Teaching for UnderstandingTeaching for UnderstandingAppalachian Math Science Appalachian Math Science

PartnershipPartnership

2007-20082007-2008

Persons with a world class education Persons with a world class education have a high degree of literacy in have a high degree of literacy in

mathematics and science.mathematics and science.

Showing the ability to do applications Showing the ability to do applications in contexts that vary from in contexts that vary from

instructional contexts can provide instructional contexts can provide important evidence of the desired important evidence of the desired

level of understanding.level of understanding.

Three important learning principles to Three important learning principles to facilitate the construction of understanding facilitate the construction of understanding

followfollow..

National Research Council, (2005). How students National Research Council, (2005). How students Learn: History, mathematics and science in the Learn: History, mathematics and science in the

classroom. Committee on How People Learn. M.S. classroom. Committee on How People Learn. M.S. Donovan and J.D. Bradford (Eds.). Washington, Donovan and J.D. Bradford (Eds.). Washington,

DC: The National Academy Press.DC: The National Academy Press.

1. Engage Students’ Prior 1. Engage Students’ Prior Understandings.Understandings.

2. Exploit the essential roles of factual 2. Exploit the essential roles of factual knowledge and conceptual knowledge and conceptual

frameworks in facilitating students’ frameworks in facilitating students’ construction of understanding.construction of understanding.

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

Desirable science learning includes Desirable science learning includes subject matter, inquiry skills, nature subject matter, inquiry skills, nature

of science and science and society of science and science and society issues.issues.

National Research Council. (1996). National National Research Council. (1996). National science education standards. Washington, science education standards. Washington,

DC: National Academy Press.DC: National Academy Press.

Desirable mathematics learning Desirable mathematics learning includes:includes:

• conceptual understanding (comprehension of conceptual understanding (comprehension of math concepts, operations and relations)math concepts, operations and relations)

• procedural fluency (utilizing procedures procedural fluency (utilizing procedures flexibly, accurately, efficiently and flexibly, accurately, efficiently and appropriately.)appropriately.)

• strategic competence (ability to formulate, strategic competence (ability to formulate, represent and solve math problems.)represent and solve math problems.)

• adaptive reasoning (capacity for logical adaptive reasoning (capacity for logical thought, reflection, explanation and thought, reflection, explanation and justification.)justification.)

• productive disposition (inclination to view productive disposition (inclination to view mathematics as sensible, useful and mathematics as sensible, useful and worthwhile, along with a belief in diligence worthwhile, along with a belief in diligence and one’s own efficacy.)and one’s own efficacy.)

National Research Council. (2001). Adding it up: National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds). Washington, J. Swafford, and B. Findell (Eds). Washington, DC: National Academy Press.DC: National Academy Press.

Some implications follow for Some implications follow for assessment and differentiated assessment and differentiated

instruction as we try to provide a instruction as we try to provide a world class education that addresses world class education that addresses

important learning outcomes important learning outcomes through the application of modern through the application of modern

learning theory.learning theory.

Formative assessment should include Formative assessment should include preinstruction assessment of the preinstruction assessment of the

understandings students bring to the understandings students bring to the setting.setting.

Many instructional tasks should have Many instructional tasks should have a built-in allowance for individual a built-in allowance for individual

differences in pursuing a problem or differences in pursuing a problem or exploration.exploration.

Heavy reliance on a traditional Heavy reliance on a traditional textbook as the major data source textbook as the major data source for instruction in mathematics or for instruction in mathematics or

science would create insurmountable science would create insurmountable needs for differentiated instruction needs for differentiated instruction and not be consistent with learning and not be consistent with learning

principles, when the varied outcomes principles, when the varied outcomes of a world class education are of a world class education are

targeted.targeted.

Formal and informal assessment data Formal and informal assessment data should be obtained seamlessly and should be obtained seamlessly and

utilized at strategic points in order to utilized at strategic points in order to make decisions about what needs to make decisions about what needs to

happen next for individuals and happen next for individuals and small groups.small groups.

A variety of differentiated learning A variety of differentiated learning outcomes should be pursued outcomes should be pursued

instructionally and assessed at levels instructionally and assessed at levels consistent with the desired outcomes.consistent with the desired outcomes.

Strategies that encourage students to Strategies that encourage students to monitor their own learning should monitor their own learning should

become a regular feature of become a regular feature of instruction.instruction.

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

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

Evidence should regularly tap Evidence should regularly tap students’ ability to do applications students’ ability to do applications

and communicate defensible results.and communicate defensible results.

All students should be expected to All students should be expected to learn and demonstrate major learn and demonstrate major

progress toward meeting minimum progress toward meeting minimum standards.standards.

All students in a class will not All students in a class will not construct the same level of construct the same level of

understanding for any particular understanding for any particular topic in mathematics and science.topic in mathematics and science.

Many students should be expected to Many students should be expected to regularly exceed minimum standards regularly exceed minimum standards

for any particular topic in for any particular topic in mathematics and science.mathematics and science.