Poster #69 - An Analysis of Textbook Problems on Percentages

• In Event: 3-159 - Poster Session 12
  In Poster Session: PS 12 Section - Education, Schooling

Integrative Statement

Mastering rational numbers is important for later mathematics achievement and career development. Unfortunately, many children do not have a good understanding of them. The importance of rational numbers, together with children’s poor knowledge of them, have stimulated a lot of research on fractions and decimals and greatly informed us about how children understand them (e.g., Behr et al., 1984; Desmet et al., 2010; Siegler & Lortie-Forgues, 2015; Vamvakoussi & Vosniadou, 2010). In contrast, little research has been done on children’s understanding of percentages (Tian & Siegler, 2017).

Many of children’s learning difficulties that are usually attributed to their intellectual failings actually are more reflective of the environments in which their learning occurs. To understand that environment for learning percentages, we conducted an analysis of textbook problems on percentages. Past examination of textbook input illuminated sources of children’s difficulty in understanding fractions (Braithwaite, Pyke, & Siegler, 2017; Siegler & Lortie-Forgues, 2017); the same seemed likely to be true for percentages.

We coded and analyzed problems related to percentages in the 3rd to 8th grade volumes of two widely used math textbook series (GO Math! by Houghton Mifflin Harcourt and enVision math by Pearson). A total of 802 problems were entered into our database: 328 from Go Math! and 474 from enVision Math. Table 1 shows the categories into which these percentage problems were coded based on the content knowledge being assessed.

In both textbook series, percentages were defined as a rate or ratio that compares a number to 100, which highlighted their relational nature. Unlike decimals and fractions, percentages were always used with reference to a whole in the textbooks. These findings suggest that assessment of children’s knowledge of percentages should focus on the relational and part-whole meaning of percentages.

Another important phenomenon in both textbooks was the unbalanced distributions of problems that examined understanding of the same mathematical relation. One set of problems that we identified concerned relations among a percent, a whole, and a part. Problems in this set specified values of two components and asked students to find the value of the third. The number of problems in which the part was the missing component was almost twice as large as the number of problems in which the percent or the whole was the missing component in both textbooks (Table 1).

An unbalanced distribution was also present among percent change problems, which involved the relations among an original amount, a percent change, and a new amount. Notably, problems that asked children to find the original amount almost never appeared in either textbook (Table 1).

These findings are informative for future assessment of children’s knowledge of percentages. Children are likely to have more difficulty solving the less frequently presented problems than the more frequently presented ones, as found previously with fractions.

Authors

• Jing Tian, Teachers College, Columbia University
  Presenting Author

• Robert Siegler, Professor
  Non-Presenting Author