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During the first 12 weeks of an applied calculus course, two classes of college students (n=39) studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Only the last 3 weeks were spent on skill development. Class transcripts, student interviews, field notes, and test results were analyzed for patterns of understanding. Students showed better understanding of course concepts and performed almost as well on a final exam of routine skills as a class of 100 students who had practiced the skills for the entire 15 weeks.

Digital technology1 is omnipresent in society. Revolutionary technological developments change the character of professional environments, and therefore put new demands on workers (Hoyles, Noss, Kent, & Bakker, 2010). Consequently, there are new demands on educational systems in order to prepare students for future professions. Importantly, technology also offers opportunities for teaching and learning (see for example, Clark-Wilson, 2010;Sacristán et al. 2010); exploiting these opportunities requires rethinking educational paradigms and strategies. With the advent of such technology, the question arises as to what the impact on education and teaching practices should be in order to prepare the next generation of students for future careers.Both in professional practice and in personal life, it is particularly striking how digital technologies such as software-controlled engines, smart phones, tablets, and GPS devices rely on mathematical algorithms that are invisible to the user, but play essential roles "under the hood". Implications of these technology-rich environments have the potential to influence the nature of mathematics education and the concepts and skills that future students will possess.Roberts, Leung, and Lin (2013) comment on the complexity of the interplay between technology, mathematics, and education, noting that this complexity related to the use of tools in mathematics is not a phenomenon that is due to current technologies, but one that has been evident whenever people use tools in mathematics. The rapid development of digital technologies features new capabilities not even considered possible in the past. Despite advances in digital technologies, there is still strong value in using a combination of physical tools and digital technologies in mathematics education (Maschietto & Trouche, 2010). Different types of technologies are available for teaching mathematics, and different technologies are appropriate for different purposes. General technologies for communication, 1 To avoid constantly repeating the terms "digital technology" in this text we will often refer to "technology"; while doing so, we refer to digital technology in mathematics education.