2013 Conference Proceedings - University of Nevada, Las Vegas

Adopts the “111” (a term coined by the authors of the paper and explained below)style when computerizing the grading of solution processes. “111” refers to aparticular style of limit computation using limit properties which intends to fosterstudents to develop an ability to solve problems in a gradual, firm, and orderlymanner, and to make the computerization of grading solution processes easier toimplement. It denotes the following: for each one (1) computation step, choose onlyone (1) property, and apply that property only once (1).Limit Computation TreesFor the problem described in the section “Structures Embedded in Expressions”, we proposean alternate method to the traditional line-by-line linear form for conducting and presenting thecomputation of limits — limit computation trees. The scheme of such computation trees isshown in Figure 1 where exp is a mathematical expression; subexp1 and subexp2 are its subexpressions;prop1 to prop3 are instances of limit properties; op1 to op3 are mathematicaloperators ( etc.); and n1 to n4 are numbers.The essential idea of the limit computation tree is to show exactly how the process ofcomputing a limit, which is entirely driven by repeatedly applying various limit properties, starts,proceeds, and terminates by displaying the structure of and the correlation between all subcomputations(induced by the original computation) in a top-down graphical manner. Anexample of the limit computation tree is given in the next section.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 138