The Common-Core Assessments: What Math Teachers Need to Know
As you surely know by now, the Common Core State Standards in language arts and math were designed to get students to engage in problem solving, communicate effectively, and think more critically. As a result, new assessments had to be developed that can effectively measure mastery of complex skills. Two state consortia—the Partnership for Assessment of Readiness for College and Careers, or PARCC, and Smarter Balanced Assessment Consortium, or SBAC—have been contracted to develop a set of literacy and math assessments to do just that starting next school year.
As a high school math teacher in Kentucky, I want to make sure that I fully understand the scope of the available assessments from both consortia. Even if my state does not use one of the consortia's assessments next year, I want to continue to be able to collaborate with high school math teachers nationwide. I need to be able to provide my students with the same high level of instruction that is available to students who are being assessed through PARCC or SBAC.
Although Kentucky adopted the common standards several years ago, the accountability assessments that my Algebra 2 students currently take contain only multiple-choice items. It is exciting to me that both the PARCC and SBAC have developed summative mathematics assessments that are expected to go beyond multiple choice to determine students' understanding and their mastery of skills.
The sample test items available online can give teachers a pretty clear understanding of what the new assessments will entail. A sample PARCC performance-assessment item for Algebra 2 requires the student to find the intersection points between a linear function and a rational function, which is something that I have never seen before on a summative math test at this level. (Usually students are required to find the intersection point between two linear functions). Students not only have to identify the intersection points; they also have to explain their reasoning and find the zeros of a third function, which is the difference between the first two functions. This requires mastery of common standard A-REI.10-11 ("represent and solve equations and inequalities graphically"), as well as common-core mathematical practices three ("construct viable arguments and critique the reasoning of others"), and seven ("look for and make use of structure").
Each assessment consortia has put forth ideas that I appreciate as a math teacher. For example, PARCC plans to release one-third of the assessment items after the tests are taken each year (similar to how the College Board releases the Advanced Placement free-response questions). SBAC plans to provide classroom activities related to each performance task that will allow students to become more familiar with the context of the problem before attempting the actual test.
For a performance task entitled "Crickets," for example, the students first learn from their teacher selected information about why crickets chirp, and have an opportunity to practice calculating the average number of chirps per minute. Then students complete the performance-task assessment, which involves determining the relationship between temperature and chirping rates of snowy tree crickets. This way, the assessment is measuring students' knowledge of content rather than context.
A Challenge for Teachers
If you're anything like me, you might be a little nervous about the new assessments and the difficulties that students will most likely encounter, given the increased rigor compared with most current state tests. This will definitely be a time of transition for both students and teachers as we get accustomed to the new expectations.
PARCC has developed two sequences of exams to be given at the end of each high school mathematics course. One follows a traditional math pathway of Algebra 1, Algebra 2, and Geometry. The other is designed for students who are enrolled in integrated math courses that combine the different strands. SBAC's approach is a bit different, containing optional interim exams for all high school grades but only providing a required exam for 11th grade students.
Similar to the College Board Advanced Placement math exams, both tests will have calculator and non-calculator sections. For the calculator-allowed portion of the PARCC assessment, students will use an online calculator that is similar in function to a TI-84 graphing calculator, which could be an issue for schools like mine that primarily use the TI-Nspire. The SBAC exam also has a pop-up online calculator for students to use on certain problems, but it doesn't mimic the TI-Nspire or the TI-84; instead, students can use the calculator in scientific, regression, or graphing mode.
In terms of how the tests will be scored, PARCC has developed performance-level descriptors, or PLDs, that describe what students know and can do relative to common-standards content. For example, the Algebra 2 PLD for equivalent expressions requires a student at the distinguished level to be able to "use mathematical properties and structure of polynomial, exponential, rational, and radical expressions to create equivalent expressions that aid in solving mathematical and contextual problems with three or more steps required." A student who has only partial command of the standard can "use provided mathematical properties and structure of polynomial and exponential expressions (not radical or rational) to create equivalent expressions." There are 15 different PLDs for the Algebra 2 assessments alone.
SBAC uses a similar system that involves achievement level descriptors, or ALDs. Five claims detail what students should be able to do during the time of the assessment—one overall claim and four separate domain claims. For 11th grade, the composite claim is that "students can demonstrate college and career readiness in mathematics." The other claims cover concepts and procedures, problem solving, communications and reasoning, and modeling and data analysis. The ALDs are then provided for each assessment item based on a student's knowledge and skill of each particular claim.
I have to say, however, that I'm optimistic that the new assessments are steering student learning in the right direction. Until now, there has been little to no connection between daily formative assessments and state-mandated summative assessments. In my classroom, I strive to assess what my students understand based on their thinking processes. I want to know more than just whether or not the student can circle the correct letter. I want to know how well my Algebra II students can think abstractly and connect new topics to prior knowledge, for example. Most math teachers will agree that this type of daily assessment is essential to both how we teach and what we teach, and is more valuable than data received from a summative multiple-choice test. It has been frustrating to me that in the past few years, students could be deemed college- and career-ready by means of the latter type of assessment.
But with this new wave of assessments, I see this starting to shift. Both consortia assessments will include some multiple-choice questions, but many items will require students to interact with the questions beyond just choosing one correct answer—and the data that teachers will receive in turn goes beyond a scale score. For example, one of the Smarter Balanced 11th grade practice items displays a set of six radical equations, and the student must select all of the equations that have integral solutions. Even though there are definite right and wrong answers, the students are scored on a continuum. If a student correctly identifies the equation that contains a rational exponent but struggles with the equation with the negative exponent, then that provides me with much more information than I could get from a multiple-choice question. To me, this looks more like a solid formative assessment activity that I might do in my classroom.
New Instructional Foundations
When I first read the common standards in math a few years ago, I was ecstatic about their rigor and the inclusion of the mathematical practices. However, I was skeptical that assessments could be written that actually measure a student's mastery of such complex standards as well as college and career readiness. Based on the sample assessments and the ALDs and PLDs, I am hopeful that both PARCC and SBAC have developed assessments that are closer than ever to assessing students' conceptual understanding as well as proficiency with mathematical practices.
If the assessments are able to truly provide teachers, students, and parents with valid data about student learning, "teaching to the test" becomes a good thing. Teachers will no longer encourage students to follow specific steps or memorize formulas because the new assessments will measure whether or not students truly understand mathematical thinking. This means that teachers will need to collaborate and develop lessons that balance procedure and understanding. The mathematical practices—which include constructing viable arguments and critiquing the reasoning of others, modeling with mathematics, and look for and make use of structure, to name a few—will have to become the foundation of instruction as opposed to add-on enrichment activities.
Many math teachers recognize the standards and the mathematical practices as simply "good teaching." Modeling with mathematics, for example, is certainly nothing new, but what is different is that now it is a standard. This, to my mind, means good instruction for all students.
My hope is that the new CCSS-aligned assessments, whether PARCC, Smarter Balanced, or new assessment that have not yet been created, will support this kind of instruction. Like many teachers, I am not afraid of being held accountable (in fact I embrace it), as long as the test is measuring the type of learning that I know is best for my students.