Text to diagram to symbol: representational transformations in problem-solving

Central to engineering problem solving is what we call representational transformation. Such transformations are built upon community-sanctioned practices often referred to as "back of the envelope" calculations. First a problem statement (text) is translated into a sketch (diagram) which visually articulates the essential problem parts. Mechanical models and free-body diagrams are instances of this first transformation. The qualitative model is then transformed into a set of mathematical formulae (symbols), which drive the problem solution. Thus, the problem is solved using three types of representational systems: textual, diagrammatic and symbolic. At each step the engineer translates information from one representational system to another, enacting an abstract cultural algorithm. The knowledge necessary to undertake these transformations is described in this paper in the context of multi-literacies. We propose that a large part of learning engineering problem solving is in fact learning the relationships between the multiple languages of problem solving.