Rounding off the cow: challenges and successes in an

interdisciplinary physics course for life science students

Dawn C. Meredith

University of New Hampshire, Department of Physics, Durham, NH 03824∗

Jessica A. Bolker

University of New Hampshire, Department of Biological Science, Durham, NH 03824

(Dated: December 19, 2011)

Abstract

We describe a four-year project designing, teaching and assessing an interdisciplinary algebra-

based physics course for undergraduate biology students. We addressed the needs of this cohort

through careful selection of topics and rich biological applications, while also attending to deeper

pedagogical concerns (students’ conceptual understanding, epistemological stance, and ability to

connect meaning and mathematics). The course provided biology/physics connections that stu-

dents valued. Students’ work indicates their ability to understand and integrate physics in biological

contexts. We offer strategies, suggestions, and some cautionary tales for faculty contemplating or

already engaged in similar endeavors.

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I. INTRODUCTION

Our title is lifted from a well-worn story: consulted about methods to increase milk

production in a dairy herd, a physicist responds, “Consider a spherical cow....” The old joke

captures one of the difficulties of designing a physics course that will better serve students

who are more interested in real cows (as well as fish, bacteria, and humans) than in the

idealized, often simplified objects and phenomena in introductory physics textbooks.

This is not a new problem: it is well known that the needs of life science students differ

from those of students in physical science and engineering.1 The search for solutions to this

problem has received new impetus in the past decade from four national reports focused on

undergraduate biology education.2–5

Bio2010: Transforming Undergraduate Education for Future Research Biologists2 de-

scribes three reasons why biology students should study physics:

First, there are the specific and quantitative principles of physics on which a

microscopic understanding of biology is ultimately based, and on which much of

the instrumentation of biological research is also based. . . Second, and more ab-

stract, physics is a more mature science with far less complexity than biology, in

which a student can more easily learn about the interactive relationship between

experiment, theory, modeling, and analysis. Third, much of physics is about the

behavior of dynamical systems. Biologists need to understand dynamics, for

biology is fundamentally a driven, dissipative system, not at equilibrium. (p.

155).

Scientific Foundations for Future Physicians3 lists expected competencies for students

entering medical programs, and proposes that defined competencies replace required courses

as pre-requisites for admission; their recommendations draw directly on Bio2010. The three

student competencies6 most relevant to college physics instructors are the abilities to

• apply quantitative reasoning and appropriate mathematics to describe or explain phe-

nomena in the natural world. (p. 22)

• demonstrate understanding of the process of scientific inquiry, and explain how scien-

tific knowledge is discovered and validated. (p. 24)

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• demonstrate knowledge of basic physical principles and their applications to the un-

derstanding of living systems. (p. 26)

The pre-health professional entrance examinations (Medical College Admissions Test

(MCAT)7 and the lesser-known Optometry Admissions Test8) are long-standing external

influences on the breadth and depth of introductory course for life science students. Some

instructors assume that preparing students for the MCAT requires teaching all the topics

in a standard college physics text, even if this demand for breadth results in superficial

coverage. Contrary to this assumption, however, Zheng et al.9 demonstrate that a large per-

centage of MCAT questions require critical thinking, not just recall.10 This focus on depth

rather than breadth is echoed in the recent MCAT Fifth Comprehensive Revision (MR5);4

a recommendation particularly important for physics instructors is the plan to “test exam-

inees’ knowledge and use of the concepts...[that are] most important to entering students’

success” (underlining added).

The Vision and Change group,5 catalyzed by recent significant changes in the field of

biology and the science of learning, have issued a call to action to undergraduate biology

educators (and presumably those in other disciplines who teach biology students). They

recommend teaching core concepts (“evolution; pathways and transformation of energy and

matter; information flow, exchange and storage; structure and function; and systems”) in

courses that are “active, outcome-oriented, inquiry-driven, and relevant.”

These national reports have helped to focus and energize efforts within the physics com-

munity to improve the standard course in Introductory Physics for Life Science Students

(IPLS), leading to the formation of a national group of physics educators interested in the

IPLS course. This group has met at AAPT meetings and at stand alone-workshops, and

identified a number of common goals and concerns,11 all focused on improving the IPLS

course.

We also heard from our own students:

Please give a lot more biological examples to relate physics to something we

bio majors understand! It captures our attention SO much more and gets us to

understand concepts so we can do better in the class. We like animals and plants

and things like that, and we want to understand these things, so if you play off

our interests more it’ll help us do better. Physics is an interesting subject for a

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lot of people, but concepts are hard to grasp without making direct connections

between it and other things we know and like.12

This is the national and local context in which we set out to transform a standard

introductory physics course populated mainly by biology students into an explicitly inter-

disciplinary course designed to better meet our students’ needs. This paper summarizes

what we learned along the way.

We begin with the context: class format, and student characteristics. We describe how we

redesigned the course and what we learned about integrating biology into a physics class. We

present data about outcomes, including an overview of student perceptions of the project.

We end with a discussion of unsolved problems, including the challenge of transforming a

local, individual initiative into a broader institutional change.

II. LOCAL CONTEXT

Our IPLS course served 250-320 students each semester, and was split into two lecture

sections that each met three times a week. Every student also enrolled in a weekly lab section.

There were no scheduled recitations or problem solving sessions; however, we provided several

options for group work outside of class, facilitated by either peers13 or instructors, and

sometimes used lab time for group problem solving.

Most of our students were juniors or sophomores. Over 85% were from the College of

Life Science and Agriculture, and taking the course to fulfill a major requirement. Although

some planned to apply to medical school, many were primarily interested in areas of biology

per se, such as marine ecology, zoology, behavior, neuroscience, and microbiology. Fifteen

to 20% of our students viewed the class as a good way to study for the MCATs, and 15-30%

perceived it as useful to their future careers. Independent of its perceived utility, 15-20%

saw physics as inherently fun and/or interesting.

Our students’ physics and mathematics background varied widely. About 25% of our

students had no previous physics instruction; 25% had taken conceptual physics, 40% had

taken college preparatory physics, and 10% had taken an AP or college level course. Al-

though 75% had taken calculus (required by many of the majors that also require physics),

18% sometimes found the mathematics in our class (algebra and trigonometry) too diffi-

cult. For 76% it was not a barrier to learning, and 5.5% would have liked more challenging

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mathematics.

III. COURSE DEVELOPMENT AND PEDAGOGY

A. Co-teaching

Our goals in the IPLS course were both to teach physics effectively, and to demonstrate the

connections between physics and biology. In particular, we wanted students to understand

how and why physics is important within biology (at levels from ecology and evolution,

through organismal form and function, to instrumentation).

With this motivation, we sought to test the hypothesis that a thoroughly interdisciplinary

IPLS course was an effective approach to teach physics to life science students, and that

developing such a course would be an interesting, though difficult, venture. Over the past

four years, our IPLS course was co-developed and co-taught by a physicist (DCM) and a

biologist (JAB).

We believe that close faculty-level collaboration across disciplines is the best way to run

an interdisciplinary course. Such visible collaboration offers students two important bene-

fits: the experience of working with faculty from different backgrounds, who have different

training, perspectives, and approaches; and a practical model of colleagues from disparate

disciplines actively collaborating on an integrative project (in this case, their class). Seeing a

biologist and a physicist working together to offer a genuinely interdisciplinary course sends

a powerful message about the value we place on integration.

B. Pedagogy

Biological applications that may improve student motivation are not in themselves suf-

ficient to produce effective learning in a physics class.14 Beyond working to integrate bi-

ology into the course content, we also focused on conceptual understanding15 using peer

instruction16, and group problem solving on challenging questions17. We chose the text

by Knight, Jones and Field18 as it supported several of our strategies: modeling, focus on

concepts, and awareness of students’ initial ideas about physics.

Students’ personal epistemologies (i.e., beliefs about learning and knowledge) were ad-

dressed through a focus on sense-making and refining intuitions.19,20. Our labs were in-

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formed by Modeling Instruction (MI)21 in order to explicitly address epistemology, allowing

students to engage in authentic scientific inquiry in the classroom. MI was adapted by

graduate student Christopher Shubert in collaboration with Prof. James Vesenka in order

to accommodate local constraints (shorter class period, less experienced instructors), and

integrate biological topics22

C. Choice of Topics

Traditional introductory physics courses acknowledge only slightly the needs of life science

students; typically the breadth of topics covered is the same as for the engineers (though

with less mathematics), and the interests of biologists are addressed only through biological

examples or homework questions.23 But this approach fails to meet biologists’ real needs:

few topics have equal value to engineers and to biologists. Treating the IPLS class as a minor

variation on the engineering course is like pouring salsa over a meatloaf and then declaring

it a Mexican dish.

We took a different approach, deliberately choosing topics with our biology students’

needs and interests in mind. To determine if a topic belonged in our course, we asked

whether it would

• have important biological applications (either in organisms or in instrumentation)

• be intellectually accessible to most students in the time available

• be essential to a coherent physics narrative (e.g. acceleration is a key concept in talking

about forces.)

The resulting list of topics differs substantially from that in a traditional syllabus. Table I

summarizes our topics. A number of traditional topics were covered in less detail, because the

biological applications were sparse (e.g. two-dimensional elastic collisions), relatively trivial

(falling maple seeds as an example of rotational motion), or too difficult to be covered well

at this level (projectile motion with drag). The list of topics we chose to omit aligns with

others.24–26 Our list is shaped by our own interests as well as our students’; we offer it as

an example, not a universal prescription. The approach we took to generating it, however,

should be widely applicable.

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Semester 1 Semester 2

Included or Stressed Kinematics Heat transfer

Dynamics Kinetic theory of gases

Static Torque Entropy

Energy Diffusion, convection, conduction

Materials (stress/strain) and fracture Simple harmonic motion and waves

Fluids (far more) (including sound, optics)

Omitted or deemphasized Projectile motion Heat Engines

Relative motion Magnetism (less)

Rotational kinematics and dynamics Induction (qualitatively)

Equilibrium with forces and torques Atomic physics

Collisions (limited to instrumentation applications)

Newton’s laws of gravitation Relativity

Kepler’s laws

TABLE I. Changes in topic emphasis compared to standard course.

Some traditional, beautiful and interesting topics in the introductory physics course must

be cut to make room for less standard topics (such as fluids) that are essential for biologists.

For a physicist, this is like being asked to choose your least favorite child. But it was made

easier by our realization that some standard topics are simply not vital for this audience.

This is an example of the constant tension between the instructor’s sense of beauty and

coherence of their chosen subject, and students in other majors whose overwhelming concern

is for its usefulness.This happens in all fields, and is a particular challenge in a service course,

whether it be for engineers or biologists. We need to find the best balance possible. While

we can reasonably expect a student to be willing to listen to an hour’s lecture on a beautiful

physics topic with no obvious application, it is unfair to ask her to invest hundreds of hours,

great effort, and inevitable pain and frustration in learning material in which she sees neither

beauty nor utility.

In cases where we retained topics (e.g. kinematics) that were needed primarily to support

a coherent story line, we focused on problems that, while not biologically-based, were acces-

sible and relevant to most students. For instance, problems based on cars (safe following or

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passing distances, accident reconstruction) are a good standby when biological applications

are lacking.

The choice of topics is complicated by the wide range of biological applications. At our

institution, biology faculty often call for a one-semester physics course that will “hit all the

high points,” but cannot agree on what those high points are. Biologists working at the

cellular level (who need diffusion, viscosity, energy, entropy, etc.) have different priorities

than those who work at the organismal level (who need energy, torque, ray optics, convection,

etc.). Covering all the topics on the combined list would require at least two and possibly

three semesters of physics instruction, not a single 15-week class. Moreover, we ignore at

our peril the extensive literature14,27 documenting the essential distinction between what we

“cover,” especially at superficial depth and high speed, and what students actually come to

understand in any useful way.

D. Biologically motivated themes

Beyond the essential topics, there are critical themes that could be woven through the

entire IPLS course: scaling, estimation, and gradient driven flows.

Size and Scale. The importance of size and scale in biology has long been recognized,28

but the standard physics course addresses neither. Most topics offer some opportunity to

point to scaling and/or size effects (for example, gravity matters a lot to us but comparatively

little to a flea; the opposite is true of surface tension).

Estimation and Quantitative Thinking. Biology students need more opportunity to gain

experience, competence, and comfort with quantitative thinking.29 The IPLS course offers

an ideal venue for practice using estimation and quantification to this end. One key use

of estimation for biologists is in assessing what elements of the system matter most: if the

viscous drag on a fish is orders of magnitude less than the pressure drag, only the latter

matters, so streamlining will be useful even if it increases total body surface area. But

for a tiny water flea, pressure drag, and therefore body shape, are insignificant. Asking

students to estimate Reynolds numbers can help them understand different flow regimes

and what matters at different size scales or in different environments, as well as exercise

their quantitative skills. The use of estimation in turn brings up a key epistemological

issue: understanding when approximations are useful, and how to decide. (See Fig. 1 for an

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example of a biological application where students must figure out what matters.)

Gradient driven flows. These are a pervasive theme in biology, with many applications,

particularly in physiology and cell biology (oxygen in lungs, exchange of nutrients and waste

across the lining of blood vessels and intestines, transport across cell membranes, etc.).30

Students readily connect physics concepts in this area to what they already know about cell

membrane structure and function.

E. Mathematics

Life science students need to strengthen their quantitative reasoning skills,2,3,5 and an

algebra-based physics course provides many opportunities. However, two issues prevent

students from taking full advantage of these opportunities. First, many students have not

used algebra or trigonometry for years, or have significant gaps in their background. Second,

for a significant fraction of biology majors mathematics is a foreign and often intimidating

language; they are not predisposed to using mathematics as a tool for understanding.

To address the issue of weak or distant background, we offered on-line tutorials (both

those in MasteringPhysics c© and several written by our mathematics colleague Prof. Gertrud

Kraut). Three quarters of the students found tutorials to be helpful; 23% already knew the

material well enough to do without, and 2% still felt ill-prepared for the mathematics in

the course. We highly recommend such tutorials on prerequisite mathematics, as we often

found significant unexpected gaps in student background knowledge.31

To address the second mathematical challenge, we sought to motivate students to see

mathematics differently: we wanted them to understand equations as ways to tell a story,

not just use them to get numbers. To many physicists, the best way to teach, learn, or

understand an equation is by deriving it; for them proofs both “convince and explain.”32

However, students have a different perspective: “the students indicated that proofs are only

convincing to teachers and others who are informed about particular formats and rituals.”32

We question whether proofs are a useful exercise for biologists (or engineers), especially for

undergraduates who might someday use the equations of physics in their work, but will

never need to derive them. It is counterproductive to spend lecture time on derivations

that we never intend or expect students to perform: it only reinforces the (erroneous, but

disappointingly pervasive) notion that physics is about manipulating equations rather than

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about understanding the world.

There are several other ways to help students connect meaning and mathematics by

seeing a story in an equation. In Modeling Instruction labs students model their own data

with an equation, and devise a verbal link between the physical world and the equation.

Quantitative relationships for which there is no convenient lab can be motivated via lecture

demonstrations or appeals to experience. For example, given the microscopic explanation

of pressure drag as the result of collisions with fluid molecules, students readily see that

surface area of the moving object matters but its mass does not.

Another alternative to formal proofs is to “unpack” equations in order to build under-

standing of physical relationships and their mathematical representation.33 This strategy

helps students see the story in the equation, familiarizing them with the characters (or

terms) and the plot (or mathematical relationships) as well as the moral: what really mat-

ters in the end, and how it’s determined. For example, we’ve used the equation for energy

conservation as the framework for a lecture on locomotion, in which we examine each term

and relate it to specific ways animals minimize the cost of moving around. Knowing that

kinetic energy depends on mass explains why gazelles have slender legs. The fact that the

velocity term is squared indicates that slowing down can significantly reduce required energy

(and power), and thus helps explain why long migrations are undertaken at moderate, not

maximum, speeds.

IV. BIOLOGICAL APPLICATIONS AND PROBLEMS

The core of our work was in developing and deploying biological applications for the IPLS

course. Life science students are not readily engaged by questions about blocks sliding on

ramps or other simple physics examples for which they can imagine no interesting applica-

tion. Improving the IPLS course requires labs and problems that are more relevant to this

cohort, both to keep them engaged and motivated, and to demonstrate that physics is, in

fact, directly applicable to biological phenomena. Simply painting a cow face on a sphere

(or pouring salsa over a meatloaf) isn’t enough. To be taken seriously by our students,

biology-related problems must

• be clearly important to/within biology,

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• be factually correct and numerically reasonable,

• match students’ prior knowledge of biology, thus reinforcing the connection (as well as

the credibility of the physics professor standing in front of a room full of biologists!),

• incorporate substantive conceptual and/or quantitative physics,

• be included on exams, and

• represent a significant fraction of the course grade

The biggest challenge in developing biologically relevant problems for the IPLS course is that

there is a very fine line between physics problems with only superficial biological connections,

and problems that invoke too much physics or are too complex.

It’s relatively easy to invent questions we would classify as “superficial applications.” For

instance, we could ask, “If animal x can jump 1.3 m high, what must its initial velocity be?”

To a biologist, this is grossly oversimplified, and does not address essential concerns such

as how the animal’s structure is related to its jumping ability (not every organism jumps

the same way: a flea, a human, and a horse have very different ways to get 1.3 m above

the ground). Disappointingly many biological applications, especially in textbooks, take

the form of an engaging color photo plus a short conceptual explanation or a few homework

questions; while these are helpful in pointing out links between biology and physics, they are

not enough to improve students’ understanding of deeper and more quantitative connections

between the fields.

But we can also err on the other side, posing questions that are so complex and full of

biological information that students are overwhelmed, or distracted from the fundamental

physics issues. In addition, although most IPLS students are biology majors, they have

diverse backgrounds, so we cannot assume any particular biological knowledge. Moreover,

the average physics instructors would not feel comfortable asking deeply biological questions.

A related complication is that questions about biological systems sometimes elicit bio-

logical, rather than physical, answers. To discourage these responses, when we write a test

question on a topic with obvious biological applications (such as gradient driven flow across

a membrane; Figure 2), we note explicitly that the question refers to a model and not an

actual biological structure, since detailed features of cell membranes (such as dynamic ion

channels) have no place in an IPLS course. The question presented in Figure 2 is an example

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of a round cow: it has clear connections to biology, but omits much of the complexity of the

real biological system.

In accordance with Bio 2010’s (page 48) exhortation, we worked with other faculty to

identify rich and meaningful applications to incorporate into the IPLS course. We consulted

with colleagues from many areas of biology in order to develop a broad range of applications,

and we drew on several biology books with strong physics components.34 A side benefit of

our conversations with biologist colleagues was getting feedback about how the IPLS course

was going, and discussing whether the physics they used in their own courses was (or should

be) covered. When biologists provided examples we used in the IPLS course, we credited

them in class not only out of gratitude, but as a way of signaling to the students that their

biology faculty also care about physics.

We focused on animal, plant and cellular applications, as human applications were already

available from the Humanized Physics Project35 and medical applications have been covered

by Amadore Kane36 Along the way, we identified key traits of good biological applications

for the IPLS course. These applications need to

• Balance tractability with applicability in the real world (simplification vs. complexity)

• Connect to central biological topics such as physiology, structure and function, and

adaptation to the environment

• Incorporate overarching concepts such as quantifying, modeling, rates, gradients, and

scaling

• Provide sufficient but not irrelevant biological context

• Relate to other problems focusing on the same key idea, such as pushing on the

environment to move (just as a traditional course offers multiple problems illustrating

core ideas such as Newton’s second law)

• Integrate concepts from many realms (e.g. geometry, forces, energy), while avoiding

cognitive overload.

The problems we wrote are complex: students need to coordinate biological, mathemati-

cal, and physical concepts and laws. The problems are by nature unique as they describe a

single biological system, though we provide several biological applications for each physics

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principle (e.g. analyzing different ways that animals push on the environment presents the

impulse momentum theorem in several guises). Writing such questions is challenging: unlike

questions in a more abstract context, it is not a simple matter to write innumerable ques-

tions that are isomorphic and still biologically realistic. Since these problems are difficult

to grade individually, and likely impossible to grade for a large class, we recommend the

methods suggested by others19,42 to grade for effort and then publish solutions that students

can analyze as a source of detailed feedback.

In addition to developing biological application problem sets, we created several other

kinds of resources that link biology and physics: lectures with clicker questions, annotated

bibliographies of biological resources, and labs. These are available on our web site33 as

source code so that they may be edited.

V. OUTCOMES AND ASSESSMENT

Our primary goal was to make the course thoroughly interdisciplinary, and thus more

relevant and engaging to life science students. Secondary goals included improvement in

students’ conceptual understanding, ability to connect meaning and mathematics, and epis-

temological stance. We collected several forms of data to measure progress toward these

goals.

A. Student Attitudes and Beliefs

To examine students’ appreciation of the role of physics in biology (and of interdisci-

plinary thinking more generally), we assessed their perception of the biological applications.

Students were asked how they viewed the integration of biology into the physics course; the

results show that we successfully matched the number and difficulty of biology applications

to student interest (Figure 3).

We then asked whether students38 found the biology applications (a) interesting, (b)

relevant to their other courses and planned career, and (c) helpful to understanding the

physics (Figure 4). Their replies were very encouraging (Figure 5 presents examples of

enthusiastic positive feedback). Additionally, one of our biology colleagues commented that

following our class, students were more willing and able to use physics in his course.

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According to Figure 4, the overall interest was greater than the perceived relevance. This

was echoed in several answers to the open-ended question “Have you used physics at all in a

biology class?” Several students answered in this vein: “Although I didn’t use [physics] that

much [in biology classes] the biology application made it MUCH more interesting for me.”

While including biology certainly makes the physics more palatable, life science students

may still question why they are required to take a year of physics.

In Spring 2009 we asked, “Have your perceptions of the connections between biology and

physics changed as a result of this course?” allowing open-ended answers. Based on the

most common responses, we asked a closed- response question in Spring 2010: Which of

these statements best describes how your perceptions have changed through this course?

1. My perception of connections has changed very little as a result of this course (17.2%)

2. It has become much more evident to me how much biology is dependent on physical

principles (28.4%)

3. My understanding of the actual physical mechanisms within biology has improved

since I’ve taken this course, though I knew before hand that they were connected

(54.4%)

Students clearly found the interdisciplinary nature of the course valuable, even though many

were already aware of connections between the disciplines.

The course was not universally well-received: 9% of students would have preferred to

have less or no biology in the physics class. They gave a variety of reasons: the biology

was confusing, didn’t help them understand the physics, made the physics harder, or simply

didn’t belong in a physics class. Some students were concerned that they were getting less

physics because class time was spent on biological topics. Comments included a simple

request to “Cease doing [biological applications],” along with the complaint that “I don’t

like biological applications in this course. I signed up to take physics, not biology.”

Another concern, voiced by 14% of the students, was that the course was not integrated

enough, mentioning the scheduling of biology-focused and regular lectures on separate days,

as well as differences in our individual teaching styles.

We administered the Colorado Learning Attitudes about Science Survey (CLASS)39 (an

extension of the Maryland Physics Expectations Survey (MPEX)40) to measure students’

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personal epistemologies in regard to science. This is a Likert-scale survey, where students

are asked to agree or disagree with statements about attitudes toward science (e.g. “To

understand physics, I sometimes think about my personal experiences and relate them to

the topic being analyzed”). The 33 questions are grouped into eight subcategories (e.g., real

world connections, sense making/effort).

Pre and post testing results are quoted as changes toward (positive) or away from (nega-

tive) the expert-like attitudes. In both traditional and reformed courses across the country,

changes range from -9.8 to +1.4 % in algebra based courses.41 However, courses with a strong

epistemological focus have produced changes on individual MPEX categories between +0 to

+30%.19,42

Overall, our students moved −3.3±1.1% away from expert beliefs. The best result was an

insignificant change (−1.3±2.8%) for the category of “real world connections,” the category

where we put the most emphasis and where loses are often the greatest ( MPEX “real world

connections” category loses are often 10-20%40). Our results show some progress, but leave

room for improvement.

There appears to be a disagreement between our own surveys on students’ appreciation

of biological applications and the results of the CLASS: our survey shows 17% of students

began to see more connections with biology, where CLASS shows no significant change in

students’ belief that physics applies to real life. We see two possible explanations. First, the

CLASS is not focused on biology in particular, so students may have been thinking about

other applications (e.g. cars, toaster ovens) about which their opinions did not change.

Second, the CLASS was administered in Fall 2010 after only one semester; our surveys

were administered in the spring semester. The second semester provided many biological

examples that students found intriguing.

B. Can students round off the cow with us?

A core question is the extent to which students are capable of integrating physics and

biology. To investigate this, we looked at student responses to the air versus water’ question

in Figure 1, asked on the final exam. We used these data to answer the following: Can

students look at a biological system through a physics lens, or are they unable (or unwilling)

to strip off the biological complexity? To what extent can they pick out which pieces of

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physics matter in a given biological situation?

Looking at student responses (N=237), only three brought in biological details that were

not introduced in the problem itself (for example, one student was concerned about breath-

ing issues). In addition, four students (mistakenly) inferred that since no organisms with

this method of locomotion existed, it was clearly not feasible. Clearly, students are able

and willing to overlook biological complexity that is not essential to the question at hand.

Moreover, they applied many relevant physics principles in their answers:

1. Half mentioned that the push from squirting out air would be far less than the push

from squirting out water due to lower density of air. Some went on to note that faster

or more frequent squirting would increase the push.

2. Nearly half of the students mentioned that buoyancy would be less in the air. A

handful then concluded that this would result in the animal being on the ground and

having to deal with friction.

3. Forty percent of the students noted that the drag force would be less in air, making it

easier to get around, though many focused on viscous drag instead of pressure drag.

In summary, 91% of the students were able to describe at least one of the above-mentioned

important physics difference between motion in air and water, demonstrating that they can

in fact see the physics in a biology question. In addition, another 6% mentioned physics ideas

that are more difficult to quantify: the effects of compression, wind, and air currents. There

were also, unsurprisingly, some common difficulties: confusion of viscosity and density (many

noted that viscosity was needed for the push), and failure to consider Reynolds number and

realize that viscosity is negligible in either fluid for an organism of this size and velocity.

A student’s answer to a different question provides additional evidence of the ability to

negotiate the physics/biology distinction:

Q: Bats, mice, dogs, and some other mammals are capable of detecting higher-

frequency sound waves than we are. Does that mean they can hear sound signals

faster or sooner than we do, assuming we are standing in the same place? Ex-

plain your reasoning. (This is not about reaction or processing time, just about

physical receipt of the signal.)

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A: Animals that hear a higher frequency do not hear sound signals faster or

sooner than we do because frequency does not affect the speed of sound signals.

They simply have ears that can detect frequencies at different vibrations than

we can, but it has nothing to do with the speed of the signals.

This student distinguished clearly between the biology and the physics: she answered the

physics first and went on to add closely related biological information. We have many

examples of similarly good answers from students who weave together physics and biology

in useful ways.33

Lastly, we have several pieces of student work that demonstrate students’ ability to make

their own connections between biology and physics (Figure 6). These data come from a final

exam question asking students to connect biology and physics, either in some situation we

described in class, or (for a bit of extra credit) in a context not mentioned in class. Another

source of data is an assignment in JAB’s evolution course, in which students invent new

species. Several students have used physics in these papers, indicating that they see physics

as one source for explaining biological form and function.

C. Connecting meaning and mathematics

We assessed students’ ability to connect meaning and mathematics through many exam

questions. For example, a question related to Newton’s law of cooling

T (t) = Be−t/C + D

was connected to a lab in which students took data from cooling temperature probes and

modeled their data with an exponential function, connecting parameters with the physical

situation. One part of the question asked which parameter changes when the insulation is

increased (if all else stays the same); 69% of students answered correctly. This parameter

was also emphasized in the study of damped oscillations, and several students explicitly

connected the cooling and damping curves. Students did less well on connecting the other

parameters to physical variables. One possible inference is that two exposures to the same

idea was significantly better than one. Anecdotal evidence that we were achieving our goal

came from a group that was videotaped during the lab. One group member commented

17

that “It’s kinda cool way to make us figure out this equation,” to which his lab partner

responded “It actually makes a lot of sense.”

D. Conceptual Understanding

To measure conceptual understanding, we used the Force and Motion Concept Evaluation

(FMCE)43 and the Test of Understanding Graphs in Kinematics (TUG-K).44 Although these

tests do not measure concepts of particular importance to biology students, they do provide

a measure of students’ conceptual learning. We chose the FMCE over the Force Concept

Inventory (FCI)45 because the FCI has many two dimensional questions (e.g. projectile

motion and circular motion) that we did not emphasize (Table 1) and tools are available to

produce a finer grained analysis of the FMCE results.46

The TUG-K pre-instruction score average was 34%, and the post-instruction average was

55%, representing a gain of 33.5% (N=752). The gain is defined as

〈g〉 =(post percent average)− (pre percent average)

100− (pre percent average)

and is designed to allow comparison between classes with different pre-test scores. The TUG-

K gains were fairly constant over the four years. The FMCE the gains are mixed. Scores

improved over the years, with the average gain in Fall 2010 of 24% (N=299). Gains varied

significantly across conceptual categories: gains in velocity graphs (42%), acceleration graphs

(28%), energy (58%), and Newton’s third law (34%) for our students were encouraging.

Gains in force graphs, force sleds, and reversing direction were closer to 15% and show

need for further improvement. For comparison, FCI gains for reformed courses are typically

around 35%.47

E. Summary

Our data on student attitudes and beliefs about the interdisciplinary features of the

course are very positive, with 90% of the students satisfied. Over 90% showed ability to

see physics in a biological situation, and many deftly combined physics and biology in

useful and/or novel ways. We conclude that the interdisciplinary nature of the course was

successful. The CLASS results indicate measurable progress toward our goal of improving

18

students’ epistemological stance, but show there is room for improvement. Although the

gains measured by TUG-K, and FMCE were modest at best, these assessments do not

sharply focus on our main objective.48 There is a clear need to develop more assessment tools

that focus on physics knowledge, skills, and attitudes that are central to biology students.49

Our data provide a starting place to review our main goals, how much we can reasonably

accomplish, and how we can best assess the outcomes.

VI. CONCLUSIONS AND DISCUSSION

There can be no general formula for an “ideal” IPLS course, since so many essential

elements, from staffing to syllabus, depend heavily on local needs and resources. Thus, you

will need to work out your own solutions to specific problems (proof is left to the reader!).

We can, however, identify some key strategies for success:

Topics and organization. Think carefully about what to cover, and how to organize it.

The traditional list of topics in a calculus-based course, or an introductory textbook, aligns

poorly with biology students’ needs. Those needs are, however, well-known to colleagues

who teach biology classes in which students should find physics useful: seek their input (see

below).

Traditional topics may be best presented in new contexts. For example, biology stu-

dents could learn kinematics and dynamics mainly in the context of fluids, where many

important (and biologically relevant) forces come into play. Thermodynamics concepts are

essential for biologists who focus at the cellular level; work with biologist colleagues to de-

velop applications of entropy and enthalpy that are accessible to IPLS students with minimal

mathematics. After deciding what to cover in the IPLS course, there remains the question

of organization. For example, it may make sense to start with energy (for which there are

many biological applications) rather than with kinematics.

Collaborate with biologists. Ideally, recruit a local biologist as a co-instructor for a truly

interdisciplinary IPLS course. If that’s not possible, invite biologist colleagues as guest

speakers. At a minimum, use them as a source of background information about biological

applications of physical topics.

Interdisciplinarity is, by definition, a two-way street. Besides making the physics course

more relevant and appropriate for biologists, we need to encourage biology faculty to call

19

upon the physics we teach in the IPLS course. As one of our students pointed out,

[B]iology professors don’t place emphasis on physical concepts, and those that do

assume no physics knowledge of their students. Perhaps requiring that physics

be taken Freshman or Sophomore year would allow upper-level biology class

professors to assume basic physics knowledge in their students, allowing them

to incorporate the concepts into their curriculum if desired.

We can provide instructors of advanced biology courses with an overview of what students

who have taken the IPLS class should already know about key topics (e.g. light, circuits,

energy, fluids). We can also encourage instructors in the freshman biology course to point

forward to these topics. Moving physics earlier in the curriculum poses a greater challenge,

as the first two years of the biology curriculum are often filled by mathematics, chemistry

and introductory biology.

Pay attention to constraints. Recognize administrative structures that pose constraints

or offer opportunities. Despite high-level calls for interdisciplinary teaching and learning,

much work remains to be done at ground level. We believe that a truly integrated IPLS

class is best taught by a physicist and a biologist together, and our local circumstances (plus

our NSF funding) enabled us to do that for several years. However, limited resources often

preclude such arrangements: what is best for students in the long run may be too costly for

departments in the short run. Institutions claiming to value interdisciplinary collaboration

need to develop ways to acknowledge and reward such activities, both for individual faculty

and for their departments. For example, a biologist helping to teach a physics class should

receive workload credit for that teaching effort (even though it is in a foreign department),

rather than have it treated as a voluntary overload.

On the positive side, where institutions (or funding sources) offer explicit support for

interdisciplinary teaching and research, we can make a strong case that improving the IPLS

course is a good investment. Physics and biology faculty benefit from sharing perspectives,

disciplinary knowledge and teaching strategies. Biology students benefit from a deeply

integrative course in which they gain not only new quantitative skills and physical knowledge,

but the ability to apply them in their chosen field.

Use the research. We say this again, because it bears repeating: draw on the extensive

research of learning and teaching to improve pedagogy.14 Such strategies are especially useful

20

in an IPLS course, where students may lack both the background and the motivation to

readily master new concepts and problem-solving skills.

Future work. While we have made progress in shaping our IPLS course to meet the

needs of our students, we see much that can still be done. Weaving in the biology themes

more extensively and smoothing the edges between biology and physics would make for a

more integrated course. We must become more realistic about what we can accomplish

in one course. Omitting many physics topics still leaves more than we can do effectively

(improving student content knowledge, skills and attitudes), yet we feel we must address

these several goals all together to make real progress. We suggest the evolutionary principle

of “correlated progression” as a possible model for on-going course development. This is

a model of evolution “in which all the traits are functionally linked and so constrained to

evolve by small increments at a time in parallel with each other.”50

In the face of diminishing resources, increased teaching requirements, and obstacles to

granting workload credit for shared courses, we have been unable to continue teaching our

collaborative IPLS class at UNH. We hope other faculty and institutions can devise a sus-

tainable model, and that our insights and resources will prove useful to that effort. Designing

and teaching a rigorous, effective, and engaging IPLS course is hard, and challenges remain.

Nevertheless, external calls for change resonate with our own conviction that we can do bet-

ter than the traditional introductory course to help life science students learn and appreciate

physics.

ACKNOWLEDGMENTS

We gratefully acknowledge the invaluable assistance of our collaborators on this grant:

Gertrud Kraut, James Vesenka, and Christopher Shubert. Helpful editorial suggestions were

provided by Ethan Bolker and Robert Hilborn. This material is based upon work supported

by the National Science Foundation under Grant No. 0737458.

∗ dawn.meredith@unh.edu

1 Otto Bluh, “Physics for the Biologist,” Am. J. Phys. 29, 771-776 (1961). Patrick Argos, “Gen-

eral Physics Course for Pre-medical Students,” Am. J. Phys. 41, 1224-1229 (1973). William G.

21

Buckman, James E. Parks, and Thomas P. Cohill, “ An introductory physics and biophysics

course for life science students,” Am. J. Phys 43, 77-80 (1975). Gerd Kortemeyer, “The Chal-

lenge of Teaching Introductory Physics to Premedical Students,” Phys. Teach. 45, 552-557

(2007).

2 Committee on Undergraduate Biology Education to Prepare Research Scientists for the 21st

Century, Bio 2010: Transforming Undergraduate Education for Future Research Biologists (The

National Academies Press, Washington, D.C., 2003).

3 AAMC-HHMI Committee, Scientific Foundations for Future Physicians (American Association

of Medical Colleges, Washington, D.C., 2009).

4 The MCAT MR5 preliminary recommendations are available on the AAMC website,

〈https://www.aamc.org/initiatives/mr5/preliminary recommendations/〉5 This site houses reports, presentations, and working group information from the 2009 meeting:

〈http://visionandchange.org/〉6 Detailed examples can be found in the AAMC-HHMI report.

7 A list of physics topics covered and a sample physics portion of the MCAT is available on-line,

〈https://www.aamc.org/students/applying/mcat/preparing/〉.8 The OAT practice test can be found on-line, 〈https://www.ada.org/oat/index.html〉. The Dental

Admissions Test (DAT) does not have a physics component.

9 Alex Y. Zheng, Janessa K. Lawhorn, Thomas Lumley, Scott Freeman, “Application of Bloom’s

taxonomy debunks the ’MCAT Myth’,” Science, 319, 414-415 (2008).

10 The MCAT exam includes passage questions that introduce physics phenomena or concepts

that few students will have learned about in class, such as bremsstrahlung (the subject of

the passage problem in the current practice test). These passages build on fundamental ideas

such as probability and conservation of energy, thus allowing students to construct a working

understanding of the new topic on the spot. Several of our students who took the exam confirmed

that it probes comprehension rather than mere recall.

11 Catherine H. Crouch, Robert Hilborn, Suzanne Amador Kane, Timothy McKay, and Mark

Reeves, “Physics for Future Physicians and Life Scientists: a moment of opportunity,” APS

News, 19, 9 (2010). IPLS course syllabi and working documents from the Fall 2009 IPLS

conference can be found at 〈http://www.compadre.org/PSRC/items/detail.cfm?ID=9797〉.12 From one of our students on anonymous course feedback.

22

13 David K. Gosser, Mark S. Cracolice, J. A. Kampmeier, Vicki Roth, Victor S. Strozak and

Pratibha Varma-Neslon, Peer-Led Team Learning: A guidebook (Prentice Hall, Upper Saddle

River, NJ, 2001).

14 J. D. Bransford, A. L. Brown, and R. R. Cocking, How People Learn: Brain, Mind, Experience,

and School, (National Academies Press, Washington, DC, 2003). Jo Handelsman, Sarah Miller,

and Christine Pfund, Scientific teaching (Roberts and Co., New York, 2007). Edward F. Redish,

Teaching physics: with the physics suite ( John Wiley & Sons,Hoboken, NJ, 2003). Randall

D. Knight Five easy lessons : strategies for successful physics teaching (Addison Wesley, San

Francisco, Calif. 2004).

15 Lillian Christie McDermott, “Millikan Lecture 1990: What we teach and what is learned -

Closing the gap,” Am. J. Phys. 59, 301-315 (1991).

16 Eric Mazur, Peer Instruction: A User’s Manual (Addison-Wesley, San Francisco, 1997).

17 Patricia Heller, Ronald Keith and Scott Anderson, “ Teaching problem solving through

cooperative grouping. Part 1: Group versus individual problem solving,” Am. J.

Phys. 60, 627-636 (1992). Their website has a library of context rich problems

〈http://groups.physics.umn.edu/physed/Research/CRP/crintro.html〉18 Randall D. Knight, Brian Jones, and Stuart Field, College Physics, A Strategic Approach (Pear-

son, Addison Wesley, SanFrancisco, CA., 2007).

19 Edward F. Redish and David Hammer, “Reinventing college physics for biologists: Explicating

an epistemological curriculum,” Am. J. Phys. 77, 629-642 (2009).

20 Open source tutorials focused on helping students refine their intu-

itions, developed by Andrew Elby and Rachel Scherr, are available at

〈http://www2.physics.umd.edu/ elby/CCLI/index.html〉. This site also has annotated

videos and instructor’s guides.

21 Malcolm Wells and David Hestenes, “A modeling method for high school physics instruction,”

Am. J. Phys. 63, 606-619 (1995).

22 James Vesenka, in preparation.

23 A new IPLS textbook (published after we began our project) that does pay close attention to

the needs of biologists is Jay Newman, Physics of the Life Sciences (Springer, New York, N.Y.,

2008). Another new text by Tim McKay is in preparation.

24 See the working documents from the 2009 IPLS conference, Competency E3, Teaching IPLS

23

Physics Content.

25 See page 37 in Bio2010 full list of recommended topics, which largely overlaps ours.

26 Tim McKay’s course outline for his IPLS course is located on the UMD-BERG webiste,

〈http://umdberg.pbworks.com/w/page/35683159/Tim%20McKay%27s%20Physics%20for%20Life%20Sciences%20Course%20-

%20Brief〉27 David Hammer, “Two approaches to Learning Physics,” Phys. Teach. 27, 664-670 (1989).

28 J. B. S. Haldane, Possible Worlds and Other Essays (Harper and Brothers, New York. 1928),

chapter “On Being the right size.” Max Kleiber, The Fire of Life: An Introduction to Animal

Energetics (John Wiley and Sons, New York, 1961). Thomas A. McMahon and John Tyler

Bonner, On Size and Life (Scientific American Library, New York, 1983). Colin J. Pennycuick,

Newton Rules Biology: A Physical Approach to Biological Problems (Oxford University Press,

Oxford, UK., 1992). E. M. Purcell, Life at low Reynolds number Am. J. Phys. 45, 3-11 (1977).

D’Arcy Wentworth Thompson, On Growth and Form (Cambridge University Press, Cambridge,

U.K., 1972). S.A. Wainwright, W. D. Biggs, J.D. Currey, and J.M. Gosline, Mechanical Design

in Organisms (Edward Arnold Reprint, London, UK; Princeton University Press, Princeton,

NJ. 1976).

29 See Bio2010, page 4.

30 Todd Cook and Joe Redish, University of Maryland, personal communication.

31 Gillian Galle and Dawn Meredith, in preparation.

32 Sharon M. Soucy McCrone and Tami S. Martin, “Formal Proof in High School Geometry: Stu-

dent Perceptions of Structure, Validity, and Purpose,” in Teaching and Learning Proof Across

the Grades: A K-16 Perspective, edited by Despina A. Stylianou, Maria L Blanton, and Eric J.

Knuth (Routledge Taylor& Frances Group, New York, 2009), p. 204-221.

33 Our website is a repository for several kinds of curricular materials: lectures, peer instruction

questions, annotated bibliographies, and problem collections. In addition we include student

work that connects biology and physics. 〈http://pubpages.unh.edu/ dawnm/phyls.html 〉34 Steven Vogel, Comparative Biomechanics: Life’s Physical World (Princeton University Press,

Princeton, NJ. 2003). Jack W. Bradbury, Sandra L. Vehrencamp, Principles of Animal Commu-

nication (Sinauer Associates, Sunderland, Mass. 1998). Mark W. Denny, Air and Water: The

Biology and Physics of Life’s Media (Princeton University Press, Princeton, N.J. 1993). Steven

Vogel, Life in Moving Fluids (Princeton University Press, Princeton, N.J., 1994). Steven Vogel,

24

Vita Circuits: On Pumps, Pipes and the Workings of Circulatory Systems (Oxford University

Press, New York, N.Y. 1992). Roland Ennos, Solid Biomechanics (Princeton University Press,

Princeton, N.J., 2012).

35 Humanized Physics Project laboratories and activities can be found at

〈http://physics.doane.edu/hpp/〉36 Suzanne Amador Kane, Introduction to Physics in Modern Medicine (Taylor and Francis, Lon-

don, 2003).

37 George Benedek and Felix Villars, Physics With Illustrataive Examples From Medicine and

Biology (AIP Press, Springer Verlag, New York, N.Y., 2000). Philip Nelson, Biological Physics:

Energy, Information, Life (W. H. Freeman and Company, New York, N.Y., 2008).

38 Not all questions were asked of students in all years.

39 W. K. Adams, K. K. Perkins, N. S. Podolefsky, M. Dubson, N. D. Finkelstein, and C. E.

Wieman, “New Instrument for measuring student beliefs about physics and learning physics:

The Colorado Learning Attitudes about Science Survey,” Phys. Rev. S. T. - PER 2, 010101-1

- 010101-14 (2006).

40 E. F. Redish, J. M. Saul, and R. N. Steinberg, “Student expectations in introductory physics,”

Am. J. Phys. 66, 212224 (1998).

41 K. K. Perkins, W. K. Adams, N. D. Finkelstein, S. J. Pollock, and C. E. Wieman, “Correlating

student attitudes with student learning using the Colorado Learning Attitudes about Science

Survey,” in 2004 Physics Education Research Conference Proceedings, 790, edited by J. Marx,

P. Heron, and S. Franklin (AIP, Melville, NY, 2005), pp. 6164.

42 Andrew Elby, “Helping physics students learn how to learn,” Am. J. Phys. 69, S54-S64 (2001).

43 Ronald K. Thornton and David R. Sokoloff, “Assessing Student Learning of Newton’s Laws:

The Force and Motion Conceptual Evaluation and the Evaluation of Active Learning Laboratory

and Lecture Curricula,” Am. J. Phys. 66, 338-352 (1998).

44 Robert J. Beichner, “Testing student interpretation of kinematic graphs,” Am. J. Phys. 62,

750-762 (1994).

45 D. Hestenes, M. Wells, and G. Swackhamer, “Force Concept Inventory,” Phys. Teach. 30, 141-

158 (1992).

46 Tools to help researchers gather and analyze data are available on the UMaine Orono Physics

Education Research web site, 〈http://umaine.edu/per/research-tools/〉

25

47 Hake, “Interactive-engagement versus traditional methods: A sixthousand- student survey of

mechanics test data for introductory physics courses,” Am. J. Phys. 66, 6474 (1998).

48 Work by D. J. Wagner on developing a fluids assessment, which is more closely linked

to needs of biology students, is available on PER-Central website, 〈http://www.per-

central.org/perc/2009/Detail.cfm?id=2688〉49 A summary of the IPLS FAll 2009 working group on the need for different assessment is located

on the IPLS wiki, 〈http://www.phys.gwu.edu/iplswiki/index.php/Assessment〉.50 T. S. Kemp, “The concept of correlated progression as the basis of a model for the evolutionary

origin of major new taxa,” Proc. R. Soc. B 7 274, 1618, 1667-1673 (2007).

26

Forces in air versus water: We talked about jellyfish that get around by taking in water and

squirting it back out. Describe at least two things that would be different if there were an

organism that got around in air by doing the same thing. Would these differences make it easier

or harder to get around?

FIG. 1. An example of a biological application.

27

Gradient-driven flows: Potential across a membrane. This is an ideal situation (as we had in lab);

it is NOT meant to describe a real cell membrane (though there are some similarities).

1. You have a membrane with pure water on the left side and K+ ions on the right side. The

membrane is permeable to K+.

(a) What gradients, if any, are present in this situation?

(b) Will the K+ move? If so, in what direction and why?

(c) If there is net motion of K+, when will it stop, if at all and why? If there is no net

motion, why not?

2. You have a membrane with Na+ on the left side and K+ ions on the right side (equal numbers

of ions on both sides). The membrane is permeable to K+ only.

(a) What gradients, if any, are present in this situation?

(b) Will the K+ move? If so, in what direction and why? Is there a net motion of K+?

(c) If there is a net motion of K+, when will it stop, if at all and why? If there is no

motion, why not?

FIG. 2. Example of a biological application stressing that the situation is idealized.

28

0  

10  

20  

30  

40  

50  

60  

70  

80  

Too  many/too  hard   Just  right   Too  few/too  easy  

number  

difficulty  

FIG. 3. Student perceptions of the appropriateness of the number and difficulty of the biological

applications.

29

0  

5  

10  

15  

20  

25  

30  

35  

40  

45  

strongly  agree   neutral   strongly  disagree  

Interes6ng  

Relevant  

Helped  me  understand  the  physics  

FIG. 4. Student answers to Likert scale questions: a) “I found the biological applications inter-

esting,” b) “I found the biological applications relevant to my other courses and/or my planned

career,” and c) “I found the biological applications helped me understand the physics.”

30

Biology applications made the class much more “worth my time” and made me feel that a

seemingly non-relevant major requirement actually did relate to my major.

The biology applications were helpful in examples to describe the physics behind it. I think I was

more comfortable with the biology explanations and by knowing how to explain it with biology I

could better understand the physics side of it.

The biological applications...were completely relevant. Not only were the applications extremely

interesting, but I think they helped students (including myself) connect adaptation abilities, and

more importantly, evolutionary sequences of the natural world of organisms. Organisms

understand physics incredibly well; this is how they thrive and survive. I think in order for a

biology student to be successful in the future, one must make these connections at an early stage

in his/her career.

FIG. 5. Favorable student comments about the relevance of the IPLS course.

31

From an exam question asking for an example of applications of physics principles: Giving a shot

too quickly is bad because the high concentration of the antibiotic or vaccine needs time to soak

in as the syringe is depressed. This is especially important in euthanasia because too great a

volume of the chemical, in too short a time could cause a non-peaceful and painful death.

From a fictional species paper in a course on evolution: Electriatus musae This species also

possesses traits unique within the Muridae family. Predominantly, it is capable of harnessing and

manipulating static electricity. The fur of this creature is a thick double coat with outer guard

hairs to shed the perpetual ocean mist about its habitat and a loose dry inner coat that keeps in

heat and generates a small static charge as the rodent moves. The rodent can release this charge

with some accuracy by pointing specialized, mobile, whiskers up to 10 inches away. The

transmission of the charge is made possible by the ever-present saltwater mist, which will conduct

electricity for small distances. The foot pads of this rodent are thick and non-conductive,

effectively trapping accumulated charge for defensive or offensive use. An over-accumulation of

static charge can stress the rodent’s cardiovascular system, despite surprising resilience to electric

overstimulation in that organ system. If that happens, E. musae will ground itself by touching its

tail to the ground, therefore dispersing the charge.

FIG. 6. Examples of students connecting biology and physics.

32