This article integrates research in intelligent tutors with psychology studies of memory and math fluency (the speed to retrieve or calculate answers to basic math operations). It describes the impact of computer software designed to improve either strategic behavior or math fluency. Both competencies are key to improved performance and both address working memory limitations as students solve math problems. This research evaluated software interventions to improve strategies and fluency and tested their relative magnitude on math post-tutor performance. We discovered that both interventions appear to complement one another, impacting math achievement. Results suggest that training both strategy and fluency provide an advantage in accuracy and speed at answering math problems, due to more available memory capacity. Mathematics fluency has an impact on students' cognitive resources that are needed for more difficult (computationally intensive) math problems. We suggest that intelligent tutors can be enhanced with math fluidity training activities that help students to make calculations automatically with minimal memory load. (Contains 3 tables, 1 footnote, and 3 figures.)