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Sample Lesson 5 - Developing Math Learning Skills

Reading Mathematics and Following Through on
Organizing for Studying Mathematics

Rationale

The language of mathematics uses words with precise meanings. To successfully read mathematics, one must know these meanings and understand the context in which the words are used.
Mathematics requires careful and deliberate reading. Students must read what is written and not interject expectations.
A daily encounter with mathematics can include overview, review, cross referencing vocabulary, or history. This encounter is something aside from normal mathematics study and homework.

Objectives

  1. Each student will experiment with suggestions on improving mathematics reading skills.
  2. Each student will examine times allocated for studying mathematics.

Materials and Resources

Index cards and scratch paper
Kogelman, S., and J. Warren, 1978. Mind over math, 163 68. New York: McGraw Hill.
Larnb, C., and N. Zeliavi. 1984, Elementary mathematics vocabulary. In Diagnostic and prescriptive mathematics issues, ideas, and insights. Ed. G. Bright and J.M. Hill, 58 61. Kent, Ohio:
Research Council for Diagnostic and Prescriptive Mathematics.

Handouts

  • "How to Study Mathematics," from Lesson 2
  • "Math Reading Test"
  • "Answers to Math Reading Test"

Instruction and Activities

  1. Review vocabulary from the previous lesson.
  2. Discuss requirements for successfully reading mathematics: From "How to Study Mathematics." read item 2, 'Read Carefully and Deliberately."
  3. Provide an example to illustrate careful reading, such as the following:

    There are 4 Arabians and 3 thoroughbreds in the pasture.
    Are there more Arabians than there are horses?

  4. Suggest that students use two index cards to avoid visual overload by blocking out all but the text they need to concentrate on, Demonstrate this method and have students practice. Suggest that students also highlight important material.
  5. Read and discuss Kogelman and Warren's suggestions for reading a math textbook.
  6. Read and discuss item 3, "Think with Pencil and Scratch Paper," from "How Mathematics." Suggest that students write big.
  7. Distribute the "Math Reading Test" Allow students to answer the first few items first three items and request that students write the solutions on the chalkboard as they solve the problems.
  8. Whenever possible check with students on their success in maintaining a schedule that allows for studying mathematics each day. Share problems and results. Tutors can review each student's schedule, skim the journal and notebook, and discuss ways of making the study of mathematics more organized.

Evaluation

  1. Have students identify the most important technique they learned about reading
  2. Ask students to identify one, new technique they will use when reading
  3. Ask students to identify one new technique they will use when reading mathematics

HANDOUT

Math Reading Test*

  1. Does England have a Fourth of July?
  2. If you had only one match and entered a room where there was a lamp, an oil heater, and some kindling wood, which would you light first?

  3. A woman gave a beggar 50 cents. The woman is the beggars sister, but the beggar is not the woman's brother. Why?
  4. Is it legal in North Carolina for a man to marry his widow's sister?
  5. A garden had exactly 50 different kinds of flowers, including 10 kinds of roses, 3 kinds sweet peas 2 kinds of alyssum, 5 kinds of carnations, 3 kinds of zinnias. 8 kinds of poppies, 4 kinds of snapdragons. 5 kinds of gladiolus, and 6 kinds of phlox. How many different kinds of flowers did the garden have?
  6. A rooster is sitting on the peak of a roof and lays an egg. Which way does the egg roll: to the right or to the left?
  7. Abbott, Baker, and Casper are a detective, and an entomologist and a farmer, although not necessarily in that order. Abbott was the proud mother of healthy twins yesterday. Casper has a deathly fear of insects and will not even get close enough to one to kill it if she sees it. The farmer is getting worried because she and her husband are getting old and will am be unable to run the farm for too many more years, and she has no children. Casper, unmarried, especially likes to date brunettes. What is the occupation of each of the three women?
  8. Three quarrelsome men registered at a hotel and paid $30 for a suite of rooms, each man contributing $10. The clerk discovered later that he should have charged them only $25 for that suite, so he gave the bellboy $5 to return to the men. Remembering how the men had quarreled when they registered, the bellboy thought they would quarrel too much about how to split the S5 refund, and so he kept $2 and returned $3 to the men. Now each man had paid $ 10, less $1 refund for the room ($9 x 3 men $27). But $27 + $2 kept by the bell boy equals only $29, and the original charge was $30 What happened to the other $1?


*Adapted from Jean Smith, Math Clinic, Wesleyan University, Middletown, Connecticut.

 


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