Mathematics Commons^™

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).

The Wright Message, 2009, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- 2009 - 2010 Tenure-Stream Faculty
-- Mathematics Education Program
-- Project and Grants
-- Summer Research for UNI Math Students
-- Student Competitions
-- The Iowa Collegiate Mathematics Competition
-- TEAM News
-- Alliance Program
-- Two Endowment Funds
-- Mathematics Contribution Form
-- Mathematics Scholarship Funds
-- Applause and Congratulations!
-- Math Walk Challenge

Empirical Development Of An Instructional Product And Its Impact On Mastery Of Geometry Concepts, Donaldson Williams

Dissertations

Problem

Relatively poor levels of mathematical thinking among American school children have been identified as a major issue over the past half century. Many efforts have been made to increase the mathematics performance of children in schools. Additionally, out-of-school-time programs have attempted to address this issue as well. Holistic development is one of the distinguishing features of Seventh-day Adventist instructional programs. Yet, as of 2007, the Pathfinder program, an informal educational program operated by the world-wide Seventh-day Adventist church, had no instructional product designed to foster participants’ cognitive development in mathematics. This study focused on the empirical development of an …

Introducing Interior-Point Methods For Introductory Operations Research Courses And/Or Linear Programming Courses, Goran Lesaja

Mathematical Sciences: Faculty Publications

In recent years the introduction and development of Interior-Point Methods has had a profound impact on optimization theory as well as practice, influencing the field of Operations Research and related areas. Development of these methods has quickly led to the design of new and efficient optimization codes particularly for Linear Programming. Consequently, there has been an increasing need to introduce theory and methods of this new area in optimization into the appropriate undergraduate and first year graduate courses such as introductory Operations Research and/or Linear Programming courses, Industrial Engineering courses and Math Modeling courses. The objective of this paper is …

Gorenstein Flat Dimension Of Complexes, Alina Iacob

Mathematical Sciences: Faculty Publications

We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for complexes; we also define a generalized Tate cohomology for complexes over Gorenstein rings, and we show that there is a close connection between the absolute, the Gorenstein and the generalized Tate cohomology.

On Fourier Parabolic And Wave Equation, Mekki Terbeche, Broderick O. Oluyede

Mathematical Sciences: Faculty Publications

This paper is devoted to a diffusion (heat) and wave equations for the function of two independent variables. We establish a criterion for existence and uniqueness of the solution of Fourier parabolic equation using Taylor series. A formal solution for a wave equation is investigated.

On Some Differential Equations, Mekki Terbeche, Broderick O. Oluyede

Mathematical Sciences: Faculty Publications

This paper investigates Cauchy and Goursat problems for partial differential operators. Successive approximation techniques for partial differential equations and the estimated results are employed to obtain the existence and the uniqueness of the solutions of such problems. An extended Darboux-Goursat-Beudon problem is studied.

Combinatorics Of Ramanujan-Slater Type Identities, James Mclaughlin, Andrew Sills

Mathematical Sciences: Faculty Publications

We provide the missing member of a family of four q-series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinatorial implications of the identities in this family, and of some of the identities we considered in Identities of the Ramanujan-Slater type related to the moduli 18 and 24.

Establishment Of Weak Conditions For Darboux-Goursat-Beudon Theorem, Mekki Terbeche, Broderick O. Oluyede

Mathematical Sciences: Faculty Publications

This paper is devoted to the establishment of weak conditions for Darboux-Goursat-Beudon (DGB) theorem in order to improve analogous results in [1, 7]. By adapting a technique proposed by [7] in another setting [8] via majorant method, we obtain the generalization of DGB theorem.

Proceedings Of The Third Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Front Matter

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Contents of 3rd Annual GAMTE Proceedings Front Matter:

• Proceedings Committee
• Officers of GAMTE
• Purposes and Goals of GAMTE
• Table of Contents
• Letter from President

Analysis Of Achievement For Understanding Geometry, Annita W. Hunt

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

The purpose of this study was to investigate the effectiveness of a mathematics professional development course. More specifically, in this study we examine whether geometric experiences have an impact on level of performance in mathematics. The van Hiele (Fuys, D., Geddes, D., & Tischler, R., 1988) model of geometric understanding provided a research framework from which to view geometric understanding. This model suggests five levels of understanding that should be taken into consideration when examining levels of geometric thinking: Visual, Descriptive/Analytic, Abstract/Relational, Formal Deduction/Proof, and Rigor. The sample under study was three cohorts of practicing elementary teachers and mathematics coaches …

Content Knowledge And Pedagogical Content Knowledge Of Algebra Teachers And Changes In Both Types Of Knowledge As A Result Of Professional Development, Joy W. Black

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

In seeking to improve the mathematics education of all students, it is important to understand the connection between the content knowledge and pedagogical content knowledge of mathematics and how professionals can influence growth in both of these types of knowledge. We do not have an answer about the interplay of content knowledge and pedagogical content knowledge in successful instructional practices in the mathematics classroom. This study involves assessing the content knowledge and pedagogical content knowledge of secondary teachers of Algebra I. In addition, how are these types of knowledge expressed in instructional practices? Last, how do content knowledge, pedagogical content …

Authentic Discovery Projects In Statistics, Dianna J. Spence, Robb Sinn

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

We report the activities and findings of a 3-year project, ―Authentic, Career-Specific, Discovery Learning Projects in Introductory Statistics,‖ funded by the National Science Foundation. The project scope includes: 1) development of teaching materials for using discovery learning projects to teach statistics; 2) training secondary teachers to use the materials developed; 3) evaluation of student outcomes, in both content knowledge and attitudes toward statistics; and 4) extending and refining teacher training. With input from an interdisciplinary team of instructors, materials were developed to assist the teacher in facilitating collaborative discovery projects using linear regression techniques and comparison techniques with appropriate t-tests. …

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 …

Addressing The Principles For School Mathematics: A Case Study Of Elementary Teachers Pedagogy And Practices In An Urban High-Poverty School, Robert Q. Berry, Linda Bol, Sueanne E. Mckinney

Educational Leadership & Workforce Development Faculty Publications

The extent to which four novice teachers assigned to an urban high-poverty school implemented the Principles of School Mathematics during their mathematics instruction program was investigated using a case study design. The research team conducted 36 unannounced observations of the participating teachers and utilized a developed assessment to guide their observations. Results indicated that only one teacher was judged proficient for all the principles. The remaining three teachers fell short in the implementation and direction of the principles. Detailed descriptions of the pedagogical practices of the teachers are provided.

The Process Of Tracking In Mathematics In Box Elder School District, Megan Haramoto Bushnell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Educational policymakers have used tracking to instruct students in a variety of subjects, including mathematics. Tracking, which has also been called ability grouping, is a process by which students in the same grade are placed into different classes based on academic ability. Few educators and sociologists have looked at the process by which students are placed in different mathematics tracks. The research design of this study focused on accumulating, evaluating, and reporting the understanding and observations of 12 teachers and 4 counselors as they discussed their knowledge and involvement in the mathematics placement procedures from the intermediate and middle school …

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 …

Ramanujan–Slater Type Identities Related To The Moduli 18 And 24, James Mclaughlin, Andrew Sills

Mathematical Sciences: Faculty Publications

We present several new families of Rogers–Ramanujan type identities related to the moduli 18 and 24. A few of the identities were found by either Ramanujan, Slater, or Dyson, but most are believed to be new. For one of these families, we discuss possible connections with Lie algebras. We also present two families of related false theta function identities.

Imagine Math Day: Encouraging Secondary School Students And Teachers To Engage In Authentic Mathematical Discovery, Darryl H. Yong, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

Research mathematicians and school children experience mathematics in profoundly different ways. Ask a group of mathematicians what it means to “do mathematics” and you are likely to get a myriad of responses: mathematics involves analyzing and organizing patterns and relationships, reasoning and drawing conclusions about the world, or creating languages and tools to describe and solve important problems. Students of mathematics often report “doing mathematics” as performing calculations or following rules. It’s natural that they see mathematics as monolithic rather than an evolving, growing, socially constructed body of knowledge, because most mathematical training in primary and secondary schools consists of …

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 …

Quantitative Literacy On The Web Of Science, 1: The Bibliography And Its Role In The History Of This Journal, H L. Vacher, Todd Chavez

Numeracy

Prior to deciding to propose in 2006 that the National Numeracy Network (NNN) publish a new journal for quantitative literacy with their support, the University of South Florida Libraries investigated the publication environment of the field on the Web of Science®. Reproducing part of that study in this paper, we present findings from topic searches (March 2008) for “numeracy,” “quantitative literacy,” and “statistical literacy.” These updated results include a combined bibliography of 338 peer-reviewed articles amongst 210 different journals, by 748 authors from 321 institutions in 25 countries, in a total of 87 subjects (34% of the subject classes in …

Abstracts For Numeracy, H L. Vacher

Numeracy

No abstract provided.