See the attached file, please.
1. The two foundations in which reasoning of justification for mathematics rest upon according to (Ball, & Bass, 2003) are a body of public knowledge, which stands as the linchpin of departure defining the granularity of acceptable mathematical reasoning in a supplied context or society. The next foundation is language or symbols, terms, and similar forms of illustrative paradigms representing definitions of what is justifiable mathematics. The rules of logic and syntax of this language dictates meaningful use in formulating claims and the networks of relationships used to justify this language. These two foundations are predicated upon knowledge of certain facts and concepts of mathematics and are prevalent in any level of math whether trigonometry, nuclear physics, or basic elementary (Ball, & Bass, 2003).
2. Teachers can first select and adapt tasks to create the need and opportunity for substantial mathematical reasoning. Teachers should ensure that reasoning of justification is a part of these tasks ...
Discusses the foundations of mathematical reasoning.