mathematical concepts that are revisited several times in a single course. Using some best practices from the mathematics education community surrounding problem solving, calculus reform, pre-college mathematics and five geoscience/math workshops, geoscience and mathematics faculty have identified five pedagogical ideas to increase the QL of the students who populate introductory geoscience courses. These five ideas include techniques such as: place mathematical concepts in context, use multiple …

Establishing The Quantitative Thinking Program At Macalester, David Bressoud

Numeracy

In November 2005, the faculty of Macalester College voted to institute a graduation requirement in Quantitative Thinking (QT) that is truly interdisciplinary. It currently draws on courses from thirteen departments including Anthropology, Economics, Geography, Political Science, Theater, Mathematics, Environmental Science, and Geology. This article describes the process that led to the creation of this program. It explains how we were able to get broad buy-in at the beginning and the long process of trial and error—informed by formative assessment—that was needed to refine the initial vision and shape it into a viable program that would be accepted by most of …

Confronting Challenges, Overcoming Obstacles: A Conversation About Quantitative Literacy, Bernard L. Madison, Lynn A. Steen

Numeracy

An edited transcript of the opening session of a workshop on quantitative literacy held Oct. 10-12, 2008 at Carleton College, Northfield, Minnesota. The workshop, which brought together interdisciplinary teams from two dozen colleges and universities, was sponsored by the Quantitative Inquiry, Reasoning, and Knowledge (QuIRK) Initiative at Carleton and the Washington-based Project Kaleidoscope. Two mathematicians in the forefront of quantitative literacy initiatives over the period 1997-2008, Lynn Arthur Steen and Bernard L. Madison, converse about attitudes, obstacles, changes and accomplishments. The conversation, structured as an interview, begins with the relationship between mathematics and quantitative literacy and moves through issues central …

All The More Reason For Qr Across The Curriculum, Bernard L. Madison

Numeracy

No abstract provided.

Rules And Insights: Connecting The Mathematical And Linguistic Abilities Of C.S. Lewis, Kim Regnier Jongerius

ACMS Journal 2008-2009

While most biographical works on C.S. Lewis give passing reference to Lewis' problems with elementary mathematics, few have made an attempt at diagnosing the difficulty or exploring its impact on his writing. A careful study of family correspondence, however, makes it clear that his learning difficulties were not with mathematics alone and suggests connections between attitudes toward and abilities in both mathematics and language. This paper will make these connections clear and will illustrate their ties to Lewis' effective mathematical references.

The Effects Of Block Scheduling On Ap Calculus Ab Student Achievement, Larry A. Lightner

Mathematics Graduate Theses

Student achievement on the AP Calculus AB Exam is always a concern for teachers and school districts that offer the exam. A factor of concern that also arises is a school’s schedule. A school’s schedule may have an affect on achievement. This study examines the comparison in achievement of students who take the AP Calculus AB Exam under a block schedule and a traditional schedule system. Block Scheduling is defined as a class period of 80-90 minutes with 4 periods each day, allowing a full year’s curriculum to be offered in one semester. Traditional scheduling is defined as a class …

Cooperative Learning In The Mathematics Classroom, Janine Regnier

Mathematics Graduate Theses

Student interactions are important which provokes the idea that cooperative learning should be incorporated into classrooms. Research states many benefits for incorporating cooperative learning and are included in the literature review. Cooperative groups were introduced and studied by the author, who ultimately concluded that cooperative learning does have a place in Mathematics classrooms and should be used when the lesson lends itself to a cooperative environment. The study results can be found in this paper following the literature review.

To What Degree Will Differentiated Instruction Impact Student Grades In A Middle School Classroom?, Maureen K. Wilke

Mathematics Graduate Theses

The middle school student population encompasses one of the widest ranges of diversity in the educational system. Besides cultural, religious, educational, economical diversity, the middle school student copes with physical and psychological changes as well. It is important to understand that reaching students successfully is not teaching one way, but providing a learning experience based on students’ needs. The five key differentiated strategies in the classroom are: knowing the student, the environment, meaningful lessons, tiered assignments, and assessment. Gather as much information on the students, such as data from past standardize tests, conversation with students, student journals about success and …

Skittles Chocolate Mix Color Distribution: A Chi-Square Experience, David R. Duncan, Bonnie H. Litwiller

Faculty Work

In teaching statistical processes, it is important that there be application to realworld settings and activities. When this is done, students are more likely to see the meaning of the steps being developed.

One such activity involves using the Chi-Square statistical test and its applications to counting Skittles Chocolate Mix candies. Many students are aware that these candies come in five different flavors: Brownie Batter (BB), Vanilla (V), Chocolate Caramel (CC), S’mores (S), and Chocolate Pudding (CP).

Problem-Based Instructional Tasks, Larry Leutzinger

Faculty Work

No abstract provided.

The Iowa Core Curriculum And Me: How My Teaching Of Mathematics Methods Will Change, Catherine M. Miller

Faculty Work

It is an exciting time to be a mathematics educator in Iowa! We are joining the other 49 states by having a set of state standards. In fact, Iowa is exceeding federal expectations by having a curriculum to inform the work of teachers and school administrators. Because of this, we enter an era of change in Iowa and, as we know, change is never easy. To succeed in implementing the Iowa Core Curriculum (ICC) in mathematics all teachers need to learn about it and have help in implementing its core ideas and content. This includes teachers who will begin their …

Meaningful Distributed Instruction— Developing Number Sense, Edward C. Rathmell

Faculty Work

What Is Number Sense?

The primary goal for elementary and middle school mathematics is to help students learn to use numbers meaningfully, reasonably and flexibly in everyday life. This means that students must develop a deep understanding of

-- numbers and operations,
-- when operations can appropriately be used to solve problems, and
-- judging the reasonableness of their solutions to problems.

They also need to develop attitudes so they

-- believe they can make sense of mathematics, and
-- habitually try to make sense of mathematics.

In other words, students need to develop number sense.

Understandings Needed for Number …

Conceptual Previews In Preparation For The Next Unit Of Instruction, Michele Carnahan, Bridgette Stevens

Faculty Work

Understanding meanings of operations and how they relate to one another is an important mathematical goal for students in fourth grade (National Council of Teachers of Mathematics, 2000). Using pictures, diagrams, or concrete materials to model multiplication helps students learn about factors and how their products represent various contexts. The foundation of understanding how operations of multiplication and division relate to one another deepens the understanding of the composition of numbers. Discussing different types of problems that can be solved using multiplication and division is important, along with the ability to decompose numbers. When students can work among these relationships …

Using Spreadsheets To Discover Meaning For Parameters In Nonlinear Models, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

Using spreadsheets one can develop an exploratory environment where mathematics students can develop their own understanding of the relationship between the parameters of commonly encountered families of functions (linear, logarithmic, exponential and power) and a natural interpretation of “rate of change” for those functions. The key to this understanding involves expanding the concept of rate of change to include percent changes. Through the use of the spreadsheet model, students can explore and easily determine which type of change is most natural for a given family of functions. This, in turn, provides a mechanism for interpreting the parameters of the function …

Parts Of The Whole: Teachers And The Work They Do, Dorothy Wallace

Numeracy

This introductory column argues the need to study our system of education with the same care we would give any complex system, pointing out some ways in which the educational system functions differently from other managed systems, and concluding that a careful study of the forces shaping education will lead to insight into what makes educational change successful.

Review Of Quantitative Reasoning: Tools For Today's Informed Citizen By A. Sevilla And K. Somers, Aaron G. Montgomery

Numeracy

Alicia Sevilla and Kay Somers, Quantitative Reasoning: Tools for Today’s Informed Citizen. (Emeryville CA: Key College Publishing, 2007). 626 pp. Softcover with Student CD. $79.95 (USA) ISBN 1-931914-90-1. http://www.keycollege.com/catalog/titles/quantitative_reasoning.html

From charts and graphs (Topic 1) to decision making (Topic 21), Quantitative Reasoning offers a good selection of topics that students in a general education mathematics course and other individuals in our society should understand. Organizing the 21 chapters (topics) under the headings of numerical reasoning, logical reasoning, and statistical reasoning, Sevilla and Somers focus their chapters on examples and devote the last 224 pages to 21 Excel activities. Parallel graphic-calculator …

Word Problems: Reflections On Embedding Quantitative Literacy In A Calculus Course, Gizem Karaali

Numeracy

Even though Quantitative Literacy (QL) programs are currently being developed and implemented in several colleges and universities, most schools still depend on traditional mathematics courses to reach their quantitative literacy goals. This note is a case study of how a traditional mathematics course sequence intended for students majoring in social and life sciences may be modified and adapted to at least partially fulfill the need in the absence of a stand-alone QL program. In particular, we focus on a freshman-level mathematics course sequence that serves various client departments. This sequence covers the traditional content of a first-year calculus sequence along …

False Positives And Referral Bias: Content For A Quantitative Literacy Course, Stuart Boersma, Teri Willard

Numeracy

An extended study of accuracy in medical screening is presented as a useful application to increase students’ quantitative reasoning skills. Two detailed examples are presented. The first explores the frequency of obtaining false positive results from a medical screening tool while the second examines the issue of referral bias and its effect on the apparent sensitivity and specificity of the screening tool. Results from student assessments indicate that the activity increases one’s ability to define terms such as “false positive” and “false negative” and increases one’s ability to read and compute with information obtained from a two-way table. Teacher assessment …

Using Local Data To Advance Quantitative Literacy, Stephen Sweet, Susanne Morgan, Danette Ifert Johnson

Numeracy

In this article we consider the application of local data as a means of advancing quantitative literacy. We illustrate the use of three different sources of local data: institutional data, Census data, and the National College Health Assessment survey. Our learning modules are applied in courses in sociology and communication, but the strategy of using local data can be integrated beyond these disciplinary boundaries. We demonstrate how these data can be used to stimulate student interests in class discussion, advance analytic skills, as well as develop capacities in written and verbal communication. We conclude by considering concerns that may influence …

Quantitative Literacy Across The Curriculum: A Case Study, Benjamin Steele, Semra Kiliç-Bahi

Numeracy

We describe a quantitative literacy (QL) program at Colby-Sawyer College, a small, residential, liberal arts college in New Hampshire. This program has grown rapidly from a traditional math curriculum to a college-wide understanding of quantitative literacy and voluntary participation by many faculty members in all departments. More than 80% of the faculty agreed that it would be useful for students to be able to use quantitative skills in their courses, but only 24 % thought students were capable of doing very well in mathematics. Twenty-three faculty members attended a summer workshop, funded by NSF, DUE # 0633133, in which they …