According to the National Council of Teachers of Mathematics (NCTM) Task Force on the Mathematically Promising, the highly able mathematics student should independently demonstrate the ability to:
- display mathematical thinking and have a keen awareness for quantitative information in the world around them.
- think logically and symbolically about quantitative, spatial, and abstract relationships.
- perceive, visualize, and generalize numeric and non-numeric patterns and relationships.
- reason analytically, deductively, and inductively.
- reverse reasoning processes and switch methods in a flexible yet systematic manner.
- work, communicate, and justify matheatical concepts in creative and intuitive ways, both verbally and in writing.
- transfer learning to novel situations.
- formulate probing mathematical questions that extend or apply concepts.
- persist in their search for solutions to complex, "messy," or "ill-defined" tasks.
- organize information and data in a variety of ways and to disregard irrelevant data.
- grasp mathematical concepts and strategies quickly, with good retention, and to relate mathematical concepts within and across content areas and real-life situations.
- solve problems with multiple and/or alternative solutions.
- use mathematics with self-assurance.
- take risks with mathematical concepts and strategies.
- apply a more extensive and in-depth knowledge of a variety of major mathematical topics.
- apply estimation and mental computation strategies.
The Committee noted that it is important to realize that these variables are not fixed and need to be continually developed.
Here are some resource links that might help with that development.
Bridges: The Math Learning Center (K-5 Math Teaching Resources | K5 Math | Math Learning Center): ALL grade levels (4th grade as example only).
Illuminations: Brain Teasers
