Abstract
Students' informal algebraic encounters in grades K–8 lay the foundation for more formalized study of algebra in the future (NCTM 2000; Yackel 1997). The study of functions and relationships is essential in algebra. Functions and relations involve variables and describe how the change in one variable causes a change in a second variable. Words, tables, graphs, and formulas can be used to describe these relationships, which can also be found in many aspects of real life. Consider the following two examples: (1) the darkness of a piece of toast is a function of the setting on the toaster (Ritchhart 1997) and (2) the length of time required to ride to school on the bus can also be a function of the distance between the bus stop and the school. These relationships were described in words, but they can also be described by using a graph, a table, and depending on the exact nature of the relationship, even a formula. Many children do not realize that their everyday lives are filled with such functions and relations (Ritchhart 1997), and they have limited opportunities to interpret and analyze change graphically. Because students experience difficulty in interpreting graphs (Janvier 1981), they must be given opportunities to both interpret and create them.
Published Version
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