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.

The Mod Squad at Pierce

Five members of the Pierce College math department--Cassie Cain, Sheri Lehavi, Brenda Rudin, Zhila Tabatabai, and Kathy Yoshiwara--are trying an experiment to improve student success in elementary algebra.

Five sections of elementary algebra, a total of 200 students, are involved.

The plan is based on the Emporium model (http://www.thencat.org/PlanRes/R2R_Model_Emp.htm ) developed at the Virginia Teach and implemented successfully at a variety of institutions nationwide, and specifically at Foothill College in Los Altos (http://www.foothill.edu/PSME/index.php ).
The course is broken into small pieces, or modules, that students can cover at their own pace (with plenty of guidance and a detailed suggested schedule for successful completion in one semester.)

The modular format is designed for active learning. "Lectures…are replaced with an array of interactive materials and activities that move students from a passive note-taking role to an active-learning orientation." (NCAT) This format should also give students more control over the pace at which they cover the material, and encourage them to take more responsibility for their own learning. If students cannot finish the course in one semester, but do complete at least half the modules, they can opt for an Incomplete and continue the following semester.

Course Structure
The five members of the "Mod Squad" have organized the material into ten modules. A module consists of a pretest, four or five lessons with worksheets for in-class practice, a sample test, and a suggested schedule. There was an initial plan to have homework problems delivered and graded by computer, but that has not been implemented this semester.

Mod Squad members authored the modules, which students can purchase at the Bookstore at cost. Students will not need to purchase a separate textbook.

Study skills are incorporated into lessons as part of the course. The study skills activities are based on the lessons designed by the Mod Squad and already in use in Pierce College Learning Communities iand the ASAP (Algebra Success At Pierce, a 10-unit math + 1 unit study skills + 3-unit Personal Development) algebra course. We hope to be able to add a 1-unit study skills class to the Modular Math classes.

When students finish the assignments in the module, an instructor verifies that the portfolios are complete, and the students are given a ticket allowing them to take the in-class module test. These tests would require mastery at 85%. (The plan to have students take a qualifying sample test on the computer has been postponed.)

Students who do not pass the module test would be required to complete a second set of worksheets (and computer drill problems) before attempting the module test again.

Pierce does not have a testing center to accommodate self-paced courses. Instead, module tests are offered twice weekly, on Tuesdays and Thursdays, with one or more of the modular classrooms used as the test room, and one of the modular team serving as proctor. All students who are eligible to take a module test would report to the test room and be given the appropriate module test. Tests are returned to the respective instructor of record for grading. Students who don't wish to take a test on that day report to one of the remaining classrooms for class as usual.

Delivery
The course is team taught by the five instructors of the Mod Squad. Each instructor is responsible for the grading and record keeping for the students on her roster. However, all modular sections meet at the same time in adjacent rooms, and students may attend class in any of those rooms, depending on which module they are studying.

Class meetings concentrate on group work, practicing the skills on the modular worksheets. Instructors also offer short mini-lectures as needed. At least one classroom keeps to a schedule that allows students to finish the course in one semester, but others work at a pace to accommodate different students. Students working on the same module are formed into groups if they wish. The modular team instructors coordinate daily to plan scheduling and room allocation.

To facilitate active learning, there is a student tutor for each classroom. Tutors help instructors interact with students individually or in small groups and assist with organization and logistics, as students move from one setting to another. "Students need human contact…to assure them that they are on the right learning path. An expanded support system…is critical to persistence, learning, and satisfaction." Tutors are also crucial for checking the steady stream of worksheets and quizzes that provide students with immediate feedback. "Shifting the traditional assessment approach toward continuous assessment is an essential pedagogical strategy. … Low-stakes quizzes motivate students to keep on top of the course material, structure how they study, and encourage them to spend more time on task."


Timeline
It is anticipated that many students will need more than one semester to be able to pass all the modules at the 85% proficiency level required. So students who have completed at least half the modules at the 85% level but do not complete the course in one semester will earn an "incomplete" grade in the course. They can pick up where they left off the following semester.

But in order to encourage reasonable progress, any student in the program who does not complete at least half of the modules in the first semester will earn a grade of F.

The modularized elementary algebra course serves as the elementary algebra component of our departmental MAP (Mediated Algebra Project, mentioned in the previous blog). We can monitor both courses via the common exam given to all Pierce College sections of elementary algebra and the common exam given to all Pierce College sections of intermediate algebra.

More on the MET, our common exams, in the future.

Developmental math projects at Pierce

Several members of the Los Angeles Pierce College mathematics department are involved in two extraordinary experiments to improve the school's developmental math program. The Mediated Algebra Project (MAP) aims to improve the success of intermediate algebra students, and the Modular Math Project is trying an alternative method for teaching elementary algebra.

MAP involves:

• reading assignments completed before coming to class (in a textbook authored by Pierce faculty and available to students both online for free, or through the bookstore at the cost of copying and binding),
• online reading and skills questions (using the open source WeBWorK homework delivery and grading system http://webwork.maa.org/moodle/, with problems coded by Pierce faculty),
• online videos (including Pat McKeague's freely available MathTV site (http://www.mathtv.com/ ) and screen capture videos made by Pierce faculty),
• an online Question and Answer student forum using the open source Moodle learning management system,
• Replacement of lectures with in-class activities that explore math concepts, (from an Activities book created by Pierce faculty and sold to the students at cost) within an environmental theme when possible ,
• written homework aligned with the in-class activities, and
• concept "clicker" questions (written by Pierce faculty).

This fall 2009 semester is the first try at the "full" MAP package, with three faculty teaching in the pilot: Kathie Yoder, Kathy Yoshiwara, and myself. The Reading and Activities books have already been class-tested by the principal author, Kathy Yoshiwara. Some of the ancillary MAP materials were created by Roya Furmuly, Sheri Lehavi, Bob Martinez, Jenni Martinez, Brenda Rudin, Ben Smith, Kathie Yoder, and me.

The "Mod Squad", team-teaching a modular self-paced elementary algebra course, consists of Cassie Cain, Sheri Lehavi, Brenda Rudin, Zhila Tabatabai, and Kathy Yoshiwara. More on their efforts later.

Most of the funding to pay for the continuing development of the two programs comes from California's Basic Skills Initiative (http://www.cccbsi.org/ ). Further funding came from a STEM grant at the college and will be supplemented this semester by a Hewlett Foundation (http://www.hewlett.org/ ) grant. The college itself has committed none of its normal budget to the effort.

Teacher Prep at Community Colleges

Although only a small proportion of the general public or even the faculty and administrators involved seem to be aware of it, community colleges are in the business of preparing future teachers.

It has been estimated that 40% of U.S. K-12 teachers took math or science at a two-year college (http://www.nsf.gov/pubs/1999/nsf9949/nsf9949.htm ) and that 46% of baccalaureates in science and engineering have attended a two-year school (http://www.nsf.gov/statistics/nsf04302/ ).

The numbers of K-12 teachers who attended two-year colleges only grows if we include courses and degrees in non-STEM disciplines.

At California State University Northridge (CSUN) , which identifies teacher preparation as one of its primary missions, more than half of their students in the multi-subject credential program (for teaching elementary school ) took math courses at a community college. Most of CSUN's math majors are considering a career in teaching, and about two-thirds of CSUN math majors took math at a community college.

Many or most universities require only 3 to 9 units of courses taught by math departments for the students preparing to become elementary school teachers. Some of these units may be taken at a community college, and considering that many students (51% at CSUN) take developmental math classes at a two-year schools, and furthermore that some students (20% at CSUN) require as much as 20 units of remediation, our prospective elementary school teachers are probably taking more math at two-year colleges than at four-year colleges and universities combined.

A number of faculty at two-year colleges take seriously their role in the recruitment and education of future teachers. The Teacher Prep Committee ( http://amatyc.dtcc.edu/ , http://teacherprep.amatyc.org/ ) is one of only eight standing national committees of the American Mathematical Association of Two-Year Colleges. Yet there are two-year colleges where the "Math for Teachers" class either does not exist or is taught primarily by adjunct faculty because the full-time faculty do not have sufficient interest to teach the course, or the institution is not sufficiently motivated to run the course.

A policy against married couples

Los Angeles Pierce College has decided that no married couples can serve together on a hiring committee. This policy was initiated by the vice-president of academic affairs and then endorsed by the Pierce Ethics Committee and the Pierce College Academic Senate.

The motivation behind the ban is putatively to reduce the possibility of Pierce receiving accusations of collusion between a married couple from a candidate who was not offered a position. The policy establishes Pierce's preference to restrict the rights of all productive married couples on the faculty over accepting any risk that a disgruntled candidate with sexist prejudices may file a complaint and thus cause Pierce the inconvenience of having to defend faculty against false accusations.

If a Pierce couple actually does engage in collusion or unfair practices, then the department should not nominate them for a hiring committee, the Vice-president should advise the senate to reject the offending couple, and the academic senate should not approve them. Further, everyone on a hiring committee, including any couple, is supervised by a dean and compliance officer.

There will be no inappropriate collaboration between any married couple if any one of the department, or the VP, or the senate, or the dean, or the compliance officer can do a responsible job, even if no married couple can act responsibly on their own.

Obviously it is simpler for Pierce to ban all couples rather than to take on the responsibility of making a hard decision to deny opportunities a specific couple if it should become appropriate. But a policy banning all married couples from serving together on hiring committees is in direct opposition to the recommendations of the American Association of University Professors (AAUP).

The 1971 position paper “Faculty Appointment and Family Relationship” called for an end to “policies and practices [that] subject faculty members to an automatic decision on a basis wholly unrelated to academic qualifications and limit them unfairly in their opportunity to practice their profession.”

This position paper was prepared initially by the Association’s Committee on Women in the Academic Profession. It was approved by that committee and by Committee A on Academic Freedom and Tenure. The statement was adopted by the Association’s Council in April 1971.

But let us assume that we support Pierce's position that trying to avoid lawsuits is more important that supporting productive faculty. Then we should consider how much better it would be if we also banned any two faculty members sharing religious beliefs from serving together on a hiring committee, because there is a chance that a rejected and disgruntled applicant may complain that the two colluded against him or her. We should also prevent any two faculty who attended the same school together from serving together on a committee. Certainly we cannot allow any two homosexuals to serve together.

Continuing this logic leads us inevitably to restricting the hiring committees to members of the Pierce community who are beyond reproach because of their unquestioned integrity and fairness, such as the Ethics Committee and the Vice-president of Academic Affairs. But the school's philosophy requires that we guard not only against rational complaints, but especially against irrational complaints of collusion. So the appropriate policy would appear to be that all personnel decisions should be decided by lot rather than allowing any human to be involved.