When Sandy Keith first invited me to join her in putting together this book, my motivation was the section on assessing the major. In our last accreditation review, Wabash College, where I began this work, had been told that it was only being provisionally accredited, pending adoption of an acceptable assessment plan. The administration then told each department to come up with a plan for assessing its activities. With little guidance, we each put together a collection of activities, hoping they would be sufficient to satisfy the accrediting association. Having wasted a lot of time trying to figure out what assessment meant and what options we might consider, I felt that by writing a book such as this one, we could save many other colleagues a similar expenditure of time. Thus, I began work on this book more from a sense of duty to the profession than from any excitement over assessment.
My attitude toward assessment reversed dramatically when, on Sandy's suggestion, I read Angelo and Cross's, Classroom Assessment Techniques. This book contained ideas which could help me in the classroom, and immediately. I began putting some of these techniques to use in my classes and have found them very worthwhile.
Most of us have had the experience of lecturing on a topic, asking if there are any questions, answering the few that the better students have the courage to ask, assigning and grading homework over the topic, and yet when a question on that topic is asked on an examination, students are unable to answer it. Classrooms Assessment Techniques (CATs) are ways to find out whether students understand a concept, and what difficulties they are having with it, before they fail the test on it. They also include ways to find out how well students are reading, organizing the material, and so on. Traditional assessment is summative assessment: give students a test to find out what they've learned, so they can be assigned a grade. CATs are formative assessment: find out where the problems are so students can learn more and better.
Not all of the assessment techniques in this section of our book are CATs; many of them can be used for both formative and summative assessment, and some are mainly summative. However, what they all have in common is that in the process of assessment, students are learning by participation in the assessment technique itself. We've always given lip service to the assertion that on the best tests, students learn something taking the test; the techniques in this section make this homily a reality. This section doesn't try to duplicate Angelo & Cross, and we still recommend that you look at that book, since many of the techniques which they don't specifically recommend for mathematics can be adapted to use in our classrooms. However, we present here a good variety of assessment techniques actually being used in mathematics classrooms around the country to improve student learning.
This section begins with variations on the traditional tests and grades. Sharon Ross discusses ways in which traditional tests can be modified to examine aspects of student understanding, beyond the routine computations which form the core of many traditional examinations. One variation on tests is Michael Fried's Interactive Questionnaires, a form of quiz taken electronically and sorted automatically to give large classes semi-individualized detailed responses to their work. Then William Bonnice discusses allowing students to focus on their strengths by choosing what percent (within a range selected by the instructor) of their grade comes from each activity.
Next comes a collection of CATs, ways of finding out how well students understand a concept or section which has been taught. David Bressoud discusses adapting Angelo & Cross' One-Minute Paper to mathematics classes, large or small. It takes a very small amount of classroom time to find out how productive a class period has been, and what topics need further clarification. Dwight Atkins also adapts an Angelo & Cross technique, Concept Maps, to mathematics classes to learn how well students understand connections between related concepts. John Koker has his students discuss the evolution of their ideas as they work on homework sets, which gives him insight into how much they actually understand and what they have learned by working the problems. John Emert offers three quick CATs: a brief version of the class mission statement (which Ellen Clay discusses, later in the section, in more detail), a way to check how well the course is going before the end of the semester, and a quick way to assess how groups are working. Sandra Keith describes a number of "professional assessment techniques," ways to encourage students to take a more professional attitude toward their studies, going beyond the individual course.
Several articles discuss helping students review and clarify concepts. Janet Barnett uses true/false questions, but has students justify their answers. These justifications bring out confusions about the concepts, but are also the beginning, for calculus students, of writing mathematical proofs. Joann Bossenbroek helps developmental and precalculus students become comfortable with mathematical language and learn how to use it correctly. Agnes Rash encourages students to look for their own applications of the methods they're studying while reviewing the material for a test.
At the opposite extreme from most CATs, which are fairly short and give helpful information on individual details, are methods used in research on teaching and learning. We have not tried to cover that field in this section, but do have one article, by Kathleen Heid, on using videotaped in-depth interviews to assess student understanding. While very time-consuming, it is a method of finding out just what students have understood, and where confusions lie.
There has been considerable attention in the last several years to having students engage in larger projects and write about mathematics as a route to learning it better. Several other Notes volumes (especially #16, Using Writing to Teach Mathematics, and #30, Problems for Student Investigation) discuss these processes in more detail; here we present additional guidance in this direction. Annalisa Crannell discusses assigning and assessing writing projects. Charles Emenaker gives two kinds of scales which can make the process of assessing project reports less tedious. Brian Winkel explains how having students work on large projects during class time gives multiple opportunities to redirect students' formation of concepts before they are set in stone in the students' minds. Alan Knoerr and Michael McDonald use two kinds of portfolios to help students aggregate and reflect on concepts studied. Dorothee Blum uses student papers in an honors, non-science majors' calculus course to integrate ideas studied. Alvin White discusses using student journal writing to expand students' vistas of mathematics. Patricia Kenschaft uses short papers and students' questions to have general education students think carefully about the readings.
As many of us move away from complete dependence on the lecture method, the issue of assessing these alternative teaching techniques arises. Nancy Hagelgans responds to the concern, when using cooperative learning, of how to ensure that individuals take responsibility for their own learning. Catherine Roberts discusses effective ways of giving tests in groups. Carolyn Rouviere discusses using cooperative groups for both learning and assessment. Annalisa Crannell explains how to give and grade collaborative oral take-home examinations. (See also the article by Emert earlier in this section for a quick CAT on discerning how well groups are working.) Sandra Trowell and Grayson Wheatley discuss assessment in a problem-centered course.
In recent years we have become more aware that not all students are 18-22-year-old white males. Some of these other students don't "test" well, but can demonstrate what they've learned when alternative assessment methods are used. Two articles discuss these special-needs students. Regina Brunner discusses what techniques she's found effective in her all-female classes, and Jacqueline Giles-Giron writes of strategies to assess the adult learner.
Turning from assessment of individual parts of a course to assessment of how a course as a whole is going, Ellen Clay helps set the tone of her courses at the beginning by developing a "class mission statement," which can be revisited as the course progresses to assess progress toward meeting course goals. William Bonnice, David Lomen, and Patricia Shure each discuss methods of finding out, during a semester, how the course is going. Bonnice uses questionnaires and whole-class discussion. Lomen uses student feedback teams. Shure has an outside observer visit the class, who then holds a discussion with the class in the absence of the instructor, and provides feedback to the instructor. Janet Barnett and Steven Dunbar discuss alternatives to the standard course questionnaire for summing up a course once it's finished. Their methods provide more useful information than do student evaluation questionnaires for improving the next incarnation of the course. Barnett has students write letters to friends describing the course. Dunbar collects data throughout the semester into a course portfolio, which can then be used by that instructor or passed on to others.
Keep in mind that as you consider using one of
these techniques, even if your course and institution are very
similar to that of the author, to make the technique work well
you will need to modify the technique to fit your personality
and the tone and level of your class. But for most of
your assessment problems, there should be at least one
technique from this assortment which can help.