Math Content Standard D: Reasoning

Key Elements

A student who meets the content standard should:

1. Analyze situations.
2. Draw logical conclusions.
3. Use models, known facts and relationships to explain their reasoning.
4. Verify conclusions, judge the validity of arguments, and construct valid arguments (Deductive Reasoning); and
5. Recognize patterns and form mathematical propositions (Inductive Reasoning).

Mathematical Reasoning for All

• Mathematical literacy involves a willingness to engage in a problem without knowing the answer in advance. For many students this requires a step into an insecure territory in which they must enter into uncertainty to gain access to success.
• Successful experiences with the habits of mind that support higher order critical thinking are crucial at an early age in order to develop a willingness to work with this uncertainty in more complex problems with larger stakes.
• Students should be asked to perform complex mathematical reasoning by extending the logic from simple patterns and models to more complex situations.
• By strategically applying different types of logic students will learn to recognize which type of logic is being used in different situations and respond accordingly.

Big Ideas in Reasoning

Non-algorithmic and algorithmic reasoning
Multiple solutions; multiple criteria for correctness
Uncertainty dominates
Requires sustained effort
Interdisciplinary usefulness of these habits of mind
Valuing debate and critique