Math teachers from across the country, already facing enormous pressure to raise scores on high-stakes tests, should embrace other, more creative forms of assessment as a way to improve their instruction, peers at their annual meeting urged.
Assessment, far from being a dirty word, was a major theme at the annual conference of the National Council of Teachers of Mathematics.
NCTM officials used the event here to highlight the ways in which math teachers can use a broad range of assessments in their classes—beyond simply paper-and-pencil tests—to gauge whether students are learning and adjust their day-to-day lessons accordingly.
New NCTM President Francis M. “Skip” Fennell chose “Assessment Is Much More Than Testing” as the title of his speech. At numerous other sessions, teachers from many grade levels described how assessment could include not only regular quizzes on math content, but also homework, in-class writing exercises, question-and-answer sessions, and games.
A 2004 survey of some 300 teachers and school administrators in Kentucky, Ohio, and Michigan found that they had different opinions on the usefulness of various types of assessment.
*Click image to see the full chart.
SOURCE:Thomas R. Guskey, University of Kentucky, College of Education
Ideally, assessments should serve as “snapshots in a much larger album of student learning,” Mr. Fennell said in an interview. Put another way, assessments are not about “inflicting pain,” he added. “It’s about thinking about what can be done to help students.”
Nonetheless, for many math teachers, the foremost assessments in mind are the annual tests required of students in that subject in grades 3-8, and once at the high school level, under the federal No Child Left Behind Act. Schools are under pressure to raise test scores in math. Many of the teachers who attended the NCTM meeting said they had come looking for strategies to help them do just that. In-class assessments, which give teachers immediate information about the concepts that are most difficult, are one such tool, some speakers suggested.
Many of the strategies outlined at the NCTM event are what researchers call “formative” assessments—activities designed to help teachers adjust their teaching techniques and lessons on the fly to improve students’ grasp of math concepts. By contrast, “summative” assessments, in the jargon of researchers and testing experts, are given after the fact to determine whether students grasped classroom material. A high-stakes test is a typical summative assessment. Such tests can be used across the curriculum. (“Benchmark Assessments Offer Regular Checkups on Student Achievement,” Nov. 30, 2005)
Ellen Dairyko, the co-director of outreach at the Center for Elementary Mathematics and Science Education at the University of Chicago, gave teachers at one session an example of a lesson to help shape their instruction. She and Karen Holly, an elementary math facilitator with the Chicago public schools, showed examples of teachers’ asking students to give written explanations for answers to math problems, which offered insights into students’ computational skills and their ability to use different strategies to come up with an answer.
Interest in using assessment to shape day-to-day lessons, rather than simply as “a final check on student learning,” grew during the 1960s and 1970s, said Thomas R. Guskey, a professor of educational policy at the University of Kentucky who has studied assessment. Over time, school officials have begun to recognize the limited value of summative assessments, he noted; by the time schools received test results, students had migrated to the next grade.
For teachers of math or other subjects to use assessment effectively, those instructors have to be willing to evaluate their classroom techniques honestly, he said.
“If I discover that a question was answered incorrectly by half of the students in my class, that’s not really a student problem, that’s a teacher problem,” Mr. Guskey said from his campus in Lexington, Ky. “No matter how carefully I taught it, it didn’t work. … You need to go back and address those concepts in a different way.”
Sue Tatman Caballero, a teacher at Villa Del Ray Elementary School in the East Baton Rouge Parish district in Louisiana, said she chooses in-class assessments that tell her something about students’ math skills—and keep them enthusiastic.
Ms. Caballero, who made a presentation at the NCTM conference, teaches a 4th grade class with 22 students, only four of whom have not repeated at least one grade level. Many of those children “have been frustrated to the point that they completely shut down as soon as you even mention the word ‘math,’ ” she said. “I need a way to catch them and teach them and not let them shut down.”
One simple assessment in her arsenal is a game called King of the Hill. Students are each given calculators and told to key in a single, relatively large number, such as 10,000. They are then asked to hit another button as many times as they can, trying to get the highest number possible, until Ms. Caballero tells them to stop.
The teacher then calls on students to read the numbers on their keypads aloud—“10,014,” one student might say. Ms. Caballero then asks if another student can top it. If someone can, that student must read out a higher number: “10,029,” or “10,042,” and so on. Other, more complicated assessments follow.
The activity gets at a skill identified in Louisiana’s state standards: the ability to read numbers, Ms. Caballero says. It tells her which students are struggling, and allows her to spend more time with them individually. The process of reading numbers aloud also builds students’ confidence, she said.
“You don’t want to just do a game and then leave them,” Ms. Caballero said. “I want it to have a purpose. I want to know what students can do, and what they couldn’t do before—and where do they go next?”
A version of this article appeared in the May 10, 2006 edition of Education Week as Math Teachers Encouraged to Assess Creatively