MATH SPIN News
Newsletter of the NADE Math Spin group Spring 2000
Greetings from the chair
It has been an interesting spring! I co-presented a workshop in Biloxi that shared technologies available to enhance teaching and learning. Then at our Georgia Chapter conference, I was part of a panel looking at communicating mathematically via the web. In the process of preparing and sharing with my co-presenters, I had an opportunity to reflect on the changes we've seen in the past few years and the opportunities awaiting us in the future. Ten years ago, I was wrestling with the impact of calculators; now I am contemplating offering a course online. Ten years ago, my computer was a word processor; now it is a telephone, production studio, and virtual library of information. I can't even imagine the changes coming in the next ten years.
It is in these times of change that I am most thankful for groups like our Math SPIN. Through the conference sessions we have the opportunity to see how others are incorporating change to their advantage. The listserv, newsletter, and website also provide opportunities for exchanging information with others about incorporating change.
With this issue of the newsletter, we continue to get good value for our Math
SPIN dues. In this issue, we have gathered summaries from many of the NADE 2000
presenters in an effort to share the conference with those unable to attend.
The presenters have a wide variety of interests and approaches. By sharing their
ideas, they also give us new strategies for dealing with change.
Please join me in a round of applause for the presenters, and for Tom Armington and Daryl Stephens for their work in sharing this information with you. And, while you are at it, give yourself a pat on the back for surviving all this change.
Roberta Lacefield, Math SPIN Chair
(Note: Roberta's conference presentations can be viewed at the following sites:
Web Site continues to evolve
The Math SPIN web site is updated regularly by Daryl Stephens. Each edition of the newsletter will be posted on-line as soon as it is available. Back issues through November 1997 can also be viewed. Recent issues have been posted as PDF documents to maintain the approximate appearance of the newsletter itself. Reading PDF (Portable document format) files requires the use of Adobe Acrobat Reader software, which can be downloaded free at www.adobe.com .
A new feature of the web site is that there are now links to various sites of interest to developmental math instructors. These include sites put up by textbook publishers and developmental math faculty, online tutorial services, general interest math sites, technology-related sites, and links to sources that might make good class activities such as Java applets that graph functions.
SPIN members who are aware of other sites of interest or who have their own web site are asked to contact Daryl ( stephen@etsu.edu ) so that he can continue adding to the page of links. Daryl hopes to develop a list of links related to developmental math content areas. He also invites suggestions for the organization of the web site itself. The Math SPIN web site can be accessed from the NADE web site or directly at www.way.peachnet.edu/devstudies/mathspin/index.htm . The direct address of the links page is www.etsu.edu/devstudy/spin/links.htm .
| Best deal in town
If you would like to become a member of the NADE Math SPIN (Special Professional Interest Network), contact Roberta Lacefield ( RSLace@mail.way.peachnet.edu ) to be placed on the list. There is a $5 membership fee to cover administrative costs such as the annual meeting, newsletter, and other SPIN activities. Contact NADE at the address below or Mike Smith ( mismith@sinclair.edu ), the SPIN Coordinator, to obtain a membership form. NADE 1234 Pembrooke Drive Warrensburg, MO 64093 |
| Best Practices in Developmental Math
The Math SPIN is proposing to produce a booklet entitled "Best Practices in College Developmental Mathematics Education." The booklet will discuss lecture, lab, and hybrid classes, as well as placement issues. If possible, we would like ideas that have been tested by some sort of evaluation process or student success rates if available. If you are interested in contributing to this effort, send your best organizational ideas and teaching suggestions to Deann Christianson ( dchristianson@uop.edu ) at the address below. A list of contributors will be included. Deann Christianson University of the Pacific Stockton, CA 95211 |
Notes/Announcements
A report entitled "Remedial Education at Higher Education Institutions in Fall 95" is available from the US Department of Education. The report, prepared by Westat Inc. under contract with the National Center for Education Statistics, can be downloaded from the Internet or requested from the following address:
National Center for Education Statistics
Office of Education Research and Improvement
555 New Jersey Avenue NW
Washington, DC 20208-5574
For the second consecutive year, the Math SPIN meeting was scheduled at the same time as other math
presentations. Consequently, many SPIN members had to choose between attending the meeting or
another presentation of interest to them. The leadership would like future SPIN meetings to be
scheduled at a time that does not conflict with other math activities. If you support this idea, please take
a minute to e-mail NADEpresident-elect Linda R. Thompson ( lthompson@harding.edu ) or current
president Martha Casazza ( mcas@whe2.nl.edu ) to express your support.
The International Conference on Technology in Collegiate Mathematics (ICTCM) is offering a 4-day
Professional Development Short Course Program that gives instructors the resources to integrate the
Web into their courses. The program will provide extensive hands-on opportunities to allow in-depth
study. Novice and intermediate tracks are available. The program will be hosted by Colorado State
University, Fort Collins, CO from May 22-25. The registration fee is $200. Graduate credit is also
available for an additional fee. For more information visit www.ictcm.org/shortcourses.
The newsletter welcomes submissions of any kind that members feel are appropriate including announcements, comments, articles, teaching tips, research, etc. Please be conscious of space limitations. Materials should be sent to:
Thomas Armington
Academic Services Dept.
Slippery Rock University
Slippery Rock, PA 16057
Approximately 30 math presentations
were given at the NADE 2000 Conference in Biloxi. In an effort to share the
conference with those unable to attend, we have collected the following summaries
of presentations. SPIN members are invited to contact presenters for additional
information. The newsletter thanks those who contributed to this effort.
Improved Success Rates in Developmental Mathematics through Alternative Learning Environments
Two programs were implemented allowing students extra time for difficult topics to increase mastery and employing an alternative testing site with no time limits to reduce test anxiety. The Flex-Pace program allows two semesters to complete algebra courses. Each class consists of four groups of eight students, a teaching assistant for each group, and an instructor. Course work is divided into six modules and an in-house workbook is used. Students must pass all modules by completing assignments and scoring 80% on all exams. Exams are taken outside of class in a Test Center. Students may retake tests on different versions until they score 80%.
Students completing all requirements in one semester are given a grade. Students completing less than four modules receive an "F" for the course. Students completing four or five modules receive an "I" and enroll in a follow-up course. These courses are pass/fail, 0 credits, and offered in five-week sessions with a fee equivalent to 1 hour. The classes are structured the same as the original course. Students completing all requirements during the first five-week session receive a grade for the original course. Otherwise they sign up for another five weeks. If they do not finish in the second five weeks, they sign up for a third and final five-week session. Students unable to complete all requirements by the end of the this session receive an "F" for the course.
The main feature of the Out-of-Class Testing program is that all exams are administered at the Math Test Center. Whenever an exam occurs, students are given a five-day period during which they make take up to three versions of the exam. Teaching assistants help students analyze their mistakes between versions. The highest score counts.
Presenter: Dianne F. Clark ( clarkd@ipfw.edu )
The Function of the Function in Developmental Math
This presentation used four components -- background, teaching, issues, and suggestions -- to address
the concept of functions in developmental math. Background information was used to develop a
rationale for the inclusion of functions, with reference to AMATYC and NCTM standards. An example
of how functions can be addressed in grades K-12 was presented, followed by a demonstration of how
functions can be taught in developmental math. This included methods of addressing definition,
representation, domain and range, and other function-related topics. The issues of basic skills and
calculator usage were also discussed. Journal names and web addresses were provided for reference.
Presenter: Selina Vásquez ( sv10@swt.edu )
Unleashing the Web in Developmental Mathematics
This session demonstrated how the Internet can be used as a powerful instructional tool to introduce students to an effective plan for studying math and for mastering math concepts. Participants were provided with assignments in which students utilize specific websites to explore mathematical concepts. The assignments were prepared by the presenters for Basic Mathematics, Elementary Algebra, and Intermediate Algebra courses.
Using web assignments promotes independent learning when students are directed to websites comprised of mathematical tutorials. Utilizing the web also enhances the critical thinking skills of students in developmental programs, and gives them an opportunity to see practical applications of concepts taught in class. One specific assignment involved tracking stock performance over a period of time, noting negative and positive fluctuations. After noting the changes, students were asked to speculate on the reasons for the fluctuations.
Developmental math instruction should prepare students to function in a world that is technology
centered. Utilizing web assignments provides an opportunity for students to employ technology while
mastering curriculum objectives.
Presenters: Marva Lucas ( mlucas@mtsu.edu )
Nancy Brien ( nbrien@mtsu.edu )
Meeting Math Standards with Graphing Calculators
This workshop described the successful integration of graphing calculators into the developmental math curriculum and demonstrated calculator activities that promote AMATYC standards, including the teaching of mathematics as a laboratory discipline. Graphing calculators have been used at the presenter's college since 1992 to implement these standards.
The following ways of meeting the standards were demonstrated. Calculators serve as discovery tools
that enable students to analyze situations through trial and error, graphing and verifying results, and
drawing conclusions about what they observe. Calculators promote the study of real-world models and
free students from laborious calculations. Graphical and tabular features enable students to explore the
meaning of mathematical identities which can be summarized algebraically. Finally, calculators are
effective tools for promoting collaborative activities through which students learn communication skills
in mathematics.
Presenter: Robert Pesut ( bpesut@pstcc.cc.tn.us )
Elementary Algebra Activities for Kinesthetic Learners
The presenter assembled 20 of the worst math students and worked with them to find different methods of learning algebra. The following are some examples of the activities she found to be successful with these students.
To simplify a square root, she began with a collection of objects, some of which were alike, in a plastic zip bag. The bag represented the radical itself, which can be seen as a container. If the bag had two identical objects, she took out the pair, putting one object on one piece of paper and the other on another piece of paper. The square roots were the contents on one piece of paper. Everything left in the bag stayed under the radical sign.
To distinguish factors and terms, she gave students scissors and strips of paper with polynomials typed on them (4x + 3y, 5xy, 9). She asked students to cut each strip into pieces containing only one term, placing positive terms on a piece of black paper and negative terms on red paper. Students then cut terms apart into separate factors.
Like terms were modeled using red and white pipe cleaners with colored beads. Red pipe cleaners
represented positive terms while white represented negative terms. One kind of bead was x, another was
y. Students modeled terms such as xyyxyyxx, then discussed the purpose of exponents. Other examples
were also discussed.
Presenter: Anita Hughes ( anitah@bbcc.ctc.edu )
Comparative Performance Standards & Retention Rates
A study was made to determine if developmental math students attending two classes per week were retained at the same level as students attending three classes per week. The study included Basic Math, Elementary Algebra, and Intermediate Algebra courses. Three variables -- performance averages, gender, and age classifications (traditional and non-traditional) -- were compared using a three-way ANOVA. Performance was measured by calculating the normalized differences between pre- and post-test scores. A two-way ANOVA was used to compare retention rates for each of the three developmental courses.
The study found no statistically significant differences in the three-way ANOVA for the three groups
compared for any course. There were also no statistically significant differences in the retention rates
for the three courses compared in the two-way ANOVA. The results suggest that, based upon gender or
age classification, students should be advised that there are no performance differences between
developmental math classes that meet twice versus three times per week. Future studies might examine
if differences exist for other groups (i.e., ethnic, marital status, or work status).
Presenter: Terrence Sundeen ( tsundeen@mtsu.edu )
Handheld Computer Systems in Developmental Algebra
This post-session workshop was an introduction to the philosophy, pedagogy, and application of a curriculum designed to work with algebraic manipulatives and the Casio Algebra FX 2.0 computer algebra system in relation to some of the topics in developmental algebra. Specific information about the pilot project and data indicating its success was also shared. Opportunities to participate in classroom testing of the curriculum are available at specific locations.
The project, funded by the National Science Foundation, takes advantage of the new handheld computer
algebra systems and new information about the ways in which students learn to revolutionize
developmental math at the college level. The curriculum builds on prior work suggesting the power of
the handheld calculator, the role of manipulatives in teaching algebraic concepts, and new information
about cognitive development in mathematical thinking. Careful attention was paid to building on
students' intuitive understanding of mathematical principles. Manipulatives were used to help students
acquire an understanding of underlying concepts. Traditional symbolic algorithms were explored and
practiced. The Casio FX 2.0 was employed to facilitate the symbolic computations. Workshop
participants were guided through the curriculum using the above approach.
Presenters: Dr. Laurie B. Hopkins ( lhopkins@colacoll.edu )
Dr. Amelia S. Kinard ( mkinard@colacoll.edu )
Mastery Learning with Self-pacing
This session presented data from a four-year evaluation of a program that uses the Keller Plan of Mastery Learning Instruction with modified self-pacing. Descriptive Tests of Mathematical Skills (DTMS) by ETS are given to all incoming students who have not met the general education requirements. Various levels of math are taught in a laboratory setting. Student tutors are trained using the CRLA Tutor Certification program.
The study, funded by the Irvine Foundation, compared pre- and post-test scores on the DTMS. Results
showed a significant and practical gain in skills. Mean gain as compared to the standard error of
measure was found to be several times higher. Completion rates ranged from 70-80% for developmental
courses. A comparison of grade distributions (by Chi-squared analysis) in subsequent math courses
showed no significant difference between non- developmental and developmental students.
Presenters: Deann Christianson ( dchristi@uop.edu )
Elaine Werner ( werner@uop.edu )
Is Sequencing of Topics Important?
Solving quadratic equations by factoring requires knowing how to factor and solve. Most developmental texts present this topic by demonstrating a factoring technique followed immediately by practice problems. Once factoring methods have been presented, solving is taught. While there have been many pedagogical changes in math texts, sequencing has received little attention. This presenter believes that factoring and solving should be taught together, not in isolation.
A study was conducted to determine if students would perform better if they were taught to solve and
factor simultaneously. Four Introductory Algebra courses were randomly divided into two groups. A
one-way ANOVA indicated that the groups were comparable on math skills before the manipulation.
One group was taught using the traditional approach and the other in a different sequence. Identical
problems were worked by all students, only in different sequence. Final scores were compared using a
t-test. A slight difference favored the experimental group, but no significant difference was found.
While this result did not support the hypothesis, an interesting discovery was made. The experimental
groups' instruction time was shortened by two days leaving time for extra activities. Other activities that
could be incorporated into the unit were also shared.
Presenter: Josette Ahlering ( jahlering@cmsu1.cmsu.edu )
Fun Math Activities to Enhance Dev. Algebra Classes
Young people of the 90's have been inundated with computers and video games that create for them a lifestyle that is lively and interactive. However, in a typical math classroom of the 90's, they have been expected to watch and learn as their teacher explains homework problems, presents lessons, and gives assignments. To these "upbeat" young people, this classroom situation seems passive and uninteresting. As a result, many dislike math and perform poorly in their math classes.
In an effort to motivate students to like math and to improve student performance in math, many
teachers are changing their teaching methods. They have begun to include group activities, to use
technology, and to model real-life problems that help students become more actively involved in doing
math. The presenters demonstrated examples of problems that allow students to participate in
"hands-on" group activities. Some of the activities require the use of a graphing calculator, others do
not. All of the activities were chosen to demonstrate problems that capture students' interest, create in
students a greater desire to do math, and help students better understand math. Materials distributed
included problems demonstrated during the session.
Presenters: Don Brown ( dbrown@gsvms2.cc.gason.edu )
Donna Saye ( dbsaye@gsvbms2.cc.gasou.edu )
Computer-aided Animations in Developmental Math
In this fast-paced, high-tech, low attention span age, instructors must compete to keep students attention in the classroom. Instructors must present material in new formats and media. Computer-aided animations are a novel approach to integrate new technology and instructional forms into the developmental math classroom.
In the spring semester of 1999, the presenter completed a project using Director 6.0 to create a series of
15 short computer-aided animation sequences to introduce developmental math topics. The sequences
were generated into multiple formats including self contained players burned on CD ROMs, Shockwave
Web movies, and videotapes. The use of multiple formats allowed more students to access the
animations. The project was evaluated by a class of 20 students. In general, the students felt that the
animations had educational value (average rating 4.525 on a Likert scale from 1-least to 5-highest). The
presenter demonstrated the use of computer-aided animations and shared personal experiences
concerning the technology and its success. The basic requirements for creating the animations using
Director 6.0 was also discussed.
Presenter: Meredith Higgs ( mhiggs@mtsu.edu )
Strategies for Teaching Rational Expressions and
Graphing Linear Inequalities of the form y = mx + b
When teaching rational expressions, teachers often focus only on the procedures given in the textbook or instructional materials. As some students have difficulty following these procedures and the examples teachers use to illustrate them on the chalkboard or overhead, teachers must be able to engage their student in tasks that promote understanding of the concepts and procedures. In addition to demonstrating knowledge of math concepts, teachers must also be able to employ alternate methods of solving problems. For students to develop mathematical power, a curriculum and learning environment must be created that promotes students' well-being. Improving the learning environment will enhance student achievement.
One teaching strategy demonstrated in the presentation was prime factorization using the "ladder
method." This is an alternative method to the tree diagram used in most math texts. Another topic
demonstrated was the test of divisibility. Determining the greatest common factor and least common
multiple were discussed using alternative methods which included an extension of the "ladder method."
Other topics demonstrated included -- Comparing fractions, Cross mean of adding and subtracting two
fractions, Single-fraction and LCM methods of simplifying complex fractions, and Graphing linear
inequalities of the form y = mx + b.
Presenter: Samuel Richardson ( srichard@aug.edu )
Enhancing the Developmental Algebra Curriculum
It's no secret that motivation is a problem for many students in developmental algebra. In addition to the motivational problems associated with developmental studies in general, prior negative experiences with math and the abstract nature of algebra heighten the problem. On course evaluations, however, students identify the curriculum itself as contributing to their motivational problem in that they find algebra to be boring and irrelevant to their academic pursuits. This presentation examined ways that instructors can address these valid student concerns by making the developmental algebra curriculum more interesting, meaningful, and fun.
Five types of curricular enhancements were discussed and demonstrated, enhancements that can be
made in any algebra course regardless of the instructional format. These included -- Linking algebra
concepts to other courses that students will take while in college, Drawing on areas of general student
interest for application problems, Turning common problems into fun problems, Providing "challenge
problems" for stronger students, and Using pictures on handouts to enliven otherwise ordinary
instructional materials. Examples of each were demonstrated. These included the linkage of algebra
concepts to the sciences, business, and economics; applications drawn from consumer affairs, social and
economic trends, and the laws of nature; and fun problems such as the Y2K and Divide-by-0 dilemmas.
Presenter: Thomas Armington ( tmarmington@aol.com )
Teaching Online Developmental Mathematics
As distance learning has expanded, so has the use of the Internet. What are the issues for teaching material on the Internet? What students will benefit from such opportunities? These are some of the questions that must be answered in creating an online course.
Over the past two years, the presenter implemented online courses in Developmental Math and College Algebra. Class notes were available on Web pages. Students were required to participate in chat rooms and discussion forums, and to contact the instructor regularly by e-mail. Testing was done in a traditional format at college testing centers.
The online course took more instructor time as students felt free to e-mail her with homework questions (usually preceded by comments about what else was happening in their lives -- sick kids, dog died, husband laid off, etc.). The presenter also noted that success in this type of course requires a higher degree of student motivation and self-discipline.
The presentation included resources and methods for teaching a math course on the Internet. Other
online math courses are in the works at the college.
Presenter: Mary S. Hall ( mhall@gpc.peachnet.edu )
Using the TI-92 Calculator in the Geometry Classroom
This presentation gave a hands-on experience of the TI-92 and its use in teaching geometry. Features of the calculator's geometry menu were shown and used to demonstrate geometric theorems. Particular points examined included -- point, line segment, angle, angle measure, polygon, sum of angle measures in a polygon, regular polygon, parallel lines, transversal, corresponding angles, triangle, concurrence of perpendicular bisectors, circumcenter, circumscribed circle, and calculating pi = circumference/diameter.
The course is taught by faculty members of the Developmental Studies Program to students who did not
complete a high school geometry course. It has been the experience of the presenters, over a period of
several years, that students building their geometry skills derive a better understanding of theorems
when they are able to visualize the geometric figures involved. The presentation demonstrated how the
TI-92 can be used to show illustrations of geometric figures and to facilitate a greater understanding of concepts.
Presenters: James Sanders ( sandersj@apsu.edu )
Patrick Perdew ( perdewp@apsu.edu )
Stepping Up: A Hands-On Approach to Slope
Slope is a rate of change, not a formula to be memorized. This presentation demonstrated how to reach the many students that are kinesthetic and visual learners by using a concrete model, a set of stairs, to visualize steepness. To climb stairs, one steps up before stepping forward. Since slope is a rate or ratio, usually written in fractional form, the numerator (vertical change - stepping up) is written first followed by the denominator (horizontal change - stepping forward). By color-coordinating the links used to build the stairs, students can easily count the blocks rising and the blocks across. To reinforce the concept, students make their own set of stairs given a certain slope.
Rulers are used as ramps to demonstrate the steepness of each set of stairs. The sets of stairs are arranged in order according to steepness of the ramp. The numerical slope values are written on the board in corresponding order. Students observe that the slopes are ordered from largest to smallest, and make the connection that the larger the slope, the steeper the ramp.
The approach then moves to graphs on the coordinate plane and an input-output table. On the graphs,
slope is determined by counting vertical spaces compared to horizontal spaces moving from one point
to another on a line. The idea of counting is carried from the concrete model of stairs to the picture of
the line. Points on the line are matched to data entries in the table. Slope is then calculated by finding
the change in output as compared to the change in input.
Presenter: Connie Rost ( crost@slcc.cc.la.us )