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Probing For Thought Processes

by Kenneth Fuller 
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In order to say how effective teaching has been it is necessary to determine what learning has taken place.  The
evidence of learning is a change of behavior.  The behavior we expect to modify involves the overt behavior of
“giving  a response to a question”, but also all the higher level thinking processes which determined what the
response would be.  It is quite possible to arrive at a correct response for a wrong reason.  Therefore, to determine to
what extent a concept has been internalized by a student, in a form usable as foundation for further conceptual
learning it is necessary to probe for the thought processes used by the student.

When thought processes are not probed

We are familiar with complaints about “Scientific Illiteracy” in American society.  We have seen surveys showing that
many graduates from Ivy League universities, and even faculty members, are completely confused concerning the
causes of seasons, a subject presumed to have been taught in every elementary school.  Even many writers of science
curriculum materials are caught in the confusion.

“Twice each year Earth’s north pole is parallel with Sun’s north pole.” (Winds of Change, a CD-ROM by the
Educational Affairs Office at JPL)
(We will disregard the confusion between axes and poles.)
Most likely, a teacher said, “In summer Earth’s north pole tilts toward Sun, and in winter Earth’s north pole tilts
away from Sun.”  Perhaps the teacher understood that Earth’s axis is always (virtually for our lifetimes) pointing the
same direction while we revolve around Sun.  In the hearers mind, Earth’s axis flip-flops between seasons.

“In addition, the Earth’s rotation affects the rays of sunlight beating upon the earth, causing them to bend.  This
motion and the bending of sunlight causes seasons. “(Interdisciplinary Lessons For The Middle School Curriculum,
Judith D. Kalish, Ed.D. , Lorraine P. Marshall, M.S. , Automated Weather Source)  “I guess, in winter sunlight is
reflected off the moon and the planets or something.” (Anonymous).. ”When the sun shines upon Earth it sends out
two kinds of rays, direct and indirect.” (tutorial on an astronomy web site)
These confusions undoubtedly started with the statement, “ In summer, the Sun’s rays strike the earth more directly.”
In the speaker’s mind “directly”  means, “The Sun’s rays hit the ground at close to a 90 degree angle,
perpendicularly.”  In the mind of the hearer “directly” means, “In a straight line”.  Therefore, “less directly” means
“indirectly”, that is, not in a straight line.  Now, in the position of  teachers, these hearers feel compelled to create
theories to explain how Sun’s light can reach Earth by an indirect path , that is, not traveling in a straight line from
Sun to Earth, during winter.

Teachers who have not developed a conceptual understanding of the subject they “teach” cannot be expected to
encourage conceptual understanding in their students.  Pressure to cover large amounts of subject matter discourages
the use of time to present and evaluate material conceptually.  Rote memory of questions with their answers is a fast
way to create a superficial appearance of understanding.  A common example is the stimulus-response memorization
of lists of vocabulary words with their definitions.  Correct matching of the pairs on a test is assumed to show
mastery of the subject.  Even higher levels of Bloom’s Taxonomy can be simulated in this way, by giving the question
with an approved answer in the review activities.

A concept may take five pages of explanation with diagrams.  It is then summarized in one paragraph for review.  The
paragraph is in turn summarized in one sentence for cramming.  In the test item, the student recognizes a key word,
and produces the associated “correct response.”  The student is then assumed to understand the five page

Comprehension does not just happen, it requires work of both the teacher and the student.

To probe for thought processes requires that the teacher has:

1. Mastered the concept in question beyond the usual text book and lecture coverage.  Has analyzed the concept in
great detail and resynthesized it.  Has assimilated it, and integrated it into an overall scheme of understanding.

2. Learned to probe own thought processes in connecting diverse concepts into a unified system.  And to recognize
gaps and inconsistencies, and live with the gaps until information becomes available to allow for their resolution.

3. Learned patience.  Probing  thought processes is a time consuming  activity.  It requires more than the normal, or
even recommended “wait time” for answering questions.  It  often requires rephrasing questions and responses as the
student works through the conceptual connections.  If  the primary objective is to “cover ground”, you do not want
to know what your students are understanding.

4. Learned to live with incomplete success.  Students come with differing backgrounds and abilities.  Some will catch
on faster than others.  Some may never completely get it.  Sometimes it will suddenly click in a students mind long
after they have left the class in which they heard it first.  And the teacher will never know.

What It Takes.

The teacher must be able, and willing to take the time to present the concept more than once, using different words,
and different examples each time.  Repeating the same wording over and over improves rote memorization, but does
nothing to clarify ambiguities, or to resolve other confusions.  Connections of the present principle with principles
previously studied will seldom be made by students unless they are made explicit by the teacher.  Transfer of skills
and knowledge between units or subjects also needs to be made explicit by the teacher.  Concepts that “Go without
saying”, go unlearned.  It is also necessary that the teacher take time to encourage students to verbalize their
confusion.  By listening carefully to student’s questions and answers, it is often possible to determine the source of
confusion or error.

“Teacher, you said that if we go outside tonight and look over that way, we can see the planet Venus.”
“That’s right.”
“And you said if we look that way, we can see the planet Jupiter in the sky.”
“You’ve got it. And it looks like it will be clear tonight.”
“But teacher, you said that Earth is a planet too.”
“A planet just like Venus and Jupiter?”
“How can Earth be a planet up there when it’s down here?”

Many middle school students have learned all about the planets in their text books.  And can pass a test.  But no one
has ever made a connection for them between what’s in the book and things they can see in real life.
I had told a teacher about the student who said in class,  “Yes , Earth rotates on its axis, and it revolves around Sun.
But NOT the Earth we live on!”  She said, “I’m glad none of my students are like that!”  Which means she had never
bothered to find out what her students were really thinking.  (She had also forgotten that my students came from her

The student must be rewarded for developing conceptual connections.  Establishing the habit of seeking to
incorporate new learning into an overall conceptual scheme with previous learning will greatly enhance the ability to
retain and use subject matter.  Even when presented by less effectual teachers.  It is the excitement of discovery as new
concepts are integrated into one’s established framework that provides the intrinsic motivation and reward for

To test for mastery of vocabulary, more effective than having the students match definitions with words, have them
restate the principle without using the key words.  For example: State Newton’s third law of motion without using
the words “action” and “reaction”, and give an example which we have not used in class yet.  One example is almost
never enough to ensure that a student has correctly isolate the aspect of the example which illustrates the concept.

A Puzzling Analogy For Educators

Suppose you had never seen such a jigsaw puzzle before.  Someone with a 1,000 piece jigsaw puzzle were to hand
you the pieces, one at a time, for your inspection.  Having shown each of them, they shove the whole pile of loose
pieces to you and announce, “Now you have the whole picture.”  How complete and accurate do you think your
mental image of the picture on the puzzle would be?  If, on the other hand, they show how the shapes, colors, and
picture elements on them can be used to sort the pieces out and place each in correct relationship to each of the
others, then indeed you may have the whole picture. (Even without looking at the box.)

Yet, much of our educational system seems too nearly to fit the first model.  The student is provided with a pile of
factoids.  A stimulus-response test is given.  Having gotten passing scores on a large number of such tests, the
student is given a degree, and told, “Now you have an education !”

It is true, all of human experience is too large for the human mind to encompass all at once.  We need to assimilate it
little bits at a time.  So we divide our massive body of knowledge and skills into “subject areas”.  These we further
divide into grade level, unit and chapter segments.  With each chapter, a vocabulary list and assorted, appropriate
factoids are assigned to be memorized.  At the end of the chapter a test is given.  Grades on the test may be high,
low, or indifferent, no matter, forget all that and go on to the next chapter.  Most of the content of the chapter  will
never be mentioned again anyway.  At least this is the perception of the student, regardless of the teacher's opinion.
And it is the students perception that drives learning.  Many middle school students do not expect to understand what
they read in the text.  They wait for the teacher to give them the correct answers to the review questions, so they will
know what to memorize.  One “A” student taught me this early in my career, as I was going over a quiz with the class
she said, “Teacher, we don’t want to know why it is the correct answer, we just want to know whether the right
answer is C or D.”  No one had ever shown them that the pieces can be fit together to make a picture larger than a
grade point average.

Some attempts to remedy this situation have resulted in trends toward, “Interdisciplinary”, or “Integrated” curricula,
often proclaimed as, “Revolutions in Education”.  These have generally been implemented by reshuffling the piles of
factoids, to be shuffled again with the next “revolution”, with no significant change in the processes of teaching or
learning.  It has been established that teachers have a strong tendency to teach in the same way they were taught.
Therefore it  is necessary to provide teachers with both the incentive and ability to teach for conceptual
understanding, or the revolutions will continue to roll around without getting anywhere.

How then can we break out of the trends?  How can we go against the current?  How can we overcome the
resistance of students, parents, and colleagues?  How can we convince students that the little pieces really do fit
together to make a bigger picture?  Now those are good questions!



Redirecting Thought Processes

According to the constructivist model of learning/teaching, we must start with
what the student already understands.  Sounds reasonable.  The problem is, how do you
find out where the student is conceptually?  Can we assume that every (or any particular)
student has mastered everything in the “Scope and Sequence” of the curriculum for each
earlier grade?  Dream on!  It gets even worse, it goes back to learning the language.

 Human language is inherently ambiguous.  The meaning of a simple statement is
quite obvious within the context of thought in the mind of the speaker.  Within the
context of thought in the mind of the hearer, the statement may have an equally obvious,
but very different meaning.  Many of the most commonly used words we learned as
preschoolers, by induction from thousands of example uses.  Since everyone knows what
the words mean, no one ever bothered to give us a definition.  Now we need to establish
a common context so that meanings of speaker and listener will coincide.

Example #1  Up and Down

Teacher: What direction is down ?
Student: That way!
T: You are talking on the telephone to a person who is just learning English.  You need to
tell them what you are pointing at.
S: The floor.
Down is toward the floor under YOUR feet?
So, people downstairs would point toward this floor when they point down.
Then, what do you always point at when you point down?
 At the ground.
By, “The ground”, do you  mean, “the surface of Earth”?  So that “down” is always
toward the surface of Earth?
Therefore, when I was in Mammoth Cave, and I pointed down toward the surface of
Earth. (Finger pointed toward ceiling.)
Then what is it that you always point toward when you point “down”.
 We point at the middle of Earth any time we point down.
Does everyone agree now that down is always toward the center of Earth?
Good .  Now , notice on our model of Earth (globe), here in Artesia you would point
down in this direction, 12 hours later pointing down is in nearly the opposite direction
because you have rotated half way around the center of  Earth.  Notice also, a student on
this island in the Indian Ocean pointing down is pointing in exactly the opposite direction
you are, because when you both point toward the center of Earth, you are pointing
directly at each other.
Does this make sense to every one?  That "down" means toward the center of Earth?  That’s nice. 
But, I have another question.

When astronauts were standing on the surface of Moon, one dropped a hammer, which
direction did it fall?
  Up ?
No, not up.
Yes, but down toward the center of...?
 Toward the center of Moon.
Right, it fell down toward the center of Moon.  They had to look up to see Earth!
Now for the next question.  When the Viking spacecraft landed on Mars, it scooped up
soil and dumped it into a hopper.  Which direction did the soil fall?
Down toward the center of...?
 Toward the center of Mars.
Very good.  Now maybe we can give a complete definition of the direction “down”.
Down is always toward the center of whatever large planet-like object you are on.  Down is the
direction any unsupported object will fall.  Is that agreeable to all?
How about when one is not on any planet, satellite, or asteroid.  For example, in the
space shuttle in orbit.  What direction will a dropped object fall?
 It won’t  fall.  It will just stay where it was dropped.
Which shows that in interplanetary space there is no “ up ” or “ down ”.

Example #2  Seasons

Teacher: Why is our weather in Artesia, CA usually warmer during July than it is in
Student: Because it’s summer.
Do you mean that if we decided to call July “winter” it would be cooler?
S: (not always the same student) No.
Then why is the part of the year we call “summer” usually warmer than the part we call
“winter”?  Why isn’t the weather the same all year round?
Because we are closer to Sun in the summer.
Look at what we just read in the book.  We are about 5,000,000 km closer to Sun in
January than we are in July.  So, if you are right, then we should have our hottest weather
in January.
(usually a different student) It’s hot in the summer because Earth is tilted.
What do you mean by the word, ”tilted”?
Not straight up and down.
Isn’t Earth round, like this ball?
Is this ball tilted now?
(Rolling it a bit) Is it tilted now?
I don’t understand how anything this shape could be tilted.  So what do you mean by,
“Earth is tilted”?
Earth’s axis is tilted.
We said that tilted means, ”Not straight up and down .”  So, If I go to the South Pole,
where the axis meets the surface of Earth, the axis will not come straight up out of the
ground, but will go off at some sort of a slant to the surface?
Well, no.
Does the axis go through the center of Earth?
We agreed that down is toward the center of Earth.  From the South pole, the axis goes to
the center of Earth, straight down, and from there it goes straight up!  So how can Earth’s
axis be tilted?
But that’s what it said in the book!
Yes, that is what it said in the book.  And the authors forgot to explain what they meant
by “tilted”.

Let’s take a look at our model of Earth (globe).  It is mounted so that its axis is not
straight up and down.  There is a reason for this.  Just as by convention (That means we
all decided to almost always do things this way instead of another equally good way, just
so it would be easier to communicate with each other.) we usually put the direction north
toward the top of a map, so with a globe we assume that a horizontal plane (level with
the floor) through the center of the globe represents the plane of Earth’s orbit around
Sun.  Of course we could put the plane of Earth’s orbit in any other direction we like, as
is done on many wall charts.  The slant in the axis of our model indicates that Earth’s
axis is not at a right angle to the plane of its orbit around Sun.

So that is what is meant by, “Earth’s axis is tilted”, but what does that have to do with
our weather?
Sometimes Earth’s axis is tilted toward Sun, and sometimes it’s tilted away from
Wait a minute, Earth’s axis is a straight line, right?  If  one end is pointing away, then the
other end must be pointing toward.  How can you say it is toward, or away?
The north end tilts toward Sun in summer, then the north end tilts away from Sun
in the winter.
Do you mean that the Earth’s axis flips back and forth, changing the direction it points?
Sorry, that won’t work.  Until you want the precision needed for interplanetary travel, the
north pole of Earth’s axis always points in the same direction - in our life times that is a
point very close to the direction of the star Polaris.

Now that most students have somewhat unlearned what they memorized in previous
years, a complete explanation, using models will generate some comprehension .

Causes Of Seasons:

During the northern hemisphere’s spring-summer, Earth is on the
other side of Sun from Polaris.  Since Earth’s north pole
points toward Polaris, the north pole is on the lighted half of
Earth 24 hours a day.  Every place on Earth north of its
equator will spend more than half (12+ hours) of each day on
the lighted half of Earth.  The more hours on the lighted half,
the more light absorbed per square meter of surface per day,
the more heat per square meter per day, the higher the
temperature.  Of course, at the same time the south pole of
Earth must be on the dark side of Earth 24 hours a day.  Every
place on Earth south of its equator will spend less than half
(12- hours) on the lighted half of Earth.  The fewer hours on
the lighted half, the less light absorbed per square meter per
day, the less heat per square meter per day, the lower the

During the northern hemisphere’s fall-winter, Earth is on the
same side of Sun as Polaris.  Since Earth’s north pole points
toward Polaris, the north pole is on the dark half of Earth 24
hours a day.  Every place on Earth north of its equator will
spend more than half (12+ hours) of each day on the dark half
of Earth.  The more hours on the dark half, the less light
absorbed per square meter of surface per day, the less heat per
square meter per day, the lower the temperature.  Of course, at
the same time the south pole of Earth must be on the light side
of Earth 24 hours a day.  Every place on Earth south of its
equator will spend less than half (12- hours) on the dark half
of Earth.  The fewer hours on the dark half, the more light
absorbed per square meter per day, the more heat per square
meter per day, the higher the temperature.

The temperature of the surface depends not only on the number
of hours of light each day, but also on the concentration
(brightness) of the light.  Light is most concentrated on a
surface which is at right angles to the direction the light is
traveling.  On level ground, that means the light is coming
straight down, Sun is directly overhead. (Hence the unfortunate
use of “direct and indirect rays ”.)

In the tropics where Sun is 90 degrees above the horizon at
noon, the level surface may receive 1,000 watts of light per
square meter.  Four hours earlier, and again four hours later,
the same level surface will receive only 600 watts of light per
square meter.  And of course, as sunset approaches, the
brightness of the light will approach 0 watts of light per
square meter.  And that’s without allowing for increased
scattering of the light due to traveling a much longer distance
through air and haze.  Similarly, at 60 degrees of latitude
north, or south of the sub solar point at noon, the brightness
will be reduced from 1,000 to 600 watts of light per square
meter, because the light is now spread over 1.7 square meters
of level surface instead of just 1 square meter.

The plane of Earth’s axis makes an angle of 23.5 degrees
from the perpendicular to the plane of Earth’s orbit around
Sun.  Therefore, in the northern hemisphere, at noon on the
summer solstice Sun will be 47 degrees higher above the horizon
than it will at noon on the winter solstice.  So, not only does
each square meter of surface get fewer hours of light each day
in winter, but the light is less concentrated (dimmer) as well.
Less light energy per square meter per day, less heat energy
per square meter per day, lower temperature.  Keeping in mind
that the dates are reversed in the southern hemisphere.  Or, to
quote Donald Duck, “Chile isn’t chilly in the winter, when
we’re chilly.  No it’s not.  Chile is only chilly in the
summer, when we’re hot.”

Example #3  Frames of reference

The class just read the section starting, “There is no truly stationary object in the
Teacher: John, that book on the table in front of you, is it moving?
Student: (with confused expression because of “obvious answer”) No.
T: John, what about Earth, is Earth moving?
S: Yes. (everybody knows that Earth moves)
T: If the Earth is moving and the book is not moving, then the distance between them
must be changing.  True?
Why not?
 Because it is not moving!
Which “it” is not moving? Earth?
 No, the book is not moving.
Is the book near Earth?
When a car is moving and you are not moving, does the distance between you and the car
remain the same?
If  Earth is moving and the book is not moving, shouldn’t the distance between them
(At this point a student once said, ”Yes, Earth is moving around Sun, and rotating on its
axis, but not the earth we live on!  Few students are so clear about the way they
understand things.)
 Oh, you mean that the book is moving along with Earth.
Yes.  Remember that the book said that we measure the motion of any object by
comparing its movement with the movement of another object.  Most often we compare
the motion of objects to the surface of Earth.  Since the floor, the table, and the book, are
all moving at the same speed and in the same direction as the surface of Earth, we say,
“They are standing still.”  Even though we know that compared to the center of Earth, we
are all going about 1300 km/hr toward the east.

Try this.  You are flying along at 800 km/hr in a large aircraft.  After your third trip to the
little room in the tail, your mother says to you, “Sit down, and be still.”  Does she mean
for you to stop moving at 800 km/hr relative to the surface of Earth?
She means for you to stop moving relative to ...?
 The airplane.
Correct.  Remember, when an object is moving the same direction and same speed as the
object we use for comparison, we say that it is not moving.  But, at the same time,
compared to a different object it is be moving.

Example #4 Failing to recognizing relationships

A mother brought  her daughter to me one day, "My daughter knows all the questions on the Q&A sheet!  She has studied  it with me at home and I know that she really knows it!  But she has retaken the meteorology test three times and not passed. Why?"

"Well, let's see if we can figure it out.  Here is the test (20 item multiple choice, different form than before).  Let her take now and  see how she does."

Putting it on the key and finding fewer than the required 15 correct, and that her first incorrect response was an item from Q&A question 5, I questioned the student.
"In what way does air pressure change going upward through the atmosphere?" (Exact wording of Q 5.)

"Air pressure is caused by the weight of air above pressing down on the air underneath.  Therefore, going up in the atmosphere there is less air above pressing down.  The higher the altitude, the lower the air pressure." (Exact wording of A 5.)

"Very good. Now suppose you were in an airplane flying upward.  How would the air pressure around you change?"

Hesitantly, "I suppose it would get less."

"True.  But on the test it asked, 'If an airplane is flying downward through the atmosphere, the air pressure around it will become ....'"

"But Mr. Fuller, you never told us about how air pressure changes when going down!"

It never entered her head that going down is the opposite of going up, and becoming greater is the opposite of becoming less.
Her mother assumed that being able to repeat the explanation verbatum she must understand what it means.

Example #5 Inability to particularize a generalization

On the Q&A sheet it says, "Eroded rock material
, such as sand, silt, and gravel, carried by a river is called sediment."
On the test it says, "The Colorado River washes many tons of sand, gravel and silt along in its water.  This material is called ...."

"Mr. Fuller, you never told us anything about the Colorado River!"
A river in general has no connection with any specific river.

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