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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.
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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.
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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.
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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.
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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.
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Students should create note cards while
reading their math textbook.
Creating these cards requires students to read,
reflect on what they’ve 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.
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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.
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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.
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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).
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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.
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1.
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?”
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2. “What’s 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 you’ve
already proven? Is it an important step in the proof
of some other theorem? Is it surprising?”
5.” What’s the motivation for the theorem? What
question does it answer?”
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The easiest way to read a proof is to check that
each step follows from the previous steps.
Once you’ve 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?”
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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.
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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.
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The following link provides examples of
annotating your math textbook and combining
lecture notes with the book.
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Reading a Math Textbook (PDF File)