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Reading a Math Textbook

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Title: Reading a Math Textbook Author: scox Last modified by: Administrator Created Date: 2/17/2012 5:32:14 PM Document presentation format: On-screen Show (4:3) – PowerPoint PPT presentation

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Title: Reading a Math Textbook


1
Reading a Math Textbook
2
Previewing
  • Before reading an assigned chapter, highlight all
    bold and italic words. Include these words and
    their definitions in a glossary in your notebook.
  • Ask What is the main topic? What does the author
    hope to accomplish in this chapter? What should I
    be able to do after reading and studying this
    chapter? Record the answers to these questions in
    your notes as you read.
  • Set up a journal with three columns containing
    the headings What I Already Know, What I Have
    Studied Before but Need to Review, What I Have
    Never Studied. New concepts (what you have never
    studied before) will require the most time and
    concentration as you read and study the chapter.

3
Reading
  • Mathematics textbooks follow this pattern
    statement, example, and explanation/summary.
  • To identify and study the statement, students
    should read only the first title or subtitle and
    predict what will come next. Then read the first
    paragraph and write a short summary phrase in the
    margin or in your notes. Repeat this process for
    each paragraph.

4
Reading, continued
  • To study examples, begin by looking at the first
    line of the sample problem. Cover up the rest of
    the problem. Predict the next line of the
    problem. Check your prediction against the
    example. Then, examine and learn from the
    difference between your prediction and the
    example.
  • For the explanation or summary, sample problems
    are often explained in the paragraph that
    follows. Work out the sample problem after
    reading the explanation. If a summary is given,
    paraphrase it in your notes.

5
Practice
  • Before continuing with the chapter, work out a
    couple of problems that follow the example just
    given.
  • Next, move on to the next section of the chapter.
    Read it and work out the problems. Include all
    steps. Check your answers, and if any are
    incorrect, go over the step to determine where
    you went wrong.

6
Review
  • Before class, students should review their
    textbook annotations, mathematical journals, and
    notes to find any concepts they do not fully
    understand. This will be the basis for classroom
    discussion of the assigned chapter.

7
Concept Cards
  • Students should create note cards while reading
    their math textbook.
  • Creating these cards requires students to read,
    reflect on what theyve read, and write the
    information in their own words. This demonstrates
    comprehension of the text.
  • These cards can later be reorganized by related
    concepts for study purposes.

8
QAR
  • The Question, Answer, Relationships strategy was
    developed to help students understand where basic
    mathematical concepts apply to the real world and
    how they connect to more sophisticated
    mathematical concepts.
  • Begin with Right There Questions. These are
    based on information given in the problem.
  • Next, Think and Search Questions require
    students to identify relationships between
    information provided and unknown information.

9
QAR, Continued
  • Finally, students answer On Your Own Questions.
    They must identify prior knowledge and
    additional information needed to solve the
    problems.
  • These types of questions make students aware of
    the different types of information provided in
    word problems and what areas they need to
    concentrate on while reading and studying.

10
QAR, Continued
  • It is also helpful if the instructor provides
    guided practice at the beginning of the course
    and models responses to the questions. Then the
    students will learn to generate their own
    questions while reading (Campbell, Schlumberger,
    and Pate).

11
Helping Undergraduates Learn to Read Mathematics
  • As students progress through their college
    education, reading materials naturally become
    more difficult to comprehend and expectations for
    the level of the students understanding
    increase.
  • The study methods and reading strategies
    necessary for understanding and learning from
    mathematics textbooks are very different from
    those involved in reading for other disciplines.

12
Helping Undergraduates, Continued
  • Theorems and proofs make up a large portion of
    advanced mathematics textbooks.
  • In order to read and understand a theorem
    effectively, Ashley Reiter of the Maine School of
    Science and Mathematics suggests considering the
    following questions
  • What kind of theorem is it? Is it a
    classification of an object, an equivalence of
    definitions, an implication between definitions,
    or a proof of when a technique is justified?

13
Helping Undergraduates, Continued
  • 2. Whats the content of the theorem?
  • 3. Why are each of the hypotheses needed? Can
    you find a counterexample to the theorem in the
    absence of each of the hypotheses? Are any of the
    hypotheses unnecessary? Is there a simpler proof
    if you add extra hypotheses?
  • 4. How does this theorem relate to other
    theorems? Does it strengthen a theorem youve
    already proven? Is it an important step in the
    proof of some other theorem? Is it surprising?
  • 5. Whats the motivation for the theorem? What
    question does it answer?

14
Helping Undergraduates, Continued
  • The easiest way to read a proof is to check that
    each step follows from the previous steps.
  • Once youve read a theorem and its proof, you
    should do the following to synthesize your
    understanding of the theorem and proof.
  • 1. Write a brief outline demonstrating the logic
    of the argument.
  • 2. Answer the question What mathematical raw
    materials are used in the proof?
  • 3. Also answer, What does the proof tell you
    about why the theorem holds?

15
Helping Undergraduates,Continued
  • 4. Finally, answer the question Where are each
    of the hypotheses used in the proof? (Reiter)
  • Employing the above strategies can improve your
    understanding and utilization of the information
    presented in your college mathematics textbooks.

16
Sources
  • Campbell, Anne E., Schlumberber, Ann, and Pate,
    Lou Ann. Promoting Reading Strategies for
    Developmental Mathematics Textbooks. 28/12/11.
  • http//www.umkc.edu/cad/nadedocs.
  • Reiter, Ashley. Helping Undergraduates Learn to
  • Read Mathematics. 28/12/11. http//www.maa.org.

17
Appendix
  • The following link provides examples of
    annotating your math textbook and combining
    lecture notes with the book.
  • Reading a Math Textbook (PDF File)
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