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Reading a Math Textbook

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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?

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?

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?

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.

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.

Appendix

- The following link provides examples of

annotating your math textbook and combining

lecture notes with the book. - Reading a Math Textbook (PDF File)