October 2007 — News

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Test Prep and Math Realities

by Patricia Deubel, Ph.D.

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.