1. Behaviorism and the Teaching of Mathematics
a brief overview…
Math 149
Spring ‘14
Burger

2. What is behaviorism all about?
Behavioral psychology is the study of external behavior
Behavior is objective and observable, where as what goes on in one’s mind can never really be known or measured (the mind is a “black box”)to a behaviorist!
Behavior is the response of an organism to stimuli.

3. History of Behaviorism
Pavlov (1927), a Russian physiologist discovered classical conditioning in dogs.

4. Classical Conditioning
Explains some learning of involuntary emotional and physiological responses.
Dog drooling when it smells food and later when it hears a bell.
It’s important for us as teachers to understand since school is often the cause of unintentional learning through classical conditioning, especially anxiety.
Test anxiety conditions us to have general school anxiety.

5. Ivan Pavlov
(1849–1936)
DiscPsy p. 166

8. Classical Conditioning
basic learning process discovered by Pavlov that involves repeatedly pairing a neutral stimulus with a response-producing stimulus until the neutral stimulus triggers the same response

9. Ivan Pavlov's Classical Conditioning
Before Conditioning
Unconditioned Stimulus
Unconditioned Response
No Response
Neutral Stimulus

10. Ivan Pavlov's Classical Conditioning
During Conditioning
Unconditioned
Response
Neutral
Stimulus
Unconditioned
Stimulus

11. Ivan Pavlov's Classical Conditioning
After Conditioning
Conditioned
Response
Conditioned
Stimulus

13. More Examples of Classical Conditioning
Kids who often get strep throat, after much swabbing of their throat, begin to gag as soon as they see the doctor with the swab.
Hearing a teacher, roommate, boyfriend/girlfriend say to you, “We need to talk”. Upon hearing this phrase your stomach “flutters”.
The point is, we learn to associate a stimulus with a response, and eventually our body does this automatically in the presence of the stimulus.
In CC, the response is involuntary.

14. Shoulder Partner Discussion topic: Examples of Classical Conditioning in the Mathematics Classroom:

15. Classical Conditioning …..
Classical conditioning can face “extinction”, where the learning is undone.
This can happen naturally (the dog stops getting meat when music is played)
Or can happen through some type of therapy in the case of severe anxiety reactions
Ex: people who are afraid to fly….
Remember: Classical conditioning is more than forming an association – it is an involuntary, physiological response

16. Classical Conditioning in the Classroom
Playing soothing music, dimming the lights to calm and relax students
Unintentional classical conditioning:
Test anxiety
Math anxiety
Public speaking anxiety
General school anxiety

17. B.F. Skinner (1904 –1990)
American psychologist - influential from the 1930’s - 60’s – developed ‘Operant Conditioning’
Skinner was interested in education
He believed that behavior is sustained by reinforcements or rewards, not by free will.
• Famous for the Skinner box & the teaching machine
• Often worked with pigeons
& rats and applied what he learned
with these animals to human learning.

18. Operant Conditioning (Skinner)
This involves conditioning voluntary, controllable behaviors, not the automatic physiological responses in Classical Conditioning
With Operant Conditioning the Response comes before the Stimulus (the opposite of CC)
R S

19. Operant Conditioning
Teachers can deliberately use operant conditioning with their students (training)
How someone reacts to our behaviors determines whether or not we continue the behavior
if we are rewarded for something we will likely do it again - do you do this as a teacher?

20. Skinner’s Operant Conditioning
Positive Reinforcement
Presence of Pleasant Stimulus
Behavior
Increases
Negative Reinforcement
Absence of Unpleasant Stimulus
Presence of Unpleasant Stimulus
Behavior
Decreases
Punishment

21. Consequences for Behaviors
Positive Reinforcement – You behave in a certain way that results in a reward, and as a result, you are more likely to repeat that behavior
Negative Reinforcement – You behave in a certain way that results in the removal of something unpleasant, and as a result you are more likely to repeat that behavior (ex: doing a paper early)
In both cases, something happened that you saw as “good” and as a result, you exhibited the behavior more.

22. Consequences for Behaviors
Punishment – A consequence that follows a behavior so that you do the behavior less often in the future.
Punishment can involve adding something (paying a fine, staying after school) or involve removing something you like (losing recess time, leaving your friends)
In both cases, adding something or removing something, you perceive it as “bad” and as a result, you exhibit the behavior less.

23. Differences Between Negative Reinforcement & Punishment
Negative reinforcement: Something unpleasant is removed & as a result you are more likely to do it again
Something happened that was “good”
Punishment: A consequence happens that you don’t like and you are less likely to do it again. The punishment can add something or take something away.
Something happened that was “bad”

24. Shaping New Behaviors
Shaping is a process of reinforcing a series of responses that increasingly resemble the desired final behavior
When a desired behavior occurs rarely or not at all, we use shaping
First reinforce any response that in some way resembles the desired behavior, then one that is closer etc.
Think of animal training or the hyper kid who can’t sit in his chair in class – do things in small steps

25. Operant Conditioning
learning process in which behavior is shaped and maintained by manipulating its consequences
Operant conditioning involves voluntary behaviors.
Operants are actions upon the environment, which may lead to reinforcement or punishment

26. B. F. Skinner Founder of Operant Conditioning Invented “Skinner Box”
Won “Sexiest Man Alive” award in 1939!

29. Reinforcement
anything that strengthens a response or increases ( ) the chance that it will occur
almost anything can act as a reinforcer – food, sex, vacation, etc.
Remember: Reinforcement INCREASES ( ) behavior.

31. Positive Reinforcement
Positive consequence that increases the chance of desired behavior because something is added (+) or presented.
Can be thought of as a reward
Represented by: positive (+), reinforcement ( )

32. Negative Reinforcement

33. Negative Reinforcement
Works to increase behavior but does this by removing an unwanted stimulus
Think of negative sign (-), REMOVING unwanted stimulus
EX: Beeping noise from car – buckle seatbelt – noise goes away – noise is the negative reinforcement to put on seatbelt.

35. Shaping - gradually molding a desired behavior by reinforcing responses that are similar or close to the final desired behavior

37. Punishment
anything that weakens a response or decreases the chance that it will occur.

38. Positive Punishment (+ )
decreases behavior by adding an unpleasant stimulus
Remember, think positive as in plus sign (+), adding something
EX: spanking, a prison sentence, or criticizing someone

39. Operant conditioning. Having received a face full of quills, a young coyote has probably learned to avoid porcupines!

40. Negative Punishment
decreases behavior by removing a pleasant stimulus ( - )
EX: taking away car keys to punish a teenager (works to decrease future behavior)

41. Negative Reinforcement v. Punishment
Many people confuse negative reinforcement and punishment.
Negative Reinforcement always increases behavior
Punishment always decreases behavior.

42. Negative Reinforcement v. Punishment Example

43. Practice Problems CC or OC? CC!
When you were still together, you and your ex used to love the same hit song. Now when you hear that song, you feel sad.
CC or OC?
CC!

44. Practice Problems
Jose did not like to do his homework. One day his mom told Jose that he could play video games for an hour after his homework was done. Jose completed his homework more often as a result.
CC or OC?
OC!

45. Practice Problems
A fourth grade teacher who was very strict and scary used to wear a strong, rose-scented perfume. The smell of roses now makes you very nervous.
CC or OC?
CC!

46. Practice Problems
Jane came home late and her parents took away her car privileges for a week. In the future, Jane made sure to come home on time.
CC or OC?
OC!

47. Practice Problems
One night you bought a meal deal at McDonald’s, you arrived home to find a burger, fries, colas, and three roaches in the bag. Now, even the sight of the McDonald’s logo makes you sick to your stomach.
CC or OC?
CC!

48. Practice Problems
Clare studies hard and gets an A on her Biology test. The teacher praises her in front of the class. As a result, Clare stops studying earns a failing grade on the next two exams.
CC or OC?
OC!

49. Practice Problems
Mike was more likely to return his rental DVD’s on time after the video store raised their late charges.
CC or OC?
OC!

50. Critiques of Behaviorism
External rewards may diminish intrinsic motivation
Studies where participants work on an interesting task (ex: puzzles) - experimental group is given a reward when finished while the control group is not.
After initial period, during a non-rewarded time participants are given a choice between continuing to work on the task or switching to another activity. Typical result is that participants in the experimental group spend less time on the activity than the control group. This is taken as indicating that reward reduces intrinsic motivation. Pizza Hut used to give away free pizza to kids who read a certain number of pages. This practice was discontinued as it actually eroded students intrinsic motivation to read!

51. More Critiques …
Behaviorism doesn’t account for anything that isn’t an observable behavior
There has to be more going on than what is observable - doesn’t there?
Behaviorism only accounts for learning through direct experience with the environment (not observational learning)

52. Classical Conditioning Positive Reinforcement Negative Reinforcement
#54 Spring Break writing assignment for your Math 149 portfolio: (2-3 pages, typed, 1.5 spaced)
Based on your experience and observations, write and reflect on at least one classroom example related to the teaching of mathematics for each below:
Classical Conditioning
Positive Reinforcement
Negative Reinforcement
Positive Punishment
Negative Punishment
Shaping