We examine the role of tasks that have the intended effect of teachers re-conceiving the mathematics they teach as comprising a coherent body of meaningful ideas. We ground our discussion in ideas of trigonometry and modular functions and draw from a professional development research project to illustrate our approach. In this project, many…

Multiplication and division have in general been much more difficult to perform than addition and subtraction. Perhaps, if we could find some device for reducing multiplication and division to addition and subtraction, computational loads could be lightened. One such device is that of logarithms of course. This note outlines another such device…