Daniel Schwartz School of Education Stanford University

1. Socializing Transfer Daniel Schwartz School of Education Stanford University

2. What I talked about last time:Transfer literature • Detterman from Transfer on Trial. • “…most studies fail to find transfer …and those studies claiming transfer can only be said to have found transfer by the most generous of criteria and would not meet the classical definition of transfer.” • Classic “stimulus generalization” view -- replication of old behavior in a new situation. • Plays into educational and psychological literature emphases on efficiency. • Faster and more accurate retrieval and application of previously learned behaviors.

3. Innovation Normalizing data Measuring variability Graphing data Optimal Corridor of Instruction Annoying Novice Adaptive Expert PFL Routine Expert SPS Novice Efficiency

4. Worked Example Embedded in Test 67% 33% Correct Solutions Preparation for Future Learning Measures(SPS v. PFL) Innovation Activities Efficiency Activities Target Transfer Problem

5. The Effect on the PERC Audience?

6. Decided to give a different kind of talk. • Poster session with Jose Mestre summarizes recent transfer findings. • Continue theme of “learning” v. “problem solving” with two micro-findings that have just been waiting for a captive audience. • In this case, not learning at test versus problem solving at test. • Discuss cognitive science more broadly.

7. Learning is not the Same Thing as Problem Solving. Daniel L. Schwartz Stanford University

8. Some General Cognitive Science Contributions • Multi-disciplinary • Verbal protocols and discourse analyses • Careful descriptions of problem solving • Formal, executable models of cognitive process.

9. Some General Risks ofCognitive Science for Education • Separation of higher order cognition from important factors in learning. • Motivation rarely appears in cognitive science journals. • Use of problem solving models to explain learning. • Search, schemas, mental models, goal decomposition, analogical reasoning, working memory, cognitive load come from problem solving research not learning research. • The fact that I achieve a correct answer in problem solving (when I could not before), does not entail I have learned. • Confusions between symbolic models of thought and thought itself. • Transfer often described as an “equivalence detection” (X = Y), instead of resonance (for example). • All told, the picture that often gets transmitted to education emphasizes verbal (symbolic) problem solving, which may not do justice to learning.

10. Not true of all cognitive science. • Separation of verbal problem solving from other mental systems, perception and affect, does not work so well for learning. • The (problem-solving) talk may only reveal one part of what enables the (learning) walk. • There are other styles of cognitive science. • Describe two (utterly unrelated and self-indulgent) instances of basic, cognitive science research that may nevertheless address important educational issues. • Non-verbal outcomes of symbolic, rule learning. • Non-verbal processes regulate verbal learning.

11. Non-Verbal Outcomes of Verbal Rules (w/ Sashank Varma) • How do people build new knowledge on a foundation of old knowledge. • Prevalent assumption: people develop well-formed abstractions from perceptual representations. • Embodied cognition • P-prims • Sensory motor  Concrete Operations  Formal Thought • Enactive  Iconic  Abstract • Propose that people can start with symbolically expressible rules that evolve into perception-like representations.

12. The case of mathematics • Some relevance to physics, because mathematics play an important role in structuring physics understanding. • Take a simpler case than physics. • Building the integers on top of natural numbers.

13. What do we know about representations of natural numbers? • People’s representations of natural numbers has a perception-like substrate. • Evidence? • The symbolic distance effect (SDE) • Neuroscience correlations.

14. Symbolic Distance Effect • Perceptual discrimination has a well-known curve. • “Near” perceptual referents take longer to discriminate than “far” perceptual referents. • Hearing: • Loud sound v. soft sound. (Fast) • Softer sound v. soft sound. (Slow) • Loud sound v. louder sound. (Slower) • Effect is general – it applies to nearly all perceptual magnitude judgments: • Saltiness, brightness, firmness, heat, weight…

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21. Natural numbers exhibit the same curve. • Moyer and Landauer (1967) • 2 v. 9 (Fast) • 2 v. 3 (Slow) • 8 v. 9 (Slower) • This finding was a big deal. • A purely symbolic task was processed perceptually. • Cognitive-neuroscience has investigated this effect.

22. IPS activation correlated with SDE. IPS active for perceptual comparisons. IPS implicated in spatial reasoning (e.g., rotation) IPS activates strongly for subtraction (not multiplication). Neuroscience findings…

23. 1 2 3 4 5 6 7 8 9 • Led to proposal that the representation of natural number uses a perception-like number line. • So, what does the adult representation of integers look like?

24. Adults (n=21) Far Near Positive 1 v. 8 1 v. 3, 6 v. 8 Negative -1 v. -8 -1 v. -3, - 6 v -8 Mixed -2 v. 6 -2 v. 1 • Other factors for balancing the stimuli • Larger number on right/left. • Choose larger/smaller of numbers

25. Give it an introspective try. • A short series of problems. • See if you can detect the effect. • Remember SDE predicts: • Near is slow. • Far is fast.

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38. How’d you do? • Can you predict study outcomes? • Hard to introspect because the difference between near and far is around 0.05 sec. • Sometimes verbal reports of one’s own problem solving do not work so well.

39. Distance Effect

40. Inverse Distance Effect

41. Summary of Results • Within-in class comparisons show SDE • Negatives increase by a constant (“flip rule”) • Between-class comparisons show inverse SDE. • What might explain this effect?

42. “Perceptualizing” Integers • Integer comparison may have recruited another general perceptual mechanism. • Categorical Comparison • People are very fast at comparisons that fall on either side of a perceptual boundary. • English speakers distinguish ‘pa’ and ‘ba’ faster than non-native speakers. • Color comparisons across boundaries are faster than within boundary. • Negative and positives have developed a boundary, and people are very fast at comparisons close to, and on either side of, the boundary.

43. Non-Negative 0 |1| |2| |3| |4| |5| |6| |7| |8| |9| near far -9- -8 7 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 Negative Reflection not extension of the number line. far: 6 v. -2 near: 1 v. -2 1 -2

44. Natural numbers. 7th-graders look like adults. Looked at rising 7th-graders. Integers introduced by 4th-grade. 2+ years practice. Equal accuracy as adults. 1 v. 3 1 v. 9 K 1st 4th 7th A Kids? Sekuler & Mierkiewicz (1977)

45. Distance Effect Adults 6th Graders

46. Distance Effect Adults 6th Graders

47. Summary of Adults vs. 7th Graders • 7th-graders same as adults for within-class comparisons. • 7th-graders show no inverse distance effect • They used rules to reason about negative and positives. • “If it has a negative sign, it is less.” • Ignore magnitudes.

48. Discussion • Guiding hypothesis • People use rules that become “perceptualized.” • Needs more (cleverer) research. • Still, a useful lesson. • Negative numbers were taught with “intuitive” representations that made sense. • At the same time, kids learned “meaningful” rules for managing integers. • Over time (into adulthood) these rules changed underlying form.

49. Relevant to physics. • Intuitions and perceptual experiences are important for instruction. • Also need mathematical rules, so it is possible to reason in more complex ways. • It may take many years before these rules transform into immediately meaningful “perceptual phenomena.” • One hypothesis is that the rules are necessary way station. • Physics for non-majors seems fine, but they will never develop the base representations that make them see the world as physicists. • When they see that ball rising in the air, they need to use rules to separate forces and velocity. You probably do not. You “perceive” the separation.

50. So, what do you think of cognitive science of learning?