American Mathematical Association of Two-Year Colleges
Opening Doors Through Mathematics
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
Please submit the implementation manuscripts using the following guidelines:
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
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)
Reviewed by Annette M. Burden, Youngstown State University
Edited by Brian E. Smith
of Several Popular Web-Enhanced
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
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
2. Learning Styles of the Student
3. Educational Environment
5. Multimedia Technologies
6. Goals of Multimedia Design
7. Goals of Multimedia Learning
The Microsoft design team summarized the theoretical focus well in the following statement:
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.
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:
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.
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.
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.
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.
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:
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.
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.
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.
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:
MXL is also a dynamic learning tool that provides students with:
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.
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.
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.
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.
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
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.
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.
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 firstname.lastname@example.org.
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Edited by Stephen Plett and Robert Stong
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
With Inflammatory Notes for the Mortification of Educologists and the Vindication of "Just Plain Folks"
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)