Quantitative reason may have a layered codification in which the innermost one is the set theoretic framework of arithmetic based mathematics. The chapter Modern Mathematics Instruction describes how this author met a modern mathematics curriculum in the late 1960s and makes observations about mathematics instruction which support the recommendations given in this work. Further support for the recommendations is given in the next chapter. The chapter The Two Ends describes primary mathematics instruction and college level mathematics service courses. For most people entering college, this represents the start and finish, the two ends, of their math education.
Observations here support earlier instructional thoughts.
The Transition details how intermediate level courses may provide a smooth transition between the two ends. This chapter offers a program to develop algebraic and deductive thought apart from geometry. Again, teachers or curriculum committees may think of further topics to add or to refine the proposed core of this program. See the companion books or their table of contents. The long chapter Elementary Instruction describes its subjects prealgebraic and predeductive, yet thought based, nature.