Conceptions of Function in Textbooks from Eighteen Countries

The concept of function has dramatically changed thelandscape of mathematics. Its introduction intoschool mathematics however has proved to bechallenging. What might students learn aboutfunctions if they were to answer all the functionstasks in their seventh- and eighth-grade textbooks? In 35 textbooks from 18 countries collected by theThird International Mathematics and Science Study(TIMSS) there were five distinct conceptions offunction: symbolic-rule ordered-pair social-dataphysical-phenomena and controlling-image. Symbolic-rule and ordered-pair were the mostfrequent. The achievement test items in TIMSS did notappear to address the same conceptions of function asthe tasks in the textbooks. The TIMSS test emphasizedsocial-data physical-phenomena andcontrolling-image conceptions over symbolic-rule andordered-pair conceptions. Some textbooks had tasksthat enacted a variety of conceptions of functionwhereas others only emphasized a few. Theseconceptions might play an important role in makingthe concept accessible if they could be used asspringboards toward a more flexible understanding offunction.