Presentation on theme: "Understanding Number Discriminate –based on number and nothing else Categorize –generalize across situations –label Conceptualize –serial learning (1,"— Presentation transcript:
Understanding Number Discriminate –based on number and nothing else Categorize –generalize across situations –label Conceptualize –serial learning (1, 2, 3, 4…) transitive inference Scanning in pigeons vs. chimps –operations (2 + 1 =3)
Early Counting Experiments Clever Hans –answers math questions
Early Counting Experiments Clever Hans –answers math questions Spontaneous Counting –not impressive
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
Generalize Across Modalities
Discriminate Number (not Time) Acquisition –RRRN –NRRRN R = Reward N = Nonreward
Categorize (Generalize) Acquisition –CPPN –PPN Shift –PCCN –CCN P = Pellets N = Nonreward C = Corn Pops
Categorize (Label) Answers Correctly: “How many blocks?”
Not Subitization Perceptual not cognitive Estimating small quantities at a glance without counting Hard with similar distractors
Three-Item Transitive Inference Train A > B B > C Test A > C But…………..A is 100% reinforced and C is 0%
Five-Item Transitive Inference Train A > B B > C C > D D > E Test B > D But…………the are alternatives!
Successful “Species” Children Monkeys Pigeons Fish “Inebriated” University Students
Why? Fewer unreinforced responses directed at B because its partner A is always reinforced (Disappointment 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
Simultaneous Chaining Ordered Series of Responses A-B-C-D-E Response Chain: Each response serves as a discriminative stimulus Serial Representation: Mental chunking
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?
Pigeons (Test Trials)
Chimpanzees (Test Trials)
(Brannon & Terrace, 1998) Basic paradigm: Touching stimuli in numerical order produces a reward.
Primates Rosencrantz and Macduff
Test with novel stimuli About 75% correct
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