Tell a person that they can think,
and they will love you.
Make a person think,
and they will hate you.
-Source unknown
What makes a good
analytical thinker?
Analytical thinkers not only make
good scientists and engineers; analytical
thinking makes people good responsible
citizens, good workers, and, most
important for you, good students.
This presentation was prepared by Dr. Ed. Vavra,
developer of the KISS Approach to teaching grammar.
Blueprint for Educational Change
In 1993, Dr. Arthur Whimbey, Dr. Mary
H. Johnson, Dr. Eugene Williams, Sr., and
Dr. Myra J. Linden published a book titled
Blueprint for Educational Change
(The Right Combination, Inc.)
This book should be much better
known than it is!
Blueprint for Educational Change
A major objective of the authors was to
determine the differences between
“strong” and “weak” analytical thinkers.
They arrived at two major differences.
Blueprint for Educational Change
1. Strong thinkers are very concerned
with details; weak thinkers are not.
2. Strong thinkers break any problem
down into steps—they learn to use an
analytical process; weak thinkers give
one-shot answers, as if either one knows
the answer or one does not.
The Nature of Analytical Ability
•
In Chapter Two of the book, they give a
number of questions from a 38-question
test—the Whimbey Analytical Skills Index.
The test was given to 500 students
entering community colleges in New
Jersey. This presentation is based on four
of those questions and the results from the
500 students.
About this Presentation
The authors make extremely
perceptive (and very helpful) observations
about how students answered the
questions.
About this Presentation
Because those observations are so
important, and so clearly explained, the
text in most of the following is quoted from
pages 6 through 15 of the book. (My
comments will be in light blue.)
Question 1
Which letter is as far away from K
in the alphabet as J is from G?
a. K
b. M
c. N
d. G
e. I
About Question # 1
Question 1 is fairly easy. However, to
answer it correctly, a person must carefully
read it and perform several mental operations.
Quoted from page 6.
About Question # 1
Research shows that good analytical
thinkers often read the question in parts,
talking to themselves and rephrasing ideas
in their own words to help grasp the ideas
completely. They may read the entire
problem through to get an overall picture,
and then reread it in sections—something
like this:
Quoted from page 6.
About Question # 1
“Which letter is as far away from K—I have
to find a letter that is some distance from
K—in the alphabet as J is from G. OK, I
need to get the distance from J to G.
Then, if I count that same distance off from
K, I should have the answer.”
Quoted from page 6.
About Question # 1
The best answer from among the alternatives
offered is N (alternative c). . . .
Seventy-seven percent of the students
answered this question correctly. But 23% did
not. Apparently the latter students had not
learned how to accurately read through a
problem such as this and then go through the
necessary steps to reach the correct answer.
Quoted from pages 6 and 8
About Question # 1
Incidentally, research on reasoning has
revealed many myths about mental skills. For
example, did you count on your fingers in
solving this problem?
Quoted from page 8
About Question # 1
After conducting workshops on reasoning, we
have been told by teachers that they counted
on their fingers but did it clandestinely under
books or desks. Several even admitted they
counted with their hands in their pockets to
avoid embarrassment--to conceal this hidden
activity.
Quoted from page 8
About Question # 1
The reason for their secrecy is that there is a
common myth that counting on one's fingers is
a childish activity, reflecting lower mental
ability when done by an adult.
Quoted from page 8
About Question # 1
However, when a group of mathematics and
science teachers was asked to solve this problem, a
number of them also counted on their fingers. Some
even wrote out a portion of the alphabet to count off
the letters in reaching their answer.
Quoted from page 8
About Question # 1
Rather than being a sign of immaturity, such
activities reflect a strong concern for accuracy in
processing information. Research shows that a major
difference between strong and weak analytical
thinkers is that strong thinkers have a much greater
concern for accuracy, and they tend to engage in more
activities to insure accuracy in solving problems.
Quoted from page 8
About Question # 1
This will be discussed again with later
problems. For now, suffice it to say that
peripheral activities like finger counting are
good not bad practices in problem solving.
They are part of actively and accurately
processing information.
Quoted from page 8
About Question # 1
Finally, although answer N (alternative c) is the
correct choice, some good thinkers initially conclude
that the letter H should be the answer. The problem
asks you to find a letter which is “as far away from K
. . . as J is from G.” H is the same distance from K as
J is from G.
Quoted from page 8
About Question # 1
When good thinkers notice this, they reread
the problem and see it does not specify
direction—only distance. They then try
counting off the distance from K in the other
direction, and arrive at N.
Quoted from page 9
About Question # 1
What’s interesting about this solution is that it
represents in miniature the way analytical
thinkers often deal with real-life problems. If,
after obtaining some information about a
problem, they find they cannot arrive at a
solution, they go back to the problem and
examine it again to look for more information
or a different perspective.
Quoted from page 9
About Question # 1
In fact, this also replicates in miniature what is
called the scientific method, in which an
investigator makes some observations,
formulates an hypothesis, makes some more
observations to see if the hypothesis is correct,
and changes the hypothesis as required by
additional new data.
Quoted from page 9
About Question # 1
This illustrates why scientists tend to score
well on tests of analytical ability. Such tests
measure the cognitive habit needed to
pursue science.
Quoted from page 9, my emphasis
A Comment about Question # 1
Making notes and counting on one’s
fingers are to math what detailed
brainstorming is to writing. A good paper is
written from the bottom (details) up. As
Ben Franklin said, “An empty sack cannot
stand upright.”
(EV)
A Comment about Question # 1
The examples (details) arrived at through
brainstorming give a writer interesting and
meaningful things to say. But weak writers
refuse to brainstorm. It is not that they
can’t. Most often, they just do not want to
take the required time.
(EV)
Question # 2
There are 3 separate, equal-size boxes,
and inside each box there are 2
separate small boxes, and inside each
of the small boxes there are 4 even
smaller boxes. How many boxes are
there altogether?
a. 24
b. 13
c. 21
e. some other number
d. 33
About Question # 2
Question 2 can be solved most readily by
making a diagram such as in Figure 2, showing
that the answer is 33.
Quoted from page 9
About Question # 2
This question also reveals a common myth
about reasoning. When a group of math and
science teachers tried solving it, several asked
apologetically whether they were permitted to
make a diagram. They explained that they
could “see” problems like this better if they
first drew a picture.
Quoted from page 9
About Question # 2
The fact that these experienced math and
science teachers meekly asked whether they
could make a diagram reflects the common
misbelief that good thinkers can solve all
problems mentally, that only poor thinkers
must resort to scratch paper and diagrams.
Often quite the opposite is true.
Quoted from page 9
About Question # 2
Many mathematicians think with a pencil
in their hand to make diagrams and
computations. It improves their understanding
of problems and their accuracy.
Quoted from page 10
About Question # 2
In contrast to this, high school physics teachers
have reported that they often cannot get weak
students to make diagrams in solving
problems, even when diagrams are useful or
necessary.
Quoted from page 10
About Question # 2
Weak students tend to be one-shot
thinkers. They habitually skim through a
question and then jump to an answer. They
have not learned to work step-by-step through
a problem, spelling out all the details and
making diagrams as needed, until they
understand the information fully in coming to
an answer.
Quoted from page 10, my emphasis
About Question # 2
The common myth that good thinkers are
purely cerebral, that they can do everything
mentally and do not require diagrams,
reinforces the poor thinking habits of
analytically weak students.
Quoted from page 10
About Question # 2
In the New Jersey Task Force study, only 37%
of the students answered this question
correctly. The most common incorrect answer
given by weak students is 24. They just take
the three numbers in the problem (3, 2, 4) and
multiply, without first spelling out the
information in a mental picture or a diagram to
see whether this multiplication is appropriate.
Quoted from page 10
A Comment about Question # 2
Note that diagrams are to math
problems what outlines are to writing.
Weak writers regularly tell me that they
don’t like to make outlines. It is not that
they can’t; they just do not want to. (Is this
because making an outline requires
thinking about what one is going to say?)
--EV
Question # 3
Ten full crates of walnuts weigh 410 lb,
while an empty crate weighs 10 lb. How
much do the walnuts alone weigh?
a. 400 lb
d. 320 lb
b. 390 lb
e. 420 lb
c. 310 lb
About Question # 3
Question 3 is fairly easy, but it must be
read and thought through carefully in order to
carry out appropriate arithmetic operations.
Quoted from page 10
[54% of the students had the correct answer. – EV]
About Question # 3
Although the correct answer is 310, the most
common incorrect answer is 400.This answer
is easy to rationalize: The person has
subtracted the weight of only one crate instead
of 10.
Quoted from page 10
About Question # 3
Still, it is symptomatic of the cognitive
style underlying low analytical ability. Weak
analytical reasoners tend to skim through a
problem and quickly jump to an answer,
frequently with the attitude that you either
know the answer to a problem, or you might as
well give up and guess.
Quoted from pages 10 and 11
About Question # 3
Some weak students answer 420 for Question 3.
This answer is more difficult to rationalize, since it
says that the walnuts alone weigh more that the crates
and walnuts combined. Students who give this answer
are the type who sometimes tell math teachers they
can do math but just can’t solve word problems. What
they mean is they can do simple arithmetic but cannot
analyze a problem to see what arithmetic operations
are needed.
Quoted from page 11
About Question # 3
I’ll interject here to note that the question includes a
subordinate clause—“while an empty crate weighs 10 lb.”
In Trevor J. Gambell’s “What High School Teachers Have
to Say about Student Writing and Language across the
Curriculum” (English Journal, September 1984), he states,
“Teachers ... found problems with texts which employed
multiple choice questions with subordinate clauses.
Students had difficulty determining the main idea of the
sentence and thus the question; the subordinate clause led
to ambiguity and confusion.” ( 43) Rather than suggesting
that students should be taught how to understand
subordinate clauses, he concluded, “This problem also
warns us that multiple choice questions need to be worded
as simple sentences so that content is being tested rather
than language.” And this was in English Journal, the main
publication for high school English teachers!? (EV)
About Question # 3
To solve this problem, one must read it carefully
and fully conceptualize the information, namely that
the total 410 pounds is made up of two parts,
walnuts and crates, and that the crate weight has 10
components, as shown in Figure 3.
Quoted from page 11
About Question # 3
Computationally, there is more than one
way to solve this problem. One can figure that
since there are 10 crates, and each crate weighs
10 pounds, the total crate weight is 100
pounds. This is then subtracted from the total
poundage to get the weight of the walnuts.
410
-100
310
Quoted from page 12
About Question # 3
Another way to solve the problem is to
figure that if 10 full crates weigh 410 pounds,
then one full crate weighs 41 pounds. Since the
crate itself weighs 10 pounds, the walnuts
inside one crate weigh 31 pounds. Therefore
the walnuts inside 10 crates weigh:
31
x10
310
Quoted from page 12
About Question # 3
While these two solutions are
computationally different, they are both based
on an accurate mental representation of the
information in the problem. Low-ability
students must learn to construct such accurate
mental representations.
Quoted from page 12
Question # 4
Cross out the letter after the letter
in the word “pardon” which is in the
same position in the word as it is in
the alphabet.
About Question # 4
Question 4 looks a bit like IRS tax
instructions. But it also looks like the
complicated sentences found in law books and
textbooks in chemistry, physics, economics
and other scholarly fields.
Quoted from page 12
About Question # 4
For example, here is a sentence from a text on
language usage.
When a compound modifier begins with a word
ending in -ly or follows the word it modifies, there
is no need for a hyphen.
Quoted from page 12
About Question # 4
If you are not already familiar with this rule, if
you have to read the sentence carefully to see
exactly what it means, you find yourself going
through the same type of step-by-step mental
gymnastics that you use in answering
Question 4.
Quoted from page 12
About Question # 4
In other words, Question 4 does not involve
just some trivial test gamesmanship. It taps the
same mental ability needed to comprehend
complicated material encountered in all
advanced academic subjects.
Quoted from pages 12 and 13
About Question # 4
An analytically strong student was asked to
think aloud as he solved Question 4, to see the
mental steps he used. Here is his response:
Quoted from page 13
About Question # 4
Cross out the letter after the letter in the word
“pardon.” That’s confusing; I’ll read it again.
Cross out the letter after the letter in the word
“pardon.” I guess I have to cross out some letter
in “pardon,” but I’m still a little confused. I’ll read
the rest of the problem and see if that helps.
Quoted from page 13
About Question # 4
...which is in the same position in the word
as in the alphabet.
I guess the word being referred to is
“pardon.”
Quoted from page 13
About Question # 4
It says, “same position in the word.” What
do I mean by “same position in the word”?
Quoted from page 13
[Note how “What do I mean” shows the student taking
meaningful possession of the question. Weak students
rarely do this; instead they just give up. (EV)]
About Question # 4
Well what does “position in the word”
mean? Let me look at the word “pardon.” I
guess “p” is in the first position in “pardon”;
“a” is in the second position; “r” is in the
third position.
Quoted from page 13
About Question # 4
In the alphabet, “a” is in the first position,
“b” in the second, “c” in the third.
I need to find a letter which is in the same
position in “pardon” as in the alphabet.
Quoted from page 13
About Question # 4
Looking at the word “pardon,” “p” is in the first
position in “pardon,” but “p” is not in the first
position of the alphabet; “a” is in the second
position in “pardon,” but it isn't in the second
position of the alphabet; “r” is in the third position
in “pardon,” but not in the alphabet; “d” is in the
fourth position in “pardon.” It is also in the fourth
position of the alphabet.
Quoted from pages 13 and 14
About Question # 4
So I have pinned down the letter “d.” But
there was something at the beginning of
the problem that confused me. Let me
reread the beginning.
Quoted from pages 13 and 14
About Question # 4
Cross out the letter after the letter in
“pardon.”
So I have to cross out the letter after the
“d” in “pardon.” That is the “o.” I’ll cross out
the “o.”
Quoted from page 14
About Question # 4
This solution is particularly interesting
because when nonanalytical students miss
Question 4 and are asked to explain their
difficulty, they often say they did not know
what “same position in the word as in the
alphabet” meant. The analytical student above
did not initially understand this phrase either.
Quoted from page 14
About Question # 4
But having an analytical habit of mind, he
broke it down by first figuring out what was
meant by “position in the word.” Once he
understood that, he was able to figure out what
was meant by “same position in the word as in
the alphabet.”
Quoted from page 14
About Question # 4
This highlights a major difference between
strong and weak analytical thinkers. Strong
analytical thinkers engage in more of the
minute mental activities that lead to
comprehension. They have learned how to
construct meaning for themselves.
Quoted from page 14
About Question # 4
Weak analytical thinkers tend to be less active
in pinpointing precise meaning. They have not
learned how to break down complex parcels of
information into manageable parts by starting
with something they can understand and
building from there.
Quoted from page 14
About Question # 4
Strong thinkers are more active in this regard.
They have a greater tendency to talk to
themselves at length while solving a problem –
asking themselves questions, answering the
questions, and rephrasing ideas into their own
words.
Quoted from page 14
About Question # 4
They work step-by-step, stopping to figure
things out and pin down exactly what
everything means. In short, they do more
analytical processing.
Quoted from pages 14 and 15
About Question # 4
People critical of tests point out that Question
4 can be rewritten so it is easier to
comprehend. This is true. Here is a simpler
version:
Cross out the “o” in “pardon.”
Quoted from page 15
About Question # 4
However, psychometricians include questions
like 4 on tests because such questions
distinguish analytical from nonanalytical
students. While Question 4 can be written
more simply, advanced chemistry, physics and
mathematics textbooks cannot be rewritten in a
way that makes them accessible to
nonanalytical students.
Quoted from page 15
About Question # 4
A great deal of research has been invested in
trying to make textbooks more readable.
Vocabulary and sentence structure can
sometimes be simplified. But there is a limit to
how simple physics and chemistry textbooks
can be made. Their difficulty lies in the
complexity of the ideas, not in the structure of
the language.
Quoted from page 15
About Question # 4
Question 4 has been written in an intentionally
complex manner so that it taps the same
analytical skill required to comprehend
advanced academic material.
Quoted from page 15
About Question # 4
In the study of these questions by the New Jersey
Task Force on Thinking, Question 4 proved to be the
most difficult: Only 33% of the students answered it
correctly. What is remarkable is that Question 4 does
not require any creative insights or cognitive leaps. It
only requires that a student work step-by-step through
the problem to pin down exactly what it says.
Apparently, this is a mental skill which many high
school students have not mastered.
Quoted from page 15
Quiz
On a piece of paper with your name
on it, answer the following question:
What are the two major differences
between “strong” and “weak”
analytical thinkers?
Conclusion
The two major differences between
“strong” and “weak” students are that:
1. “Strong” students break problems down
into smaller ones and work their way
through them, step-by-step. “Weak”
students take the attitude that either one
knows the answer or one does not.
(EV)
Conclusion
2. “Strong” students are concerned with
details. They make diagrams and notes
when appropriate to help them understand
the questions. “Weak” students won’t take
the time to do that.
(EV)
Conclusion
Note that both of these differences are
matters of habit, attitude, and willingness
to put in time and work. If you are currently
a “weak” student, you can train yourself to
be stronger.
(EV)
Just for Fun
 A genius is someone who is screwed up in a useful way.
 A grownup is someone who suffers from responsibility.
 Good Health is merely the slowest possible rate at which
one can die.
 I chose the path less traveled, but only because I was
lost.
 Work when you should and play all the time.
 Not he, who has much, is rich . . . but he, who gives
much.
 One must wait until evening to see how splendid the day
has been.
A Note about Art Whimbey
I corresponded with Art Whimbey for several years. He
generously gave me permission to make an electronic, interactive
version of his Analyze, Organize, Write, an excellent book for
students. (Unfortunately, the program doesn’t run on newer
computers.)
Dr. Whimbey sent me a copy of Blueprint, and to this day I still
think that it is the most insightful book on what needs to be done to
improve education.
I also owe him a debt. In the course of our correspondence, he
asked to see a manuscript that I had written about KISS grammar.
The manuscript had lain in a drawer for fifteen years, but Dr.
Whimbey’s enthusiasm about what I had written encouraged me to
renew my efforts to develop the KISS Approach. For that, I sincerely
thank him.
Dr. Ed Vavra (July 11, 2011)
A Note about KISS Grammar
Most grammar textbooks teach students what subjects and
verbs are, but they do not even try to teach students how to identify
the subjects and verbs in their own writing.
Fourth grade teachers have told me that they are supposed to
teach their students “clauses,” but many students can’t understand
them. The reason they cannot understand clauses is that a clause is
a subject/verb pattern (and all the words that go with it). If the
students cannot identify subjects and verbs in their own writing, they
will have major problems with clauses.
This is only one of the numerous problems in the teaching of
grammar that the sequential KISS Grammar Approach directly
addresses. For more information about KISS, go to the KISS
Grammar site at http://home.pct.edu/~evavra/KISS.htm, or search
the web for “KISS Grammar.”
Dr. Ed Vavra (July 11, 2011)