Mathematics is a subject noted for “drill and practice,” where learning is often equated with the quantity of problem solving. Over the past three years, teachers at Holt High School in Holt, Michigan, have tried to shift our emphasis toward conceptual understandings and the active demonstration of learning. In particular, we have had great success with a panel performance assessment in Algebra II and Precalculus.
We began changing our curriculum in response to a new conceptual change model, developed by the Holmes Group at Michigan State University. The model requires us to learn whether students understand the concepts behind the subjects being taught rather than simply being able to recount facts and knowledge. Central principles of the model include: teach for understanding; organize the school and its classrooms as a community of learning; hold ambitious learning goals; teach adults as well as children; make reflection and inquiry central features; and invent a new organizational structure for the school.
One of our teachers of Algebra II and Precalculus, Michael Lehman, began to alter his teaching and testing style to reflect these principles. Because he realized that multiple-choice or problem/answer exams would not effectively assess learning based on the conceptual change model, Lehman developed a panel performance assessment process.
How Panel Assessment Works
For their midsemester and semester exams, students in Algebra II and Precalculus discuss before a panel of three judges the solutions to complex problems. Several days prior to the exam date, students receive six problems based on the main concepts discussed during the semester. The problems require some computation along with opportunities to make judgments based on the results of the computations.
Students work in cooperative learning groups of three or four to solve the problems and to practice presenting their understanding of each one. They use their books and notes and ask questions of the teacher or other classmates as they feel the need. They often meet outside of class time as a group to continue their preparations. Parents assist with practice sessions before exam day arrives.
To assess the students, we recruit panels of judges from the business community, from Michigan State University (with which we have a strong partnership because of our role as a professional development school), from our school board, and from among parents and other district administrators. Educators from nearby school districts who are curious to know more about the panel assessment process also sometimes serve as judges.
Each panel consists of one “math expert” (usually a math teacher, a university math faculty member, or a math-related professional) and two “laypersons” (judges who may not necessarily be well versed in either algebra or precalculus). Having laypersons on the panel allows us to check for understanding in everyday language; students need to articulate and explain the math concepts to those who may not have the background for understanding them well. Prior to the exam, the panel judges receive the complete set of problems, the answers, and the scoring procedures.
On the day of the exams, student groups go before the panels of judges as a team. Currently, the assessments take place in the classroom and the school library, where tables are arranged so that no two groups of students are able to see each other. Each panel assesses only one team for Algebra II and one team for Precalculus.
The judges randomly select one of the problems and ask a team member to explain the problem. The students must be comfortable with all of the problems, as each will be asked to answer one of the six individually. After the judges hear a student discuss the problem, they may probe more deeply, or they may open the discussion to other students on the team.
After the panel assessment, each judge rates the individual students on both their understanding of the mathematics concepts described and on their ability to present what they know. Each student receives a letter grade based on a point system, as well as written descriptions of his or her abilities to communicate, to make sense of the problem, and to relate it to other “real-world” examples. This form of assessment gives students a much broader picture of their mathematical understanding, as well as of their teamwork and communication skills.
Students wait anxiously for the results of their panel assessment. A student who had never scored above a C on a traditional math test and who had failed more tests than he had passed told the math teacher he was grateful that the judges took the time to ask questions; he knew the information, but had trouble finding the right words. When this student found out that he had received a B on the exam, he jumped two feet off the ground and ran down the hall shouting the results!
The Payoffs
Organizing panel performance assessment does require a considerable amount of time. The time, however, is a trade-off against the time spent grading traditional exams, as the grading is completed on the spot. More important, this form of assessment is a rich supplement to the written methods used in the math classes.
The panel assessment process offers students an alternative to the traditional paper-and-pencil tests. Many students do not memorize information well, or they freeze when faced with a sheet full of complex computational exercises. During the performance assessment, these students have the opportunity to seek clarification from the judges and to express themselves orally as well as in writing or with other visual aids. Students gain a confidence that some of them have seldom experienced.
Performance assessment also provides students with a more meaningful way to demonstrate what they have learned. Students organize themselves and focus on what they need to know or do to successfully demonstrate their learning. This relevant, real-world assessment empowers students to construct knowledge and apply complex thinking skills.
Several teachers in other content areas such as global studies and American studies are now exploring using a similar technique in their classes. As we move forward to make performance assessment the norm rather than the exception at Holt High School, we anticipate that assessment, instruction (driven by performance assessment), and student achievement will improve, pointing students toward future success in their learning and work experiences.
