Calculators Not Required: The Importance of Intuition in Physics Education
Sherry-Vy Gould
Sherry-Vy Gould
Richard Feynman, one of the most prominent theoretical physicists in modern history,
had two children, Carl and Michelle. Feynman taught Carl through discussion, using small
concepts like ants to gather perspective on problems and issues. Michelle, however, struggled to
learn using the same methods (Feynman and Sykes). Here are two children, raised by a
groundbreaking physicist, who had vastly different needs when it came to learning. Obviously,
learning is not like buying clothes. There is no “one size fits all,” let alone nice sizes to fit into
no matter where you go (or in learning’s case, what you’re learning). The percentage of the
world that learns using critical, analytical thinking are largely the same people who prosper in
math classes. Subjects such as math and physics just seem to make sense. The opposite, students
who flourish in creative thinking courses such as those in the humanities, may struggle when
given a math problem. In recent years this has become increasingly apparent and teachers and
professors in fields across the nation have responded accordingly. They have changed their
teaching methods to fit both types of students, and all that fall in between, however the field of
physics lags behind. As it has for years, the focus lies in equations and intensive applications of
math. Lectures come first to show students the concepts they need to understand in order to
successfully complete experiments, which are done following the lectures in order to supplement
the math, rather than show the science in action. Why, if it has been established that not everyone
learns material in the same way, are physics academia insisting on maintaining the status quo?
Students may learn a concept during lecture that will then be applied during an experiment, but is
that truly the best way to learn physics? There is a continuing conversation about whether
physics should be taught with a strong mathematical foundation, through lecture and formal
education, or with a focus on physical intuition. Many physics professors would argue that, yes,
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in order to fully understand physics, students must first master the math behind the concepts.
Others would disagree, claiming the only true way to understand physics is through exploration
and experimentation. However according to research into both the benefits and risks of physical
intuition, neither of those solutions are entirely correct. Only by combining the two different
pedagogies of physics can a true knowledge be gained. In order to achieve a full understanding
of physics, both physical intuition and math-based teaching must be present and nurtured in
formal education.
I. Defining Physical Intuition and the Current Atmosphere
In order to discuss arguments supporting or denying the importance of physical intuition,
it is necessary to define both physics as a science and intuition’s role in learning. The National
Institute of Physics, a charity aiming to advance physics research and understanding, defines
physics as “the study of matter, energy, and the interaction between them” (“What Is Physics?”).
In less scientific words, physics is the study of how everything interacts with everything else. It
stands as the foundation for other sciences like biology and chemistry and includes subjects both
smaller than any microscope could see to larger than any mind could fathom. The vastness of
physics both contributes to and minimizes its difficulty. On one hand, it is impossible to fully
understand everything there is to know about the science. On the other hand, the simple fact that
physics is everywhere lends itself to observation. Through those observations, physical intuition
is born. In a study discussing the necessity of physical intuition, Chandralekha Singh defines it as
the possession of a large bank of rules and heuristics that can be called upon in less familiar
circumstances to accelerate problem-solving (1103). The presence of those heuristics is the
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difference between intuitively knowing that objects fall when dropped and needing to apply a
formula to determine in which direction it will accelerate. A more scientific example would be
the ability to look at a problem detailing the reactions of a particle traveling through a circuit and
understanding how the values change when it travels through different areas. In upper-level
physics classes, physical intuition serves as an alternative to formulaic algorithms that may take
days to understand. In Feynman’s own words, physics is “not just mathematical problems”
(Feynman and Gottlieb 52). Just as children learn to count with abstractions, tangible blocks and
candies, physics students must first learn physics through visuals. In order to succeed in physics,
it is almost a requirement to be able to look at a problem and have a basic understanding of what
is happening and why before numbers and formulas are even taken into account.
Since physical intuition is so necessary, one would think physics professors would be
encouraging its formation. However that is not the case. Not only are professors not allowing
students the opportunity to gain physical intuition, but they then claim that students should have
that intuition naturally. When a student has trouble understanding physics, it is their fault for not
being naturally good at the subject. The phrase “they just aren’t cut out for it” prevails. Looking
at both research and using first-hand observations, it is clear to see that physical intuition is not
something that people are just born with. Established physics professors, when faced with a
problem they have no experience solving, act in similar ways to students (Singh 1104). Through
the application of math it needs to be nurtured and grown in order for students to have
experience and knowledge from both methods of learning. Neither physical intuition nor math
alone can create a large enough bank of information for students to draw from when problemsolving, however professors are quick to argue over which method produces the best results.
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Prominent physicists are not spared from this conversation; even Feynman ensured his
voice was heard. He once observed a student ignoring all of the obvious answers to a practical
problem, how to stop a table from wobbling, because the student was too focused on attempting
mathematical calculations to find a solution (Feynman and Gottlieb 52). While the story may
have been exaggerated, it still illustrates a common occurrence in physics. Students who lack a
true, deep understanding of physics and its mechanics will not understand even how to start
solving problems. Students will either look for answers on a level that is far too shallow or too
deep, but will not know where the right answer lies. Feynman responds to this occurrence, saying
that physics may be manageable when concepts are constructed using math, but “as problems get
more and more difficult, and as you try to understand nature in more and more complicated
situations, the more you can… understand without actually calculating, the better off you are!”
(Feynman and Gottlieb 52).
II. Benefits of Physical Intuition
Without physical intuition, physics is nothing but rules and mathematical formulas.
Physics is exceptionally more relatable when the student can begin to understand the conceptual
patterns behind the numbers. This was made clear through experimental changes made at the
University of Maryland, where biology students taking physics were consistently scoring lower
than their physics major counterparts. When the class structure resembled a basic algebra-based
physics class, students struggled to understand what was really being taught. After the physics
department made a conscious effort to appeal to the students rather than the usual teaching
methods- lecture after lecture, with brief interludes for math problems- positive changes occurred
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across the board. Professors, instead of teaching physical concepts through lecture, applied the
same concepts to biological situations. By appealing to the interests and experiences of the
students, there was a drastic change in the way students viewed the subject. The same concepts,
applied in scenarios familiar to a biology major, changed the outlook completely. Students who
reportedly saw physics as “useless and irrelevant” prior to the change (Redish 19) said that “I
now see that physics really is everywhere” (64) after their experiences were taken into account.
What was being taught now had value beyond rote memorization and test-taking. The difference
between the two methods was an awareness of the importance of physical intuition. When the
biology students were shown the biological examples they knew and understood in the context of
physics, it made it that much easier to form connections. They knew how the scenarios would
play out, they just had to apply the physics terminology. The alternative would be to take a room
full of students, give them unfamiliar concepts and complicated formulas to match, and then
coach them into applying those concepts (usually incorrectly) to whatever situations they can
think of. Nothing that was unfamiliar would ever truly be understood, rather it would be
remembered at face value. The formula for force is mass times acceleration, but why? When a
student can explain why something is happening rather than simply what is happening, they have
gained an understanding that extends deeper than memorization- the ability to apply the
knowledge.
As is to be expected, the benefits of promoting physical intuition extends to more than
biology majors. Priscilla Laws, in her article “Calculus-Based Physics Without Lectures,”
discusses the factors that cause students to turn away from physics and how the presence of
physical intuition can change that. Out of all the students across the nation who are required to
take physics as a prerequisite, a generous estimation of half will fail (Laws 24). Usually
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engineering or science majors, these students are not the normal suspects for failure. But not only
that, students in the humanities who were required to take physics described the course as
“uninteresting, time consuming…fixated on the procedures of textbook problem solving, devoid
of peer cooperation… crammed with too much material, and biased away from conceptual
understanding” (21). If there is a course that otherwise great students are consistently failing,
there is obviously a problem with the course, and those phrases are all very clear- current physics
classes are not up to the standard the nation holds for its other courses. That does not leave
physics professors with no hope, however. Instead, by encouraging the growth of physical
intuition in students using techniques such as “workshop physics” (Laws 25), or physics taught
through experiments, there is a greater success rate when teaching students concepts that were
previously hard to master. Students become more actively involved in class, even going so far as
to take leadership roles in both the classroom and lab, and performance on formal exams matches
or exceeds students in lecture-based classes (28). According to Laws’s analysis of this new sort
of workshop physics, most students do not have enough prior experience with the concepts
represented in class to understand mathematical explanations. It is necessary, therefore, to aid the
students by teaching them through activities and models that represent the actual physical events.
Without these demonstrations, students would lack an understanding of what was conceptually
happening, therefore finding it more difficult to assign mathematical equations to those concepts.
The benefits found through Laws’s research are reflected further in Chandralekha Singh’s
article “When Physical Intuition Fails.” Rather than teaching concepts exclusively, Singh shows
that “explicitly teach[ing] problem-solving heuristics” (1107) allows students to solve more
problems on their own, using critical thinking skills. Even professors, when encountering a
problem with which they have no prior experience, cannot quickly deduce a method to solve the
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problem (1104). They behave similarly to introductory-level students, regardless of how many
years of experiences they had with solving problems using math. The necessary component is
physical intuition, which must be gained through experience. The benefits of physical intuition
are undeniable, however it is important to remember that all of the findings are based on
including physical intuition in math. Physics, at its most basic, is applied math and therefore
math is an integral part of any curriculum. Physical intuition serves to supplement the math, just
as the math supplements the intuition. Neither piece on its own would act as a sufficient body of
knowledge for any student to be successful when math is used to accurately comprehend
experiences to the point where that knowledge can be manipulated and applied.
III. How to Nurture Physical Intuition
While the benefits of physical intuition have been explored, there has been no intensive
discussion into how the findings can be applied in universities. As mentioned above, there have
been multiple experiments into the pedagogy of physics and physical intuition. Perhaps the most
simple change for universities to adopt would be a physics curriculum more heavily focused on
student-centric problems. Designing problem sets with relevancy is the first step to appeal to the
students as more than simply “someone who’s not cut out for physics.” In the case of Dickinson
College in Pennsylvania, the inclusion of physical intuition into the curriculum was done by
redesigning the entire curriculum through the removal of all lecture-based physics classes.
Instead, classes were transformed and intended to be as focused as possible on hands-on
experimentation. Class time was spent carrying out experiments with the ultimate goal of
“acquiring transferable skills of scientific inquiry” (Laws 25). Only after experiments- some as
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simple as dropping bean bags and recording the time it takes to reach certain distances in order to
calculate velocity and acceleration- was the math brought into play. Students had images in their
mind and muscle memory of actually completing the action, which in turn made applying
formulas much easier. Consequently, students were able to remember and recall not only the
formulas but their applications when it came time to test (28). The same results were apparent in
every single experiment- teaching students through experimentation promotes a more thorough
understanding of the material. Furthermore, by allowing students to gather their own
observations and use the math to make sense of them, their scientific inquiry skills grow stronger
and more capable of answering questions beyond the semester-long course. According to David
Hestenes, a failure to take seriously the applications above will result in an ever-widening gap
between physics professors and their students, which has led to a decline in students who (as
mentioned in Laws study) turn away from the science. Hestenes reemphasizes the already
existing chasm and succinctly summarizes a possible source of frustration with the following
claim: “When an instructor takes certain basics for granted and fails to teach them, the students
flounder until they rediscover those basics for themselves or, more likely, develop inferior
alternatives to cope with their difficulties” (2).
IV. Considerations
Not every physicist agrees that physical intuition is necessary. Some even argue that it is
counterproductive for students, causing more harm than good. David Keeports, in the article
“Addressing physical intuition: A first-day event,” discusses the necessity of “thoroughly
develop[ing] the topics of mechanics, waves, electricity, and magnetism” (318) before
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integrating any aspect of intuition into the classroom. Because those are the main tenants of
introductory-level physics and they are the most observable in every day life, Keeports claims it
is important to approach those topics with care to rearrange students’ existing intuition.
Furthermore, according to Keeports, his experience has led him to not only warn students that
their intuition would be challenged but to “address the issue of physical intuition head-on” (318).
He explains to students why “untrained physical intuition is often flawed and incomplete,” due to
our observations existing only in a “very specific and limited physical environment” (318). For
example, an observation such as “an object in motion will slow down unless an outside force is
applied to it” would be correct in the world students exist in. In the vacuum that is physics
classrooms, however, Newton’s first law states that an object in motion will stay in motion. The
experience that students have is the complete opposite of what is taught in physics, which not
only creates confusion but slows down future learning. This is why Keeports places such
emphasis on telling his students not to trust their intuition. He even questions whether or not
there is a better strategy than using observations to build intuition yet does not provide a
solution. Although Keeports has valid criticisms, namely the fact that intuition can be wrong,
that should not stop professors from nurturing it. It is presumptuous to claim physical intuition
can be wrong and therefore it has no place in the classroom, and then teach the math behind the
concepts, fully understanding that most students do not have an adequate background in math to
understand what is being taught. David Hestenes also addresses concerns such as that which
Keeports raised, however Hestenes shows a different view- one with a solution.
Hestenes argues that while physical intuition may not be counter-productive, it does not,
and should not, have a significant presence in an introductory physics class. In breaking down
scientific knowledge into two separate branches- factual knowledge and procedural knowledge-
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he acknowledges the existence of intuition in learning yet highlights the necessity of a strong
mathematical foundation (3). Factual knowledge stands as the foundation, constructed of a deep
understanding of mathematical equations and the laws of physics, that procedural knowledge
(which could also be called physical intuition) stands on. Before students can be expected to
accurately express an understanding that is reliable enough to apply to other situations, the
essentials must be learned through formal education. That formal education serves as the
previously mentioned “large bank of rules and heuristics” (Singh 1103) that can be used when
necessary. Hestenes and Keeports both provide similar claims to refute the inclusion of physical
intuition into physics curricula, however what Hestenes outlined has a simple solution. He
already split knowledge into procedural and factual, it is only necessary for physics professors to
encourage both. Rather than ignoring physical intuition under the guise that it preys on
knowledge, it would be prudent to use the math, the factual knowledge, the formal lectures and
conceptual physics, to support intuition. When intuition fails, as it will, students will have the
support of the math to lean on. On the other hand, by ignoring physical intuition in favor of
math, students will lack the understanding of physics that is necessary should the students ever
attempt to apply their knowledge. There is a compromise that needs to be made between physical
intuition and math, but both clearly need to be present or students will have a knowledge that is
both incomplete and lopsided.
V. Conclusion
Richard Feynman, one of the most prominent theoretical physicists in modern history,
had two children, Carl and Michelle. Feynman taught Carl through discussion, using small
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concepts like ants to gather perspective on problems and issues. Michelle, however, struggled to
learn using the same methods (Feynman and Sykes). Carl was able to learn through the use of
physical intuition, looking at everyday objects and applying his observations to other scenarios.
Michelle needed much more concrete information to process in order to understand her
observations, and that’s okay. Not every student learns in the same way, in the same way that not
every physics student can learn from just math or just experimentation. Unlike Feynman teaching
his two children, physics professors have a much larger audience to cater to. There cannot be
one-on-one help for every student, therefore professors must dedicate their time to an even
spread of both pedagogies. Creating physics curricula that can nurse both a student’s logical,
math-based thinking and their observational, intuition-based reasoning is the only solution. In
finding that solution, however, more questions are raised. The most direct effect of a changing
curriculum in higher education would be different standards of learning prior to university.
Incoming students would be expected to have a different education in order to fully benefit from
the new methods of teaching; most notably, students would need to be self-sufficient in lab
settings and able to experiment through mistakes in order to answer questions. That ability is not
something schools currently prioritize. Students from other majors, engineering and other
sciences, would also be expected to take greater responsibility for their education. Hands-on
physics is more beneficial, but leaves the student to read the textbook and practice whatever
math is necessary on their own. It would be prudent to question the increased demands that new
physics methods place on students in order to enact them most effectively.
Questions and implications aside, it is clear that in order to gain a full understanding of
physics both physical intuition and math must be taught. In that way, students have the
opportunity to learn material in one way and support the information in another. When one fails,
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the other can act as a crutch. The absence of one problem-solving method leaves a student
vulnerable to situations in which they have no prior experience, not to mention problems they
should be able to solve but cannot due to a narrow understanding. Whether physics makes more
sense through observing and experimenting or deriving math equations, both approaches together
create a fluid body of knowledge that can be both internalized and applied.
Word Count: 3521
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Works Cited
“What is Physics?.” What Is Physics?|Explore|physics.org. Institute of Physics, n.d. Web. 11
Apr. 2015.
Feynman, Richard P., and Michael A. Gottlieb. Feynman's Tips on Physics Reflections, Advice,
Insights, Practice : A Problem-solving Supplement to the Feynman Lectures on Physics. New
York: Basic, 2013. 52-53. Print.
Feynman, Richard P., and Christopher Sykes. No Ordinary Genius: The Illustrated Richard
Feynman. New York: Norton, 1994. Print.
Hestenes, David. "Toward a modeling theory of physics instruction." American journal of
physics 55.5 (1987): 440-454.
Keeports, David. "Addressing physical intuition—A first-day event." The Physics Teacher 38.5
(2000): 318-319.
Laws, Priscilla W. "Calculus-based physics without lectures." Physics today 44.12 (1991): 2431.
Redish, Edward F. Reinventing Introductory Physics for Life Scientists. Publication. National
Experiment in Undergraduate Science Education, 16 Oct. 2014. Web. 23 Mar. 2015.
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Singh, Chandralekha. "When physical intuition fails." American Journal of Physics 70.11
(2002): 1103-1109.
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