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.
鈥淗aving these really good performance tasks as targets is great, because then students get to do more of these problems in class,鈥� said Diane J. Briars, the president of the Reston, Va.-based National Council of Teachers of Mathematics. 鈥淭hey get to think about what鈥檚 the criteria for a good explanation鈥攊t really does support the students鈥� deeper understanding of mathematics.鈥�
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 91制片厂视频, for example, a group of 20 high-profile scholars expressed the hope that the consortia tests .
鈥淲hile 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,鈥� the paper said.
Preparing for Bias
While the tasks are expected to involve 鈥渞eal world鈥� problems, students鈥� 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 鈥渃lassroom activity鈥� 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.
鈥淚n the real world, if you were really solving a math problem, you could go look up anything you wanted, right?鈥� said Shelbi Cole, the deputy director of content for Smarter Balanced. 鈥淚n a secure testing environment, that is just not possible. So we were trying to reconcile those two things.鈥�
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鈥� 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 . The tasks are designed to test multiple standards simultaneously, which supporters say creates a necessary complexity that has been missing from standardized tests.
鈥淲e鈥檝e 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,鈥� Ms. Briars said. 鈥淎nd most high-stakes assessment since No Child Left Behind came in has not done that.鈥�
But critics are not so easily convinced that these tasks are the ones students need.
鈥淲hat we have seen thus far of these tests does not leave me inspired,鈥� said educator Anthony Cody . 鈥淨uite the opposite. When tests are designed to be 鈥榤ore rigorous,鈥� the outcome seems to be to drastically lower the number of students rated as proficient.鈥�
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. 鈥淭his is a new concept for most states,鈥� she said.
PARCC鈥檚 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.
鈥淯nless the standard changes, the test is measuring the standard,鈥� he said. 鈥淯nless the standards change, you test those things.鈥�
But Mr. Nellhaus made it clear that he expects the performance tasks to take math assessment to a new level.
鈥淭hey鈥檙e the part of the assessment we鈥檙e most excited about,鈥� he said. 鈥淣ot all math items come in short little questions. [This is] what math is all about.鈥�
