“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
does not just happen, it requires work of both the teacher and
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.
“Teacher, you said that if we go outside tonight and look over that
way, we can see the planet Venus.”
“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.
Yet, much of our educational system seems too nearly to fit the
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!
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.
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
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 .
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.”
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 ...?
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.