Deep mastery of key STEM concepts requires the ability to transition with ease from one representation to another. Students should, for example, be able to think about acceleration and Newton’s Second Law using verbal, diagrammatic, graphical, and algebraic models, and to deal effectively with both natural and designed physical examples.
Unfortunately, many math and science classes (and some engineering and technology classes) fail to achieve effective integration of multiple representations. It is far too common, for example, to find students who are quite competent at solving equations or word problems based on “F = ma,” but who experience great difficulty applying that relationship to interpret and explain physical events or to design a practical, physical process.
Grounded in decades of interdisciplinary collaboration at Sinclair Community College in Dayton, Ohio and in a series of grants from NSF’s Advanced Technological Education Program, Math Machines software and hardware can be effective tools for increasing student use of multiple representations in modelling-based instruction.