2) Heuristics are rules of thumb for effective problem solving. They are fairly broad strategies for making progress on unfamiliar or difficult problems. Examples are exploiting analogies and working backward. While the mathematics education community has generally accepted the idea that such strategies are useful and worth teaching, until recently there has been little understanding of their complexity and little evidence that students can reliably learn to use such strategies.
3) Control deals with the question of resources management and allocation during problem solving attempts. In this context it is reserved for major decisions regarding planning, monitoring, and assessing solutions on-line, and the like. With good control, problems solvers can make the most of their resources and solve rather difficult problems with some efficiency. Lacking it, they can squander their resources and fail to solve problems easily within their grasp.