Overarching question: What should schools teach? n What’s the problem? u Not a problem of mastering repetitive, routine procedures u Weakness centers on inference, problem- solving, comprehension; critical thinking skills n Breuer: Making intelligent novices u Develop expertise u Develop expertise at becoming an expert n What is expert problem-solving?

GO USA!!! Why patriotic back-patting shows low standards: n A Nation at Risk (NCEE 1983): u “Unilateral educational disarmament” u 1986 NAEP results: F Math: multi-step problems w/ variables; exponents & roots; basic functions & coordinate systems passed by 6% of 17-year-olds F Science: how data support a theory; exper. design passed by 41% of 17-year-olds F Reading: comprehend, summarize, elaborate moderately difficult text: passed by 42% of 17-year-olds

Can Problem-Solving be Taught? Problem of transfer… n Learning X vs. Learning to learn 1 Can general problem solving skills be learned? 2 Can metacognition be taught/fostered? F Metacognition in problem solving...

1. No: Problem-solving can’t be taught n Content knowledge is critical: u Johnson-Laird IF-THEN problem (Bruer pp ): F In math/logic, novices don’t transfer what they learn (e.g., conditional reasoning). u Adult experts vs. novices solving physics problems: F Categories: “Newton’s 2nd law” vs. “Springs” u Child dinosaur experts: F Infer properties of new dinosaurs, logical connectives, more comparison

Categorizing physics problems...

Child dinosaur experts... n Infer diet of new dinosaurs: u Experts used specific physical feature (i.e., teeth); novices cited visible features n Logical connectives in reasoning: “…if they saw a giant meateater, they would duck their heads…so it couldn’t take a bite out of them, or else they’d get the big prickles in them” n Comparisons: n Experts do better inductive inference!

2. Yes: Problem-solving can be taught n Bloom & Broder (1950): Good students failed exams at U. Chicago: u Focus on problem-solving strategies: F Remedial student solved problem, F then read transcripts of model answers, F then induced principles: “What should I do if…?” F training sessions u Training improved scores (vs. control students) u But did it transfer to other disciplines, etc? n Science strategies (covered in Module 3)

So how do we improve problem solving for all students? n Is lots of specific content info necessary? u Experts make different discrimination; conceptualize problems differently (not distracted by irrelevant info!) u Siegler balance scale: Make children aware of relevant features F Might be induced from lots of experience, but more efficient to point it out! [But: doesn’t always work] n What about metacognition? n Can general skills be induced from expertise in another domain?

Metacognition and high-level problem-solving n Metacognitive practices/standards: u Standards of performance (self-assessment) u Knowing when & how to learn more (Wineburg) u Can these be taught? We don’t know

…continued n Naïve reflection; errors prep for “deep” learning/transfer: u Schwartz & Moore: Compare distribution cases F [2,4,6,8,10] vs. [4,5,6,7,8] F [2,4,6,8,10] vs. [2,2,10,10] u Schwartz & Bransford: Learning about memory F Summarize  lecturevs. F Compare  comparevs. F Compare  lecture F Transfer correct predictions: ≈ 20% vs. 45%!

Creating Intelligent Novices n Critical role of metacognition u Self-tests; self-evaluation u Comprehension monitoring n Learn by discussion (include “expert”) u Finding out more using others’ expertise F Let students become “local” mini-expert n Focus on critical information to encode; Focus on why (role of theories!) u Balance scale u Teaching force vectors: ThinkerTools

Example: ThinkerTools for teaching force vectors n Force vectors errors (just counting!) continue after 1 semester of college physics

ThinkerTools continued... c

Schools for Thought summary n Weak methods in schools n Problem of transfer… n What makes experts experts? u Expose students to experts’ thinking; foci; strategies u Model expert problem solving; make p.s. explicit n Make students aware of relevant info (useof multimedia) u Good error feedback

…continued n Problems: u What’s missing? THEORIES! u “to get ahead, get a theory!” (Karmiloff-Smith): Knowing “why’ vs. knowing “that” u Metacognition n Examples exist of this approach in classrooms, but no unified large scale effort u Teacher expertise in content & metacognition u Resources to pose realistic problems u Time for content, theory, & reflection