New EDC Book Helps Teachers Explore Students’ Mathematical Thinking

There are things kids need to understand about mathematics that are not at all the things we have traditionally taught them. The traditional focus has been on skills, but skills are just a means, not an end. So kids were learning the material in the book but missing the point of mathematics. One of the most useful things a kid can take away from class is a style of work—a set of mathematical methods—rather than a collection of results.

—Al Cuoco, director of EDC’s Center for Mathematics Education

Al Cuoco might have added that there are things kids need to understand about mathematics that do not show up on the traditional mathematics tests. And that touches on a particularly difficult issue for mathematics educators today: How can we evaluate students’ understanding of mathematical methods and concepts as well as their command of specific skills? What new tools and strategies do we need? And what roles should teachers play in employing these tools and strategies?

Questions like these lie at the heart of a series of teacher development projects directed by EDC’s Mark Driscoll and Deborah Bryant. Driscoll and Bryant are leading researchers in the emerging field of mathematics assessment, which refers to the process teachers use to understand, respond to, and evaluate student thinking.

In their new book, Learning About Assessment, Learning Through Assessment—commissioned by the Mathematical Sciences Education Board of the National Research Council and published by National Academy Press—Driscoll and Bryant provide a framework for teachers interested in learning “the professional craft of assessment” through ongoing, collaborative work with their colleagues.

The book grows out of three projects Bryant and Driscoll directed involving hundreds of teachers across the country. As part of these projects, staff developers engage groups of teachers in analysis and discussion of student work drawn from a variety of classrooms and showing varying degrees of mathematical knowledge. “We’ve found that the most successful professional development programs involve teachers working together to analyze real pieces of evidence, such as case studies or student work,” Driscoll explained.

“The central point of our programs is not just to provide teachers with missing knowledge but rather to help them develop their taste and judgment in selecting worthwhile mathematics tasks,” he added.

In Learning About Assessment, Learning Through Assessment, Driscoll and Bryant identify seven core learning challenges that teachers encounter when they begin to build this kind of judgment:

Seven Core Learning Challenges

Judgment about the quality of mathematics in tasks

• Challenge 1:Reaching consensus about quality when looking at mathematics tasks.
• Challenge 2:Framing questions and structuring tasks so that what is important and intended is elicited.

Judgment about the appropriateness of tasks

• Challenge 3:Aligning classroom assessment with curriculum, instruction, and external assessment.
• Challenge 4: Ensuring that tasks involving important mathematics elicit from the broadest range of students what they truly know and can do, and that there are no unnecessary barriers due to wording or context.

Judgment about the quality of student responses

• Challenge 5: Deciding what are reasonable student answers to a problem when there is no one “correct” answer.
• Challenge 6: Using evidence to make valid inferences about student understanding.

Judgment about consequent actions

• Challenge 7: Determining appropriate actions in light of conclusions from student evidence.