Research in the Teaching and Learning of Physics

Part I: Survey of Cognitive Science

Motivation

• Scientific approaches to science education– Research-based vs. seat-of-the-pants

• Is teaching an art?

Cognitive “Science”

• Caveat: Why the “science?”– Context of results

• What is it?• Why study it?

– Intellectual curiosity (how does the brain work? What is “genius?”)

– Practical applications (HCI, AI, education)– Implications for other fields (sociology, economics,

political science…)

History• Plato, Aristotle (~400 B. C.)

– Empiricism vs. Nativism

• Scientific beginnings of psychology (1879)– Research by introspection– Free association experiments

• Behaviorism (1920)– Consciousness is neither definable nor useful

• Information-processing model (1960)– Research on human factors– Rise of computer science, artificial intelligence– Inadequacy of behaviorism in linguistics

Information processing

• Sternberg (1969)– Subject given a

string of one to six digits (e.g., 397)

– Measure time to determine if a single digit is in the string

Perceivestimulus 9 = 3? 9 = 9? 9 = 7? Make

decisionGenerateresponse

9 Yes

Features of IP model

• Discussion of what is going on in the brain, with no reference to physiological processes

• No reference of how symbols are encoded in brain

• Use of a computational metaphor

• Time measurement important

Domain of analysis

• Cognitive science <==> physiology

• Computer science <==> electrical engineering

• Emerging field: Cognitive neuroscience

Recent controversies

• Ecological approach (situated cognition)– Structure of the mind, environment, or both

• Connectionism– How can high-level functions be achieved by

connections of neural-like elements

Some areas of research

• Perception and attention– How do we recognize what we see and hear?

• Memory– How do we remember and forget things?– How does memory work?

• Problem solving– How do we solve problems we’ve never seen before?

• Development of expertise– How do we become skilled at cognitive tasks?

• Others: language, knowledge representation, child development, etc.

What is memory?

• How is it organized?• How do we get stuff in and out?• How is stuff stored?

Sensory store

Attention

Short-term memory

Rehearsal

Long-termmemory

Organization of memory

• Rehearsal was necessary for getting ideas into long-term memory

• More rehearsal resulted in better memory

• Many experiments showed decrease in accuracy of recall with time

Memory

• Craik and Lockhart (1972)– Subjects given a 4-digit number– They then rehearsed a word for 2, 6, or 18 seconds– They were then asked what word they rehearsed– Subjects recalled 11%, 7%, and 13% of the words

• Rehearsal time is not the key, crucial part is processing of material

Working memory

• Contents can originate from sensory memory

• Contains information that one is conscious of at the moment

• Contents can be acted on and processed, or maintained by rehearsal

• 7 ± 2 elements

5 0 7 2 3 6 1 2 4 8 2 9

1 7 7 6 1 8 6 5 1 9 4 1

dogrockchairbayropestinkdark

universityaluminum

biographicalconstitutional

auditoriumorganizationuntargetable

Rehearsal and working memory• Has an articulatory loop• Holds 1.5–2 sec of infoOther evidence (Conrad 1964):• When subjects asked to recall

a string of letters (HBKLMW)– Mistakes consisted of

replacing a letter by one that sounds alike (T with G), as opposed to looks alike (Q with G)

– Harder to memorize letters that rhyme (BCTHVZ) than ones that don’t (HBKLMW).

30

40

50

60

70

80

90

1.2

1.4

1.6

1.8

2

2.2

1 2 3 4 5

Number of syllables

% correct

# words readable

(Baddeley 1986)

37x 28296

+ 7401036

374x 288

Working Memory

• Consists of a visuospatial sketchpad and a phonological loop, both controlled by a central executive.

• Physiological evidence--frontal cortex

Central executive

Phonologicalloop

Visuospatialsketchpad

Area 46• Test:

– Monkey shown food item that is hidden in 1 of 2 covered wells

– Monkey is prevented from looking at wells for 10 seconds

– Monkey allowed to retrieve food

• Human infants unable to perform similar task until 1 year (maturation of frontal cortex)– Increased blood flow to area 46 when retaining working-

memory information

• Monkeys with damage to frontal cortex unable to perform task– Neurons in area 46 fire only during delay period

Memory and meaning

• We normally remember the meaning of a linguistic message, rather than its exact wording.

• We tend to remember a meaningful interpretation of a picture.

• Less meaningful material can be remembered better by converting it to meaningful material.

What do we remember?

• When you score your results, do nothing to correct your answers but mark carefully those answers which are wrong.

• When you score your results, do nothing to correct your answers but carefully mark those answers which are wrong.

• When you score your results, do nothing to your correct answers but mark carefully those answers which are wrong.

• When you score your results, do nothing to your correct answers but mark carefully those answers which are wrong.

To begin the test, please turn to page 2 of the answer booklet and judge which of the sentences printed there occurred in the instructions you just heard.

(Wanner 1968)

(Wanner 1968)

Target picture(77% recog.)

Token change(60% reject)

Type change(94% reject)

(Mandler and Ritchey 1977)

Subjects studied 8 pictures for 10 sec each

• 70% correctly reconstructed when given labels with which to study the picture

• 51% correctly reconstructed without labels

(Bower, Karlin, Dueck 1975)

Implications of memory for meaning

• Mnemonic techniques can be useful for learning things that don’t initially have much meaning– associating nonsense syllables– learning a foreign language (carciofi, Atkinson

and Raugh, 1975)– telephone numbers, names for faces, etc.

• Good memory for material results when it is processed more elaborately

Processing for memory

• Bobrow and Bower (1969)– People memorized simple subject-verb-object

sentences– Condition 1: Sentences provided by

experimenter– Condition 2: Sentences generated by people– Task: Given subject, supply object – Success rate was 29% and 58%

Processing and meaning

• Subjects’ show better memory for sentences printed upside down (Kolers 1979).

• Slamecka and Graf (1978):Generating vs. reading synonyms or rhymes for words

• Processing need not be focused on meaning of material.

Processing and intention

• Subjects shown 24 words spaced 3 seconds apart

• Half of the subjects told to check whether word contained an “e” or “g,” other half told to rate word for pleasantness.

• Half of the subjects told that the purpose of the test was to check for letters or to rate the words, other half told that purpose was to memorize the words

rate check e/gincidental 68%intentional

39%69% 43%

(Hyde and Jenkins 1973)

• Whether or not you intend to learn doesn’t matter! It’s the level of processing in which you engage.

Implications of processing for memory

• Study strategies (SQ3R, PQ4R)– Preview: Survey chapter, identify sections

– Questions: Make up questions about each section

– Read: Read section with questions in mind

– Reflect: Reflect on text, construct examples, relate to prior knowledge

– Recite: Recall info, answer questions for section

– Review: Review main points, answer questions for chapter

• Strategies designed to encourage deep processing

Some studies

• Frase (1975)– Control: Nothing special (50%)– Group 1: Make up study questions while

reading (70% / 52%)– Group 2: Answer study questions while reading

(67% / 49%)

• Rothkopf (1966)– Control: Nothing special (30%)– Group 1: Interspersed preview Q’s (72% / 29%)– Group 2: Interspersed review Q’s (72% / 42%)

Application

• Reciprocal teaching– Student/teacher play both roles inventing

questions

Practice effects

• Time to recognize sentences vs. number of days of practice (Pirolli and Anderson, 1985)

• Power law of learning y = A xB

Physiological basis

• When a neural pathway is stimulated with high frequency current, cells on that pathway become more sensitive to further stimulation.

• Measured percent increase in excitory postsynaptic potential (decrease in difference of electric potential between inside and outside of neuron) due to stimulating the hippocampus of rats

Barnes (1979)

Non-practice effects

• Success at word recognition (from a learned list) as a function of delay T

• Power law

y = Ax–B

Physiologically…

Barnes 1979

But forgetting is not just a matter of time…

Interference effects

Pre-existing knowledge• Subjects learned 0-4 fantasy

facts about well-known people (e.g., Napoleon Bonaparte was from India)

• Subjects then judged three types of sentences, (a) fantasy facts, (b) actual facts, (c) false statements

• The more fantasy facts learned, the longer the delay in recalling actual facts (fan effect).

Lewis and Anderson (1976)

Redundancy

• Subjects learned:– a single fact (92% immediate recall, 62% recall after one week)

• Newton became emotionally unstable and insecure as a child

– a single fact + 2 irrelevant facts (80%, 45%) • Locke was unhappy as a student at Westminister• Locke felt fruits were unwholesome for children• Locke had a long history of back trouble

– a single fact + 2 related facts (94%, 73%)• Mozart made a long journey from Munich to Paris• Mozart wanted to leave Munich to avoid a romantic entanglement• Mozart was intrigued by musical developments in Paris.

• Additional knowledge can sometimes be helpful (but not always…)

Bradshaw and Anderson 1982

Retrieval and inferences

• “She was deaf, dumb, and blind.”– Carol Harris: 5%– Helen Keller: 50%

• Evidence for inference being made at test

Carol Harris’ Need for Professional Help

Carol Harris was a problem child from birth. She was wild, stubborn, and violent. By the time Carol turned eight, she was still unmanageable. Her parents were very concerned about her mental health. There was no good institution for her problem in her state. Her parents finally decided to take some action. They hired a private teacher for Carol.

The heir to a large hamburger chain was in trouble. He had married a lovely young woman who had seemed to love him. Now he worried that she had been after his money after all. He sensed that she was not attracted to him. Perhaps he consumed too much beer and french fries. No, he couldn’t give up the fries. Not only were they delicious, he got them for free.

Retrieval and plausibility

Retrieval and plausibility• The heir married a lovely

young woman who seemed to love him.

• The heir got his french fries from his family’s hamburger chain.

• The heir was careful to eat only healthy food.

Reder 1982

• Judged for recognition or plausibility.• Recognition time increases with # facts. Plausibility time decreases

Elaboration and inferences

Nancy went to see the doctor. She arrived at the office and checked in with the receptionist. She went to see the nurse, who went through the usual procedures. Then Nancy stepped on the scale and the nurse recorded her weight. The doctor entered the room and examined the results. He smiled at Nancy and said, “Well, it seems my expectations have been confirmed.” When the examination was finished, Nancy left the office.

Nancy woke up feeling sick again and she wondered if she really were pregnant. How would she tell the professor she had been seeing? And the money was another problem.

Elaboration and inferences

• Studied propositions recalled:– 29.2 for theme condition– 20.3 for neutral condition

• Inferred propositions:– 15.2 for theme condition– 3.7 for neutral condition

• Many in the theme condition reported that the doctor told Nancy she was pregnant.

Implications for advertising

“Wouldn’t it be great,” asks the mother, “if you could make him coldproof? Well, you can’t. Nothing can do that.” [Boy sneezes.] “But there is something that you can do that may help. Have him gargle with Listerine Anti-septic. Listerine can’t promise to keep him coldfree, but it may help him fight off colds. During the cold-catching season, have him gargle twice a day with full-strength Listerine. Watch his diet, see he gets plenty of sleep, and there’s a good chance he’ll have fewer colds, milder colds this year.”

Replaced “Listerine” with “Gargoil.” After hearing this commercial, all 15 subjects checked “gargling with Gargoil Anti-septic helps prevent colds” as a true statement.

Schemas

• A representational structure in memory that includes characteristics of an object.

• House– Isa: building

– Parts: rooms

– Materials: wood, brick, stone

– Function: human dwelling

– Shape: rectangular, triangular

– Size: 100-10,000 square feet

Schemas and inference• Thirty subjects brought to room shown and told it was

experimenter’s office. Asked to wait there while experimenter checked on previous subject. Left for 35 seconds.

• Subject taken to nearby room, asked to write down everything they could recall about experimenter’s office.

• Descriptions influenced by “office schema”– nearly all recalled desk, chair, walls– only 8 recalled skull, bulletin board– 9 recalled books (there weren’t any)

Minerals

Metals

Rare Common Alloys

Stones

Precious Masonry

PlatinumSilverGold

AluminumCopperLeadIron

BronzeSteelBrass

SapphireEmeraldDiamondRuby

LimestoneGraniteMarbleSlate

Misc.: Organization and recall

Organization and recall

• Subjects studied 4 trees for one minute each– Words either organized or random– 4 trials

• Results:– Organized: 73.0, 106.1, 112 (max), 112– Random: 20.6, 38.9, 52.8, 70.1

Bower, Clark, Lesgold, and Winzenz 1969

Contextual effects• Divers learned a list of 40 unrelated words either

while sitting on shore or 20 feet under the water.• Divers asked to recall words in same environment

or different environment.

Godden and Baddeley 1975

State-dependent learning

• Subjects learned a free recall list after smoking either a marijuana cigarette or an ordinary cigarette.

• Subjects tested 4 hours later after smoking one or the other

Study Tobacco Marijuana Average

Tobacco 25% 20% 23%

Marijuana 12% 23% 18%

Test

Summary

• The crucial factor determining how well new material is learned is how deeply it is processed by functions such as elaboration, question posing, comparison with prior knowledge, organizing hierarchically, etc.

• Prior knowledge has a great effect on what we think we learn and also on what we infer about the information we are presented with.

• Don’t smoke marijuana while studying.

Problem Solving

• What is problem solving?– When there is a goal you want to accomplish,

you don’t immediately know how to achieve the goal, and you devise and carry out a set of steps to meet the goal.

• IP model: Problem solving consists of moving through a problem space using operators

Modeling Problem Solving

• IP approach uses production systems• Production rules for multi-column subtraction problems

– If the goal is to solve a subtraction problem,Then make the subgoal to process the rightmost column

– If there is an answer in the current column,Then make the subgoal to process the column to the left

– If the goal is to process a column and there is no bottom digit,Then write the top digit as the answer

– If the goals is to process a column and the top digit is not smaller than the bottom digit,Then write the difference between the digits as the answer.

Early Research

• Cryptarithmetic puzzles

(Newell and Simon, 1972)

• Analyze protocols in terms of production rules

• Production rules explain 80 - 90% of protocols

CROSS+ROADSDANGER

Problem-solving strategies

• Difference reduction

• Means-end analysis

• By analogy

• Working backwards

Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. It is impossible to operate on the patient, but unless the tumor is destroyed, the patient will die. There is a kind of ray that can be used to destroy the tumor. If the rays reach the tumor, all at once at a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity, the healthy tissue that the rays pas through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor either. What type of procedure might be used to destroy the tumor with the rays, and at the same time avoid destroying the healthy tissue?

A small country was ruled from a strong fortress by a dictator. The fortress was situated in the middle of the country, surrounded by farms and villages. Many roads led to the fortress through the countryside. A rebel general vowed to capture the fortress. The general knew that an attack by his entire army would capture the fortress. He gathered his army at the head of one of the roads, ready to launch a full-scale attack. However, the general then learned that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely, since the dictator needed to move his troops and workers to and from the fortress. However, any large force would detonate the mines. Not only would this blow up the road, but it would also destroy many neighboring villages. It therefore seemed impossible to capture the fortress. However, the general devised a simple plan. He divided his army into small groups and dispatched each group to the head of a different road. When all was ready he gave the signal and each group marched down a different road. Each group continued down its road to the fortress so that the entire army arrived together at the fortress at the same time. In this way, the general captured the fortress and overthrew the dictator.

Analogies

• Similar to learning from examples

• However, subjects often try to use analogies based on surface similarities

• Implications for solving physics problems

Representation

• Mutilated checkerboard problem

Representation

• Imagine 27 apples packed in a crate 3 x 3 x 3 apples. A worm is in the center apple and its ambition in life is to eat its way through all the apples in the crate, but it does not want to waste time by visiting any apple twice. The worm can only move from apple to apple by going directly up, down, or to the side. It cannot move diagonally. Is such a path possible? If not, can you prove it?

Representation

• You and an opponent take turns picking a number 1 through 9. No number can be picked twice. The winner is the first person to have a collection of numbers such that exactly three of them can be combined to add up to 15.

Set effectsProblem Jug A Jug B Jug C Desired

1 21 127 3 100

2 14 163 25 99

3 18 43 10 5

4 9 42 6 21

5 20 59 4 31

6 23 49 3 20

7 15 39 3 18

8 28 76 3 25

9 18 48 4 22

10 14 36 8 6

Insight problems

• Control group (given 30 minutes): 55%• Experiment 1 (half hour break in which they

performed other activities): 64%• Experiment 2 (4 hour break): 85%• Interviews showed that subjects did not come back

to problem with finished solutions.

You are given four separate pieces of chain that are each three links in length. It costs $0.02 to open a link and $0.03 to close a link. All links are closed at the beginning of the problem. Your goal is to join all 12 links of chain into a single circle at a cost of no more than $0.18.

Development of expertise

• Like memory, expertise develops on a power law

• Experiment in training to read inverted text

Expertise

• What differentiates experts from novices in chess?

QuickTime™ and aGIF decompressor

are needed to see this picture.

Recall of pieces

722Master

612Intermediate

56Novice

RandomMeaningful

Expert memories

• Untimed chessboard-reproduction task (move pieces in meaningful chunks)

• No loss in recall after 30-second delay (better long term memory)

• Estimated that masters have 50,000 chess patterns stored

• Timing information: Masters recall more and larger patterns

Transfer

• After 200 hours of practice, subject was able to remember a string of 81 digits, repeated 1 per second.– Transfer to recall of letters = zero

• Brazilian children’s math skills– Situated context–– 98% accuracy– Lab context–– 37% accuracy– Word problems–– 74% accuracy

Expert problem-solving

• Development of useful strategies suited to a given domain– Physics and geometry: Working forward vs.

means-end analysis• Efficient use of working memory–no need to keep

track of goals and subgoals

– Computer programming: Breadth-first vs. depth-first

• Subgoals of a problem may interact

• Use of more abstract representations well-suited to problem-solving operations

Summary

• Problem-solving is typically analyzed from an information-processing point of view involving a problem space, operators, and production rules

• Generating an effective representation of a problem is a key step in its solution

• Transfer of skill is hard!

Implications for instruction

• LISP tutor– Guides students closely on relatively simple

programming problems– Monitors student performance on 500 production

rules– Research showing students learn faster using tutor

than ordinary university classroom instruction.– Same principle now used in algebra, geometry

tutors

Perception and attention

• What is attention?“Everyone knows what attention is. It is the taking possession

by the mind, in a clear and vivid form, of one out of what seem several simultaneously possible objects or trains of thought. Focalization, concentration of consciousness are of its essence. It implies withdrawal from some things in order to deal effectively with others.” William James (1890)

• Automatic processes

red orange blue orange

purple black green black

blue purple green red

green blue orange purple

red orange blue orange

purple black green black

blue purple green red

green blue orange purple

Stroop effect• Congruent: Shape has same ink

color as its associated color

• Control: White shapes or unassociated shapes

• Conflict: Shape has different ink color than its associated color 450

500

550

600

650

700

750

Congruent Control Conflict

Color namingShape naming

Condition

450

500

550

600

650

Congruent Control Conflict

Color namingShape naming

ConditionMcLeod and Dunbar (1988)

Interference depends on use of common resources (hard to disprove)

RepresentationA label machine cuts labels and prints a letter on one side (either an A or a B) and a number on the other (either a 2 or a 3). It has no other characters and never prints anything but these and on the proper side. However, on every label that has an “A” it is supposed to print a “2” on the other side. Sometimes it slips, however, and makes a mistake on this.

If you are a checker checking labels as they come past you on the assembly line out of the machine, which of the following labels flowing past you would you have to turn over to check that they are done correctly?

A 3 B 2

Representation

In a crackdown against drunken drivers, state police are revoking liquor licenses left and right if they find out that persons under the age of 21 are being served alcohol. You are a bouncer in a bar and it is your job to enforce the law. When a person orders a drink, the wait-staff writes the drink on one side of a napkin and the person’s age on the other.

Below are 4 napkins for the people at one table. Which napkins must you turn over to check if a person is breaking the law?

beer coke 25 16

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