# What Textbooks Offer for Instruction in Fraction Concepts

By Dorgan, Karen | Teaching Children Mathematics, November 1994 | Go to article overview

# What Textbooks Offer for Instruction in Fraction Concepts

Dorgan, Karen, Teaching Children Mathematics

Fraction concepts are among the most complex and important mathematical ideas that children encounter before their secondary school years (Behr et al. 1984). Perhaps because of their complexity, fractions are also among the concepts least understood by students. On the 1990 National Assessment of Educational Progress, for example, only 50 percent of eighth graders could express in decimal form a fraction with a denominator of 10. Only 49 percent could tell the weight on the Moon of an object that weighs thirty pounds on Earth, given that a weight on the Moon is 1/6 the weight on Earth (National Assessment Governing Board 1991). American students are not alone in having trouble (Strang 1990; Kerslake 1986). Why do students have so much difficulty with this area of mathematics?

Part of the difficulty lies in the nature of fractions. The word fraction may have any one of several meanings. The fraction-bar symbol itself may express several distinctly different mathematical ideas, and the concept of rational number has several different subconstructs (Ohlsson 1988; Behr et al. 1992). Fairly sharing a pizza among four friends is conceptually different from predicting the likelihood of rain, given the past record of rain on an average of one day in four. Using four eggs from a carton of a dozen is quite different from cutting a third from a stick of butter. The "simple" fraction that we try to teach our students turns out to be not so simple on closer examination.

Of How Much Help Is the Textbook?

Because most teachers rely on the mathematics textbook in planning their instruction, looking at what is available from textbook publishers seems appropriate. What meaningful learning experiences with fractions do textbooks offer? A recent examination of three 1992 textbook series for grades 1 through 5, randomly selected from those published by major companies and available for adoption in the state of Virginia, gives some indication of what today's textbooks offer.

This investigation of textbooks' treatment of fractions was guided by several ideas from recent research. For example, Lesh's model (adapted from Bruner and discussed in Behr et al. [1992]) suggests five modes of representation (see question 2 that follows): it was noted whether these modes were reflected in the textbooks. Also noted was the presence of a reasonable balance in the inclusion of different subconstructs of rational number, for example, part-whole, ratio, and decimal.

Questions Considered in the Textbook Examination

Question 1: How much of a textbook is devoted to instruction in fractions?

Rationale. One indication of the importance the authors place on fractions is the amount of space they allot to them.

Results. As expected, the percent of pages devoted to fractions increases along with the grade levels, from an average of 2 percent of the pages in the first-grade textbook to an average of 34 percent in the fifth-grade textbook. The numbers were fairly consistent across the three series, and, in general, the number of fraction-related pages increased sharply from the fourth to the fifth grade.

Question 2: Did the textbook address the various modes of representing fractions?

Rationale. Lesh has described five different modes of representing rational number: spoken symbols, written symbols, manipulative materials, pictures, and real-world situations. The processes of transforming among these five modes of representation and translating within each mode make the mathematical ideas meaningful to the child (Behr et al. 1992).

```TABLE 1
Percent of Pages Devoted to Fraction Instruction

Series 1              Series 2              Series 3
Percent               Percent               Percent
No. of    of Total    No. of    of Total    No. of    of Total
Pages     Pages       Pages     Pages       Pages     Pages

Grade 1       8        2%           6        2%          10        2%
Grade 2      16        4%          16        4%          23        5%
Grade 3      58       12%          37        7%          61       12%
Grade 4      68       14%          86       19%          93       18%
Grade 5     146       29%         154       34%         197       38%
```

Results. …

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes

#### Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited article

What Textbooks Offer for Instruction in Fraction Concepts
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
• Highlights & Notes
• Citations
Some of your highlights are legacy items.

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.