11
AN INTRODUCTION TO
CRITICAL THINKINGby Steven D. Schafersman January, 1991
Critical thinking is an important and vital topic in modern
education. All educators are interested in teaching critical thinking to their
students. Many academic departments hope that its professors and instructors
will become informed about the strategy of teaching critical thinking skills,
identify areas in one's courses as the proper place to emphasize and teach
critical thinking, and develop and use some problems in exams that test
students' critical thinking skills. This critical thinking manual has been
prepared to inform and aid you to accomplish these things, and it has been kept
brief and straightforward so that all faculty members will have the time and
opportunity to read it and follow the suggestions it contains.
Purpose and Rationale
of Teaching Critical Thinking
The purpose of specifically teaching critical thinking in
the sciences or any other discipline is to improve the thinking skills of
students and thus better prepare them to succeed in the world. But, you may ask,
don't we automatically teach critical thinking when we teach our subjects,
especially mathematics and science, the two disciplines which supposedly
epitomize correct and logical thinking? The answer, sadly, is often no. Please
consider these two quotations:
"It is strange that we expect students to learn, yet
seldom teach them anything about learning." Donald Norman, 1980, "Cognitive
engineering and education," in Problem Solving and Education: Issues in
Teaching and Research, edited by D.T. Tuna and F. Reif, Erlbaum
Publishers.
"We should be teaching students how to think. Instead, we
are teaching them what to think." Clement and Lochhead, 1980,
Cognitive Process Instruction.
Perhaps you can now see the problem. All education consists
of transmitting to students two different things: (1) the subject matter or
discipline content of the course ("what to think"), and (2) the correct way to
understand and evaluate this subject matter ("how to think"). We do an excellent
job of transmitting the content of our respective academic disciplines, but we
often fail to teach students how to think effectively about this subject matter,
that is, how to properly understand and evaluate it. This second ability is
termed critical thinking. All educational disciplines have reported the
difficulty of imparting critical thinking skills. In 1983, in its landmark
report A Nation at Risk, the National Commission on Excellence in
Education warned:
"Many 17-year-olds do not possess the 'higher-order'
intellectual skills we should expect of them. Nearly 40 percent cannot draw
inferences from written material; only one-fifth can write a persuasive essay;
and only one-third can solve a mathematics problem requiring several steps."
While we as professors have the ability ourselves to think
critically (we had to learn these skills to earn advanced degrees in our
disciplines), many students--including our own--never develop critical thinking
skills. Why? There are a number of reasons. The first goal of education, "what
to think," is so traditionally obvious that instructors and students may focus
all their energies and efforts on the task of transmitting and acquiring basic
knowledge. Indeed, many students find that this goal alone is so overwhelming
that they have time for little else. On the other hand, the second goal of
education, "how to think" or critical thinking, is often so subtle that
instructors fail to recognize it and students fail to realize its absence.
So much has become known about the natural world that the
information content of science has become enormous. This is so well known that
science educators and science textbook writers came to believe that they must
seek to transmit as much factual information as possible in the time available.
Textbooks grew larger and curricula became more concentrated; students were
expected to memorize and learn increasingly more material. Acquisition of
scientific facts and information took precedence over learning scientific
methods and concepts. Inevitably, the essential accompanying task of
transmitting the methods of correct investigation, understanding, and evaluation
of all this scientific data (that is, critical thinking) was lost by the
roadside. This situation became especially severe in primary and secondary
education, and over the last decades there has been a well-known decline in the
math and science ability of students in our country compared to other
industrialized countries. Studies have shown that our students abilities in math
and science begin on level with students in other countries, but then
progressively decrease as they make their way through our educational system. By
the end of high school, United States students rank among the lowest in the
industrialized world in math and science achievement. We in introductory college
science education inherit these students and have to deal with their
deficiencies in scientific and critical thinking.
In retrospect, it seems obvious that when the information
content of a discipline increases, it becomes even more vital to spend time, not
learning more information, but learning methods to acquire, understand, and
evaluate this information and the great amount of new information that is not
known now but will surely follow. Frankly, it is counterproductive to simply
memorize and learn more new and isolated facts when future facts may eventually
displace these. Thus, our science education policy has been completely backward,
teaching more science facts and less scientific method rather than the converse.
The errors of primary and secondary education in math, science, and other
disciplines during the last forty years are now well known and are currently
being addressed. The latest science books, for example, emphasize critical
thinking and the scientific method. They focus on teaching students the proper
ways to obtain new reliable knowledge for one's self, not on engendering factual
overload. Curriculum reforms in science, such as Project 2061 of the AAAS and
Scope, Sequence and Coordination of the NSTA, are also being instituted. It will
be another generation before these textbook and curriculum reforms will have
achieved results, if ever, and until then we must be aware of students' lack of
critical thinking skills and of our need to enhance them. (It is accepted, one
assumes, that students entering college should already have mastered all basic
critical thinking skills; that is, they should have learned these skills during
their primary and secondary education and thus be able to bring them with them
into the college math and science classroom. The fact that this manual has been
prepared is an indication that students have not learned these skills. We may be
the last opportunity such students have to appreciate and learn critical
thinking.)
A final rationale for critical thinking is explained by
William T. Daly (1990) in a short article, "Developing Critical Thinking
Skills." He says that
"the critical thinking movement in the U.S. has been
bolstered and sustained by the business community's need to compete in a
global economy. The general skill levels needed in the work force are going up
while the skill levels of potential employees are going down. As a result,
this particular educational reform movement . . . will remain crucial to the
education of the work force and the economy's performance in the global arena.
This economic pressure to teach critical thinking skills will fall on
educational institutions because these skills, for the most part, are rarely
taught or reinforced outside formal educational institutions. Unfortunately,
at the moment, they are also rarely taught inside educational institutions."
Definition of
Critical Thinking
Critical thinking means correct thinking in the pursuit of
relevant and reliable knowledge about the world. Another way to describe it is
reasonable, reflective, responsible, and skillful thinking that is focused on
deciding what to believe or do. A person who thinks critically can ask
appropriate questions, gather relevant information, efficiently and creatively
sort through this information, reason logically from this information, and come
to reliable and trustworthy conclusions about the world that enable one to live
and act successfully in it. Critical thinking is not being able to process
information well enough to know to stop for red lights or whether you received
the correct change at the supermarket. Such low-order thinking, critical and
useful though it may be, is sufficient only for personal survival; most
individuals master this. True critical thinking is higher-order thinking,
enabling a person to, for example, responsibly judge between political
candidates, serve on a murder trial jury, evaluate society's need for nuclear
power plants, and assess the consequences of global warming. Critical thinking
enables an individual to be a responsible citizen who contributes to society,
and not be merely a consumer of society's distractions.
Children are not born with the power to think critically,
nor do they develop this ability naturally beyond survival-level thinking.
Critical thinking is a learned ability that must be taught. Most individuals
never learn it. Critical thinking cannot be taught reliably to students by peers
or by most parents. Trained and knowledgable instructors are necessary to impart
the proper information and skills. Math and science instructors have precisely
this information and these skills. Why?
Critical thinking can be described as the scientific method
applied by ordinary people to the ordinary world. This is true because critical
thinking mimics the well-known method of scientific investigation: a question is
identified, an hypothesis formulated, relevant data sought and gathered, the
hypothesis is logically tested and evaluated, and reliable conclusions are drawn
from the result. All of the skills of scientific investigation are matched by
critical thinking, which is therefore nothing more than scientific method used
in everyday life rather than in specifically scientific disciplines or
endeavors. Critical thinking is scientific thinking. Many books and papers
describing critical thinking present it's goals and methods as identical or
similar to the goals and methods of science. A scientifically-literate person,
such as a math or science instructor, has learned to think critically to achieve
that level of scientific awareness. But any individual with an advanced degree
in any university discipline has almost certainly learned the techniques of
critical thinking.
Critical thinking is the ability to think for one's self
and reliably and responsibly make those decisions that affect one's life.
Critical thinking is also critical inquiry, so such critical thinkers
investigate problems, ask questions, pose new answers that challenge the status
quo, discover new information that can be used for good or ill, question
authorities and traditional beliefs, challenge received dogmas and doctrines,
and often end up possessing power in society greater than their numbers. It may
be that a workable society or culture can tolerate only a small number of
critical thinkers, that learning, internalizing, and practicing scientific and
critical thinking is discouraged. Most people are followers of authority: most
do not question, are not curious, and do not challenge authority figures who
claim special knowledge or insight. Most people, therefore, do not think for
themselves, but rely on others to think for them. Most people indulge in
wishful, hopeful, and emotional thinking, believing that what they believe is
true because they wish it, hope it, or feel it to be true. Most people,
therefore, do not think critically.
Critical thinking has many components. Life can be
described as a sequence of problems that each individual must solve for one's
self. Critical thinking skills are nothing more than problem solving skills that
result in reliable knowledge. Humans constantly process information. Critical
thinking is the practice of processing this information in the most skillful,
accurate, and rigorous manner possible, in such a way that it leads to the most
reliable, logical, and trustworthy conclusions, upon which one can make
responsible decisions about one's life, behavior, and actions with full
knowledge of assumptions and consequences of those decisions.
Raymond S. Nickerson (1987), an authority on critical
thinking, characterizes a good critical thinker in terms of knowledge,
abilities, attitudes, and habitual ways of behaving. Here are some of the
characteristics of such a thinker:
- uses evidence skillfully and impartially
- organizes thoughts and articulates them concisely and
coherently
- distinguishers between logically valid and invalid
inferences
- suspends judgment in the absence of sufficient evidence
to support a decision
- understands the difference between reasoning and
rationalizing
- attempts to anticipate the probable consequences of
alternative actions
- understands the idea of degrees of belief
- sees similarities and analogies that are not
superficially apparent
- can learn independently and has an abiding interest in
doing so
- applies problem-solving techniques in domains other than
those in which learned
- can structure informally represented problems in such a
way that formal techniques, such as mathematics, can be used to solve them
- can strip a verbal argument of irrelevancies and phrase
it in its essential terms
- habitually questions one's own views and attempts to
understand both the assumptions that are critical to those views and the
implications of the views
- is sensitive to the difference between the validity of a
belief and the intensity with which it is held
- is aware of the fact that one's understanding is always
limited, often much more so than would be apparent to one with a noninquiring
attitude
- recognizes the fallibility of one's own opinions, the
probability of bias in those opinions, and the danger of weighting evidence
according to personal preferences
This list is, of course, incomplete, but it serves to
indicate the type of thinking and approach to life that critical thinking is
supposed to be. Similar descriptions of critical thinking attributes are
available in the very extensive literature of critical thinking. See, for
example, Teaching Thinking Skills, 1987, edited by J. B. Baron and R. J.
Steinberg; Developing Minds: A Resource Book for Teaching Thinking, 1985,
edited by A. L. Costa; The Teaching of Thinking, 1985, edited by R. S.
Nickerson and others; Critical Thinking, Fifth Edition, 1998, by B. N.
Moore and Richard Parker, and Critical Thinking, Second edition, 1990, by
John Chaffe. These books are representative of the genre.
Relationship of
Critical Thinking to the Scientific Method
Because of the identification of critical thinking as
scientific thinking, it is reasonable to conclude that math and science courses
are a good place to learn critical thinking by learning the scientific method;
unfortunately, this is not always true. Good scientists who conduct science must
practice critical thinking, and good science teachers usually teach it, but few
ordinary individuals learn the scientific method, even those who successfully
take a number of science classes in high school and college. This is because, as
discussed above, science in the United States is often poorly taught as a
fact-based discipline rather than as a way of knowing or method of discovery. As
incredible as it may seem, studies reveal that 3% of the U.S. population is
scientifically literate, down from 5% about twenty years ago. Thus, it does not
appear that science alone will teach critical thinking to the masses. In fact,
critical thinking programs are almost always designed by social scientists and
directed toward improving thinking in the humanities and social studies, but the
same can be accomplished with math and science courses. Properly taught
university courses should teach a student critical thinking in addition to the
disciplinary content of the course.
It is useful to ask why the scientific method--now
recognized, in its guise of critical thinking, as so important to modern
education that hundreds of critical thinking programs exist in thousands of
schools across the nation--is so valuable for an individual to learn and
practice. The reason is because the scientific method is the most powerful
method ever invented by humans to obtain relevant and reliable knowledge about
nature. Indeed, it is the only method humans have of discovering reliable
knowledge (knowledge that has a high probability of being true). Another name
for this type of knowledge is justified true belief (belief that is probably
true because it has been obtained and justified by a reliable method). Nobel
Prize-winner Sir Peter Medawar claimed that, "In terms of fulfillment of
declared intentions, science is incomparably the most successful enterprise
human beings have ever engaged upon." Other methods of gaining knowledge--such
as those using revelation, authority, artistic and moral insight, philosophical
speculation, hopeful and wishful thinking, and other subjective and
authoritarian means--have historically resulted in irrelevant and unreliable
knowledge, and they are no better today. These nonscientific methods of
discovering knowledge, however, are more popular than scientific methods despite
their repeated failures in obtaining reliable knowledge. There are many reasons
for this, but two of the most important are that nonscientific methods are (1)
more congenial to emotional and hopeful human nature, and (2) are easier to
learn and practice than scientific methods. Despite these reasons, however, the
value and power of possessing reliable knowledge--as contrasted with the usual
unreliable, misleading, irrelevant, inaccurate, wishful, hopeful, intuitive, and
speculative knowledge most humans contend with--have caused modern government,
business, and education leaders to place the scientific endeavor in high regard,
and caused them to promote teaching the scientific method and its popular
manifestation: critical thinking.
Humans are conditioned from birth to follow authority
figures and not to question their pronouncements. Such conditioning is done by
parents and teachers using a wide variety of positive and negative reinforcement
techniques. Most individuals reach adulthood in this conditioned form. The
result of such conditioning is the antithesis of both scientific investigation
and critical thinking: individuals lack both curiosity and the skills to perform
independent inquiry to discover reliable knowledge. Individuals who think
critically can think for themselves: they can identify problems, gather relevant
information, analyze information in a proper way, and come to reliable
conclusions by themselves, without relying on others to do this for them. This
is also the goal of science education. Critical thinking allows one to face and
comprehend objective reality by gaining reliable knowledge about the world.
This, in turn, allows one to better earn a living, achieve success in life,
better solve life's problems, and be reconciled to existence, mortality, and the
universe. If a person is happier possessing reliable knowledge and living in
objective reality, rather than living in ignorance and possessing false or
unreliable beliefs, this is as good a reason as any for teaching and learning
critical thinking.
Formal Critical
Thinking Programs
There are two ways to teach critical thinking in the
classroom. The first method, and the one we will find endorsed in this manual,
is also the easiest, least time-consuming, and the least expensive. This method
is to simply modify one's teaching and testing methods slightly to enhance
critical thinking among one's students. This method is explained in the
following two sections.
The second method--more difficult, time-consuming, and
expensive--is briefly described now. This method makes use of formal critical
thinking exercises, programs, and materials that have been prepared by
specialists and can be purchased for immediate use by the teacher or instructor.
These materials are the dominant means by which critical thinking is now being
taught in primary and secondary education. For a single classroom, school, or
school district, such formal critical thinking materials cost hundreds to
thousands of dollars. The fact that critical thinking programs exist today is a
sad commentary on the decline of education in the United States, for students
apparently once learned critical thinking in our country without such materials.
Dozens of formal critical thinking programs exist. Here are
just three that arrived unsolicited in my faculty mailbox:
First, the "CORT Thinking Program" by Dr. Edward de Bono,
is a set of 60 "thinking lessons" that promise to "succeed in motivating
students of all ages and abilities to: think--and develop creative solutions
to problems--both inside and outside the classroom, improve the quantity and
quality of their creative writing, and see themselves as active thinkers, and
therefore able to hold a better self image of themselves and have confidence
in their own ability to succeed."
Second, the "Strategies for Teaching Critical Thinking
Across the Curriculum" from Education Testing Service consists of a two-phase
professional development program for secondary-level educators that will
enable them to "integrate the teaching of thinking skills into their
instructional program, and train teachers in their schools and/or districts to
do the same." Phase I teaches "introduction to thinking skills, concept
formation, finding patterns, making inferences, formulating and testing
hypotheses, and understanding and constructing meaning." Phase II teaches the
teachers to train other teachers.
The third program, from Teacher's Press, asks "Are you
concerned when American teenagers lack logical thinking skill, equate
influence with tricks and bribery, are unable to evaluate the reliability of
data?" They have prepared high school course materials that actively address
these concerns. For example, the description of their unit on "A Study of
Logical Fallacies" states that, "Teaching critical thinking skills has long
been accepted as a major goal of most teachers. Most probably say that they
want to develop in their students a trusting, but questioning, world outlook.
Most want students to actively investigate the world in a structured,
scientific way--as opposed to blind acceptance of tradition, authority or folk
wisdom."
Course Areas In Which to Emphasize Critical Thinking
The prior sections of this manual were written to describe
critical thinking, to inform you about the pressing need to promote it among
students, and to encourage you to make it part of your course curriculum and
teaching method. Now you will learn where and how to do this in your own
courses. Critical thinking can be presented or emphasized in all classroom
areas: lecture, homework, term papers, and exams. We will examine each in turn.
Some slight extra effort on the part of the instructor will be necessary, but
the effort will be worthwhile because the results are so valuable for the
student. Remember, as you teach critical thinking, teach also why it is
worthwhile.
Critical thinking can be taught during:
1. Lectures You may of course directly teach critical
thinking principles to your students during lecture, but this is neither
required nor advisable. Stay with your subject matter, but present this is such
a way that students will be encouraged to think critically about it. This is
accomplished during lecture by questioning the students in ways that require
that they not only understand the material, but can analyze it and apply it to
new situations.
2. Laboratories Students inevitably practice critical
thinking during laboratories in science class, because they are learning the
scientific method.
3. Homework Both traditional reading homework and special
written problem sets or questions can be used to enhance critical thinking.
Homework presents many opportunities to encourage critical thinking.
4. Quantitative Exercises Mathematical exercises and
quantitative word problems teach problem solving skills that can be used in
everyday life. This obviously enhances critical thinking.
5. Term Papers The best way to teach critical thinking is
to require that students write. Writing forces students to organize their
thoughts, contemplate their topic, evaluate their data in a logical fashion, and
present their conclusions in a persuasive manner. Good writing is the epitome of
good critical thinking.
6. Exams Exam questions can be devised which promote
critical thinking rather than rote memorization. This is true for both essay
question exams and multiple-choice exams.
Your mission, if you decide to accept it, is to use one or
more of the following classroom strategies or techniques to teach critical
thinking in one or more of the above four course areas. You are encouraged to
explore the possibilites and use as many as you wish. If you are already using
some of these techniques, and many of you are, then you don't have to change a
thing.
Critical Thinking Teaching Strategies and Classroom
Techniques
Critical thinking cannot be taught by lecturing. Critical
thinking is an active process, while, for most students, listening to lectures
is a passive activity. The intellectual skills of critical thinking--analysis,
synthesis, reflection, etc.--must be learned by actually performing them.
Classroom instruction, homework, term papers, and exams, therefore, should
emphasize active intellectual participation by the student.
Lectures: Enhancement of critical thinking can be
accomplished during lecture by periodically stopping and asking students
searching and thoughtful questions about the material you have just presented,
and then wait an appropriate time for them to respond. Do not immediately answer
such questions yourself; leave sufficient time for students to think about their
answer before they state it. If you constantly answer such questions yourself,
students will quickly realize this and not respond. Learn students' names as
quickly as possible and ask the questions of specific students that you call
upon by name. If an individual cannot answer a question, help them by
simplifying the question and leading them through the thought process: ask what
data are needed to answer the question, suggest how the data can be used to
answer the question, and then have the student use this data in an appropriate
way to come up with an answer.
You may, of course, ask simple questions that merely ask
students to regurgitate factual information that you have just given them in
lecture. Many students have trouble with these factual questions because they
are not paying attention in class, they simply have never learned how to listen
to a lecture and take mental and written notes, or they don't know how to review
their notes and the textbook in preparation for an exam. Perhaps the most basic
type of critical thinking is knowing how to listen to a lecture actively rather
than passively; many students don't know how to do this because they were never
taught it and they were able to get through the educational system to their
present situation--your class--without having to practice it. (A good book to
read or suggest to students that they read is How to Speak, How to Listen
by Mortimer J. Adler.) It is probably wise to begin asking the factual type of
question so that students will realize that they have to pay attention. However,
the goal of critical thinking requires that you eventually ask questions that
require students to think through a cause and effect or premise and conclusion
type of argument. This obliges them to reason from data or information they now
possess through the lecture to reach new conclusions or understanding about the
topic. For example, in chemistry, after presenting information about chemical
reactions, you could ask students to describe chemical reactions that occur to
them or near them everyday by the combination of commonplace chemical materials.
Ask them to explain what type of reaction it is (oxidation, reduction, etc.)
using whatever knowledge they possess of the reactant materials and their new
knowledge of chemical reactions.
Dr. Dennis Huston of Rice University, winner of numerous
teaching awards, recommends asking such questions in class. He complains that we
teach students to be mere receivers of information from the instructor, rather
than getting them to talk about and trust their own thoughts about the subject
matter. Huston states that thoughtful and searching questions often have
uncertain and ambiguous answers; this is more true in his area of study
(literature) than in math and science, but the concept is the same. Rather than
condition students to value only what the instructor says, get them to think
deeply about the topic and value what they think and feel. Teach so that
students think their ideas matter. Ask them to make connections and recognize
patterns. They will experience a responsibility for their own education and
think about what they learn and read. Students will be involved with their own
learning, will feel deeply about it, and learn to value and trust their own
thoughts and ideas. These recommendations are a perfect application of promoting
critical thinking.
After lecture but before the class ends, ask students to
write one-minute papers on the most significant thing they learned in class
today and what single thing they still feel confused about. Dr. Huston says this
is the single most important exercise you can do. You get immediate feedback
about what the students are learning and what they still need to understand
(technically, this is an application of what is called "classroom research" or
"classroom assessment," the deliberate discovery of what and how much students
are learning and of how you are teaching). He says it also improves their
writing. In our present case, of course, this exercise improves critical
thinking.
In class, encourage questions from students. Always respond
postively to questions; never brush them off or belitte the questioner. Instead,
praise the questioner (for example, say "Good question!" or "I bet a lot of you
want to know that"). Questions from students mean they are thinking critically
about what you are saying; encourage that thinking!
During lecture, bring in historical and philosophical
information about math and science that enables students to understand that all
scientific and mathematical knowledge was gained by someone practicing critical
thinking in the past, sometimes by acts of great courage or tedious painstaking
work in the face of seemingly insurmountable difficulties.
Laboratories: Many science courses have laboratories
connected with them. Science laboratory exercises are all excellent for teaching
critical thinking. The reasons should be obvious. Here, the student learns the
scientific method by acually practicing it. This method of teaching critical
thinking is so clear and obvious that it seems odd that critical thinking is not
promoted more in primary and secondary education by simply beginning science
instruction in the first grade and requiring that students take more science
courses. You will have to decide for yourself why this isn't the case. Since
laboratories automatically teach critical thinking to some degree, we will spend
no more time on this topic.
Homework: Innumerable opportunities exist to promote
critical thinking by homework assignments. For reading homework, Dr. William T.
Daly recommends that you provide students the general questions you want
answered before they begin reading, and insist that they organize their notes
around these questions. Require that students transform the information and make
it their own by requiring them to paraphrase, summarize, or outline all reading
assignments. He suggests that you can grade their written efforts with oral
quizes that can be structured to require abstract conceptualization and graded
as students speak, for most students will prepare carefully in order to avoid
failing repeatedly in public. You may also, of course, collect, grade, and
return their written efforts.
As stated above, getting students to write more is the
best, and perhaps the easiest, way to enhance critical thinking (this is also
the answer to the question, "How did students learn critical thinking before
there were formal critical thinking exercises and modules?"). Writing forces
students to organize their thoughts and think critically about the material. Ask
students to write short papers about pertinent topics, review science articles,
even paraphrase news articles and textbook chapters. These exercises can be as
elaborate as you wish to make them. For example, Drs. Robin W. Tyser and William
J. Cerbin (1991, Bioscience, v. 41, no. 1, p. 41-46, "Critical thinking
exercises for introductory biology courses") propose the assignment of "science
news exercises" designed to promote critical thinking. Students are asked to
read a short science news article taken from the popular media (newspaper,
science magazine, etc.), contemplate a list of take-home questions that include
one or two hypothetical claims about the article, and a week later take a short
quiz made up of questions selected from the list. The instructor prepares the
questions and copies and distributes them and the news article to the students
at biweekly intervals about six or seven times a semester. The authors state,
"The ultimate goal of these exercises is to improve students ability to compose
a concise, logically persuasive line of reasoning about why a claim should be
either conditionally accepted or not accepted." They point out that their's and
others' critical thinking exercises have been empirically demonstrated to
develop science-related thinking skills in a course without sacrificing the
disciplinary content. For other examples of this type, please see W. R.
Statkiewicz and R. D. Allen, 1983, "Practical exercises to develop critical
thinking skills," Journal of College Science Teaching, vol. 12, p.
262-266, and M. P. Donovan and R. D. Allen, 1989, "Critical thinking questions
for examinations and exercises," p. 13-16, in L. W. Crow, editor, Enhancing
Critical Thinking in the Sciences, Society for College Science Teachers.
Quantitative Exercises: Problem solving is critical
thinking; thus, courses such as mathematics, chemistry, and physics, that
require the solution of various mathematical problems, automatically teach
critical thinking to some extent just by following the traditional curriculum.
When students are required to solve math problems, they are practicing critical
thinking, whether they know it or not. Mathematics, chemistry, and physics
problems belong, of course, to only a limited subset of critical thinking, but
this subset is an important one. Indeed, all science courses--including those
that do not traditionally require mathematical problem-solving skills at the
introductory level, such as biology, geology, oceanography, astronomy, and
environmental science--should begin to incorporate some mathematical problems in
the curriculum. Asking students to solve math problems in a science gets them
thinking about nature and reality in empirical and quantitative terms, key
components of critical thinking.
One point, however, has been made by mathematics professor
Dr. Robert H. DeVore. Do not, he says, make the mistake of believing that
teaching mathematical manipulation alone will lead to critical thinking. Many
arithmetical and mathematical problems and exercises will give the student the
facility to manipulate numbers, but will not teach critical thinking. Dr. DeVore
believes that mathematical word problems, that ask the student to approach the
empirical world from a numerical or quantitative viewpoint, are essential to
enhancing critical thinking. Indeed, he feels that math students who do not
intend to take higher-level math courses should be educated in the context of
word problems to the greatest extent possible. Obviously, students who are given
math problems to solve in the sciences are essentially working on word problems,
so the point is automatically made here.
Here are some examples of mathematical word problems
prepared by Dr. DeVore (1-5) and Dr. John B. Scott (6-10) that were specifically
devised to enhance critical thinking:
1. Show that to convert a Celsius temperature (C°) to a
Fahrenheit temperature (F°), you can double C°, deduct 10% from the result,
and add 32°.
2. Bob buys an item for X dollars. He raises the price
15% and sells to Tom. Tom lowers the price he paid by 15% and sells back to
Bob. Bob's gain on the two transactions is $2,812.50. What is the value of X?
3. Does a(bc) = (ab)c on a calculator? First, use
variables of your own choosing. Then, try using a = 10-60, b = 10-60, and c =
1060. On my calculator (Sharp EL-506A), the left side of the equation is 10-6
and the right side is 0.
4. Does a+(b+c) = (a+b)+c on a calculator? Again, use
variables of your own choosing. Now, try using a = 1, b = 1020, c = -1020. On
my calculator, the left side of the equation is 1 and the right side is 0.
5. Is any law of algebra correct on a calculator?
6. Using a standard non-digital watch or clock, at what
exact time in hours, minutes, and seconds are the hour and minute hands
precisely coincident after 3:00 ?
7. A merchant has a square carpet priced at $1.00 per
square foot and a rectangular carpet, with length three times its width,
priced at $1.50 per square foot. The combined area of the carpets is 112
square feet, and the value of the rectangular carpet is $8.00 more than the
value of the square carpet. Find the dimensions of each carpet.
8. Two airports A and B are 400 miles apart, and B is due
east of airport A. A plane flew from A to B in 2 hours and then returned to
airport A in 2 1/2 hours. If the wind blew from due west with a constant
velocity during the entire trip, find the speed of the the plane in still air
and the speed of the wind.
9. A boat can travel 36 miles downstream in 1 hour and 48
minutes, but requires 4 hours for the return trip upstream. Assuming the boat
and the stream have constanat velocities, find the velocity of the stream and
the velocity of the boat in still water.
10. The periods of time required for two painters to
paint one square yard of floor differ by one minute. Together, they can paint
27 square yards in one hour. How long does it take each painter to paint one
square yard?
Term Papers: Term papers promote critical thinking among
students by requiring that they acquire, synthesize, and logically analyze
information, and that they then present this information and their conclusions
in written form. Term papers are not traditionally required in math and science
courses, although they may be and perhaps should be. We math and science
instructors really don't require that students write very much and, when we do,
don't requre that they use correct spelling, punctuation, grammar, and syntax.
At the very least, we should allow term papers as extra credit to give students
a means to make up poor exam grades. Students who are doing poorly always ask if
there is anything they can do to make up their grade; tell them from the first
day that an optional term paper--of appropriate style, content, and length--will
enable them to improve their grade in the course. Tell them that poor spelling,
grammar, punctuation, syntax, and form will result in lesser credit. This
technique can be used in any math or science course and is strongly recommended
as a way to improve students' critical thinking skills. Perhaps as they research
and write it, they will begin to think critically about the benefits of keeping
up with lectures and studying for exams.
Examinations: Examinations should require that students
write or, at least, think. For written exams, short- and long-answer essay
questions are the obvious solution. For example, Dr. James T. Hunter, a biology
professor, typically uses a few short-answer essay questions on each exam that
test the ability of students to analyze information and draw conclusions. This
commonly-used technique, by itself, helps to teach critical thinking. Some
examples of these questions are as follows:
1. Using diagrams and/or descriptions, describe the
synthesis of a protein beginning at the DNA level and ending with a finished
protein.
2. Contrast the relative advantages and disadvantages of
the light and electron microscopes.
3. Explain the importance of plasmids, biologically and
in genetic engineering.
4. In your own words, give at least six ground rules for
the collection of clinical specimens for microbiological studies.
But other possibilities exist. For example, Dr. Hunter
modified some of his essay questions to challenge the student's critical
thinking even more. He changed Question 4 above to the following:
4. Lab technician Jim collects a culture from a patient
on which the doctor previously operated. Jim carefully collects pus from a
wound on the leg of the patient using a toothpick and then, seeing another
wound on the face of the patient, washes the face wound with iodine and, using
the same toothpick, collects serum from that wound. Jim drops the toothpick
into a tube of nutrient broth, puts the name of the doctor on the broth
culture tube, and takes it to the lab on the way home from work. List the
mistakes Jim made.
In an experiment designed to further encourage critical
thinking among students, Dr. Hunter included a take-home bonus question. These
questions were chosen "to go beyond the lecture material and to force use of the
book and lecture notes to arrive at and phrase a reasoned answer to a
complicated question." This is an example of an essay question written
specifically to enhance critical thinking. But please remember, almost any essay
question, including those less elaborate than this, will serve to promote
critical thinking. This is because writing, in itself, promotes critical
thinking.
Finally, let us consider multiple-choice questions.
Although these are constantly characterized as being inimical to the
promulgation of critical thinking, the fact remains that they must often be used
for exams. Large class sizes and student expectation of impartial grading are
the two primary reasons to rely on multiple-choice questions. It is therefore
encouraging to learn that multiple-choice questions can serve to enhance
critical thinking if they are designed correctly. Let us examine some examples
prepared by Dr. Steven D. Schafersman. First, as counter-examples, the following
two questions do not promote critical thinking, because they rely solely
on simple memorization:
1. The nucleus of an atom is composed of
a. protons and ions
b. neutrons and electrons
c. protons and electrons
d. isotopes and ions
e. neutrons and protons
2. The most abundant rock-forming mineral in the Earth's
crust is
a. quartz
b. clay
c. feldspar
d. calcite
e. olivine
The following questions do promote critical
thinking, because they ask the student to perform some reasoning along with the
memorization:
3. If you drilled a well 8 kilometers deep and encountered
rock of the mantle, your drilling rig would be
a. far offshore in the deep ocean
b. on the coastal plain near a continent's shoreline
c. on a mountain range
d. in a deep valley or basin near the center of a continent
e. nearshore in a subduction zone
4. Although 95% of the crust of the Earth is composed of
either igneous or metamorphic rock, 75% of the exposed surface of the
continental crust is sedimentary rock. This is because
a. erosion of surface soil and rocks has produced a
veneer of sediments over most of the Earth, and lithification of these
sediments has produced sedimentary rock strata
b. the temperature of the Earth increases downward, leading to the creation of
vast amounts of igneous and metamorphic rocks
c. oceanic crust, which covers about 70% of the Earth's surface, is largely
composed of igneous rocks, such as basalt, which forms at oceanic ridges
d. constitute such a small percentage of the surface of the Earth that they
contribute much less material to the surface than do physical and chemical
precipitation of sediment
5. Of the following areas, the one least likely to be
affected by a catastrophic mudflow is
a. the Ozark Mountains of SW Missouri and NW Arkansas
b. the central Argentine Andes
c. the Cordilleras of Colombia
d. the Cascade Range of N California, Oregon, and Washington
e. the Texas Hill Country west of Austin
6. Which of the following is least likely to either trigger
or enhance a mass-wasting process?
a. an earthquake
b. a prolonged period of drought
c. marine erosion of a cliff face
d. rapid tectonic uplift
e. abundant precipitation in a brief period
7. Which of the following desert proceses is most essential
to the production of loess?
a. deflation
b. saltation
c. rolling
d. oxidation
e. solution
The idea here is not profound. Many of you probably use
this type of multiple-choice "think question" already. They simply ask that the
student read the information provided in the question, examine the alternative
answers, and perform one or more acts of reason in addition to any memorization
necessary. Choosing among alternatives in multiple-choice exams, as in real life
and any other intellectual pursuit, should involve more than memorization.
Please design some of your multiple-choice questions in the future with this in
mind. |
