NCTM president: Test your test sense

Diane Briars
Diane Briars

Test Your Test Sense
by NCTM President Diane J. Briars

As we move into the second half of the school year, many of us are feeling increasing pressure to engage in special "test prep" activities intended to help our students do well on end-of-year high-stakes tests.

How knowledgeable are you about effective actions to prepare yourself and your students for upcoming high-stakes tests? Take this short test and find out!

Test Your Test Sense

1. It is valuable to analyze released assessment items from the PARCC and SBAC assessment consortia, in addition to your district and state standards and curriculum documents, even if your students will not be taking these assessments in the spring. True or False?

2. It is important to cover all the content standards that will be on the test, even if doing so means having time for only superficial instruction of some topics. True or false?

3. Which of the following practices are likely to improve your students' test performance? (Select all that apply.)
Stop teaching to review and give practice tests during the weeks prior to the test.
Provide opportunities for ongoing review and distributed practice within effective instruction.
Provide opportunities for students to develop clear expectations about the test—for example, becoming familiar with question types, characteristics of high-quality responses, and technology that the tests will use.
Teach students how to become effective self-assessors who take an active role in monitoring their own learning.
4. Good instruction is the best test preparation strategy. True or false?

Let's see how well you did.

1. True.

Analyzing the standards and related curriculum documents, such as the Common Core State Standards for Mathematics (CCSSM) progression documents, is an essential foundation for understanding what students are expected to know and be able to do. However, examining tasks can further clarify those expectations in a number of ways, including illuminating the types of problems that students are expected to solve, the reasoning they should be able to demonstrate, and the quality of explanations they should provide. Tasks released by PARCC and SBAC are particularly valuable to examine because these two consortia are developing assessments to measure all aspects of mathematical proficiency: conceptual understanding, procedural fluency, applications and problem solving, reasoning, and important habits of mind for using mathematics (that is, the Standards for Mathematical Practice).

For example, consider the following CCSSM standard for seventh graders in the domain Ratios and Proportional Relationships: "Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error" (7.RP.A3). What content does this standard encompass? And what tasks would you expect students to solve to demonstrate proficiency as expected by this standard?

Consider the released PARCC task TV Sales (2013) below:

Grade 7: TV Sales
A store is advertising a sale with 10% off all items in the store. Sales tax is 5%.

Part A
A 32-inch television is regularly priced at $295.00. What is the total price of the television, including sales tax, if it was purchased on sale? Fill in the blank to complete the sentence. Round your answer to the nearest cent. The total cost of the television is $___________.

Part B
Adam and Brandi are customers discussing how the discount and tax will be calculated.

In both equations, T represents the total cost of the television and p represents the regular price. Are they both correct? Use the properties of operations to justify your answer.

Would your interpretation of the standard have encompassed a task that calls for applying both a discount and tax to the same price, as in Part A of the PARCC task? Did it encompass evaluating and explaining two different methods for calculating price, as in Part B? And did your interpretation encompass representing the sale price and price including tax as a product, that is, as 0.9p and 1.05p respectively?

As the TV Sales item illustrates, tasks provide valuable information about how to interpret the standards, and about content and reasoning that students should have the opportunity to learn. They are also valuable examples that you might incorporate into your own assessments or instruction, even if your students will not be taking the PARCC or SBAC assessments or if you teach in a state not implementing CCSSM.

Of course, PARCC and SBAC released tasks are not the only sources of high-quality assessment tasks that illustrate expectations related to standards. NCTM has many publications that include such tasks, including the growing Putting Essential Understandings into Practice Series. Also NCTM will soon be releasing the Discovering Lessons for the Common Core State Standards e-book series, which explicitly links CCSSM to articles and resources in the NCTM practioner journals. Other sources include the Balanced Assessment in Mathematics Project, Inside Mathematics, the Mathematics Assessment Project, the National Assessment of Educational Progress (NAEP) Questions Tool, and the Illustrative Mathematics Project.

2. False.

Ideally, teachers give students the opportunity to learn with understanding all the content on the end-of-year test. But sometimes, despite our best efforts, we can't make that happen. We fall behind in our intended pacing and have too little time to teach everything. In this situation, it is more productive to teach fewer of the remaining topics with understanding than to try to cover all of them superficially. The value of depth over breadth is illustrated by the Trends in International Mathematics and Science Study (TIMSS) study (Ginsburg and Leinwand 2005). The Singapore curriculum contains a smaller percentage of the TIMSS test topics than does the typical U.S. curriculum; yet Singapore outperforms the United States. Why? A partial answer is that Singapore teachers teach the topics that are in their curriculum in more depth.

Monitoring your pacing and adjusting it periodically are also helpful, so that students have adequate time to learn the most important content before the test.

3. (b), (c), and (d) are likely to improve your students' test performance; (a) is not.

Although (a)—stop teaching new content and spend the weeks before the test reviewing and giving practice tests—may appear to be an effective way to increase test scores, research indicates just the opposite—test scores are actually lower in schools where teachers spend large amounts of time on this type of test preparation (see, for example, From High School to the Future: ACT Preparation—Too Much, Too Late).

Instead, providing opportunities for ongoing review and distributed practice, along with feedback, as suggested in (b), helps students solidify their knowledge and promotes retention, reflection, generalization, and transfer of knowledge and skill (Rohrer 2009). Review problems can be incorporated into daily warm-ups, nightly homework, quizzes and tests, or classroom questions. Regardless of how you build in the practice, be sure to provide feedback, both to ensure that students are practicing correct content and to help them take responsibility for their own learning. The sooner you start providing distributed practice, the more your students will benefit.

Test scores are also higher when students know what to expect—the types of questions that will be on the test and how their responses will be evaluated, as described in (c). For example, White and Frederiksen (1998) found that teaching seventh-grade science students the characteristics of high-quality work, and showing them how their work was likely to be evaluated, reduced the achievement gap between the highest- and lowest-achieving students by half. In addition, on average, the weakest students in the "clear expectations" classes were outperforming all but the very strongest students in the control classes who had not had such instruction.

Since both PARCC and SBAC tests feature new item types, you and your students will benefit from experience with them well before the test is administered, especially those calling for the use of new technology. On test day, you'll want students to know what to expect, and not become flustered by an unfamiliar type of task, tool, or response mode. Familiarity doesn't require spending inordinate amounts of class time on practice tests, but it does involve providing opportunities for students to experience the different types of items and tools, and receive feedback.

Teaching students to take ownership of their learning and assess the quality of their work, as outlined in (d), is another effective strategy for increasing test performance. Student ownership needs to be an explicit expectation, supported by regular opportunities for students to analyze the quality of their work and reflect on their progress toward stated learning goals. Clear expectations and ownership of learning are two of Dylan Wiliam's key strategies for effective formative assessment (Benefits of Formative Assessment, NCTM, 2007).

4. True.

Consistently providing your students with high-quality instruction and assessment that incorporates the effective mathematical teaching practices identified in Principles to Actions: Ensuring Mathematical Success for All is the most effective way to prepare your students to do well on high-stakes assessments. Such instruction takes students beyond rote learning of facts and procedures to learning with understanding, which enables them to apply and transfer their knowledge and skills to new problems, as well as apply them to familiar situations—exactly what is needed to perform well on high-stakes tests.

Developing your test sense in the ways suggested by this short test can have tangible benefits for you and your students alike. Implementing these ideas can lower everyone's stress and increase confidence and test performance—and, most importantly, improve teaching and learning every day in the classroom.