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

6. 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

7.                                             
Generalize Across
Modalities

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

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

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

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

13. How Many?
Squares
Ovals

14. Conceptualize (Serial Learning)
Transitive inference
Simultaneous chaining

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

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

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

18. 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

19. Simultaneous Chaining
Ordered Series of Responses
A-B-C-D-E
Response Chain: Each response serves as a discriminative stimulus
Serial Representation: Mental chunking 19

20. 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?

21. Pigeons (Test Trials)

22. Chimpanzees (Test Trials)

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

24. Primates Rosencrantz and Macduff
Trained on 1-5, Generalize 1-9

25. Test with novel stimuli
About 75% correct

26. Number Operations

27. 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

28. But can’t do
2+2

29. Nonverbal Counting Models