How Good Are Students at Testing
Alternative Explanations of Unseen Entities?
Anton E. Lawson Nicole Drake Jennifer Johnson
Yong-Ju Kwon Christopher Scarpone
T
HE purpose of the present study is to test
the hypothesis that a fifth stage of intellectual
development characterized by the ability to test
alternative explanations involving unseen theoretical
entities exists. This fifth-stage hypothesis will be
tested in the context of a nonmajors, college-level
biology course in which the assumption is made that
some, but by no means all, students have acquired
stage-five reasoning skills.
Jean Piaget’s well-known developmental theory
proposes that the development of thinking skills,
which most would characterize as ‘‘scientific,’’ takes
place in a stage-like fashion. Stage one, the sensorymotor stage, lasts from birth to about 18 months.
As the name suggests, the stage involves the development of sensory-motor knowledge and acquisition
of practical knowledge such as the fact that objects
continue to exist even when out of sight. Stage two,
the pre-operational stage, lasts until seven years of
age. This stage primarily involves development of
the ability to speak and understand the spoken word.
Stage three, concrete operations, which begins at
age seven, involves the development of descriptive
thinking skills in which the child acquires an understanding of class subclass relationships and begins
to understand the world in terms of specific variables
such as weight, length, area and volume (e.g. Flavell
1963; Inhelder & Piaget 1958; Lawson & Renner 1975;
Piaget & Inhelder 1969; Trifone 1991). Potential for
moving into Piaget’s fourth and highest stage of
thinking, called formal operational, generally occurs
between 11 and 12 years of age. Inhelder and Piaget
(1958) invented several widely used tasks to find
out whether or not students have developed formal
thinking patterns. A prototype task is the pendulum
task. The pendulum task asks students to identify
variables that may cause differences in the rate at
which pendulums swing. If a student conducts controlled experiments to test the possible effects of
Anton E. Lawson, Ph.D., is Professor of Biology and Nicole
Drake, Jennifer Johnson, and Christopher Scarpone are in
the Department of Biology, Arizona State University, Tempe,
AZ 85287-1501. Yong-Ju Kwon is at Pohang University of Science and Technology, Pohang, Kyungbuk 790-784, Korea.
variables such as pendulum weight, string length,
and release angle on swing speed, s/he is classified
as formal operational.
An important point in terms of the present study
is that the pendulum task characterizes stage-four
thinking by the presence of a hypothetico-deductive
thinking pattern. In other words, to test the hypothesis
that weight differences cause differences in swing
speed, one generates the following argument:
If . . .
differences in swing speeds are caused
by differences in the amount of weight
hanging on pendulums (hypothesized
cause)
and . . .
the weights are varied, while holding
other possible causes constant (proposed
experimental test),
then . . .
the speed of pendulum swing should
vary (deduced expected result).
But . . .
when the proposed experiment is actually carried out, we find the swing speed
does not vary (observed result).
Therefore . . . changes in swing speeds are probably
not caused by weight differences
(conclusion).
Piaget’s theory implies that all formal stage tasks
with the same ‘‘logical’’ form should be of equal
difficulty. Note that the stage is called ‘‘formal’’
because the thinker presumably is able to separate
form from context in reasoning (Piaget 1957). Thus,
the well-documented phenomenon that not all logically identical tasks are equally difficult (referred to
as horizontal decalage or separation) contradicts the
theory. In hopes of eliminating this contradiction,
the present view proposes the existence of a fifth
stage characterized by the use of a similar reasoning
pattern, but applied to situations in which the possible
causes are no longer seen, hence are theoretical, more
complex, and more difficult.
The idea of fifth stage is not new among psychologists (Arlin 1975; Commons, Richards & Armon 1982;
Kramer 1983; Riegel 1973, 1975). However, psychological evidence for a fifth stage is hard to come by.
Nevertheless, evidence suggestive of a fifth stage can
be found in the neurophysiological literature. Perhaps
the most compelling comes from a study reported
in Science by Thatcher, Walker & Giudice (1987).
EXPLANATIONS TO UNSEEN ENTITIES 249
They report electroencephalographic data from 577
people, age two months to adulthood. A variety of
measures were obtained for each person, including
a neurological and developmental history, full-scale
intelligence test, skull size, motor development,
school achievement, and 19 lead-coherence and
phase-electroencephalographic (EEG) readings. Based
on these measures, discrete brain growth spurts that
appeared at specific anatomical locations at specific
ages were found. Further, the left and right hemispheres developed at different rates with the timing
of growth spurts overlapping the timing of the major
developmental stages described by Piaget. Most
importantly, from the point of view of stage theory
in general, and fifth-stage theory in particular, five
growth spurts, not four, with the last occurring at
about 18 years of age, were found. Neurophysiological evidence suggestive of the existence of a fifth stage
has also been reported by Epstein (1986), Hudspeth &
Pribram (1990), and Thatcher (1990).
As mentioned, the basic hypothesis of the present
study is that reasoning of the if/and/then/but/therefore form is present at both stages four and five,
thus intellectual development during adolescence and
early adulthood presumably does not involve changes
in this thinking pattern, rather it involves changes
in what the thinking pattern can be applied to. We
have seen how this sort of reasoning can be applied
to solve the pendulum task—presumably a stagefour task. Let’s see how it might be used to solve
a stage-five task.
Cover the bottom of a bowl with water. Place a
candle in the bowl using a small piece of clay. Now
light the candle and cover it with an inverted drinking
glass so the rim of the glass is submerged in the
water. When you do this you will notice that the
candle quickly goes out and the water rushes up
into the glass. Question: What caused the water to
rise? How would you go about trying to answer this
question? If you are like many people, you would
guess that the candle burned up the oxygen in the
inverted glass creating a partial vacuum. So when
the oxygen was gone, the candle went out and the
water rushed in to fill the space that was previously
occupied by the oxygen. Let’s call this a theoretical,
rather than hypothetical, explanation because it
attempts to explain something by invoking the existence of unseen imaginary entities, such as oxygen
molecules. How would you test this theoretical explanation? Consider the following:
If . . .
and . . .
then . . .
oxygen is burned up creating a vacuum
in the glass (theoretical explanation)
the experiment is repeated varying only
the number of burning candles (test),
the amount of water that rises in each
case will be the same (expected result).
The amount of water that rises should
be the same because only a certain
amount of oxygen exists under the glass.
So more candles will burn that oxygen
up faster, but more candles will not
burn up more oxygen, thus the same
partial vacuum should be created in
each case (theoretical rationale).
But . . .
when the test is conducted, more water
rises when more candles are lit
(observed result).
Therefore . . . this theoretical explanation appears to
be incorrect and a new one should be
generated and tested (conclusion).
Regardless of what actually causes the water to
rise, the key point in terms of stage-five reasoning
is that, although identical to stage-four reasoning in
terms of the underlying reasoning pattern, it differs
from stage-four reasoning in two important ways.
First, as mentioned, the proposed causes in stage
five are unseen, rather than the seen proposed causes
of stage four. And second, unlike stage-four reasoning
where the proposed causes and the independent
variables of the experiments designed to test them
are one and the same, this is no longer the case
at stage five. In the above candle experiment, the
independent variable was the ‘‘number of lit candles,’’
while the proposed cause was a partial vacuum
created by the burning of oxygen. Because the proposed cause and the independent variable are not
the same, a theoretical rationale must be generated
to link the two so that a ‘‘reasonable’’ test can be
conducted. Hence, even following instruction in
which students (many of whom have presumably
not yet developed stage-five thinking patterns)
attempt such tests, the tests should be more difficult
to design, conduct and interpret than stage-four tests.
Method
Sample
Participants were 82 students (45 males and 37
females, 18.1 to 49.2 years of age, mean age ⳱
22.8 years) enrolled in a nonmajors, one-semester
introductory college biology course at a major southwestern university.
Design
During the semester, students conducted a series
of weekly two-hour labs in which they were explicitly
asked to design, conduct and interpret a series of
experiments in which alternative explanations to be
tested involved familiar/observable entities or unfamiliar/unseen entities. Quizzes were administered
either at the start of the next lab session or during
the final week of the semester. Students were tested
to determine whether they could: 1) successfully
propose an experiment complete with a set of
expected (predicted) results to test the alternative
explanations that had actually been tested, or had
250 THE AMERICAN BIOLOGY TEACHER, VOLUME 62, NO. 4, APRIL 2000
at least been discussed, in lab; and 2) state observed
results that would show that the alternative explanations were probably wrong. In other words, students
were tested to determine whether they could successfully generate if/and/then/but/therefore arguments
to reject the alternative explanations.
Laboratory & Field Exercises
The laboratory and field exercises, in order of
presentation, are presented in Table 1. Also included
in the table are brief discussions of the reasoning
(either stage four, stage five, or a mixture of both)
presumably required by each exercise.
Quizzes
The quizzes that followed each exercise are shown
in Table 2.
Scoring
Each quiz was scored either correct (a score of 1)
or incorrect (a score of 0), depending on the extent
to which students successfully generated complete
if/and/then/but/therefore arguments and evidence
to reject the alternative explanations. Scores of 1 were
awarded for responses in which the student described
an experiment that satisfactorily tested the explanation in question including predicted results, observed
results and appropriate conclusions. If the quiz called
for two contradictory results (to test two explanations), both had to be included to be awarded 1 point.
Results & Discussion
Results are shown in Figure 1. The figure shows
the percentage of students responding correctly to
each of the six quizzes. As you can see, percentages
ranged widely from 93.9% on the Pendulum Quiz
to 18.3% on the Osmosis Quiz. As predicted, students
were much more successful on the two stage-four
quizzes, Pendulum (93.7%) and Mealworm (81.7%),
than they were on the two stage-five quizzes, Osmosis
(18.3%) and Candle (20.7%). Also as predicted, the
two quizzes that presumably involved a mixture of
stage-four and stage-five reasoning were of intermediate difficulty, ‘‘A’’ Mountain (57.3%) and Cactus
(61.1%).
Because these results are essentially those predicted
by the fifth-stage hypothesis, they provide evidence
that supports the hypothesis. Further, one can assume
that the 10% to 20% of students who failed the two
stage-four quizzes (i.e. the Pendulum and Mealworm
Quizzes) are still operating at stage three (Piaget’s
concrete operational stage), while the approximately
20% of students who were successful on the two
stage-five quizzes (Osmosis and Candle) are operating
at stage five. This leaves about 60% of the present
Table 1. Laboratory and field exercises.
How Smart Are Animals?
This lab asked students to generate and test
explanations about the causes of movements of isopods.
Possible causes included the amount of light, food and
moisture in various locations in their environment. These
possible causes are observable, hence presumably involve
stage-four reasoning.
How Can a Burning Candle Cause Water To Rise?
The objective of this lab was to generate and test
alternative explanations to account for water rise in an
inverted cylinder. The lab begins with a burning candle
held upright in a pan of water using a small piece of clay.
Shortly after a cylinder is inverted over the burning
candle and placed in the water, the candle flame goes out
and water rises in the cylinder. These observations raise
two major causal questions: Why did the flame go out?
and Why did the water rise? Students generated and
tested several explanations to answer the second
question—presumably requiring stage-five reasoning.
What Variables Affect the Passage of Molecules Through
Cell Membranes?
This lab involved the generation and test of alternative
explanations that required imagination of the existence of
unseen atoms and ions in solution to account for increases
and decreases in cell sizes when bathed in salt solutions,
glucose solutions, and in distilled water. This lab
presumably involved stage-five reasoning.
How Does the Environment Affect the Distribution of
Organisms?
Students sampled vegetation on the south- and northfacing slopes of a small mountain near campus called ‘‘A’’
Mountain. Students discovered, among other things, that
cacti were more abundant on the south-facing slope and
grasses were more abundant on the north-facing slope.
Students were then asked to generate alternative
explanations to account for these differences and suggest
how their explanations might be tested. Student
explanations involved potentially observable factors such
as lack of water on the south-facing slope and more shade
on the north-facing slope. An explanation involving
intense sunlight disrupting the grasses’ ability to conduct
photosynthesis—an unseen theoretical process—was also
involved. Thus, this field study presumably involved a
mix of stage-four and stage-five reasoning.
What Adaptations Do Plants Have for Life in the Desert?
In the field, students observed several desert plants and
tried to identify characteristics that might represent
evolutionarily derived adaptations for life in the desert.
Observable characteristics such as the presence of spines,
tiny leaves, waxy surfaces, green bark, and thick waterfilled stems were identified. Students were asked to
propose experiments that would test the effectiveness of
these characteristics in terms of desert survival. Although
characteristics such as spines, tiny leaves, and waxy
surfaces are observable (hence stage four), the process of
evolution is theoretical and unseen, hence presumably
involves stage-five reasoning. Like the previous field
study, this study presumably involved a mix of stage-four
and stage-five reasoning.
EXPLANATIONS TO UNSEEN ENTITIES 251
Table 2. The quizzes.
Pendulum Quiz
A swinging string with a weight on the end is called a pendulum. What causes pendulums to swing fast or
slow?
Hypothesis 1: A change in the amount of weight hanging on the end of the string will cause a difference in the
swing speed—the lighter the weight, the faster the swing.
Hypothesis 2: A change in the length of string will cause a difference in the swing speed—the shorter the string,
the faster the swing.
How could you test these hypotheses? 1. Describe your experiment. 2. What are the predicted results of your
experiment (assuming that the hypotheses are correct)? 3. What result would show that Hypothesis 1 is probably
wrong? 4. What result would show that Hypothesis 2 is probably wrong?
Mealworm Quiz
A student recently placed some mealworms in a rectangular box to observe their behavior. She noticed that the
mealworms tended to group at the right end of the box. She also noticed that the right end had some leaves in it
and that the box was darker at that end. She wondered what caused them to group at the right end.
Hypothesis 1: They went to the right end because it had leaves in it.
Hypothesis 2: They went to the right end because it was darker than the left end.
How could you test these hypotheses? 1. Describe your experiment. 2. What are the predicted results (assuming
that the hypotheses are correct)? 3. What result would show that Hypothesis 1 is probably wrong? 4. What result
would show that Hypothesis 2 is probably wrong?
Candle Quiz
When a jar is placed over a lighted candle, which is held upright in a pan of water, the flame soon goes out and
the water rises into the jar. What causes the water to rise in the jar? State one hypothesis, an experimental plan, a
predicted result, an observed result, and a conclusion based on an experiment you conducted in lab.
Osmosis Quiz
When a thin slice of red onion cells is bathed in salt water, the red portion of each cell appears to shrink. What
causes the red portion to appear to shrink?
Hypothesis 1: Salt ions (i.e. NaⳭ and Clⳮ) enter the space between the cell wall and the cell membrane and push
on the cell membrane.
Hypothesis 2: Water molecules (i.e. H2O) are charged (i.e. thus leave the cell due to attractive forces of the salt
ions).
Question: How could you use model cells made of dialysis tubing, a weighing device, and solutions such as salt
water, distilled water, and glucose to test these hypotheses? 1. Describe your experiment. 2. What are the
predicted results assuming that the hypotheses are correct? 3. What result would show that Hypothesis 1 is
probably wrong? 4. What result would show that Hypothesis 2 is probably wrong?
‘‘A’’ Mountain Quiz
A recent survey of organisms on ‘‘A’’ Mountain revealed more grass on the north-facing slope than on the
south-facing slope. In response to the causal question, ‘‘Why is there more grass on the north-facing slope?’’ a
student generated the following hypotheses:
Hypothesis 1: Lack of moisture in the soil on the south-facing slope keeps grass from growing there (i.e. north is
better shaded from the sun’s drying rays).
Hypothesis 2: The sunlight itself is too intense for good grass growth on the south-facing slope (i.e. very intense
rays disrupt the grasses’ ability to conduct photosynthesis).
How could you test these hypotheses? 1. Describe your experiment(s). 2. What are the predicted results of your
experiment(s), assuming that the hypotheses are correct? 3. What result would show that Hypothesis 1 is
probably wrong? 4. What result would show that Hypothesis 2 is probably wrong?
Cactus Quiz
On our field trip to the Desert Botanical Gardens we observed several types of cacti with spines. One answer to
the question ‘‘Why do cacti have spines?’’ is that the spines have been acquired over several generations through
the process of natural selection. But of what possible survival value are the spines for the cacti today? Assuming
that you have a large grant with unlimited funds from the National Science Foundation, how could you conduct
research to answer this question? State a hypothesis, an experimental plan, a predicted result, an observed result
(you will have to make up some data), and a conclusion.
sample operating at stage four—a percentage similar
to those reported in previous studies (e.g. Dawson &
Rowell 1986; for a review see Lawson 1992; Walker
1979).
In spite of the fact that the present results clearly
reveal that testing explanations involving unseen,
imaginary entities is considerably more difficult than
testing explanations involving observable causal
252 THE AMERICAN BIOLOGY TEACHER, VOLUME 62, NO. 4, APRIL 2000
Figure 1. Percent of students responding correctly to each
of the six quizzes.
agents, the study does not establish a link (either
correlation or causal) between theory-testing ability
and the neurological maturation that presumably
takes place at age 18. Nevertheless, previous research
has linked earlier spurts of neurological maturation
to earlier stage-wise shifts in cognition (e.g. Dempster
1993a, 1993b; Diamond 1990; Lawson 1993). Thus,
the possibility exists that future research might establish such a link.
Although the present results support the fifth-stage
hypothesis, one could argue that they merely suggest
that Piaget’s formal stage can be divided into substages—the first substage involving hypothesis testing and the second involving theory testing. For
example, consider the following remarks by Inhelder
and Piaget (1958) regarding adolescent thinking:
defined). If true, then Piaget’s response to the present
study might be that stage five is merely an advanced
substage within his formal stage.
On the other hand, perhaps Piaget’s stage four is
about hypothesis testing (where the hypotheses are
about observable causes) and about theory building,
while stage five is about theory testing. Note that
Piaget mentions that the adolescent builds theories,
but he fails to mention anything about theory testing.
It does seem reasonable to suspect that adolescents
must first build two or more competing theories (e.g.
evolution and special creation) prior to asking which
is the better theory, and only then trying to figure
out how to test them.
How could the Piagetian two-substage possibility
versus the present fifth-stage possibility be tested?
This is a question not easily answered. Perhaps it
really does not matter in practice, provided that
instructors conceptualize the apparently important
distinction between hypothesis testing and theory
testing. On the other hand, it would matter if it
turns out that neurological maturation at age 18 is
in some way necessary for theory testing.
Conclusions & Implications
Given that few college students in this study gave
evidence of ‘‘theoretical’’ reasoning skills (perhaps
The adolescent differs from the child above all in that he
thinks beyond the present. The adolescent is the individual
who commits himself to possibilities—although we certainly
do not mean to deny that his commitment begins in reallife situations. In other words, the adolescent is the individual
who begins to build ‘‘systems’’ or ‘‘theories’’ in the largest
sense of the term (pp. 339–340).
Later Piaget (1966) had this to say regarding the
formal thinker: ‘‘The formal thinker is an individual
who thinks beyond the present and forms theories
about everything, delighting especially in considerations of that which is not’’ (p. 148). Thus, it seems
quite possible that Piaget was thinking about the
formal stage in terms of peoples’ abilities to think
about unseen theoretical entities, i.e. in terms similar
to those presently used to characterize stage-five
thinking. This could be Piaget’s position regardless
of the fact that none of the standard Piagetian tasks
seems to require theoretical thinking (as presently
EXPLANATIONS TO UNSEEN ENTITIES 253
as few as 20%), the key pedagogical question is this:
How can we help the other 80% develop theoretical
reasoning patterns? If intellectual development is
truly stage-like, then for stage-three students it would
appear that we need to immerse them in hypothesistesting contexts and provide repeated opportunities
for direct physical experience, for social interaction
with others, and for equilibration (Karplus et al. 1977;
Lawson 1994; Piaget & Inhelder 1969; Trifone 1991).
Once these students develop stage-four reasoning
patterns, we then need to repeat the process in theorytesting contexts. For example, we have found that
the burning-candle and moving-molecules exercises
listed in Table 1 appear to help, but many similar
‘‘theory-testing’’ inquiries are probably necessary
before substantial progress can be expected. Details
on how to use the burning-candle exercise to this
end appear in Lawson (1999); details on using the
moving-molecules exercise appear in Lawson (1998b,
in press). However, if the final brain growth spurt
that occurs during late adolescence is in fact a prerequisite for theoretical thinking, then it may not be
reasonable to expect students to become skilled at
theory testing prior to their college years. This may
seem like a rather pessimistic view (after all, it brings
into question the value of introducing theoretical
concepts to high school students—a common practice
even in many elementary classrooms), but perhaps
not a surprising one, given the considerable difficulty
some graduate students encounter when they finally
reach the research phase of their education and
embark on a theory-testing venture.
Another problem is that many instructors are so
concerned with content coverage that they are hesitant to take the necessary time to discuss hypothesis
and theory testing. Also, the lab is often thought of
as a place to verify lecture claims rather than to
conduct ‘‘real’’ inquiries. In hopes of solving this
problem in our nonmajors course, we try to make
sure that topics arise in labs prior to lectures; and
we no longer try to closely articulate lab and lecture
topics. Thus, when students need two or three weeks
to conduct a particularly difficult inquiry, we can
allow them the time to do so. In this sense, we try
to keep the American Association for the Advancement of Science’s central teaching principle in mind.
It states: ‘‘Teaching should be consistent with the
nature of scientific inquiry’’ (AAAS 1989).
Many biology courses suffer from still another
problem. Having been designed by subject-matter
experts—who often know little about developmental
psychology—topics are typically sequenced from the
instructors’ perspective, rather than from the students’. Consequently, topics often are introduced
following a ‘‘micro-to-macro’’ sequence beginning at
the highly-abstract and theoretical atomic/molecular
levels and only later moving to the more-familiar and
less-abstract organism, population and community
levels. A few recent textbooks have tried to solve this
problem by employing a ‘‘macro-to-micro’’ sequence.
Thus, they begin at the biome level and work their
way down through ecosystems, communities, populations, organisms, etc. But this sequence also fails to
recognize that learning probably occurs best when
topics are sequenced from the familiar to the abstract.
Students are organisms, not biomes, so it seems
reasonable that they will learn better when the course
begins at the organism level and then inquires into
either progressively smaller and/or progressively
larger levels of organization and abstraction. Here
the history of science may have much to offer in
terms of helping us identify ‘‘natural’’ sequences of
inquiry, sequences that past biologists have taken
and that present students can also take. Employing
such sequences should lead to scientifically literate
students—that is, to students who understand the
theoretical nature of science and how to think about
and test theories involving unseen entities.
Note
This material is based upon research partially supported by the National Science Foundation under
grant No. DUE 9453610. Any opinions, findings, and
conclusions or recommendations expressed in this
publication are those of the authors and do not
necessarily reflect the views of the National Science
Foundation.
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