Fall 1997
Vol 6 Issue 1
IN THIS ISSUE...
A First Year Editor's Perspective
Wu Yi - MCCD Business Initiative
More Than Cosmetic Surgery
Alternative Assessment in Mathematics
The Library Tour is Gone, Long Live Live Instruction
SEE ALSO...
The Labyrinth
Maricopa Center for Learning and Instruction
More Than Cosmetic Surgery
Ted Corley, GCC
In the Maricopa Community College District, Mathematical Concepts and Applications (MAT 102) has always been a terminal mathematics course designed to meet the requirements for some associate degrees and for most certificate programs. MAT 102 also acts as a prerequisite for specialized programs in areas such as business and nursing. Over time, however, this non-transferable course had degenerated primarily to just another arithmetic review, with little or no resemblance to the original course intent. Mathematics and client discipline instructors had become dissatisfied with it, and the Glendale and Mesa mathematics department chairs were confronted with the task of giving the course a "facelift."
We, the teachers representing four campuses and at least five disciplines, were recruited to incorporate a number of meaningful applications into the existing course content. The challenge was to make MAT 102 a more valuable mathematics course for our students' future occupational coursework. We began a process we thought would be a one to two month summer effort -- plenty of time for a tuck here, a few wrinkles smoothed there.
During the first joint meeting to organize this "minor" surgery, it soon became apparent that we were, instead, in for a major reconstructive effort. Because many of the mathematics instructors involved have had previous knowledge and experience with the national mathematics reform movement, ideas about changing the course reflected many of the ideas found in the NCTM Standards and AMATYC Crossroads documents. Movement towards problem solving and away from memorizing procedures, coupled with active hands-on experiences, were now seen as two of the guiding ideas behind curriculum and materials development. The use of appropriate and available technology would also be emphasized along with a greater focus on communication-especially communication of mathematical reasoning. There would also be an attempt to produce activities that encouraged students to work in cooperative groups. Incorporating these ideas forced us to rethink the entire instructional delivery system of the course-a process that expanded the vision and scope of the project.
The client discipline instructors, particularly those from the nursing and business programs, welcomed these reform ideas. They particularly encouraged the use of appropriate technology and the inclusion of cooperative learning techniques. They also emphasized the need for "teamwork" in their respective fields.
The first summer's work included daily campus meetings and periodic district-wide meetings. The course content was the main meeting focus. We did began by simply trying to include some meaningful applications from the client disciplines. However, discussions naturally led away from isolated applications to the creation of lessons that teach all of the core mathematics concepts -- and use teaching methods that most students would not have previously encountered in mathematics courses. All students would benefit from a varied set of applications springing from a variety of occupational fields. But, they would also benefit from mathematics instruction that differed from ways they had experienced previously.
The following is an example of the kind of dialogue that developed during many of these campus and district-wide disciplinary group meetings.
"What do we really want students to know about ratios and proportions?"
"Well, we want them to know what they are and how to use them."
"So we want them to distinguish between a ratio and a proportion. Do we want them to distinguish between a ratio and a rate?"
"Well, I don't know if they need to know the difference. But, as we're writing these applications we need to make sure we use correct mathematical language. By the way, shouldn't interest rates be called interest ratios instead? The units are both dollars!"
"Do we really want them to know what the difference between a rate and a ratio is, or is that just mathematics teacher trivia?"
"I think we could start with a nursing problem that asks them to find how many pills a person should get, if you know how much drug is in each pill, and the prescribed dosage."
"Sounds like a good starting place or at least a good application of proportions. We could start the unit with an activity to estimate the height of one of the light poles outside."
"How do you do that? And, will students ever really use that?"
"This is a mathematics course and there is some mathematics that is beautiful and important even if we never expect students to use it in their careers."
We did eventually reach some agreement by deciding which mathematical concepts we wanted students to know and what problems we wanted them to be able to solve.
Here is an example of our results.
Ratios and Proportions
Ratios and proportions, an obvious inclusion in developmental mathematics
courses, were also seen by both nursing and business instructors as a
major component in the mathematics portion of their disciplines. Practical
applications were developed as part of the curriculum materials.
The concept of proportions is introduced with a two-part "Group Survey" activity. First, students are surveyed as a class for some simple identifying characteristics, and then again in groups of seven or eight. One question asks, "How many of you are left-handed? Right handed?" The results of the surveys (sample) are then used to make predictions about the student body (population). Flaws in the sampling procedure and methods for improving it are discussed. Students are also asked to determine which data-class or small group-is the better predictor of population trends and to explain why. Then, we included applications involving dosages, property taxes, vehicle operational expenses, similar triangles, unit pricing, measurement conversions, and many others which directly tie the mathematical concept of ratios and proportions to students' lives or their desired occupations. These applications were spread throughout the remainder of the course to demonstrate the non-isolated value of mathematics
Of course, it is not enough just to produce new instructional materials with the hope of improvement. On-going assessment plays an essential role in determining the effectiveness of any reform, and positive outcomes are the measure of any reconstructive effort. To date, our formal assessment shows that the course materials developed and the instructional strategies used have affected student achievement and attitude. In the most recent semester, MCC students who were taught with the new materials scored significantly higher on the achievement posttest than students in all but one section, who were taught with the old materials. And, GCC students taught with the new materials scored higher on a number of the attitude assessment items. Our assessment continues this semester with a different cadre of teachers. With more data and a greater variety of instructors involved, we will get a clearer picture of the effectiveness of the newly developed materials. The district-wide meetings of mathematics instructors who are using the new materials have yielded clear evidence that the attitudes of instructors have changed-perhaps more dramatically than the students' attitudes.
During the first year of implementation, each campus held weekly meetings to monitor and adjust instructional materials and strategies. These meetings were instrumental in shifting teacher attitudes about resources and pedagogy. After the first year of these meetings, a GCC instructor remarked, "In this course, the roles of the text and the supplementary materials have been reversed for me." In other words, the text is used for practice and for students who need extra help with specific procedures. The project materials themselves now are the centerpiece of the course. Another instructor commented that their weekly MAT 102 sessions were the best professional development he had ever attended. This positive attitude not only has permeated the meetings and discussions of the reform project, but has found its way into the classrooms. Similar meetings continue now with a new set of instructors.
Our work was a response to a specific set of problems. It reflects the strengths and limitations of the participants. For us, the early hope that change would be quick and painless was not to be. Now, over three years later, the effort continues. We have found that, in the end, true reform is more than a face-lift. It is bone-deep.