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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

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behaviorism and the teaching of mathematics

Behaviorism and the Teaching of Mathematics

a brief overview…

Math 149

Spring ‘14



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 physiologistdiscovered classical conditioning in dogs.
classical conditioning
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



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

Unconditioned Response

No Response

Neutral Stimulus


Ivan Pavlov's Classical Conditioning

During Conditioning








Ivan Pavlov's Classical Conditioning

After Conditioning





more examples of classical conditioning
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, theresponse is involuntary.

shoulder partner discussion topic examples of classical conditioning in the mathematics classroom
Shoulder Partner Discussion topic: Examples of Classical Conditioning in the Mathematics Classroom:
classical conditioning1
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
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
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)


operant conditioning
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

Presence of Unpleasant Stimulus




consequences for behaviors
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 behaviors1
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
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 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 conditioning1
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

B. F. Skinner

  • Founder of Operant Conditioning
  • Invented “Skinner Box”
  • Won “Sexiest Man Alive” award in 1939!
  • 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 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 ( )
negative reinforcement1
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
  • anything that weakens a response or decreases the chance that it will occur.
positive punishment
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
Operant conditioning. Having received a face full of quills, a young coyote has probably learned to avoid porcupines!
negative punishment
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
Negative Reinforcement v. Punishment
  • Many people confuse negative reinforcement and punishment.
  • Negative Reinforcement always increases behavior
  • Punishment always decreases behavior.
practice problems
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 problems1
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 problems2
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 problems3
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 problems4
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 problems5
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 problems6
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
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
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
#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
    • PositiveReinforcement
    • NegativeReinforcement
    • PositivePunishment
    • NegativePunishment
    • Shaping