Computer-Human Interaction in Symbolic Computation

Reasoning by Equivalence: The Potential Contribution of an Automatic Proof Checker

“…(Bundy, 1983), and these are commonly taught in school mathematics. The Mathpert system of Beeson (1998) avoids the problem of deciding if a student's step is legitimate by providing a menu of steps from which the student must choose. It is certainly possible to infer some of the steps a student has made, and so some analysis of students' steps is a valuable addition to the reasoning by equivalence described here.…”

“…Mathpert is intended to replace paper-and-pencil homework in algebra, trig, and calculus, retaining compatibility with the existing curriculum while at the same time supporting innovative curriculum changes; to provide easy-to-use computer graphics for classroom demonstration in those subjects, as well as for home study; to replace or supplement chalk-and-blackboard in the classroom for symbolic problems as well as graphs. (Beeson, 1998) Students either pick a built-in topic or enter the problem they wish to solve. Students then use the calculation window to solve the problem in a step-by-step fashion.…”

“…To put it another way: it is not possible to entirely separate "interface" considerations from "kernal" considerations. (Beeson, 1998) Other important works in this area are Heeren, Jeuring, and Gerdes (2010) and Prank (2011). In particular, Aplusix focuses on reasoning by equivalence, see Nicaud et al (2004).…”

“…In this situation it is difficult to select the sub-expression x 4 − 9 from x 4 − x 2 − 9 without re-ordering some of the terms. More detailed discussion of these issues is given by Beeson (1998) and Beeson (2004).…”