MET: the Math Exit Test at Pierce

At Pierce College there is an MET for elementary algebra and an MET for intermediate algebra. All instructors of those classes are required to have their students participate, but each instructor determines how the MET scores will be weighted in the students' grades.

The MET has both multiple choice and "essay" parts, all submitted on a Scantron form. Instructors volunteer to meet after the exam to team grade the essay questions--the volunteers may but need not be instructors of the relevant courses.

The MET was designed as way to measure the department's success at achieving its stated Student Learning Outcomes (SLOs) in elementary and intermediate algebra. Each instructor is given summaries of his/her students' performance, as well as the summaries across all sections.

The department learns on which problems students overall perform well and on which they perform poorly. Individual instructors can compare their students performance with those of the entire department.

The department chair announced to the department that one intermediate algebra instructor (Kathy Yoshiwara) had far more students in the top 10% than any other instructor. Not officially discussed was the fact that one (anonymous) elementary algebra instructor had an unusually large number of students finishing the semester for a grade, with all scoring below the department MET mean, and providing a class average a few standard deviations below the department MET mean.

Guess which algebra instructor is a favorite among students, the counseling department, and our Special Services faculty and staff?

My favorite free math stuff

Winplot

Although I have licensed copies of Mathematica, Mathcad, and Maple, my favorite grapher is Winplot. Plots are easy to create and highly customizable. Winplot handles parametric, polar, and implicit 2D graphs and wireframe 3D plots, with numerous other nifty features.

Winplot is one of several clever programs written by Rick Parris of Phillips Exeter Academy. You can download his free programs from http://math.exeter.edu/rparris/.

GeoGebra

Another under-utilized program is Markus Hohenwarter's GeoGebra. If you ever wanted to use (or are using) Geometer's Sketchpad or Cabri, you might want to give this one a try. Like GS or Cabri, GeoGebra allows you to make a geometric construction based on points and/or lines of your choice, then shows you how the constructed object changes as you use the mouse to alter the defining points or lines.

But unlike GS or Cabri, GeoGebra also has an algebra window that records the algebraic representation of the geometric objects. You can either modify an algebraic definition and watch in real-time the change in the figure, or alter the figure and see how parameters change in the algebraic description.

Read more about GeoGebra in articles in the online journal Loci (http://tinyurl.com/yk8w3ks and http://tinyurl.com/yz2yjkj), or download the free program directly from http://www.geogebra.org/cms/ .

Flash Forum

Barbara Kaskosz and Doug Ensley's Flash Forum has lots of clever applets for free download or use online. I particularly like the "Visualizing Regions for Double Integrals" (http://tinyurl.com/ygcfulh) by Barbara and Lewis Pakula. You enter the limits of a double integral (in rectangular or polar coordinates) and the appropriate region is sketched. Or you can ask for a practice problem, and you are given a region for which you need to determine the coordinate system and corresponding limits to define it.

The Flash Forum also has a 3D function plotter, and graphers for surfaces defined parametrically in rectangular, cylindrical, or spherical coordinates (http://tinyurl.com/yhx45lx).

But my favorite applet is "Terminate the Terminator!", (http://tinyurl.com/yzn9m25) a game to introduce radian measure and polar coordinates. It was originally created by my colleague Bob Martinez in Mathcad, but the online version is in Flash.

Algebra Success at Pierce

Algebra Success at Pierce (ASAP) is a program that allows students to take both elementary algebra and intermediate algebra in one semester.

Whereas our school (and state) typical success rate is around 50% in each of the two courses, Kathie Yoder has had a 70% success rate at getting students through both classes in one semester.

Her students score higher on the department's standardized intermediate algebra exit exam than students in the regular or online intermediate algebra classes.

In addition to having an exceptional teacher, the students in ASAP have several advantages over their peers in other intermediate algebra classes. ASAP students are all enrolled in both elementary algebra and intermediate algebra (5 units each), Personal Development 40 (3 transferable units taught by counseling faculty), and a 1-unit math study skills course. (Yes, the students meet with Kathie for more than 2.5 hours per day, 4 days per week.) The students are not permitted to enroll in other classes during that semester.

In other words, they are immersed in math for the semester.

The course materials are written by Pierce faculty, designed specifically for this course. There is a Supplemental Instruction (SI) leader who holds study sessions outside the assigned class hours.

Pierce has also had students in a Learning Community experiment that had prealgebra, elementary algebra, or intermediate algebra, teamed with the PD 40 class and 1-unit of study skills. Results were not consistently better than for students in ordinary sections of those courses.

We have had previous experiments with SI leaders in algebra classes, but again with no convincing evidence of effectiveness.

This semester we have a second section of ASAP, and the new instructor, Jenni Martinez, reports very encouraging success on the first two exams.