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NSF-DRK-12: Creating Better Math Assessments

Fourth-graders routinely do a lot of math exercises. And sometimes it seems like James W. Pellegrino and his fellow researchers have seen every last sheet of it.

They are searching for clues about the effectiveness of the teaching strategies and tools that influence learning. Pellegrino’s Evaluation of the Cognitive, Psychometric, and Instructional Affordances of Curriculum Embedded Assessment, a $3 million, National Science Foundation-funded grant, is uncovering just how well embedded assessment tools in math curricula are working.

Embedded assessments are tasks built into the curriculum materials and lesson plans that teachers use to gauge how well students comprehend key concepts. They allow for immediate feedback, unlike summative assessments, which wait until the end of a unit to test knowledge, so that teachers can revise their strategies and adjust the focus of lessons when it’s necessary.

“We’re learning a lot about how well teachers understand the assessment tools embedded in these curricula and some of the challenges they face in trying to make use of them to track student learning and adapt their instruction,” Pellegrino explained.

The major challenge is to help teachers make the most of assessment opportunities, and improve the tools they use to do so. To accomplish this, they are focusing on two of the most popular, comprehensive curriculum programs for grades K to 5/6, University of Chicago’s Everyday Mathematics and LSRI’s Math Trailblazers. Studying two curricula allows for a comparison in their approaches to assessment and how valid and useful the assessment tools are in each program, he added.

What makes LSRI’s study different is that most other research on assessment is focused on state tests or tests that someone from outside the classroom has designed and might administer to students to find out how much math knowledge they have amassed in total. These kinds of tests are removed from the daily experiences of the classroom and aren’t focused on student comprehension during the course of the school year, Pellegrino said.

The project has collected thousands of pages of math exercises, classroom observations, and interviews with students and teachers from 18 schools across Chicago, its suburbs, and Delaware and Kansas. Analysis has already begun, with beneficial preliminary results.

“We see certain assessment activities out of alignment with a curriculum’s learning goals,” said Reality S. Canty, a researcher with DRK-12. He also explained that children might successfully complete an activity without actually engaging in the forms of reasoning the curriculum is trying to develop. For example, in a problem where they are asked to order fractions, a student may arrive at the correct answer by omitting a common denominator. This method is called a whole number strategy, but the intent of the lesson might be to learn rational number theory – where the fractions are left intact. With a correct answer, the teacher may be compelled to move on unaware that the child did not actually grasp the material accurately, Canty explained.

Embedded assessment has not been well understood, but researchers are learning more about what it takes to makes it valid and useful. This is all part of an effort by researchers and educators to focus on the “formative uses,” of assessment or what has been called “assessment for learning.” Pellegrino noted that assessment can be a very powerful tool to help teachers help students learn. But that means the assessments must be well designed well to get that job done.

The findings from the research are helping to design better assessments, and the data are being shared with another of Pellegrino’s grants on embedded assessments funded by the Institute of Educational Sciences.

One outcome of that work will be to suggest changes in assessments that can then be used by teachers to enhance learning for a wider range of children beyond those currently impacted, Canty said.

For Pellegrino’s part, he also hopes to involve technology in DRK-12 to make the processes of data collection, scoring and management easier for the teacher. In addition to providing teachers with quicker diagnostic information, this technology would also cut down on all the paper that ends up getting pushed around by both students and teachers.

— Andrew Gregory Krzak