1. Teaching for Understanding Appalachian Math Science Partnership 2007-2008

2. Persons with a world class education have a high degree of literacy in mathematics and science.

3. Showing the ability to do applications in contexts that vary from instructional contexts can provide important evidence of the desired level of understanding.

4. Three important learning principles to facilitate the construction of understanding follow. National Research Council, (2005). How students Learn: History, mathematics and science in the classroom. Committee on How People Learn. M.S. Donovan and J.D. Bradford (Eds.). Washington, DC: The National Academy Press.

5. 1. Engage Students’ Prior Understandings.

6. 2. Exploit the essential roles of factual knowledge and conceptual frameworks in facilitating students’ construction of understanding.

7. 3. Promote self monitoring/meta- cognition by students.

8. Desirable science learning includes subject matter, inquiry skills, nature of science and science and society issues. National Research Council. (1996). National science education standards. Washington, DC: National Academy Press.

9. Desirable mathematics learning includes: conceptual understanding (comprehension of math concepts, operations and relations) conceptual understanding (comprehension of math concepts, operations and relations) procedural fluency (utilizing procedures flexibly, accurately, efficiently and appropriately.) procedural fluency (utilizing procedures flexibly, accurately, efficiently and appropriately.) strategic competence (ability to formulate, represent and solve math problems.) strategic competence (ability to formulate, represent and solve math problems.)

10. adaptive reasoning (capacity for logical thought, reflection, explanation and justification.) adaptive reasoning (capacity for logical thought, reflection, explanation and justification.) productive disposition (inclination to view mathematics as sensible, useful and worthwhile, along with a belief in diligence and one’s own efficacy.) productive disposition (inclination to view mathematics as sensible, useful and worthwhile, along with a belief in diligence and one’s own efficacy.) National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds). Washington, DC: National Academy Press.

11. Some implications follow for assessment and differentiated instruction as we try to provide a world class education that addresses important learning outcomes through the application of modern learning theory.

12. Formative assessment should include preinstruction assessment of the understandings students bring to the setting.

13. Many instructional tasks should have a built-in allowance for individual differences in pursuing a problem or exploration.

14. Heavy reliance on a traditional textbook as the major data source for instruction in mathematics or science would create insurmountable needs for differentiated instruction and not be consistent with learning principles, when the varied outcomes of a world class education are targeted.

15. Formal and informal assessment data should be obtained seamlessly and utilized at strategic points in order to make decisions about what needs to happen next for individuals and small groups.

16. A variety of differentiated learning outcomes should be pursued instructionally and assessed at levels consistent with the desired outcomes.

17. Strategies that encourage students to monitor their own learning should become a regular feature of instruction.

18. What counts as evidence of learning must be given major attention.

19. Hitting a target that is set too low would be a shallow victory.

20. Evidence should regularly tap students’ ability to do applications and communicate defensible results.

21. All students should be expected to learn and demonstrate major progress toward meeting minimum standards.

22. All students in a class will not construct the same level of understanding for any particular topic in mathematics and science.

23. Many students should be expected to regularly exceed minimum standards for any particular topic in mathematics and science.