Notes for chapter 1: "What is computation?"
Video courses explaining basic arithmetic are provided by the Khan Academy. It is instructive to follow them with an eye on the algorithmic symbol-processing aspect of each technique.
Computation as an aid for understanding
The Bootstrap project uses games programming for teaching mathematical concepts to students in the 12-16 year age range.
The book Structure and Interpretation of Classical Mechanics teaches classical mechanics using a computational notation. The full text is available (HTML, PDF), as is complementary material from the corresponding MIT course. The authors have later used the same computational approach for teaching Functional Differential Geometry, which is also avaiable on-line (PDF).
The paper Domain-Specific Languages of Mathematics: Presenting Mathematical Analysis using Functional Programming by Ionescu and Jansson describes how a programming point of view can help in teaching mathematics.