2. Concept Map

3. “Concept Map Activity”
Example of a Concept Map
Concept Term list
Rose
Flower
Fragrance
Love
Florist
Feeling

4. For science & mathematics what does it mean to KNOW/ UNDERSTAND/GRASP
The NRC understands there to be 4 strands of scientific proficiency:
The NRC understands there to be 5 strands of mathematical proficiency
know, use, and interpret scientific explanations of the natural world;
generate and evaluate scientific evidence and explanations;
understand the nature and development of scientific knowledge; and
participate productively in scientific practices and discourse.
conceptual understanding
procedural fluency
strategic competence
adaptive reasoning
productive disposition

5. “Concept Map Activity”
Example of a Concept Map

6. Key Principles of Experts' Knowledge
Experts notice features and meaningful patterns of information that are not noticed by novices.
Experts have acquired a great deal of content knowledge that is organized in ways that reflect a deep understanding of their subject matter and this allows them to notice different things.

7. “Concept Map Activity”
Example of a Concept Map

8. Key Principles of Experts' Knowledge
Experts' knowledge cannot be reduced to sets of isolated facts or propositions but, instead, reflects contexts of applicability: that is, the knowledge is ''conditionalized" on a set of circumstances.
Experts are able to flexibly retrieve important aspects of their knowledge with little attentional effort.

9. “Concept Map Activity”
Example of a Concept Map

10. Key Principles of Experts' Knowledge
Though experts know their disciplines thoroughly, this does not guarantee that they are able to teach others.
Experts have varying levels of flexibility in their approach to new situations.

11. “Concept Map Activity”
Example of a Concept Map

12. Five Strands of Mathematical Proficiency

13. “Shaping Up” What did you learn?