# 3. Construct Viable Arguments and Critique the Reasoning of Others; ARGUMENTS

Einstein

3.  Construct Viable Arguments and Critique the Reasoning of Others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Being able to utilize a common algorithm to solve a simple problem remains a skill to be taught and practiced in the classroom. Many parents and teachers are confused regarding this issue. Students must know basic facts and algorithms prior to completion of the fourth grade. This has not changed due to implementation of the Common Core for Math. Being able to solve simple, one-step problems by using common algorithms is only a part of understanding mathematics. A true understanding, and the ability to apply math requires much more.

Solving a real world problem generally requires multiple steps, and can often be approached in more than one way.  This standard encourages students to look at problems in different ways, and occasionally find solutions using unconventional methods.  The ability to apply previous knowledge to problem solving is essential, as well as the ability to solve problems in different ways utilizing analytical reasoning.

The main thrust of the third standard is “argument.” Students need to be able to construct viable arguments of why their problem solving processes work. The ability to argue for a method requires the ability to recognize counterexamples that lead to the same solution. Finding flaws in method is equally important. Those proficient in mathematics must be able to justify their methods and critique those of others. This can often be accomplished through the use of “concrete referents”, such as objects, drawings, diagrams and actions. The ability to reason and write mathematical arguments has becom a necessity for today’s student. Critical thinking, a requirement for today’s information driven world, is being practiced through this method.

James Wheeler – commoncoremath.net