2013 Conference Proceedings - University of Nevada, Las Vegas

Mathematics Teacher Candidates’ Understanding of FunctionStacy ReederUniversity of Oklahomareeder@ou.eduRachel BatesRedlands Community Collegerachel.m.bates-1@ou.eduFunctions play in integral and important role throughout mathematics. Many studies havefocused on college student understanding of function and have found them to be lacking. Fewstudies however, have focused on teacher candidates’ understanding of function. Given thatmiddle school and high school mathematics teachers help students develop what we hope will bea deep and flexible understanding of function it is important that their own understanding offunction be rich and well-developed. This study examined one group of mathematics teachercandidates’ understanding of function. The results indicate that their understanding was limited.The idea of a function, or at the very least, the anticipation of the idea of function can bedated back as far 2000 B.C.E. and is evidenced in the work of the Babylonians and ancientGreeks with one-to-one correspondence for counting and their extensive use of tables. However,the notion of function, as we know it, did not arrive on the mathematics landscape until the early1300’s and had its beginnings as a way of designating the correspondences between geometricalentities. Over time the notion of function continued to develop and become associated with thestudy of analytical expressions, thus securing a central place in mathematics (Burnett-Bradshaw,2007).The work of Oreseme (1323 – 1382) included “general ideas about independent anddependent variable quantities seem to be present” (Ponte, 1992, p. 4). Some two hundred yearslater Descarte (1596 – 1650) indicated a dependence between variable quantities in his work withequations in two variables marking the emergence of the notion of functions as an individualizedmathematical entity. Furthering the idea of function was Newton (1642 – 1727) whodemonstrated how functions could be developed in infinite power series. While Leibnitz was thefirst to use the term “function” in 1673, the study of function as a clearly individualized conceptdid not arise for a few more decades at the end of the 17 th century. Finally, as a result of “thedevelopment of the study of curves by algebraic methods, a term to represent quantities that weredependent on one variable by means of an analytical expression was increasingly necessary”(Ponte, 1992, p.4), the term “function” was adopted. This was decided somewhere between1694 and 1698 in an exchange between Leibnitz (1646 – 1716) and Bernoulli (1667 – 1748).Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 24