1. Cognitive Theory: Powerful Tools for Educators? HAL Online Mar 2, 2010 HAL Online Mar 2, 2010

2. Goals for Topic 8: Understanding Children’s Thinking 1. To better understand relationships and differences among cognitive science, brain science and sociocultural theory; to be able to discuss these views in terms of tools they provide for educators. 2. To use ideas from cognitive science to analyze the problem solving of learners and to better understand and improve your own problem solving. 3. To understand and be able to discuss some important relationships between problem solving and learning. 4. To enhance your awareness of how it feels to be a naive learner; to be able to take a learner's perspective and empathize with a learner's struggle to understand. 1. To better understand relationships and differences among cognitive science, brain science and sociocultural theory; to be able to discuss these views in terms of tools they provide for educators. 2. To use ideas from cognitive science to analyze the problem solving of learners and to better understand and improve your own problem solving. 3. To understand and be able to discuss some important relationships between problem solving and learning. 4. To enhance your awareness of how it feels to be a naive learner; to be able to take a learner's perspective and empathize with a learner's struggle to understand.

3. Goals for Topic 8: Understanding Children’s Thinking 1.To better understand relationships and differences among cognitive science, brain science and sociocultural theory; to be able to discuss these views in terms of tools they provide for educators.

4. Course Perspectives  Social (Sociocultural)  Lecture, instructional method  Brain Science  Blakemore & Firth Text  Cognitive  Halpern Text  Social (Sociocultural)  Lecture, instructional method  Brain Science  Blakemore & Firth Text  Cognitive  Halpern Text

5. Socio-cultural View  Soviet psychology (Vygotsky)  Learning in communities/culture  Family, school, social, neighborhood, church, Internet, global...  Acquiring cultural “artifacts”  Language, tools, social norms  Developing community identity  Learner = apprentice

6. Mentoring in the “Zone” (of proximal development)  Model good thinking/performance  Share problem solving  Find learner zone  Scaffold thinking/performance  Fades scaffolding  Reset the “bar”  Model good thinking/performance  Share problem solving  Find learner zone  Scaffold thinking/performance  Fades scaffolding  Reset the “bar”

13. Long Term Memory Prior Knowledge: Ideas, Beliefs,Skills... Cognitive Effort Senses Eyes Ears Etc. Focuses Attention Constructs Knowledge Information... Information... Cognitive Theory Working Memory

14. Example Cognitive Theory: Piaget  Active prior knowledge (schemas): Interprets incoming experience  If experience consistent with known:  Assimilation  If experience challenges known:  cognitive dissonance  reflection  accommodation (old schemas change)  Active prior knowledge (schemas): Interprets incoming experience  If experience consistent with known:  Assimilation  If experience challenges known:  cognitive dissonance  reflection  accommodation (old schemas change)

15. Cognitive Theory: What Controls Learning?  Learning Environment  Teacher, instructional design features, etc.  Other Stuff  Intelligences, habits of mind, cultural background, situational variables, opportunities to learn  Learner  Metacognitive “self-regulation”  Strategies for self-motivation, memory, etc.  Reflection  Learning Environment  Teacher, instructional design features, etc.  Other Stuff  Intelligences, habits of mind, cultural background, situational variables, opportunities to learn  Learner  Metacognitive “self-regulation”  Strategies for self-motivation, memory, etc.  Reflection

16. Cognitive Science Metaphors  Information Processing  Mind like computer  Active knowledge construction  Effortful meaning making  Successful learning is schematic, organized  Abstract knowledge transfers to life  Justification for most school disciplines  Information Processing  Mind like computer  Active knowledge construction  Effortful meaning making  Successful learning is schematic, organized  Abstract knowledge transfers to life  Justification for most school disciplines

17. Misconceptions About Cognitive Science  Myth: Advocates direct Instruction (versus) active learning environments  Truth: ALL learning effortful, active; may (or may not) occur during lecture or hands- on activity  Myth: Advocates direct Instruction (versus) active learning environments  Truth: ALL learning effortful, active; may (or may not) occur during lecture or hands- on activity

18. Social Learning Environment: Discourse... Tasks... Activities... Illustrations...Learning Tools... Guidance... Norms Effort After Meaning Senses Eyes Ears Etc. Focuses Attention Construct Knowledge Prior Knowledge Ideas, Beliefs Skills... Sociocultural + Cognitive

19. HAL Online  How does this course try to model a blended socio-cultural, cognitive and brain-based approach?

20. The Towers Problem You have two colors of stacking cubes available with which to build towers. Your task is to make as many different looking towers as is possible, each exactly four cubes high. A tower always points up, with the little knob on top. Solve the problem inductively with your group, then: 1.Convince yourself and others that you have found all possible towers four cubes high and that you have no duplicates. 2.Represent your solution to share with the class. 3.Devise a formula that would enable you to solve the problem for towers of 2 colors and any height (advanced: with any number of colors and any height) You have two colors of stacking cubes available with which to build towers. Your task is to make as many different looking towers as is possible, each exactly four cubes high. A tower always points up, with the little knob on top. Solve the problem inductively with your group, then: 1.Convince yourself and others that you have found all possible towers four cubes high and that you have no duplicates. 2.Represent your solution to share with the class. 3.Devise a formula that would enable you to solve the problem for towers of 2 colors and any height (advanced: with any number of colors and any height)

21. After Exercise  Any member of your group should be able to:  Explain an inductive strategy for solving the 2- color/4 tall towers problem and be able to convince others the solution is correct.  Explain a general formula for the 2-color towers problem that works for towers of any height  Using your work on the towers problem, explain the relationship between deductive and inductive reasoning.  Any member of your group should be able to:  Explain an inductive strategy for solving the 2- color/4 tall towers problem and be able to convince others the solution is correct.  Explain a general formula for the 2-color towers problem that works for towers of any height  Using your work on the towers problem, explain the relationship between deductive and inductive reasoning.

22. Things to consider  Expert blind spots  Inductive versus deductive reasoning  Math anxiety  Should peer mentors provide answers?  Expert blind spots  Inductive versus deductive reasoning  Math anxiety  Should peer mentors provide answers?