The architects of the Common Core State Standards for mathematics explicitly aimed to sacrifice breadth for depth, but that proposition has raised questions about whether assessments can be developed to accurately measure the problem-solving acumen now expected of students.
To address the issue, the state consortia developing common-core-aligned assessments, the Smarter Balanced Assessment Consortium and the Partnership for Assessment of Readiness for College and Careers, have designed complex performance tasks meant to gauge whether students can apply their math knowledge and work through multiple standards simultaneously. Among other things, students will be required to use diagrams and write explanations for solutions in narrative form.
With common-core-aligned testing set to begin this school year, experts are eager to see whether the performance tasks will live up to high expectations, and perhaps even bring positive instructional changes.
“Having these really good performance tasks as targets is great, because then students get to do more of these problems in class,” said Diane J. Briars, the president of the Reston, Va.-based National Council of Teachers of Mathematics. “They get to think about what’s the criteria for a good explanation—it really does support the students’ deeper understanding of mathematics.”
Performance tasks have long been in demand by those disappointed by standardized assessments used in connection with the No Child Left Behind Act, under which performance assessment floundered. In a June 2013 report published by the Stanford Center for Opportunity Policy in Education, for example, a group of 20 high-profile scholars expressed the hope that the consortia tests would offer meaningful performance items.
“While it is possible to ask students to select an answer to a mathematical problem that is given in a familiar format [such as multiple-choice], this will not demonstrate whether the student could take a real-world problem and identify the kind of mathematics needed to solve it,” the paper said.
Preparing for Bias
While the tasks are expected to involve “real world” problems, students’ experiences of the world vary widely, and to that end, the consortia are attempting to control for cultural biases.
PARCC formed working groups of educators to detect bias in questions during the development stage, and it plans to analyze the task results afterward to see if one student demographic did disproportionately better than another.
The performance tasks will require a certain level of reading proficiency, but Jeff Nellhaus, the chief assessment officer at PARCC, said that PARCC designs its tasks using principles of universal design, an approach that aims to make content accessible to students with diverse learning needs.
Smarter Balanced plans to take a more hands-on, instructor-driven approach. Schools using that assessment will have a half-hour “classroom activity” section right before the performance section of the test in which the supervising teacher will discuss the elements and topic of the task. For example, if a high-school-level task were about driving, the teacher would work students through the process of getting a license, which might be an abstract concept to urban students.
“In the real world, if you were really solving a math problem, you could go look up anything you wanted, right?” said Shelbi Cole, the deputy director of content for Smarter Balanced. “In a secure testing environment, that is just not possible. So we were trying to reconcile those two things.”
The classroom activity also gives educators more of a role in the test, she added.
Levels of Difficulty
Some educators have expressed concerns that the computer-based testing platforms will hamper students’ ability to show their work effectively. The consortia admit that cost and other issues have hindered improvement of the technological aspects.
The bigger question, perhaps, is whether the tasks themselves will be too hard, being based on math standards that some early-childhood experts say are developmentally inappropriate for young students. The tasks are designed to test multiple standards simultaneously, which supporters say creates a necessary complexity that has been missing from standardized tests.
“We’ve long advocated that assessments need to address the full range of student proficiency in mathematics, so they need to assess conceptual understanding, problem-solving, standards for mathematical practice, as well as procedures,” Ms. Briars said. “And most high-stakes assessment since No Child Left Behind came in has not done that.”
But critics are not so easily convinced that these tasks are the ones students need.
“What we have seen thus far of these tests does not leave me inspired,” said educator Anthony Cody on his Living in Dialogue blog. “Quite the opposite. When tests are designed to be ‘more rigorous,’ the outcome seems to be to drastically lower the number of students rated as proficient.”
Ms. Cole said that Smarter Balanced has a revision process to determine whether a question is too hard for a certain grade level, but said that negative reactions may change as schools acclimate to the standards. “This is a new concept for most states,” she said.
PARCC’s Mr. Nellhaus contended that if people have concerns about whether assessments are too hard, then they should really be looking at the standards, not the test.
“Unless the standard changes, the test is measuring the standard,” he said. “Unless the standards change, you test those things.”
But Mr. Nellhaus made it clear that he expects the performance tasks to take math assessment to a new level.
“They’re the part of the assessment we’re most excited about,” he said. “Not all math items come in short little questions. [This is] what math is all about.”
Coverage of efforts to implement college- and career-ready standards for all students is supported in part by a grant from the Bill & Melinda Gates Foundation, at
A version of this article appeared in the November 12, 2014 edition of Education Week as Math-Exam Performance Tasks Ratchet Up Expectations, Anxiety