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COMPLEX LEARNING TASKS (Part B)

COMPLEX LEARNING TASKS (Part B). Chapter 12. Understanding Number. Discriminate based on number and nothing else Categorize generalize across situations label Concept serial learning (1, 2, 3, 4…) transitive inference serial order and mental lines operations (2 + 1 =3). Clever Hans.

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COMPLEX LEARNING TASKS (Part B)

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  1. COMPLEX LEARNING TASKS (Part B) Chapter 12

  2. Understanding Number Discriminate based on number and nothing else Categorize generalize across situations label Concept serial learning (1, 2, 3, 4…) transitive inference serial order and mental lines operations (2 + 1 =3)

  3. Clever Hans

  4. Early Counting Experiments Clever Hans answers math questions Spontaneous Counting not impressive

  5. Early Counting Experiments Clever Hans answers math questions Spontaneous Counting - not impressive Mechner (1958) press lever “X’ times pigeons can tell the difference between 45 and 50 pecks time passed and not number? Other examples of responding based on counts which seem to generalize

  6. Generalize Across Modalities

  7. Discriminate Number (not Time) Acquisition RRRN NRRRN R = Reward N = Nonreward

  8. Categorize (Generalize) Acquisition CPPN PPN Shift PCCN CCN C = Corn Pops P = Pellets N = Nonreward

  9. Categorize (Label) Answers Correctly: “How many blocks?”

  10. Not Subitization Perceptual not cognitive Estimating small quantities at a glance without counting Hard with similar distractors

  11. How Many? Squares Ovals

  12. Conceptualize (Serial Learning) Transitive inference Simultaneous chaining

  13. Three-Item Transitive Inference Test • A > C But…………..A is 100% reinforced and C is 0% Train • A > B • B > C

  14. Five-Item Transitive Inference Test • B > D But…………the are alternatives! Train • A > B • B > C • C > D • D > E

  15. Successful “Species” • Children • Monkeys • Pigeons • Fish • “Inebriated” University Students

  16. Some Simple Explanations Fewer unreinforced responses directed at B than D because its partner A is always reinforced (Reinforcement Hypothesis) B reminds you of A and C, D reminds you of C and E. A and C have much more strength than D and E (Value Transfer Hypothesis). So, transitive inference does not imply the learning of a mental sequence

  17. Simultaneous Chaining • Ordered Series of Responses • A-B-C-D-E • Response Chain: Each response serves as a discriminative stimulus • Serial Representation: Mental chunking

  18. Serial Order Learning Simultaneous Chaining Task All stimuli appear simultaneously in random locations Press numbers or objects in a specified order Stimuli disappear when pressed and trial finishes with reinforcement Trial immediately ends if a mistake is made Tests Trials With Missing Items Mental Line? S-R sequence?

  19. Pigeons (Test Trials)

  20. Chimpanzees (Test Trials)

  21. (Brannon & Terrace, 1998) Basic paradigm: Touching stimuli in numerical order produces a reward.

  22. Primates Rosencrantz and Macduff

  23. Test with novel stimuli About 75% correct

  24. Number Operations

  25. Sheba Taught to look in three different locations and choose a number for the total, 0+2+1=3 Maybe just counting not adding? Numbers always added to less or equal to 4

  26. But can’t do 2+2

  27. Nonverbal Counting Models

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