Mathematics Problem-based Learning through Spreadsheet-like Documents

Problem-based learning is particularly suitable in fields like Mathematics. It is quite usual to find abstract descriptions of solving methods to express mathematical knowledge. However, these descriptions happen to be somewhat hard for students. For instance, when a learner faces the integration-by-parts method, one possibility is to try to understand the general formula (by using the abstract description), while on the other hand another possible scenario is to learn by watching particular examples. Both approaches are complementary and, in fact, teachers usually move back and forth in order to manage their students to understand the underlying concepts. In this paper we introduce ConsMath (CONStraint-based MATH teaching), a computer system that includes an authoring tool for the creation by the teacher of interactive Mathematics documents. The teacher can establish spreadsheet-like relations between the different mathematical formulae that appear in the document, and require certain conditions to be held when used by the student. The documents are dynamic and their contents changes depending on the formulae filled in by the student. ConsMath can be used in a particular style of problem-based learning in a context where each document is a problem pattern, and students can work on those problems by practicing with them repeatedly, and deciding in each case about the different steps that are necessary for their resolution. ConsMath runs both as a standalone application and in an applet within a web page. An important feature of ConsMath is the possibility for the teacher to create interactive documents starting from static ones. Besides, the student can also ask ConsMath to generate specific problem statements from a given problem pattern. Consequently, students can choose between working on a problem posed directly by themselves, or asking the system to generate different problems corresponding to some given problem patterns.