Standard A: Content of Math
Standard B: Problem Solving
Standard C: Communication
Standard D: Reasoning
Standard E: Connections
Math Content Standard D: Reasoning
A student who meets the content standard should:
- Analyze situations.
- Draw logical conclusions.
- Use models, known facts and relationships to explain
- Verify conclusions, judge the validity of arguments,
and construct valid arguments (Deductive Reasoning);
- Recognize patterns and form mathematical propositions
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
- 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
Requires sustained effort
Interdisciplinary usefulness of these habits of mind
Valuing debate and critique