Test Prep and Math Realities

• By Patricia Deubel
• 10/01/07

As another school year is getting well under way, educators are faced with starting the process all over again for preparing students for standardized testing. It's not something that can be put off until the last moment. Failure to pass "the test" sometimes prevents high school students from receiving their graduation diplomas. Elementary students might be retained in a grade. There is the usual dilemma of teaching to the test versus incorporating activities that help students develop 21st century skills valued in the real world.

The state-mandated mathematics test is often the most difficult for students. I'd like to offer some test prep tips and thoughts for math educators to consider in their teaching. Of course, I advocate using technology to support instruction. These suggestions might also be of value to educators of other content areas.

1. Use diagnostics and post benchmarks.

Students need to have clear knowledge of which benchmarks they have not yet mastered. As not every benchmark is tested, be sure to know which have greatest importance to address in your curriculum. Post standards and benchmarks for mastery in the classroom. To emphasize students taking some responsibility for their own learning, provide each with a copy from which to monitor their progress. Parents should have access to that information, too.

Use a diagnostic tool, preferably one that is state-specific. Some smaller companies develop their products only for one state and, therefore, are very aware of which benchmarks to emphasize. Alternatively, use a formative assessment tool (screening, progress, and diagnostic), such as Pearson Education's PASeries for grades 3 through 12, which will help educators identify specific areas of weakness that students might have, and will also help them to tailor classroom instruction to meet students' needs.  The Northwest Evaluation Association's Measures of Academic Progress might also be used.  These are state-aligned computerized adaptive assessments that provide information about student achievement and growth. 

While a diagnostic test with item analyses reveals weaknesses in concepts and content related to strands tested, teachers will still need to delve deeper into an analysis of why students missed certain questions.  At a second level, student literacy skills might play a role in not answering a question correctly. 

Benchmarking tests should be given periodically, perhaps every nine weeks, to monitor progress in mastering objectives.  Districts might develop such tests.

2. Teach how to read a math text.

Many students rely on their teachers to provide all the techniques for completing math assignments and rarely read their texts because they find it more difficult to do so than for other subjects. They need tips, such as Reading a Math Textbook by Cynthia Arem of Pima Community College. In short, students need to read slowly, as every word counts. They should read a lesson before and after class, reread for mastery, and avoid skimming illustrative material. As they read, they should write and work out examples provided, then compare. Creating 3" x 5" cards with formulas, key vocabulary, properties, examples, and facts will be helpful for review. They should test themselves, write or say aloud important points. Other math books should be available for reference, and a glossary to clarify terms. There are several fine math glossaries online. For example, A Maths Dictionary for Kids by Jenny Eather is an attention-getting, animated collection of more than 500 terms found in K-8 math. Connecting Mathematics from the University of Cambridge is a thesaurus of terms and ideas, which might be more appropriate for upper grades. Various multimedia galleries with images, animations, dynamic geometry diagrams, and 3D views are also included.

3. Incorporate writing and problem-solving strategies in instruction.

Writing helps students to make sense of mathematics and helps them to identify what they know or don't know. According to Reeves (2004), "Even if the state test is dominated by lower-level thinking skills and questions are posed in a multiple-choice format, the best preparation for such tests is not mindless testing drills, but extensive student writing, accompanied by thinking, analysis, and reasoning" (p. 92). Writing assignments fall into four categories, which are:

• Keeping journals,
• Solving math problems,
• Explaining concepts and ideas, and
• Writing about learning processes. 

Teachers might provide initial statements, prompts, and guidelines for topics of the day for when students write to a journal (Burns, 2004). Graphic organizers, such as at the Enhance Learning with Technology website, help learners to visually organize and interrelate information.

Be sure students understand key action words typical of short answer and extended response questions, such as determine, identify, compare, contrast, explain, analyze, describe.  Such words are not typical of everyday speech.  Also note specialized math terminology used within the questions posed.  Ask students to define these in their own words.  You might be amazed at how many students have difficulty with key action words and math vocabulary, particularly those learning English as a second language. Imagine their possible confusion upon encountering homophones like "pi/pie, plane/plain, rows/rose, sine/sign, sum/some" (Bereskin, Dalrymple, Ingalls, et al., 2005, p. 3). Key vocabulary must be explicitly taught and reinforced by posting symbols with definitions and examples to clarify meaning. 

Review problem-solving strategies, such as provided by MathCounts.org, and solve problems that specifically use those strategies. Emphasize there is often more than one way to solve a problem. Stress understanding the problem, devising a plan, carrying out the plan, and looking back, which are George Polya's problem-solving steps. The Washington Assessment of Student Learning practice problems for K-8 and High School at Port Angeles (WA) School District are a good resource.  All of the problems at this site, which are separated into strands and strategies, are designed to help students learn to write in mathematics.

4. Review test-taking strategies.

Students should know techniques for taking multiple choice and essay tests and how to deal with anxiety. Southwestern University's Preparation for a Successful Exam Day and Study Guides and Strategies: Multiple Choice Tests will be helpful.

They also need to know the mechanics of test taking, such as identifying distracters, adhering to time limits, working with bubble sheets, reading and following test directions, and using deductive thinking to eliminate incorrect answers.  They might plan their essays using graphic organizers and write on every other line, which leaves room for revision when the response is reread. It is helpful to provide at least one multiple choice or short answer question on each exam during the school year, which would be typical of that encountered on the standardized test. This will help reinforce strategies, making them a part of long-term memory.

Dealing with anxiety is an often neglected area in instruction and test preparation, yet nearly everyone has experienced it at one time or another. It's an emotional learned response that often comes from negative experiences working with teachers, tutors, classmates, or family members.  Symptoms include panic, paranoia, passivity, and no confidence.  Identifying the source of the problem is a first step in overcoming it. Tim Grosse's Tips for Making Mathematics Your Friend are useful at any math level for relieving test and math anxiety. Chicago Public Schools produced Preparing Your Elementary Students to Take Standardized Tests and Preparing Your High School Students to Take Standardized Tests. These address test-taking skills, student attitudes and motivation, assessing thinking skills in the classroom, and general tips for classroom, homework, and assessment activities with content area preview.

5. Develop a database of content resources.

Have a series of technology resources at hand with content related to benchmarks students must master. According to Schneiderman (2006), digital content types for teaching mathematics fall within several categories, including tutorials, skill building/drill and practice, problem-solving, test prep, simulations and visualization, educational or serious games, and comprehensive courseware. The value of the latter is that skill mastery is often tracked and there is a student data management and reporting system to inform instruction.

Include virtual manipulatives for investigating concepts. Valuable resources include the National Library of Virtual Manipulatives, Project Interactivate, and Thinking Blocks, the last for interactive exploration of word problems. Many textbook publishers also provide online versions of their texts and/or free online resources with engaging interactive activities, multiple choice questions, video and guided explanations, and homework help, which are of value. Holt, Rinehart, and Winston, Glencoe Online Study Tools, and Saxon Student Online Activities (http://saxonpublishers.harcourtachieve.com/en-US/saxonpublishers.htm) are among those. Although some districts have banned YouTube.com because of its diverse offerings, there are some excellent math videos posted by classroom teachers and professors who explain concepts and provide examples for problem solving.

6. Provide intervention for learners in need.

Learners will benefit from a variety of intervention/remediation programs offered at various times during the school day and before and after school. Some districts are able to hire intervention specialists or reassign teachers to intervention classes or pay qualified individuals to conduct remediation programs. However, just as in the classroom, tutors need subject-matter expertise.  Certification and prior teaching experience are plusses.  Gordon (2006) suggested that a good tutoring program begins by checking whether the student has learning disabilities and ensures that tutoring is individualized and that tutors are recording progress and following the written curriculum. It also ensures parental support for good study habits and motivation for learning at home.

7. Use practice tests.

Don't be afraid to use practice tests from other states, as benchmarks in math are often similarly stated. As a starting point, you might consider Ohio's new portal to its statewide testing in grades 3 through 8 and high school and the Texas Education Agency's online interactive versions of its released tests and end of course examinations, some of which are in Spanish at grades 3 through 6. When students feel confident that they have mastered the objectives, they should take a few practice tests from your own state shortly before actual state testing.

8. Relate content to the real world.

It does not take long to totally turn off learners to math, if they see no practical use of it. TheFuturesChannel.com contains highly motivating videos, many shorter than five minutes, that link math and science to real-world applications and careers. For example, the section on Teaching & Learning contains Algebra in the Real World (by topics covered within a typical algebra course), Hands on Math (by strands), Problem Solving (by strategies), and more.  Each video is accompanied by a lesson that delves into the video's content.  Best of all, videos and classroom activities are free.

Consider using math projects that link learners with experts in the field. Electronic Emissary from the University of Texas began in 1993 to connect students to projects involving professional experts and uses e-mail for mentoring.  The online conversations typically take place anywhere from six weeks to a full academic year, based on students' needs and interests. The Center for Improved Engineering and Science Education sponsors and designs projects for K-12 students that utilize real-time data available from the Internet and that enable global collaboration with peers and experts.

Strong, Thomas, Perini, and Silver (2004) said that "any sufficiently important mathematics topic requires students to learn the topic in four dimensions: procedurally, conceptually, contextually, and investigatively" (p. 75). So, reducing the process of teaching and test preparation to a set of tips is simplistic, I know. Teaching for understanding is complex. In reality good instruction that includes attention to individual student needs is the best advice. After all this preparation, hopefully, the only thing left to do will be to remind students to get a good rest the night before and to eat a good breakfast on test day.  These strategies have given them the confidence they need to do well. Finally, along the way, celebrate success.

References

Bereskin, S., Dalrymple, S., Ingalls, M., et al. (2005). TIPS for English language learners in mathematics. Ontario (CA) Ministry of Education and Partnership in School Boards. Available: http://www.edu.gov.on.ca/eng/studentsuccess/lms/files/ELLMath4All.pdf

Burns, M. (2004). Writing in math. Educational Leadership, 62(2), 30-33.

Gordon, E. E. (2006, November 29). America needs to wise up about need for quality tutoring. Chicago Sun Times. Available: http://findarticles.com/p/articles/mi_qn4155/is_20061129/ai_n16871758

Reeves, D. B. (2004). Accountability for learning: How teachers and school leaders can take charge.  Alexandria, VA: Association for Supervision and Curriculum Development. ISBN: 0-87120-833-4.

Schneiderman, M. (2006, Nov. 6). Software & Information Industry Association: Written testimony of Mark Schneiderman before the U.S. Department of Education's national math panel. Palo Alto, CA. Available: http://www.siia.net/govt/docs/pub/siiatestimonymathpanelfinal2.pdf

Strong, R., Thomas, E., Perini, M., & Silver, H. (2004). Creating a differentiated mathematics classroom. Educational Leadership, 61(5), 73-78.

READ MORE FEATURES, INTERVIEWS, AND CASE STUDIES, AND TIPS

Proposals for articles, news tips, ideas for topics, and questions and comments about this publication should be submitted to David Nagel, executive editor, at [email protected].