The document discusses the challenges of cross-disciplinary STEM instruction. It uses a case study of developing an introductory physics course for life science students to illustrate some of the key issues. Some of the main challenges discussed are: 1) Different disciplines have distinct cultures with different goals, assumptions, uses of language, ways of building knowledge, and meanings assigned to concepts. 2) The way mathematics is used in physics is different than in mathematics, with physical concepts blended with mathematical symbols. This difference in approach can cause misunderstandings for students from other disciplines. 3) Disciplines have their own preferred epistemological resources or ways of knowing. For example, biologists value authentic examples and numbers

1. The challenge
of cross-disciplinary
STEM instruction
E. F. (Joe) Redish
University of Maryland
Department of Physics
𝐸 =
𝐹
𝑞
𝑓 𝑥 = 𝜆
1 + 𝑥
𝑥! + 1
9/6/22 Pi' dBSERC 1
2𝐴
𝐵𝑑
> 𝑅
Wait…
What?
Theme song:
Bill Staines, “Bridges”

2. Outline
• A problem: Non-majors often don’t like our classes!
• Case study: NEXUS/Physics:
A introductory physics class for life science students
• Theoretical framework: Epistemology and ontology
• 1. Math: Two cultures separated by a common language
• 2. Biology: An example of disciplinary epistemology
• 3. Chemistry: An example of disciplinary ontology
• What can we do to improve what we do
with students in other disciplines?
9/6/22 Pi' dBSERC 2

3. Crossing disciplinary boundaries
• Modern cutting-edge science often brings
multiple disciplines together.
• Physics
• Chemistry
• Biology
• Math
• Cross-disciplinary instruction is common
in STEM programs at universities.
• There are challenges to cross-disciplinary
communication at any level, from elementary school
to professional collaborations.
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These are not always
perceived as successful.

4. A problem:
Non-majors o1en
don’t like our classes!
The challenge of interdisciplinary STEM education
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5. This can’t be a problem...
• We know how to teach physics.
• Physics is physics is physics ... for everybody.
• We have a working model – and dozens of standard
texts we can use with all kinds of resources.
• This makes teaching non-majors straightforward
– even if time consuming due to the difficulty
of administering large-classes.
• No thinking required!
5
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🤷
🤦

6. Unfortunately...
Our non-physics STEM students often don’t like our classes.
• They see it as a hoop to jump through
rather than something that will help them professionally.
• Even if we “make physics fun” and they enjoy the class,
they often view physics as being “unrealistic and irrelevant”
to their professional goals.
• They may do the minimum needed to “get through”
and not engage intellectually.
• As a result, they may not bring to their professional classes
what they were supposed to get from physics.
6
9/6/22 Pitt dBSERC 😱
While this is most commonly observed
with life-science and health-care students,
it also often is true of engineering students as well!

7. A case study
• Over the past decade I worked with
a multi-disciplinary team to create
an introductory physics course
for life-science students. (IPLS)
• This experience provided numerous examples
of the challenges of cross-disciplinary instruction.
• I present today my analysis of
some of the things I’ve learned.
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8. Case study
NEXUS/Physics:
A introductory physics class for life science students
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9. A personal trajectory
• My department first asked me to teach
algebra-based physics with pre-meds in 1975.
• In 1992 I turned my research efforts from
Nuclear Theory to Physics EducaMon Research.
• Between 2000 and 2009 I did research
on student learning in algebra-based physics
with emphasis on scienMfic skill development.
• In 2006 I began a close interacMon with a biologist
and worked with him on adding acMve engagement
to his class in biological diversity.
9/6/22 Pi' dBSERC 9
E. F. Redish and D. Hammer, Am. J. Phys., 77, 629-642 (2009) “Todd the biologist”

10. NEXUS/Physics
• In 2010, building on that our work
in algebra-based physics and biology,
we were given a challenge grant from HHMI.
• Our charge was to reform the physics class
for life science students as part of a national effort
to increase pre-med’s skill development
and multi-disciplinary strengths. (National Experiment
in Undergraduate Science Education – NEXUS).
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E. F. Redish, et al. (17!) Am. J. Phys. 82:5 (2014) 368-377. doi: 10.1119/1.4870386

11. Deep research
• We brought together a large team of physicists,
biologists, chemists, curriculum developers,
and education researchers.
• We spent a year discussing what physics could do
for biologists and pre-health care students.
• We spent two years teaching small classes,
videotaping everything in sight and learning
from listening to (and interviewing) the students.
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12. We learned some things that surprised us
• We had not expected to meet serious issues
of disciplinary culture and communica]on.
• I know the key to teaching is to learn
to listen to my students.
• But I had to learn how to listen both
to my students and to my colleagues
in biology, chemistry, and math.
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The problems weren’t restricted to students!
Faculty in other disciplines were often hostile
to physics and didn’t appreciate its value
in their discipline.

13. Using our experience as a case study
• I have tried to generalize what we have learned
about the barriers to interdisciplinary
communica8on.
• I’ll present examples from:
• Math
• Biology
• Chemistry
• I’ll analyze these using some general tools
borrowed from the social sciences
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14. Theoretical framework:
Culture
Communication and culture
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15. How do we know what we mean?
• We communicate through language,
but what ma^ers is not just words.
We make meaning through associa]ons
to a rich set of knowledge that we bring
from experience.
• Meaning is built through the individual’s
social and physical knowledge and on their
personal interpreta]on of their situa]on:
culture and context.
9/6/22 Pitt dBSERC 15
Michael Agar, Language Shock: Understanding the Culture of Conversation (Perennial, 1994)

16. Communication successes
… and failures
• We understand others
through our common experience and humanity.
• We misunderstand others
when we are unaware of our cultural differences.
• When we communicate, we are always translaMng,
inferring the speaker’s meaning.
• But our interpretaMons are cultural and depend on
our own percepMon of the context.
• If others bring a different culture or interpretaMon
of the context than we do, we can have serious confusion.
9/6/22 Pi' dBSERC 16
Alexander’s horned sphere
A topological fractal

17. Wait…what?
• When we’re communicating across cultures, we may
run into a surprising difficulty —a “Wait…what?” moment.
• We need to understand it as two distinct cultures
reaching for each other. (Agar calls this a “rich point”)
• We have to put our own culture and assumptions
under scrutiny as well as the one we are observing
in order to understand a rich point’s implications.
• Working through a rich point often reveals hidden assumptions
about our own culture.
“If you hit a rich point, think you’ve solved it, and haven’t
changed [yourself], then you haven’t got it right.” (Agar)
9/6/22 Pi' dBSERC 17
Wait…
What?

18. Different scienLfic disciplines
are disLnct cultures
• They have different broad goals.
• They make different unstated assumptions.
• They use language in different ways
(both English and mathematical symbology).
• They have different ways of building knowledge
(distinct epistemological resources).
• They may put different meanings to concepts
(distinct ontological resources).
• They (and we) are often unaware of these differences.
9/6/22 Pitt dBSERC 18

19. Beyond concepts:
Epistemology and ontology
• Content usually focuses on concepts, but how concepts
are built in a discipline depends on the discipline’s handling
of epistemology and ontology.
• Epistemology: Knowledge about knowledge
• How do we know when we know something?
• The tools we use to decide we now something
(epistemological resources) are discipline specific.
• Ontology: Knowledge about things
• What are the objects and concepts into which we parse the world?
• Categories and the way we think about them
are also discipline specific.
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20. Wait … what?
1. The way math does math doesn’t match physics:
Two cultures separated by a common language
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21. Pi' dBSERC
Epistemological and ontological problems
• Many problems that students experience in physics
has to do with the role of math in science,
an ontological misconception about what a symbol means.
• Here’s the key:
The way we use math in science
is different from the way it is done in math.
• We blend physical concepts with math
and this changes the way we interpret the symbols
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🔑
E. F. Redish, The Physics Teacher 59:5 (2021) 314-318. hNps://doi.org/10.1119/5.0021129
Wait…
What?

22. Really? Consider two examples.
A. 1 inch = 2.54 cm is a legiMmate equaMon but 3 second = 3 cm is not.
B. The Electric field is defined by 𝐸 = 𝐹/𝑞 where 𝑞 is the charge on
the test (probe) charge. If 𝑞 is replaced by 𝑞/3. 𝐸 does not change.
The numerical quantities we deal with in physics are typically NOT numbers,
but stand for something physical that can be quantified in a variety of ways
depending on choices we make. (Dimensional analysis)
The symbols in the equation are not arbitrary mathematical placeholders.
𝐹 is not just a symbol; it’s the electric force felt by the charge 𝑞.
Changing 𝑞 implies that 𝐹 will change as well.
9/6/22 Pi' dBSERC 22
Redish & Kuo, Language of physics, language of math, Science & EducaAon (2015-03-14)
When asked what happens to E when q→q/3
a majority of both biology AND ENGINEERING
students say it becomes 3E (after instruction).

23. Many problems arise in physics
if you don’t make the blend.
• Our equations tend to have many more symbols
than in intro math classes. Without the blend,
picking out what you should focus on
can be difficult.
• Which symbols are constants, variables,
and parameters can change in the same equation
depending on what question we ask.
• If you put numbers into your calculation right away
and drop units until the end, you lose the chance
of catching errors or reasoning about
the reasonableness of your answer.
9/6/22 Pitt dBSERC 24

24. A particular problem with not blending
• It’s not enough to recognize that
a concept belongs to a par]cular symbol.
The blend has to be more contextual than that.
• We o`en use the same le^er to represent mul]ple
concepts. We figure out which is which by context
and understanding the blend as describing a
par]cular physical situa]on.
9/6/22 Pitt dBSERC 25
p = pressure
momentum
dipole moment
Q = charge
heat flow
volume flow
V = velocity
volume
voltage T = tension
temperature
period

25. So what did I learn
about my own culture?
• I had taken for granted that students thought about
symbols in our equa>ons the same way I did.
• I failed to appreciate how difficult it was
to learn to build the blend.
• How did this change my instruc>on?
• I became much more explicit about
the use of symbols as models for rela5onships.
• I was more explicit about dimensions and units.
• I gave homework and quiz problems focusing on
blending physics concepts with math symbols —
throughout the course!
9/6/22 Pitt dBSERC 26

26. Wait … what?
2. The biologists way of looking at math:
An example of disciplinary epistemology
9/6/22 Pi' dBSERC 27

27. Starting NEXUS/Physics for real
• For our first week of NEXUS/Physics,
I asked Todd the biologist to provide me
a problem on scaling
(surface and volume effects) for a discussion
of measurement and functional dependence.
• He came up with a great problem about worms.
It looked like this:
9/6/22 Pitt dBSERC 28
“Todd the biologist”

28. A problem posed
by a biologist for a bio class
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A typical earthworm has the following dimensions:
weight = 3.7 g, length = 12 cm, width = 0.64 cm.
Oxygen consumption of the body = 0.98 μmole O2/g
Oxygen absorption across the skin = 2.4 nmole O2/mm2.
Model the shape of the worm as a solid cylinder. Calculate
its surface area (ignore the blunt ends), volume, and density.
Worms absorb oxygen through their skin, proportional to their area, but all of the cells
use oxygen in respiration, proportional to their volume. Assuming the rates above,
show whether or not this typical worm can absorb enough oxygen to maintain
the respiratory rate of its entire body.
Organisms can grow in two ways: by increasing its length, keeping other dimensions
the same, or isometrically — by increasing all of its dimensions by the same factor.
Calculate whether a worm that doubles a length can survive and whether a worm
that doubles isometrically can survive.

29. Added by a physicist
for a physics class
9/6/22 Pi' dBSERC 30
Consider worm of density d, length L, and radius R. If the rate
of oxygen absorption through the skin is A, and the rate it
uses oxygen in the volume is B, write a symbolic expression
for the total rate of oxygen used by the worm. Find the
maximum radius the worm could be
before it would have a problem taking in enough oxygen.
Rate oxygen is absorbed = 𝐴𝑆 = 𝐴(2𝜋𝑅𝐿)
Rate oxygen is used = 𝐵𝑑𝑉 = 𝐵 𝑑 𝜋𝑅!
𝐿
Condition for survival: 𝐴𝑆 > 𝐵𝑑𝑉
2𝜋𝑅𝐿𝐴 > 𝜋𝑅!
𝐿𝐵𝑑
2𝐴
𝐵𝑑
> 𝑅

30. The reaction of the development team
to my suggested changes surprised me.
• The physicists around the table to a person,
responded, “Oooh! Neat!” 👍
• The biologists around the table
reacted differently.
• They said, “Yuck! You’ve removed the biology!
That’s not the way worms grow. 👎
The radius never grows by itself.”
9/6/22 Pitt dBSERC 31
Wait…
What?

31. The compromise: Add this
• Our analysis was a modeling analysis. An earthworm
might grow in two ways: by just ge8ng longer or by scaling up in all
dimensions. What can you say about the growth of
a worm by these two methods?
• In typical analyses of evolu@on and phylogene@c histories,
earthworm-like organisms are the ancestors of much larger
organisms than the limit here permits. What sort of varia@ons in the
structure of a worm-like ancestor might lead to an organism that
solves the problem of growing isometrically larger than the limit
provided by the simple model?
9/6/22 Pitt dBSERC 32

32. Understanding biologists
– and ourselves as physicists as well
• Biologists, both students and faculty,
value biological authen1city and real world examples.
• Numbers make the connecMon
between math and reality.
• Physicists, on the other hand, value abstrac1ons,
simplifica1ons, and universal mathema1cal principles
that help understanding relaMonships.
• We analyzed the differences we saw as disciplinary choices
for epistemological resources (ways of knowing).
9/6/22 Pi' dBSERC 33
E. F. Redish and T. J. Cooke, CBE-LSR, 12 (June 3, 2013) 175-186. doi:10.1187/cbe.12-09-0147.

33. An analytical tool: Epistemological resources
• The epistemological tools of knowing — epistemological
resources — can be disciplinary dependent.
9/6/22 Pi' dBSERC 34
D. Hammer and A. Elby,” in Personal Epistemology: The Psychology of Beliefs
about Knowledge and Knowing, Erlbaum, 2002, pp. 169-190.
Physical mapping
to math
(Thinking with math)
Value of
toy models
By trusted
authority
Intro
Physics
context
Life is complex
(system thinking)
Intro
Biology
context

34. So what did I learn about my own
culture?
• I had used symbolic reasoning to gain insights
without filling in steps or drawing (biologically)
authentic conclusions
• I took for granted the value of toy models
and did not motivate them or embed them
in a realistic context
• I presented homework and exam problems that
• Made tacit assumptions ignoring factors that the students
did not have the sophistication to assume.
9/6/22 Pitt dBSERC 35

35. How did this insight change my instruc9on?
• I reframed the entire course
to make modeling a central factor.
• I discussed explicitly the value of symbolic reasoning
and functional dependence.
• I reformulated Newton’s laws as a framework
for creating models of motion.
• I included symbolic reasoning problems in homework,
quizzes, and exams.
• I introduced parts to homework and exam problems
asking students to consider and discuss assumptions
and corrections to toy models.
9/6/22 Pi' dBSERC 36

36. Wait … what?
3. The source of chemical energy:
An example of disciplinary ontology
9/6/22 Pi' dBSERC 37

37. The energe9cs of chemical bonding
– A tale of cross-disciplinary reconcilia9on
• In introductory chem and bio classes,
students learn about the role of energy
made available by chemical reac]ons.
• But students learn heuris]cs by rote
that feel contradictory in a way
that they don’t know how to reconcile.
1. It takes energy to break a chemical bond.
2. Energy stored in ATP bonds is the “energy currency”
providing energy for cellular metabolism.
9/6/22 Pitt dBSERC 38
Wait…
What?

38. Many students bring a “piñata” model
of a chemical bond.
"But like the way that I was thinking of it… whenever
chemistry taught us like exothermic, endothermic, …
I always imagined like the breaking of the bonds
has like these little [energy]
molecules that float out,
but like I know it’s wrong.
But that's just how
I pictured it from
the beginning."
9/6/22 Pi' dBSERC 39

39. Huh! If it takes energy to break
a chemical bond, where DOES
the energy come from?
(Like we get from food)
Isn’t it chemical energy?
9/6/22 Pitt dBSERC 40

40. Here’s a classical model. (The Gauss Gun)
9/6/22 Pitt dBSERC 41
https://www.youtube.com/watch?v=fiSd91sLtS4

41. Here’s how it works:
The energy comes from potential energy!
9/6/22 Pi' dBSERC 42

42. Distinct disciplinary perspectives
• Chemists and biologists make different
tacit (cultural) assumptions.
• Chemists tend to isolate a system
to focus on a particular physical phenomenon
(a reaction) and mechanism.
• Biologists tend to assume the natural
and universal context of life
– a fluid environment
(air and water taken for granted).
9/6/22 Pitt dBSERC 43

43. Using physics to reconcile
•We explicitly discussed with our students
the different ways different disciplines
looked at the same phenomenon
– and why.
•Can physics help resolve the conflict
between the way chemists and biologists
talk about energy? What’s really the issue?
Why is this so hard for students?
9/6/22 Pitt dBSERC 44
W. C. Galley, J. Chem. Ed., 81:4 (2004) 523-525.
M. Cooper and M. Klymkowsky, CBE Life Sci Educ 12:2 (2013) 306-312

44. To set up an instructional path
to clarify this, let’s analyze
how meaning is made
in abstract situations
using some tools from
cognitive linguistics
and semantics.
9/6/22 Pitt dBSERC 45
G. Lakoff and M. Johnson, Metaphors We Live By (U. of Chicago, 1980/2003)
G. Fauconnier and M. Turner, The Way We Think (Basic Books, 2003)

45. Building up abstract concepts
• According to L&J and F&T, we build up
abstract and complex concepts by beginning with
concrete knowledge gained from direct experience,
and using metaphors that gain meanings
of their own to create new mental models.
• We then blend different mental models (schemas)
to create even more complex ideas.
• Often, in physics, we deal with constructed quantities
that do not easily match everyday experience
by cognitive blending.
9/6/22 Pitt dBSERC 46

46. Ontological metaphors for energy: 1
Energy as a substance (works for kine8c energy)
Scherr et al. 2012 science.howstuffworks.com
47
9/6/22 Pitt dBSERC
B. W. Dreyfus, et al., Phys. Rev, ST-PER 10 (2014) 020108
Energy is in objects
Objects have energy
Energy is conserved
Students have
seen this
many times
since
elementary school.

47. Energy as a loca8on (works for poten8al energy)
phet.colorado.edu
Objects are at energies
Objects go to higher/lower energy
Ground state
Excited states
48
9/6/22 Pi' dBSERC
Ontological metaphors for energy: 2
Life science students
may not have not seen
this outside of physics

48. 49
9/6/22 Pitt dBSERC

49. 50
9/6/22 Pi' dBSERC
This blend is hard.
The location
metaphor
naturally includes
negative numbers —
And that conflicts
with the metaphor
of energy as
substance

50. So what did I learn about my own culture?
51
9/6/22 Pitt dBSERC
Adding a photon (”stuff”),
excites the molecule to
an excited (“higher”)
energy state.
• I learned that I tacitly used ontologically
complex mental models, assuming they
were obvious.

51. How did this insight change my instruc9on?
• O`en we say: “Students don’t like
nega]ve numbers” and do all we
can to avoid them.
• Instead, we built a coherent story
using toy models star]ng early
in the course, scaffolding to help
students build the requisite
mental models and blends.
9/6/22 Pitt dBSERC 52

52. A series of questions (PhET based)
helps students get comfortable with negative PE
and with the concept of binding energy.
9/6/22 Pitt dBSERC 53
Same problems analyzed
with shifted zero of PE –
one positive E, one bound.

53. We created homework problems and activities
to apply the concepts in real chemical contexts
of biological relevance (to maintain authenticity).
• Calculating the energy balances in the light and dark
reactions in a toy model of photosynthesis.
9/6/22 Pitt dBSERC 54

54. So what can we do
to improve what we do
with students in other disciplines?
Some sugges]ons
9/6/22 Pitt dBSERC 55

55. Reaching students in other disciplines
• Articulation
• How does this course fit into the program
of the students in the class?
• What can we do in physics that can be of real value
to them in their professional classes?
• Authenticity
• There have to be examples where learning physics
helps them better understand things
that they have only been told and learned by rote.
• Assumptions (unhiding)
• Often physics relies on unstated assumptions about what we
are doing and the skills the students are expected to have.
We need to be explicit about some things we take for granted.
9/6/22 Pitt dBSERC 56
🔑

56. But we have too much content to cover already!
We don’t have time to add a lot of new stuff.
• Adding a focus
on developing skills
doesn’t add new topics.
• It modifies the way we
teach topics we already
include.
• It does require us to be
“meta” — to be explicit
about tools since
students don’t easily
generalize.
9/6/22 Pitt dBSERC 57
Redish, Using math in physics: Overview, The Physics Teacher, 59 (2021) 314-318

57. Cross-disciplinary communicaLon
• In NEXUS/Physics we met many “wait … what?”s
in exploring the interac]on between the cultures of
physics, biology, chemistry, and math.
• We not only learned to respect the culture of other
sciences as dis]nct from the culture of physics —
we learned a lot about how
we as physicists do physics
that we had not previously
understood!
• Cross-disciplinary communica]on
can be a challenge, but it’s worth
the effort!
9/6/22 Pitt dBSERC 59

58. My biologist colleague, Todd Cooke and I,
summarized our interdisciplinary experiences
in a paper in CBE-LSE. Here’s our conclusion.
• While we have detailed our experience, each
interdisciplinary explora6on is bound to be unique to
the individuals and ins6tu6ons involved. But what we
expect will be common to such ac6vi6es will include:
showing respect for each other's discipline and
insights; a willingness to reconsider one's own
discipline from a different point of view; and finally,
pa6ence, persistence, and humor.
9/6/22 Pi' dBSERC 60
E. F. Redish and T. J. Cooke CBE-LSE, 12 (June 3, 2013) 175-186. doi:10.1187/cbe.12-09-0147.

59. Thanks for listening!
9/6/22 Pitt dBSERC 61

60. References
• E. F. Redish and D. Hammer, Am. J. Phys., 77, (2009) 629-642
• E. F. Redish, et al. (17!) Am. J. Phys. 82:5 (2014) 368-377.
• Michael Agar, Language Shock (Perennial, 1994)
• E. F. Redish, The Physics Teacher 59:5 (2021) 314-318.
• E. F. Redish & E. Kuo, Science & Educa>on 24:5-6 (2015) 561-590
• E. F. Redish and T. J. Cooke, CBE-LSR, 12 (June 3, 2013) 175-186.
• D. Hammer and A. Elby, in Personal Epistemology: The Psychology of
Beliefs about Knowledge and Knowing, Erlbaum, 2002, pp. 169-190.
• E. F. Redish, The Physics Teacher, 59 (2021) 683-688.
• W. C. Galley, J. Chem. Ed., 81:4 (2004) 523-525.
• M. Cooper and M. Klymkowsky, CBE Life Sci Educ 12:2 (2013) 306-312.
• G. Lakoff and M. Johnson, Metaphors We Live By (U. of Chicago,
1980/2003).
• G. Fauconnier and M. Turner, The Way We Think (Basic Books, 2003).
• B. W. Dreyfus, et al., Phys. Rev, ST-PER 10 (2014) 020108.
9/6/22 Pitt dBSERC 62