Mathematical Proofs Middle School Mathematics

Mathematical Proofs middle school mathematics teacher seems at first to gain little from absorbing an article like Kleiner & Movshovitz-Hadar's "Proof: A Many Splendid Thing." However, the authors' explication on the origin of mathematical truth-finding and the changing role of the proof in mathematics reveals several key points that can incorporated into general math classrooms. For example, Kleiner & Movo*****z-Hadar discuss the confluence of philosophy and math throughout history, pointing out especially their shared use of logic and dependence on the successive logical proof in explaining their mutual discoveries to colleagues. Similarly, junior high students may be able to appreciate, if not the details of the Enormous Theorem, at least the process of thinking that underlies mathematical proof. The gap between the seemingly abstract world of theoretical math and everyday reality may not be as great as we all think. Students of math can especially benefit from a deeper understanding of the proof for the satisfaction it can bring. Mathematics is not only about measurements, calculations, and counting. Rather, mathematics form the building blocks of rational thought: our work is about process and proof.

With a firm foundation in logic, mathematics cannot be argued with. As Kleiner & Movo*****z-Hadar show, the burden of proof lies with the mathematician eager to uncover some unknown universal law or theorem. His or her colleagues will, as the authors point out, be harangued and criticized because of a general resistance to new ways of thinking or profound revelations. Because of the difficulty in obtaining proof and subsequently communicating those proofs to the academic community, math remains one of the last bastions of reason in our society. Mathematics stimulates analysis and critical thinking, essential components of a good life. Philosophers use proofs too, such as to illustrate the existence or non-existence of God. Perhaps the most salient issue brought out by Kleiner & Movo*****z-Hadar in their article and the one most relevant to modern classrooms is their celebration of diversity of thought. While mathematics may occasionally manifest as speculation or even intuition, ultimately mathematicians demand proof: evidence, firmness, and rigorous standards. In a world in which "fuzzy math" and unreal "reality TV" have taken over the public consciousness, proof might be our last hope.