Science paper - American Psychological Associationsupp.apa.org/.../a0031931/XAP-Kaminski20120778-R-F1.docx · Web viewSD = 1.17 years) from the Ohio State University participated

Cost of Concreteness -- 1

Supplemental Material

The Cost of Concreteness: The Effect of Nonessential Information on Analogical Transfer

Jennifer A. Kaminski, Vladimir M. Sloutsky, and Andrew F. HecklerThe Ohio State University

Experiment A-1: Concreteness of Elements

Experiment A-1 examined the concreteness of elements used in the reported

experiments by obtaining measures of the amount of communicated information and

measures of concreteness. In addition to the stimuli used in the reported experiments, we

also included objects that vary (according to our intuitions) from very abstract to very

concrete.

Method

Participants. Sixty-eight undergraduate students (28 female, 40 male, age M = 19.4

years, SD = 1.17 years) from the Ohio State University participated in the experiment and

received partial credit for an introductory psychology course.

Materials and Design. Participants were randomly assigned to one of two

conditions, Rate Concreteness or Rate Information. In the Rate Concreteness condition,

participants were presented with a series of 24 objects on the computer. The task was to

rate the concreteness of each object on a scale from 1 to 5. The instructions given to them

were similar to instructions used in previous studies in which participants rated the

concreteness of words (Paivio, Yuille, & Madigan, 1968; Spreen & Schulz, 1966). The

objects presented are shown in Tables A-1 and A-2. Five categories of objects were used.

The members of each category were the elements of the instantiations used in


Experiments 1 - 5 (sets Concrete 1, Concrete 2, Generic, Number, and Reduced Concrete

1, see Table A-2). Eight additional objects were included which varied in the amount of

perceptual detail (see Table A-1); four instantiations of a person, two of a cat, and two of

a pie were considered.

In the Rate Information condition, participants were presented with the same series of

24 objects as in the Rate Concreteness condition. The task was to rate on a scale from 1

to 5 the amount of information communicated by each object.

Procedure. Participants were seen individually in a lab on campus. In the Rate

Concreteness condition, participants were told they would be shown a series of images on

the computer and asked to rate the concreteness of each on a scale from 1 (very abstract)

to 5 (very concrete). As with previous studies which measured the concreteness of words

(Paivio, et al., 1968; Spreen & Schulz, 1966), participants were told that the word

“concrete” is often used to describe entities that can be directly experienced and they

were given two anchoring examples. They were shown an image of a chair and told that

the image is of something we can experience and therefore should be rated highly (at or

close to 5). They were then shown an image of an “X” and told that it is an image of

something that cannot be experienced and should be rated low (at or close to 1). The

images were then presented individually; and participants entered a rating for each. The

first image presented was of the real cat. The second image was the stick figure of a cat.

The remaining images were presented in random order.

In the Rate Information condition, participants were told that they would be shown a

series of images on the computer and asked to rate each for the amount of communicated

information. A scale of 1 (no information or very little information) to 5 (a lot of


information) was used. Participants were told they could think about their response in

terms of how much they would need to say in order to describe the object to someone

who could not see it. Participants were shown the images of the two cats in Table 1 as

examples. Then they were asked to enter a rating for the real cat and then a rating for the

stick figure cat. The remaining images were presented in random order; and participants

entered a rating for each. In both conditions, participants proceeded at their own pace,

with their responses recorded by the computer.

Results and Discussion

Mean ratings of information and concreteness were calculated for each object. Three

participants (two from the Rate Information condition and one from the Rate

Concreteness condition) were eliminated from the analysis because their responses for

three or more objects were greater than 2.5 standard deviations from the mean.

For the objects which varied in the amount of perceptual detail (instantiations of

person, cat, and pie), higher ratings for both concreteness and information were given to

the more perceptually detailed objects than to the less detailed objects (see Table A-1).

Specifically, on the trials presenting instantiations of persons, concreteness ratings

significantly increased with the amount of perceptual information present, repeated

measures ANOVA F (3, 96) = 158.3, p < .001, p2 = .83. Similarly, for cats and pies,

participants gave higher ratings to the more perceptually rich objects than to the less

perceptually rich objects, paired samples, ts (32) > 6.56, ps < .001. A similar pattern was

found for ratings of information. Higher ratings were given to perceptually rich objects

than to less perceptually rich objects, repeated measures ANOVA F (3, 93) = 63.9, p

< .001, p2 = .67 for instantiations of person and paired samples, ts (31) > 6.60, ps < .001


for the cat and pie instantiations. The correlation between information ratings and

concreteness ratings was high (r = 0.84) which supports our contention that the objects

which are typically labeled more concrete also communicate more information than those

which are considered more abstract.

Additional analysis focused on the categories of objects that were used in

Experiments 1 – 5 (sets Concrete 1, Concrete 2, Generic, Number, and Reduced Concrete

1). Mean ratings were calculated for each category (see the second and third columns of

Table A-2). For ratings of information, significant differences were found between each

pair of categories, repeated measure ANOVA, F (4, 124) = 119.4, p < .001, all pair-wise

comparisons were significantly different ps < .006. Most importantly with regard to the

following experiments, Generic objects were rated lower than Concrete 1 objects and

Concrete 2 objects; Numbers were rated lower than Concrete 1 objects; and Reduced

Concrete 1 objects were rated lower than Concrete 1. Differences were also found

between concreteness ratings, repeated measure ANOVA, F (4, 128) = 192.4, p < .001,

p2 = .86. Pair-wise comparisons found equivalent ratings for Generic, Number, and

Reduced Concrete objects, ps > 0.66. However, Concrete 1 and Concrete 2 objects were

rated significantly higher than each of the other categories, ps < .001. There was also a

strong correlation between concreteness ratings and information ratings (r = 0.93).

Taken together, the results support our intuitions; there is a high correlation between

concreteness and the amount of communicated information.

However, as mentioned earlier, information can be communicated not only by

individual elements, but also by the relations or systems of relations in which the

elements are placed. The results of Experiment A-1 provide a measure of the


concreteness of the individual elements that were used in the following experiments. The

goal of Experiment A-2 is to provide a measure of the concreteness of the system of

elements for the instantiations used in the experiments. This measure was designed to be

an indicator of the amount of information about the relational system that is easily

communicated to the participant in the absence of explicit, in-depth instruction.

Table A-1: Stimuli and mean ratings of concreteness and of amount of communicated

information for objects of varying perceptual richness used in Experiment A.


Person Cat Pie

Concreteness M = 2.03 M = 2.06 M = 2.45 M = 4.82SD = 0.85 SD = 0.75 SD = 0.83 SD = 0.73

M = 1.55 M = 4.94SD = 0.67 SD = 0.24

M = 1.55 M = 3.06SD = 0.79 SD = 1.09

Information M = 1.72 M = 2.25 M = 3.31 M = 4.34SD = 0.73 SD = 0.88 SD = 0.86 SD = 1.18

M = 1.81 M = 3.41SD = 0.74 SD = 1.29

M = 2.34 M = 3.47SD = 0.48 SD = 0.84

Table A-2: Mean ratings of concreteness and amount of communicated information for

elements and systems in Experiments A and B. Note the Summed Total Rating of

Communicated Information was used as the Concreteness Ratings for Experiments 1-5.

6.971.22= SD

= 4.00M1.10 = SD

= 2.97M0.86= SD

= 2.30MConcrete 1

6.711.27= SD

= 2.35M0.90 = SD

= 4.36M0.28= SD

= 4.81M2Concrete

5.371.54=SD 3.19= M

0.78= SD= 2.18M

0.59= SD= 1.63M

Reduced Concrete 1

4.811.73= SD

= 3.54M0.45 = SD

= 1.27M0.78= SD

= 1.56M

0 1 2(Modular Addition)

Number

4.04= 1.33SD

= 2.49M0.74= SD

= 1.55M= 0.55SD

1.59= M Generic

(Elements + System)

SummedTotal

Of the System(Experiment A-2)

Of the Elements(Experiment A-1)

Rating of Communicated InformationMean

Of the ElementsConcreteness

Mean Rating of

Instantiation


Experiment A-2: Concreteness of System

Method

Participants. Thirty-seven undergraduate students (17 female, 20 male, age M = 19.2

years, SD = 2.60 years) from the Ohio State University participated in the experiment and

received partial credit for an introductory psychology course.

Materials and Design. Participants were presented with short descriptions of six

different systems and asked to rate how much information is communicated to them by

each. They were told that they could base their answers on how much they might already

know about the system as well as the information presented to them.

Five of the systems presented (Generic, Number, Concrete 1, Reduced Concrete 1,

and Concrete 2) were used in the following experiments and will be explained in detail in

the reporting of those experiments. The sixth system was real number multiplication; and

examples were shown involving the numbers 1, 3, and 5. Descriptions were 1-page in

length and presented information including the elements, several statements, and an

example question. Figures A-1 and A-2 present the descriptions for the Concrete 1 and

Generic instantiations, respectively. The Number, Reduced Concrete 1, and Concrete 2

descriptions were isomorphic. The real number multiplication instantiation presented an

analogous amount of information.


Figure A-1. Description of the Concrete 1 instantiation.


System

In a mixing process, these amount of liquid are combined:

A combined or left-over amount is determined.

Here are some examples:

1. If and are combined, then is left-over.




Here is an example of a question that could be asked about this system:

What is left-over when the following cups of liquid are combined?

Based on your prior knowledge and the information presented above, how much do you feel you know about this system? Enter a number from 1 to 5

1 52 3 4

Nothing A lot

Figure A-2. Description of the Generic instantiation.


System

In a symbolic language, statements involve these three symbols.

A resulting symbol appears on the right.

Here are some example statements:

1. , .

2. , .

3. , .

4. , .

Here is an example of a question that could be asked about this system:

Find the resulting symbol: , , ? .

Based on your prior knowledge and the information presented above, how much do you feel you know about this system? Enter a number from 1 to 5

1 52 3 4

Nothing A lot

Procedure. Participants were seen individually in a lab on campus. They were told that

they would be asked to read about several different situations that will be presented on

the computer. After reading each one, they were asked to give a rating of how much they

felt they knew about the situation. The rating scale was 1 (I know nothing about this

system; if I had to answer questions about this situation, I would surely get them wrong.)

to 5 (I know a lot about this system; if I had to answer questions about this situation, I

would surely get them right). Participants were first presented with the situation

describing real number multiplication. The remaining systems were presented randomly.

They proceeded at their own pace; and their responses were recorded by the computer.

Results and Discussion


Mean information ratings were calculated for each system (see Table A-2). The

highest rating was given to Real Number Multiplication (M = 4.92, SD = 0.49). Mean

ratings for the five systems used in the reported experiments (Generic, Number, Concrete

1, Reduced Concrete 1, and Concrete 2) were submitted to a repeated measure ANOVA.

Difference in ratings were found across systems, F (4, 144) = 10.1, p < .001. Post-hoc

pair-wise comparisons found statistical difference in all ratings except the following:

Number and Reduced Concrete 1, Number and Concrete 1, and Generic and Concrete 2.

Most importantly for the reported experiments, both Generic and Reduced Concrete 1

were rated lower than Concrete 1, p < .001 and p < .004 respectively.

The results of Experiments A-1 and A-2 support the argument that systems can

communicate varying amounts of information through both the elements individually and

the structure that relates the elements. In very concrete situations, such as Concrete 1,

both the elements and system communicate much information. Such instantiations would

typically have recognizable elements related through a familiar structure. In other

situations, such as Generic, the elements may be devoid of particular referents and the

structure relating these elements may be unfamiliar. Such instantiations communicate

little information through their elements and their structure. Other situations may be a

combination, more or less concrete elements with more or less concrete system. For

example, Concrete 2 involves perceptually rich objects that were rated highly on amount

of communicated information. However, the structure relating these elements is

unfamiliar. Similarly, Number had a low concreteness rating of the elements and a high

concreteness rating of the system (which presented modular addition).


These results establish that the instantiations referred to as “concrete” in the

following experiments communicate more information than the instantiation referred to

as “generic”. Table A-2 presents combined element and system information scores of the

five systems used in the experiments presented below. These scores are presented in

ascending order and will be used to qualitatively predict transfer from a given system.


Learning Domains

Excerpt from training of the Generic Instantiation:

On an archaeological expedition, tablets were found with inscriptions of statements in a symbolic language. The statements involve these three symbols: and follow specific rules.

Rules for combining symbols.

Rule 1. The order of the two symbols on the left does not change the result.For example , is the same thing as ,

Rule 2. When any symbol combines with , the result will always be the other symbol. For example:

, and

,

Rule 3. ,

Rule 4. ,

Rule 5. ,

Rule 6. The result does not depend on which two symbols combine first. For example: , , It does not matter if we do

, first and then or , first and then .

Test Questions for Generic Domain:

1. Find the resulting symbol: , _____

Choose: 1.) 2.) 3.)

2. Find the resulting symbol: , , _____


Choose: 1.) 2.) 3.)

3. What symbols go in the blanks to make a correct statement?__ , __ ,

Choose: 1.) and 2.) and 3.) and 4.) and

4. What goes in the blanks to make a correct statement?

___ , ___

Choose: 1.) and 2.) and

3.) and 4.) and

5. What goes in the blank to make a correct statement?

, ___

Choose: 1.) 2.) 3.)

6. What can go in the blank to make a correct statement?

___ ,

Choose: 1.) , 2.) , 3.) , 4.) ,

7. What expression has the same result as the following expression?

, , , ____

Choose: 1.) , 2.) , 3.) , 4.) none of the above

8. Some of my team members were discussing what symbol could be placed in the first blank below. Which of their responses do you agree with?

___ , , , ___


Choose: 1.) any symbol 2.) any symbol except

3.) any symbol except 4.) any symbol except

9. When we were analyzing tablets, I overheard two of my team members talking. They were arguing about whether these inscriptions mean the same thing (have the same result). What do you think?

, , , , , ,

Choose: 1.) same 2.) different

10. How about the following? Do they mean the same thing?

, , , , , ,


11. Do the following give the same result?

, , , , , , , ,

, , , , , , , ,


12. What goes in the blanks to make a correct statement?

___ , , ___,


3.) and 4.) and

13. Which of the following symbols combine to give ?


3.) and 4.) none of the above

14. How many ‘s could combine with themselves to get ?

Choose: 1.) four 2.) five


3.) six 4.) seven

15. Find the resulting symbol:

, , , , , , , , , , ,

Choose: 1.) 2.) 3.)

16. What symbol goes in the blank to make a correct statement?

, , , , , , , , , ____

Choose: 1.) 2.) 3.)

17. When we were working, a tablet was broken. We tried to figure out what it stated.

We did not know the result, but we did know that there were two symbols on the

left; one of them was . We were trying to figure out what the result could be. Here are some opinions of my team members. Which do you agree with?

Choose: 1.) the result could be any symbol

2.) the result could only be or

3.) the result can only be

18. Find the resulting symbol:

, , ____

Choose: 1.) 2.) 3.)

19. Do the following statements mean the same thing?

, , , , , , , , ,



, , , , ,


, , , , ,



, , , , , ,

, , , , , ,



, , , , , ____

Choose: 1.) 2.) 3.)

23. What is the result of the following?

, , , , , , , , , , , ,

Choose: 1.) 2.) 3.)


, , ___ ,

Choose: 1.) , 2.) , 3.) , 4.) none of the above


Excerpt from training of the Concrete Instantiation:

A company makes detergents by mixing three different quantities of solutions,

represented as , , and . The company is testing the mixtures and wants to know what amount of solution is left-over in the mixing process.

Rules for finding left-over quantities:

Rule 1. The order by which two cups of solution are combined does not change the left-

over result. For example, combining with has a left-over quantity of

. And combining with has the left-over quantity .

Rule 2. and will fill a container, but we need a quantity of solution to test, so

we consider as the left-over.

Rule 3. When any kind of cup of solution combines with , the result will always be the other solution cup. For example:

When and combine, is left-over.

And when and combine, is left-over.

Rule 4. A combination of and does not fill a container, so the left-over is

.

Rule 5. A combination of and fills one container and has left-over.

Rule 6. Finally, you need to know that when mixing more than 2 cups of solution, the order of combining solutions does not matter. The left-over is the same no matter which cups are combined first. For example:

When we combine , and , the left-over is .

It does not matter if we do and first and then

OR and first and then .

Test Questions for Concrete Domain:


1. What is left-over when and combine?

Choose: 1.) 2.) 3.)

2. What is left-over when the following cups of solution are combined?

Choose: 1.) 2.) 3.)

3. What possible cups of solution can combine with to have a left-over of

?


3.) and 4.) and

4. Which cups of solution can combine to have left-over?


3.) and 4.) and

5. What can combine with to have left-over?

Choose: 1.) 2.) 3.)

6. What can mix with to have as a left-over?

Choose: 1.) 2.)

3.) 4.)

7. What combination of cups has the same left-over as the following?

Choose: 1.) 2.)

3.) 4.) none of the above


8. Some of the Bubblinski employees were analyzing a batch of detergent. The left-

over was . There were 4 cups of solution that were mixed. Two of these cups

were and , but the other two cups were not known. The guys were discussing which other cups could possibly have been involved in the mix. Which of their responses do you agree with?

Choose: 1.) any cup 2.) any cup except

3.) any cup except 4.) any cup except

9. Later I overheard two employees talking. They were arguing about whether these two mixtures of solution (below) would have the same left-over. What do you think?

Mix 1:

Mix 2:


10. True or false…When the cups are mixed, mix 1 and mix 2 will have the same left-over.

Mix 1:

Mix 2:

Choose: 1.) true 2.) false

11. How about these mixtures, will they have the same left-overs?

Mix 1:

Mix 2:

Choose: 1.) true 2.) false

12. What cups can combine with and to result in a left-over of ?


3.) and 4.) and


13. Which cups can combine to give a left-over of ?



14. How many ‘s could combine with themselves to get ?

Choose: 1.) four 2.) five3.) six 4.) seven

15. What is left-over when the following cups are mixed?

Choose: 1.) 2.) 3.)

16. What cup can mix with the following and have left-over?

Choose: 1.) 2.)

3.) 4.) we need more information to answer

17. One day, a batch of detergent was spilled. We did not know the left-over quantity, but we did know that there were two cups in the mixture; one of them was

. We were trying to figure out what the left-over could have been. Here are some opinions of the employees. Which do you agree with?

Choose: 1.) the left-over could be any cup

2.) the left-over could only be or

3.) the left-over could only be

18. What is left-over when the following cups of solution combine?

Choose: 1.) 2.) 3.)


19. Do the following mixtures have the same left-overs?

Mix 1:

Mix 2:

Choose: 1.) yes 2.) no

20. Do the following mixtures have the same left-overs?

Mix 1:

Mix 2:


21. How about the following, do they have the same left-over?

Mix 1:

Mix 2:


22. What cup needs to mix with the following

to have a left-over of ?

Choose: 1.) 2.) 3.)

23. What is left-over when the cups below are mixed?

Choose: 1.) 2.) 3.)

24. What cups need to mix with to have left-over?

Choose: 1.) 2.)



Transfer Domain

Excerpt from the Introduction:

In another country, children play a pointing game that involves these three objects:

. Children point to objects and the winner points to the correct final object. The rules of the last system you learned are like the rules of this game.

Test Questions for Transfer Domain:

The examples in the table below were presented with each of the following test questions.

If the kids point to these:

Then the winner points to this:

1. What object do you think the winner will point to when the other kids point to

then ?

Choose: 1.) 2.) 3.)

2. What object does the winner point to when the other kids point to then

then ?

Choose: 1.) 2.) 3.)

3. If a group of kids wants the winner to point to , and they first point to , what other objects do they need to point to?


3.) and 4.) and


4. If the winner pointed to , what objects might the other kids have pointed to?


3.) and 4.) and

5. What object do the children need to point to along with , so that the winner

points to ?

Choose: 1.) 2.) 3.)

6. What objects can the kids point to along with so that the winner points to

?

Choose: 1.) 2.)

3.) 4.)

7. Suppose that a group kids points to these objects: If other groups (in different games) point to the objects below, which group would have a winner pointing to the same object as the group above?

Choose: 1.) 2.)



8. A group of kids wants the winner to point to . They have already pointed to

and ; and they want to point to two more. What can their next object be?

Choose: 1.) any object 2.) any object except

3.) any object except 4.) any object except

9. Two groups of children were playing separate games.

One group pointed to these objects:

The other group pointed to these: Will the winner point to the same object in each case?


10. How about these objects? In separate games,

If one group points to these:

And another group points to these: Will the winner point to the same object in each case?


11. In separate games, suppose that the one group of children points to these:

And another group points to these:

Will the winner point to the same object in each case?



12. A group of children want the winner to point to .

They first point to and . What objects should they point to next?


3.) and 4.) and

13. What objects should the kids point to so that the winner points to ?



14. How many times could the kids point to so that the winner points to ?

Choose: 1.) four 2.) five3.) six 4.) seven

15. After the children point to these objects:

What will the winner point to?

Choose: 1.) 2.) 3.)

16. The children point to these objects:

What additional object should they point to so that the winner points to ?

Choose: 1.) 2.)

3.) 4.) we need more information to answer


17. Three children were playing together. One child pointed to . They were going to point to one more object, but before they did, they were trying to decide which object the winner would point to. Here are their opinions about the winning object. Which do you agree with?

Choose: 1.) the left-over could be any cup

2.) the left-over could only be or

3.) the left-over could only be

18. If the kids point to these objects: What object will the winner point to?

Choose: 1.) 2.) 3.)

19. In separate games, one group of kids pointed to these objects:

And another group pointed to these:

Will the winners of each game point to the same object?


20. How about these objects? In one game, the kids point to these objects:

and in another game, the kids point to these:




21. How about these objects? In one game, the kids point to these objects:

and in another game, the kids point to these:



22. A group of children pointed to these objects:

What additional object do they need to point to so that the winner will point to

?

Choose: 1.) 2.) 3.)

23. What will the winner point to if the children point to these?

Choose: 1.) 2.) 3.)

24. If the group of children point to these objects:

What additional objects should they point to so that the winner will point to ?

Choose: 1.) 2.)




Descriptions of the Domains used in the Similarity Judgment Experiment referred to In Experiment 1A

Generic Domain

A symbolic language was discovered in an archaeological expedition.This language uses these three symbols:

Statements are made by combining symbols.Specific combinations of symbols have a predictable resulting symbol that is written on

the right side of the statement.

Here is an example.

,

Concrete Domain

At a detergent company, different types of solution are mixed together. These three containers of solution are used:

After the mixing process, an amount is tested to make sure the detergent is being made correctly.

The tested amount can be determined from the specific amounts of solution mixed.

Here is an example. If and are mixed, then is tested.

Transfer Domain

In another country children play a pointing game.

The game involves these three objects: Children point to two or more objects and then a different child who is “it” points to

a final object. If that child points to the correct final object, then he/she is a winner.Here is an example.

Children pointed to then ; and the winner pointed to .

Documents

Science paper - American Psychological Associationsupp.apa.org/.../a0031931/XAP-Kaminski20120778-R-F1.docx · Web viewSD = 1.17 years) from the Ohio State University participated