Behaviorism and the
Teaching of
Mathematics
a brief overview…
Math 149
Spring ‘14
Burger
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.
History of Behaviorism
• Pavlov (1927),
a Russian
physiologist
discovered
classical
conditioning in
dogs.
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.
Ivan Pavlov
(1849–1936)
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
Ivan Pavlov's Classical Conditioning
Before Conditioning
Unconditioned
Stimulus
Neutral Stimulus
Unconditioned Response
No Response
Ivan Pavlov's Classical Conditioning
During Conditioning
Unconditioned
Neutral
Unconditioned
Stimulus
Stimulus
Response
Ivan Pavlov's Classical Conditioning
After Conditioning
Conditioned
Conditioned
Stimulus
Response
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.
Shoulder Partner Discussion
topic: Examples of Classical
Conditioning in the Mathematics
Classroom:
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
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
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.
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
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?
Skinner’s Operant Conditioning
Positive
Reinforcement
Presence of Pleasant
Stimulus
Negative
Reinforcement
Absence of Unpleasant
Stimulus
Punishment
Presence of
Unpleasant Stimulus
Behavior
Increases
Behavior
Decreases
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.
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.
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”
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
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
• Founder of
Operant
Conditioning
• Invented “Skinner
Box”
• Won “Sexiest
Man Alive” award
in 1939!
B. F. Skinner
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.
)
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: +
reinforcement ( )
positive (+),
Negative Reinforcement
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.
Shaping - gradually molding a desired
behavior by reinforcing responses that
are similar or close to the final desired
behavior
Punishment
• anything that weakens a
response or decreases the
chance that it will occur.
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
Operant conditioning. Having received a face full of
quills, a young coyote has probably learned to avoid
porcupines!
Negative Punishment
• decreases behavior
by removing a
pleasant stimulus ( - )
• EX: taking away car keys
to punish a teenager
(works to decrease future
behavior)
Negative Reinforcement v.
Punishment
• Many people confuse negative
reinforcement and punishment.
• Negative Reinforcement always
increases behavior
• Punishment always decreases
behavior.
Negative Reinforcement v.
Punishment Example
Practice Problems
• 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!
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!
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!
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!
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!
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!
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!
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!
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)
#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