Computational Triangulation in Mathematics Teacher Education

The term computational triangulation grew out of the author's experience using computers with teacher candidates preparing to teach K-12 mathematics in the schools of United States and Canada. The use of commonly available digital tools by the candidates allows them to appreciate the role of intrinsic complexity of the tools in the development of deep mathematical knowledge required for teaching the subject matter. The word triangulation has mathematical origin going back to antiquity as a geometric technique of indirect measurements. The idea of triangulation is commonly used by sociologists as a means of bringing rigor into scholarship by integrating different perspectives and alternative epistemologies. In mathematics, the idea of validation of mathematical propositions and simplification of their proofs using alternative reasoning strategies is a commonplace in pure and applied research. The book provides mathematics education examples of computational triangulation as multiple ways of solving a problem in the context of spreadsheets, Wolfram Alpha, Maple, the Graphing Calculator, and GeoGebra. It covers topics from arithmetic, algebra, geometry, trigonometry, probability, number theory, and discrete mathematics. The book may be of interest to faculty assigned teaching courses for future teachers of mathematics. It can support graduate/doctoral level mathematics education programs and motivate using the ideas of computational triangulation within a variety of tertiary courses in STEM disciplines.