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The AMATYC Review

A refereed publication of the American Mathematical Association
of Two-Year Colleges

Editor: Barbara S. Rives, Lamar State College

Production Manager: John C. Peterson

Abstracts

Fall 2007 issue, Vol. 29, No.1

Table of Contents

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From the Editor’s Keyboard

The fall semester is underway and hopefully, you and your colleagues have carefully read Beyond Crossroads, and have begun implementing the content of this document into your departments and classrooms. Another article focusing on Beyond Crossroads is included this issue—see the article written by Ham. Due to the importance of Beyond Crossroads, articles focusing on implementation are welcomed for review and consideration for possible publication in future issues of The AMATYC Review. Each issue for the foreseeable future will have at least one article published that shares the implementation
successes at your campuses.

Please submit the implementation manuscripts using the following guidelines:

  • Length: 5–8 pages, typed in 12 point font
  • Style: APA Publication Manual, 5th edition—this means the tables, figures, and references should be in APA (American Psychological Association) Style. If they are not in APA format, your materials will be returned to you to make the changes. This slows the review process even more, so please use APA format in your submission. For more information on the APA Style go to http://apastyle.apa.org/.
  • Submission: Submit five hard copies of the manuscript to Barbara Rives, Editor, 204 Hardin Administration Building, Box 29140, Abilene, Texas 79699-9140. Please also include the following in the lower left corner of the package—“Attention: Beyond Crossroads implementation article.”
  • Send a digital copy of the manuscript as an e-mail attachment to ReviewEditor@amatyc.org. List the following in the subject line of the e-mail: [<Author’s last name>; Beyond Crossroads implementation article: <Article title>]. For example, if I submitted a manuscript, the subject line would read—Rives; Beyond Crossroads implementation article: Implementing the Standards for Student Achievement and Success.

A special “thank you” goes to all the authors who have submitted manuscripts for possible publication. The review process has taken much longer than the authors (and the editor too) would like; however, there is “light at the end of the tunnel.” If all goes as planned (manuscripts reviewed and returned), all authors who submitted manuscripts prior to June 1, 2007 should know the final determination of their manuscript by the time you receive this journal. Many excellent articles have been received for review and consideration. I wish more manuscripts could be published; however, this is not possible due to page limitation of each issue of The AMATYC Review. Have a wonderful fall semester. See you in Minneapolis.

Barbara S. Rives, Editor
E-mail: ReviewEditor@amatyc.org

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Successful Developmental Mathematics
Education: Programs and Students— Part I

Irene M. Duranczyk

Irene is an assistant professor in the Department of Postsecondary Teaching and Learning with an EdD from Grambling State University, Louisiana. She taught developmental mathematics since 1990 and was an administrator of developmental programs for over 20 years. Irene is the recipient of the 2007 National Association for Developmental Education’s (NADE) Outstanding Research Conducted by a Developmental Education Practitioner Award.
E-mail: duran026@umn.edu

This article, the first in a three-part series, will explore the existing body of research regarding successful developmental mathematics education. The three-part series will present qualitative research conducted at a large Midwest public university. The qualitative study was conducted three to five years after students completed their developmental mathematics course work. The purpose was to collect students’ points of view regarding what, if any, aspects of the developmental mathematics program contributed their success. Students do not read the literature that professional educators read and educators often do not check back with students after program completion to assess what parts of the educational experience have contributed the students’ growth once they have completed their educational requirements. The second and third articles in the series will report on the research methods and results. The second article will specifically address aspects of the developmental mathematics program that students attributed to their successful experiences in life as well as their subsequent successful educational experiences. The last article in this series will provide some of the research tools used in this study and identify specific implications—what do developmental educators need to consider as they evaluate the effectiveness of their developmental mathematics programs.(back to top)

Differintegration: The One Branch of Calculus

Andrew J. Berry
Andrew J. Berry received his BS and MS degrees in mathematics at the University of Illinois at Urbana-Champaign, and his PhD at New York University. He is associate professor of mathematics at LaGuardia Community College, City University of New York.
E-mail: ajberry@nyc.rr.com

How might one define a functional operator DIf (x), say for f (x) = 1 + x2 + sin x, such that D+1(1 + x2 + sin x) = 2x + cos x and D-1(1 + x2 + sin x) = x + x3/3 − cos x? Our task in this article is to describe such an operator using a single formula involving the limit of a sum which depends only on a single parameter specifying the order of the operation of differintegration. (back to top)

How to Compute the Partial Fraction
Decomposition Without Really Trying

Richard Brazier and Eugene Boman

Richard Brazier received his BA from Bath University in the UK and his Masters and PhD degrees in applied mathematics from University of Arizona in Tucson. His interests include his family, seismology, gardening, home remodeling and philately.
E-mail: rab27@psu.edu

Eugene Boman received his BA in mathematics from Reed College in 1984 and his MS and PhD in applied mathematics from the University of Connecticut in 1986 and 1993 respectively. He has been teaching at the Dubois campus of Penn State since 1996.
E-mail: ecb5@psu.edu

For various reasons there has been a recent trend in college and high school calculus courses to de-emphasize teaching the Partial Fraction Decomposition (PFD) as an integration technique. This is regrettable because the Partial Fraction Decomposition is considerably more than an integration technique. It is, in fact, a general purpose tool which crops up naturally in a wide range of applications.

The techniques for computing the Partial Fraction Decomposition are numerous to say the least and tend to fall into two categories, general methods which will work for any decomposition and specialized methods which work only for special cases. Unfortunately, the general techniques are often cumbersome and tend to make relatively simple decompositions seem complex, and the specialized techniques, while often very easy to use, tend to roliferate to the point of chaos because there is a lot of variation in the kinds of decompositions that occur.

We present an algorithm for computing the Partial Fraction Decomposition that is based on Heaviside's "cover-up" method-possibly the simplest of the known specialized techniques. The "cover-up" method is extended to a general technique which can be used for any decomposition. Our algorithm is simple to use and teach and is usually more efficient than other known algorithms, specialized or general.(back to top)

An Alternative Method to the Classical Partial Fraction Decomposition

Chokri Cherif

Chokri Cherif is an assistant professor of mathematics at the Borough of Manhattan Community College (BMCC) of the City University of New York (CUNY) and a 2006-2007 (Cohort 3) Project ACCCESS Fellow. He earned his MA in Pure Mathematics from the City College of New York and his PhD in Pure Mathematics from the Graduate Center of the City University of New York. His primary area of interest is functional analysis and its application to image processing.
E-mail: ccherif@bmcc.cuny.edu

PreCalculus students can use the Completing the Square Method to solve quadratic equations without the need to memorize the quadratic formula since this method naturally leads them to that formula. Calculus students, when studying integration, use various standard methods to compute integrals depending on the type of function to be integrated. Before integrating rational functions, students often need to know how to decompose the function by using the Partial Fraction Decomposition. In some cases, extending the Completing the Square Method beyond polynomial functions, to include rational functions, can be very helpful in avoiding lengthy computations where the potential of error is high. In this manuscript we propose an alternative method to the lengthy Partial Fraction Decomposition, used in standard calculus textbooks, to compute the indefinite integral of a family of rational functions. We will also demonstrate how the integral of the rational function, one over one plus x to the fourth power, can be thought of as a special case of the integral of the family of rational functions. (back to top)

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A Couple of "lim (h=>0)-is-missing" Problems
Ko Hin Lau
Ko Hin Lau is an assistant professor in the mathematics department at State University of New York (SUNY), College of Agriculture and Technology at Cobleskill. He obtained his PhD in mathematics from Indiana University. His academic interests include analysis, operator theory, and mathematics education.
Email: laukh@cobleskill.edu
Since most students "hate" the concept of limit, in order to make them "happier," this article suggests a couple of naive "lim (h=>0)-is-missing" problems for them to try for fun. Indeed, differential functional equations that are related to difference quotients in calculus are studied in this paper. In particular, two interesting observations are made in this article, namely, (1) it is possible to solve a differential functional equation just by some basic algebra; and (2) a certain class of smooth functions is characterized by imposing a simple condition on the value c, where c is guaranteed by the Mean Value Theorem for any smooth functions defined on any interval [a, b]. (back to top)

Beyond Assessment

Jim Ham

Jim Ham is a professor of mathematics at Delta College in University Center, Michigan, near Saginaw. He served on the Beyond Crossroads National Advisory Committee and was a section writer for Beyond Crossroads. He is also actively involved in MichMATYC and AMATYC's Placement and Assessment Committee.
E-mail: jaham@delta.edu
Stakeholders are interested in accountability in public education. College professors are doing innovative things in the classroom to help students learn mathematics and, when required, are documenting this learning. This article provides several hypothetical examples of how documented assessments of student learning at the classroom, course and programs levels, can provide evidence of accountability. A well-documented collection of assessment results and actions responding to these results can be the bridge between assessment and accountability. If we take care of the little things (documented classroom, course, and program assessments), the big thing (accountability) will take care of itself. (back to top)

Exploring Measurement Error with Cookies: A
Real and Virtual Approach via Interactive Excel

Scott A. Sinex, Barbara A. Gage, and Peggy J. Beck

Scott A. Sinex is professor and chair of the physical sciences and engineering department of Prince George's Community College in Largo, MD. He received a PhD in geochemistry from the University of Maryland at College Park. He is involved with using technology to develop dynamic and interactive visualization of science and mathematical concepts for guided-inquiry instruction.
E-mail: ssinex@pgcc.edu

Barbara A. Gage is professor in the physical sciences and engineering department of Prince George's Community College in Largo, MD. She received her PhD in curriculum and instruction with emphasis in chemical education from the University of Maryland at College Park. When she's not in a chemistry classroom, she is designing activities for and teaching pre- and in-service teachers in Earth and space sciences.
E-mail: bgage@pgcc.edu

Peggy J. Beck is professor in the mathematics department of Prince George’s Community College in Largo, MD. She received her MA degree in mathematics from The Pennsylvania State University. She has used the cookie module in both intermediate and college algebra, as part of the Peer-Led Team Learning approach to teaching mathematics.
E-mail: pbeck@pgcc.edu
A simple, guided-inquiry investigation using stacked sandwich cookies is employed to develop a simple linear mathematical model and to explore measurement error by incorporating errors as part of the investigation. Both random and systematic errors are presented. The model and errors are then investigated further by engaging with an interactive Excel simulation and a variety of what if scenarios. A conceptual understanding is developed by hands-on manipulation combined with further virtual experimentation. Numerous higherorder thinking and science process skills are used throughout the investigation. (back to top)

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A Study on Student Performance in the College
Introductory Statistics Course

Jen-Ting Wang, Shu-Yi Tu, and Yann-Yann Shieh




Jen-Ting Wang has a PhD in statistics from University of California at Santa Barbara. She is an associate professor in the department of mathematics, computer science, and statistics at the State University of New York College at Oneonta. Her research areas includes applied statistics, Bayesian statistics, and statistical education.
E-mail: WangJ@Oneonta.Edu

Shu-Yi Tu received her PhD in mathematics from University of California at Santa Barbara. She is an assistant professor of Mathematics at University of Michigan, Flint. Her research interests include applied mathematics, nonlinear wave equations, and statistics.
E-mail: sytu@umflint.edu

Yann-Yann Shieh is a statistician at Office of Special Education and Rehabilitative Service, US Department of Education. She has a PhD in educational psychology. Her areas of specialization are multilevel modeling.
E-mail: yshieh@air.org

Introductory Statistics is a required course for most college students in order to graduate. Research has been conducted for determinants of achievement in college mathematics courses; however, there has been little investigation for statistics courses.

In this exploratory study, data concerning students' grades received in this course, the academic performance in high school and in college, as well as numbers of collegiate credits earned were collected from a public four-year liberal arts college. This study aims to identify the most significant factors of students' grades in this course. In addition, a comparison between performances of male and female students, as well as those of freshmen and non-freshmen was also examined. Class size effect was discussed as well. In addition to searching for the most important factors, the prediction model for the course grade was also established from multiple linear regressions. Findings suggest that a student with a good college and high school GPAs, as well as high SAT math score may perform well in the introductory statistics course. High school math grades were also found to be an important predictor. (back to top)
Book Reviews

Edited by Sandra DeLozier Coleman

THE PARROT”S THEOREM: A Novel, Denis Guedj, Translated by Frank Wynne, Thomas Dunne Books, an imprint of St. Martin's Press, New York, 2000, ISBN 0-312- 30302-5 (pbk).

CRIMES AND MATHDEMEANORS, Leith Hathout, Illustrated by Karl H. Hofmann, A.K. Peters, Ltd., Wellesley, Massachusetts, ISBN-10: 1-56881-260-4.(back to top)

Software Reviews

Reviewed by Annette M. Burden, Youngstown State University

Edited by Brian E. Smith

An Overview of Several Popular Web-Enhanced
Instructional Products: Part I

In order to better understand the products that will be discussed here, one needs to be aware of the three systems that were developed for use in an e-learning environment.

The first system, a Course Management System (CMS), was designed primarily for use in academia. This system offers its users the ability to place course materials online, create various assessment features such as tests and quizzes, communicate with students, and track student and course statistics. The most common CMS products on the market are WebCT, Blackboard, e-College, and ANGEL. Because the high price of these products can be prohibitive, free "Open Source" products such as Moodle and Saki have surfaced.

The second system, a Learning Management System (LMS), is similar to the CMS but was designed primarily for use in corporate training. This system offers its users the ability to register students, track student participation and completion, transfer information to other systems, process course charges and tuition payment/transfers, manage skill development, and create reports. A few of the most common LMS products on the market are NetDimensions EKP, Saba, and SumTotal Systems.

The third and newest system, a Learning Content Management System (LCMS), was designed to combine the learner and administrative capabilities of an LMS with the content creation and storage capabilities of a CMS (see Figure 1).

With the increase in popularity of CMS, the desire to add text specific ready made content available for use within CMS increased as well. Instructional designers were employed to create products that would satisfy this need. Of course, the popularity for these products grew with the increase in distance learning offerings and the need to easily manage multiple section offerings of a course. Hence, it became a major challenge to make these products more dynamic (interactive), more robust, and web-compatible. Due to the efforts and vision of the major players in education: Pearson Education (Addison-Wesley/Prentice Hall), McGraw-Hill, and the ALEKS Corporation, many of these challenges have been realized. The most common web-enhanced instructional products currently on the market (in order of their development) are ALEKS® (ALEKS Corporation 1965), MyMathLab® (Pearson Education 2000), Math Zone® (McGraw-Hill 2004), Thompson NOW® (Thompson
2005), and Eduspace (Houghton Mifflin 2006). More recently, Thompson-Brooks/Cole has introduced WebAssign®. However, this product tends to fall under the LMS category and is, therefore, not discussed here.

As in most web-enhanced instructional products, there is both a student module and an instructor module to the product. The instructor module of the product includes all of the necessary tools for development, assessment, and implementation of a course whether it is tied to a specific text or not. In many instances, it permits cloning of a course, making management of multiple sections of a course possible. The student module of the product minimally includes instructor prepared practice quizzes/tests and course documents. However, the more sophisticated product also includes algorithmically generated interactive practice problems, quizzes, and tests, mini-lecture video clips, animations, power points, and access to an e-book.

To create a good web-enhanced instructional product, instructional designers need to consider the functionality of the product within the following theoretical context:

1. Learning Theories

  1. Behaviorism
  2. Constructivism
  3. Cognitivism

2. Learning Styles of the Student

  1. Visual/Haptic
  2. Visual/Verbalizer
  3. Leveling/Sharpening
3. Educational Environment
  1. Traditional
  2. Distance Education (e-learning)
  3. Computer Supported Collaborative Work
  4. Computer Aided Instruction
4. Technology
  1. Use (how and where)
  2. Assessment (is it working well?)

5. Multimedia Technologies

  1. Communication
  2. Inquiry

6. Goals of Multimedia Design

  1. Information Acquisition
  2. Knowledge Construction

7. Goals of Multimedia Learning

  1. Remembering: recall & retention
  2. Understanding: transfer

The Microsoft design team summarized the theoretical focus well in the following statement:

User experience and interface design in the context of creating software represents an approach that puts the user, rather than the system, at the center of the process. This philosophy, called user-centered design, incorporates user concerns and advocacy from the beginning of the design process and dictates the needs of the user should be foremost in any design decisions [5].

With the theory of web-enhanced instructional product design in mind, an overview of each of the most popular products (in order of their development) is presented here.

ALEKS® 2.0 Overview

ALEKS is an acronym for Assessment and LEarning in Knowledge Spaces. A bulk of the development of the ALEKS online interactive system began as a result of a multimillion dollar NSF grant. The ALEKS system was based on Knowledge Space Theory which basically asserts that a complete conceptual knowledge of a subject like Algebra can be separated into various disjoint and/or overlapping elements of knowledge within the subject area. Using a series of complex algorithms and interactive math problems, ALEKS is theoretically able to determine a student's knowledge state at any particular time within the learning process and "intelligently" lead the student into the concept that he/she is most ready to learn next. A more detailed discussion of the theoretical basis of ALEKS can be found in "Knowledge Spaces" by Jean-Paul Doignon and Jean-Claude Falmagne, (Springer, 1965). ALEKS requires the appropriate Java Runtime environment and a math plug-in to run properly. These items are automatically detected and downloaded upon registration.

Administrator Module

Administrators are required to register for their course using an instructor access code. An ALEKS instructor access code can be obtained by contacting your local sales representative. After registration and upon login, ALEKS will detect and install the required plug-ins and then present the instructor with a new message board. Instructors can read messages or go on to the Main page where they can select from the following options:

  • How Do I: where instructors can obtain help for all features of ALEKS
  • Course Administration: where instructors can:
    º Create a new course
    º Display the number of students in each course and its corresponding course code
    º Change the name or topic of a course
    º Change the password of a student
    º Change personal preferences (password, message options, e-mail forward, etc.)
    º Change account preferences of a student
    º Move a student from one course to another
    º Un-enroll a student from a course
    º Delete a course containing no student
  • College Administration: where instructors can: º Create a new instructor account
    º Change the password of another instructor, or of a teaching assistant.
    º Change account preferences (name, messaging options, e-mail forwarding, etc.) of an instructor.
    º Move a course from one instructor to another.
    º Delete an Instructor Account
  • Reporting: where an instructor can generate a status report (progress, time spent on ALEKS, etc.) in a variety of styles
  • Taking Actions: where an Administrator can:
    º Schedule a new assessment
    º Cancel an assessment
    º Change the name, date, grading scale of an assessment
    º Edit the grading scale, date or name of a past or upcoming scheduled/requested assessment
    º Create a Quiz
    º Edit a Quiz
    º Delete a Quiz
    º Send a message to communicate with students or instructors.
  • Advanced: this economical mode contains all of the above features and is available for the more experienced ALEKS user.

From an administrative standpoint, the Results & Progress menu gives the course administrator the ability to create a quiz for all sections of a course, e-mail all students from a specific section of a course, create a new course section, add a new instructor, review student progress for all sections of a course, and obtain reports for all sections of a course. Students can also be conveniently "draged and dropped: from one section of a course to another (see Figure 2).

Also from an administrative standpoint, the Standards & Syllabi menu gives the course administrator the ability to set standards for the sections as well as to adjust the course syllabus for each section.

Student Module

Students are required to register for their course using a purchased access code. The student would generally purchase this access code from their campus bookstore bundled with a text order from the instructor or course administrator. The student module of the ALEKS product consists of both an assessment and a learning mode. Each will be discussed separately below.

Assessment Mode

Upon registration and plug-in check and installation, each student is required to navigate through a tutorial on proper data entry and use of the ALEKS system. This tutorial takes approximately 10-20 minutes depending upon the computer skills of the student. When the tutorial has been completed the student is given an initial assessment test. The first question that a student encounters is always based upon the course content, but each question thereafter is selected by the system according to the way the student has answered a previous question. The number of questions within an assessment varies depending upon the answers to questions within the assessment. Although no feedback is provided during an assessment, when the assessment has been completed, ALEKS generates an individualized pie chart report that tells the student what knowledge elements ALEKS has deemed the student knows.

Learning Mode

Once the student has seen the ALEKS generated report, the student must then exit the report pie and enter the learning mode pie. By selecting an available element (concept) within a slice of the pie, a student is able to navigate through the course material. The student can attempt to solve the problem or can read an explanation of the problem's solution. The student is then presented with a similar problem. If the student incorrectly answers the new problem, the ALEKS system evaluates the type of error that could have occurred and then offers the student options. Students are given an assessment when ALEKS perceives that the student is ready for one, unless an assessment has been assigned by the Administrator. Students always have access to an overview of items that they can do and items that they need to learn next.

Product Functionality—Comments

Administrator Module

ALEKS has a robust administrative component. Multiple sections of a course can be created with relative ease. Although students can be easily "dragged & dropped" from one section of a course to another, their work was, at the time of this review, not able to be moved with them. It is unclear at this time whether the product revision provides this functionality. ALEKS generates a variety of useful student and class reports that give a quick overall view of the class's progress.

ALEKS has recently undergone a revision adding the following enhancements:

  • Automatic Textbook Integration
  • New Instructor Module
  • Instructor-Created Quizzes
  • New Message Center

It is difficult for instructors to follow a text since students are usually in different chapters or sections of a chapter at any given time.

Student Module

Although the student assessment module of ALEKS is typically only supposed to offer the student between 15-25 questions, some students have found themselves taking assessments that have contained over 80 questions. In the learning mode, students have found themselves sent back to elements that they had previously learned. Students have been known to be caught in infinite loops and had difficulty moving forward in the course. It is not readily apparent how to exit the initial assessment pie and enter the learning mode. Students are instructed to click on "Exit," but in doing so, are immediately logged out of the product. It is hard for students to follow a textbook since they are permitted to select from any section of the pie that ALEKS has deemed them ready to learn.

General

Norton Antivirus has presented a problem for ALEKS users! In general, the overall design and functionality of this product appears to be theoretically strong in items 3, 4, 6, and 7 but weak in items 1, 2 and 5.

 

MYMATHLAB Overview

Course Compass (CC) is an easy to use Course Management System (CMS) environment developed by Pearson Education using Blackboard technology. Addison-Wesley and Prentice Hall offer a wide variety of textbooks within the CC environment, with 250 of these titles enhanced by MyMathLab (MML). MML is a series of text-specific, customizable courses for Addison-Wesley and Prentice Hall textbooks in mathematics and statistics. MML is powered by CC andMathXL (MXL), Pearson Education's robust stand-alone online homework, tutorial, and assessment system (see Figure 3).

As a stand-alone system, MXL is fully functional outside of the CC/MML environments and is used primarily in the development of single courses. MXL is placed within the CC/MML environment when more control over multiple sections of a course is necessary. MML permits the delivery of online courses using the content of MXL and the online tools within CC. Moreover, instructors who wish to add their own content, documents, and videos, or want to customize the learning environment for their students can only do so in MML. Thus, MXL is the essence of the dynamic course materials for selected mathematics and statistics courses. MXL provides instructors with the following rich set of course options:

  • a powerful homework and test manager
  • a custom exercise builder
  • comprehensive gradebook tracking
  • complete online course content and customization tools
  • the ability to copy or share courses and manage course groups

MXL is also a dynamic learning tool that provides students with:

  • interactive tutorial exercises
  • an e-book with multimedia learning aids
  • individualized study plans
  • tutoring service

In order to operate properly, MXL requires the MXL player which is a proprietary program developed by Pearson Education to deliver mathematics online. Although Java is used to deliver mathematics for older statistics and calculus titles, new editions of these texts will require the MXL player as well.

Administrator Module

Administrators are required to register for their course using an instructor access code. The access code is provided to instructors who adopt the MML product through their local sales representative or their course administrator. After registration and upon login, instructors are given the opportunity to take a tour of the product. As in most web-enhanced instructional products, certain plugins are necessary. These plugins can be user installed or installed by a computer administrator in the event that the instructor does not have administrator access to the computer. The administrator can create a Master Syllabus within a "coordinator" course and copy the coordinator course as many times as necessary to a "member" course. The instructor of the member course enrolls as a student and is given TA status by the course administrator.

From within a selected course, the administrator and TA have both student and instructor access, although the TA privileges are restricted. Instructor access is gained by selecting the tab labeled "Control Panel". In the control panel area, an instructor can upload or modify course documents, send e-mails, and manage the course menu. However, only the administrator has the ability to modify chapter contents and delete students from the course. The administrator can also modify MML components of the course; assign text specific algorithmically generated homework and tests, set gradebook options, etc. One should note that there are two gradebooks available from within the control panel. The first is CC dependent while the second is from within MML and keeps track of all web-enhanced assignments (see Figure 4).

Although the CC gradebook can be used for additional assignments, since it does not track student work done in MML, most instructors do not use it.

Student Module

Students need to have an access code in order to use the MML or MXL product. The course materials are generally purchased as a complete bundled package that includes the textbook and MML or MXL student access kit. Additional resources can be packaged but must be specially requested. A standalone access code can be purchased online via credit card. MML access codes remain active as long as the instructor keeps the course open. MXL student codes are good for 12 months or 24 months depending on the text (one term or two term course). Students have access to a variety of features like "Help Me Solve This", "View an Example", section lecture video, animations, and power points. An individualized study plan is generated for the student after every test to allow students to work on material that needs to be studied further.

Product Functionality—Comments

Administrator Module

MML has a clean Administrator appearance. Navigation from one stage of course/section development to another is relatively easy and cloning of a course can be done fairly quickly. Algorithmically generated assignments and tests can be copied and/or modified using the samples provided from within the product, or algorithmically generated problems can be selected from a test bank. Static or algorithmic tests can be uploaded from a Test Generator and made available for the web; however, the tests must be in multiple choice format. All interactive problems coincide with the selected text. Material that has been deleted from the course syllabus is automatically inaccessible from the MML test bank, homework, or study plan. The Administrator has the ability to simplify the course management interface.

Student Module

Students have complained that the math palette occasionally disappears, however, the new MXL player release appears to have diminished or resolved this issue. Having an MML access code remain active after it has been redeemed for as long as the instructor keeps the course open is helpful to students who have for some reason not completed the course on time. For students who have either not done well in the course or needed to drop the course, there is no need to purchase another code if they enroll in another course using the exact same text. The student interface appears to be easy to navigate and assignments
easy to access.

General

In general, the overall design and functionality of this product appears to be theoretically strong in items 1, 2, 3, 4, 5, 6, and 7.

Summary

Table 1 on the next page provides the reader with a quick overview of the instructional products that were discussed in Part I of this manuscript. A complete table of all of the instructional products discussed will be provided in Part II.


References

Reviewed by Annette M. Burden, Associate Professor, Mathematics and Statistics, Youngstown State University, College of Arts and Sciences, (Youngstown, OH). Burden is an associate professor of mathematics at Youngstown State University. She is beginning algebra coordinator and coordinator of the mathematics distance program. Annette also develops upper level mathematics courses for Empire State College. She is a member of numerous mathematics associations and the recipient teaching and service awards. She also serves on several multimedia advisory panels. Her e-mail address is aburden@as.ysu.edu.

Send software reviews to:

Brian E. Smith
AMATYC Review Software Editor
Department of Management Science
McGill University
1001 Sherbrooke St. West
Montreal, QC, Canada H3A 1G5

or e-mail: brian.smith@mcgill.ca (back to top)

The Problems Section

Edited by Stephen Plett and Robert Stong

New Problems

The AY Problem Set consists of five new problems.

Set AW Solutions

Solutions are given to the four problems from the AW Problem Set that were in the
Fall 2006 issue of The AMATYC Review. (back to top)

Mathematics For Learning

With Inflammatory Notes for the Mortification of Educologists and the Vindication of "Just Plain Folks"

Alain Schremmer

In the Spring 2004 issue of The AMATYC Review, Schremmer introduced his idea for an open-source serialized text: Mathematics For Learning. The Preface to the text appeared in the Spring 2004 issue with a new chapter in each subsequent issue of The AMATYC Review. This issue contains Chapter 6: Repeated Multiplications and Divisions, with sections on "A Problem With English" and "Templates." (back to top)

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