Common Core Standards for Mathematical Practice (Part II)
This is Part Two of a three part article [Part One] which provides the description of each of the Standards for Mathematical Practice as written in the Common Core math standards. It discusses aspects of each SMP that can be interpreted along conventional or traditional approaches to math teaching and contrasts this with how each one may be implemented under the math reform interpretation.
SMP 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.