Modeling Children's Mathematics: The Case of the Linear Function x + y = a

• In Event: 72.049 - Roundtable Session 34
  In Roundtable Session: 72.049-9 - Research on Algebraic and Proportional Reasoning

Abstract

When given a situation represented as x+y = a, if a student plots discrete points of x+y= a, does this necessarily imply an ability to construct a graph of the situation as a continuous line? Two ninth grade students showed differing constructions of x+y = a. Carl, with two levels of units coordinating scheme, failed to envision the points as forming a line while he could conceptually generate a plurality of points of x+y = a. Maggie, with three levels of units coordinating scheme, could simultaneously coordinate changes in two quantities and construct a graph of x+y = a as a line. Essential mental operations when constructing a graph of x+y = a as a line will be discussed.

Author

• Jiyoon Chun, University of Georgia