Fall 1997
Vol 6 Issue 1

IN THIS ISSUE...

Welcome!

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

Egypt Calling

Bag of URLs

Upcoming Events

What's New in MCLI Resources?

SEE ALSO...
The Labyrinth

Maricopa Center for Learning and Instruction

Alternative Assessment in Mathematics
Melinda Rudibaugh, CGCC

Many MCCD mathematics instructors are using assessment devices other than traditional tests and quizzes. These devices include presentations, projects, journaling, interviews, and portfolios. Why bother, you might ask, when it is so easy to grade those right vs. wrong kind of problems? Heck, even partial credit on a math problem is not a big deal - one just finds where the student went wrong . . .

Instructors have responded to the standards set forth by the National Council of Teachers of Mathematics (NCTM) and the American Mathematical Association of Two Year Colleges (AMATYC) by implementing new classroom strategies. Harder still is the process of changing assessment tactics. Using alternative assessment techniques requires much more time and dips into the subjective realm where analytically-minded math teachers often feel most uncomfortable.

The standards written for two-year college mathematics (Cohn, pp. 4-5) include statements such as:

• All students should grow in their knowledge of mathematics while attending college.
• Study should be meaningful and relevant and taught as a laboratory discipline.
• The use of technology is essential.
• Introductory college mathematics should significantly increase students' options in educational and career choices.

Although the AMATYC documents do not address assessment per se, they should leave the feeling that old, yellowed tests of algorithmic skill and speed, do not assess the outcomes sought in the spirit of the new standards.

As the predecessor to the AMATYC documents, the NCTM Curriculum and Evaluation Standards addressed a broader span of mathematical learning. Still, we evaluate for many reasons: to make decisions about classroom content, instructional methods, and, of course, to assign grades. Santel-Parke and Cai (1997) state that we need to assess to see if students really understand. They encourage us to provide opportunities for multiple solutions and processes that demonstrate mathematical cognition.

Recently, in a graduate research class, the instructor asked how we encouraged critical thinking in our classrooms. My immediate response was "through our assessment devices." My belief is that one can model critical thinking and use good questioning techniques, but students do what you "pay" them to do. If you get them climbing Bloom's ladder in class and in projects, but shut them down with a test on rationalizing denominators and simplifying radicals ad nauseum, what message is sent about the value of critical thought in mathematics?

So, if you want to try something different, more in-depth, more probing, what can you do? Lester and Kroll (1991) suggest beginning with smaller steps. However, so many interesting and innovative ways to evaluate are available that it is possible to get overwhelmed (p. 7). Time is the ever-present obstacle. Though interviewing has been shown to provide critical information on student understanding, most faculty do not have time to conduct them on a regular basis. They might try to conduct informal chats while monitoring group work or cut time when students linger after class. Lester and Kroll suggest keeping such information on note cards in a box for quick reference and updates. I have not tried interviews but applaud a colleague who did. His students were so impressed with this concern that they really worked hard for him - much harder than they did for me.

Journaling has been shown to provide a vent for math-anxiety. Some instructors use them just at the beginning (to lay those anxieties on the table) and at the end of the semester (to look back at what's been conquered). I have requested brief journals, which almost look like cover letters, to accompany the submission of "competency packets." The student tells me a little about his or her personal path to accomplishing tasks demonstrated in the folder then works on, say, decimals and percents.

If portfolios are something you wish to try, be advised by someone who learned the hard way; they are not just folders of student work. Like an artist's portfolio, they represent accomplishments and must include tests and selected assignments. In addition, mathematics portfolios could also include self-reflection and work that the student has done to help him or her gain understanding. Students must think and reflect about what goes into the portfolio and instructors must evaluate them on the variety and quality of entries. I use them in calculus classes as a means for students to rework the tests for final presentation and to show the incorporation of technology into the curriculum. I also use them in MAT156 , a class for pre-service elementary teachers in which portfolios serve a greater use than as an assessment device for me; they send the students off with a packet of goodies to start their own files and bulletin boards. Most importantly, portfolios celebrate student accomplishments in a subject many have feared.

Whatever you try, remember that effective assessment is just part of effective instruction. Share your plan with your students. Let them know your expectations so that they may be successful. The availability of a variety of techniques allows for a more complete picture of student understanding, but the choice is yours and needs to fit the class and your goals.

References

Cohn, D. (Ed.). (1995). Crossroads in mathematics: Standards for introductory college mathematics before calculus. Memphis, TN: American Mathematical Association of Two-Year Colleges. http://www.richland.cc.il.us/imacc/standards/