Semantic Reading in Mathematics and Mathematics Teaching

This author already published one paper about semantic reading in mathematics teaching (Naziev, 2014). The paper contained short instructions on what semantic reading is and several more or less simple examples of the application of semantic reading in school algebra, geometry, probability, and calculus. In this paper, we will give a more instructive definition of semantic reading and several more complicated and, we hope, more interesting examples. Our work is connected with the results in artificial intelligence (Garrido, 2017). An important subject in the artificial intelligence is the automated (or mechanical) theorem proving, and, in particular, mechanical geometry theorem proving (Chou, 1988). The development of this last area has showed the evidence that in order to carry out proofs of geometry theorems mechanically, we have to strictly follow some rules and axioms (Chou, 1988). This is the main goal of our article, to show how important it is in mathematics, not only in artificial intelligence, to strictly follow axioms, definitions and theorems, that is, to read them semantically.