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Biology, especially physiology, includes quantitative relationships that explain key concepts, yet many biology students have poor math skills or math anxiety which might hinder their learning. We propose that students who are motivated to learn but are intimidated by math may benefit from in-class activities such as singing or listening to content-rich jingles that make the relevant math more accessible. Here we describe a three-part process by which we have used feedback from 231 students in four college physiology classes to develop math-related jingles suitable for use in similar classes. In Part 1, we report three classes' overall reactions (>60% positive) to educational songs as reported in standard multiple-choice surveys, while noting the limitations of this approach. In Part 2, we mine open-ended survey comments for common themes among students' reactions. Among music-related comments, we repeatedly find three main constructive suggestions: songs should be kept very short; connections between lecture material and songs must be obvious; and songs must be heard or sung more than once to be maximally helpful. In Part 3, we present seven mathematical physiology jingles (with URLs for online access) whose development was driven partly by insights from Part 2.
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Journal of Mathematics Education © Education for All
December 2015, Vol. 8, No. 2, pp. 56-73
Integration of Math Jingles into
Physiology Courses
Gregory J. Crowther
University of Washington, Bothell, USA
Katie Davis
University of Washington, Seattle, USA
Lekelia D. Jenkins
Arizona State University, USA
Jennifer L. Breckler
San Francisco State University, USA
Biology, especially physiology, includes quantitative relationships that explain
key concepts, yet many biology students have poor math skills or math anxiety
which might hinder their learning. We propose that students who are motivated
to learn but are intimidated by math may benefit from in-class activities such
as singing or listening to content-rich jingles that make the relevant math more
accessible. Here we describe a three-part process by which we have used
feedback from 231 students in four college physiology classes to develop math-
related jingles suitable for use in similar classes. In Part 1, we report three
classes’ overall reactions (>60% positive) to educational songs as reported in
standard multiple-choice surveys, while noting the limitations of this approach.
In Part 2, we mine open-ended survey comments for common themes among
students’ reactions. Among music-related comments, we repeatedly find three
main constructive suggestions: songs should be kept very short; connections
between lecture material and songs must be obvious; and songs must be heard
or sung more than once to be maximally helpful. In Part 3, we present seven
mathematical physiology jingles (with URLs for online access) whose
development was driven partly by insights from Part 2.
Key words: content-rich songs, educational music, physiology mnemonics,
musical equations.
The Next-Generation Science Standards and Vision and Change report
representing current best practices for K-12 and undergraduate education,
respectively state unequivocally that mathematical literacy is a central
component of biology education (American Association for the Advancement
of Science, 2011; NGSS Lead States, 2013). Thus, quantitative reasoning
should be included in all high school and college biology courses, yet this is
more easily said than done. Among the sciences, biology has a reputation for
harboring students and faculty who dislike or fear math (Sorgo, 2010). Indeed,
at the college level, performance on standardized multiple-choice math tests is
lower among college biology students than in their counterparts studying
Crowther et al. 57
computer science, physical science, and engineering (Wai et al., 2009). We and
others have observed that many college biology students struggle with many
aspects of simple algebraic equations: remembering them, solving them,
grasping their conceptual meaning, embracing their relevance to biology, and
so forth (Breckler et al., 2013; Watkins & Elby, 2013).
Numerous possible strategies for improving biology students’ math
skills have been noted by authors such as Madlung et al. (2011). These include
incorporating more math problems into biology classes, incorporating more
biology problems into math classes, creating more math-centric biology
textbooks, getting biologists and mathematicians to team-teach biology, and
developing new hybrid biology/math courses. These approaches could perhaps
be complemented with efforts to make math more fun and engaging for the
students, thus reducing barriers to learning. In the context of teaching statistics,
Lesser & Pearl (2008) offer a “taxonomy of fun” including such modalities
as humor, kinesthetic activity, music, and poetry and advice on implementing
fun activities. More specifically, the use of music to enliven mathematics and
statistics courses has been discussed cogently by others (Robertson & Lesser,
2013; Lesser, 2014) and is a primary theme of this special issue.
Here we explore a somewhat different use of music: to emphasize and
clarify important mathematical relationships found in biology courses. In
particular, we show how simple equations can be presented and sometimes
explained in the form of song lyrics, potentially promoting both memorization
and understanding. Our efforts are focused on physiology, a core component of
biomedical science taken annually by hundreds of thousands of high school,
undergraduate, and graduate/professional students in North America alone
(Human Anatomy & Physiology Society, 2006).
Our long-term goal is to determine whether content-rich STEM songs
can improve students’ academic performance, as suggested by some previous
reports (VanVoorhis, 2002; McCurdy et al., 2008; Smolinski, 2011; Lesser et
al., 2014). However, the answer to this question may depend heavily on whether
students like the songs and the pedagogy in which they are embedded. Thus, as
a preliminary step toward our ultimate goal, we have used students’ feedback
on classroom song interventions to guide the creation of short math jingles that
may be broadly useful to physiology teachers and students. The purpose of this
paper, therefore, is to report on this feedback-guided song development process
and the songs resulting from it; we plan to assess actual learning gains in future
General Methods
Courses and students studied. As part of our ongoing exploration of
educational science music (Crowther, 2012a; Crowther & Davis, 2013;
58 Math Jingles in Physiology Courses
Crowther et al., 2016), we collected and examined feedback on educational
songs used by the lead author in teaching quarter-long (11-week) undergraduate
physiology courses on three different campuses during 2014 and 2015. The
courses and campuses are as follows: Biology 220 (Introductory Physiology),
University of Washington-Seattle (UWS; 145 to 573 students); Biology 241-
242 (Human Anatomy & Physiology for pre-nursing students), South Seattle
College (SSC; 18 students) and University of Washington-Bothell (UWB; 27
students); Biology 352 (Anatomy & Physiology for biology majors), UWB (30
students). The 200-level courses (220 and 241-242) are considered introductory
courses and are taken mostly by freshmen, sophomores, and juniors of various
majors; the 300-level course (351) is taken predominantly by junior and senior
biology majors. While detailed demographic information on the students was
not obtained, the proportion of “non-traditional” (older) students is relatively
low at UWS, somewhat higher at UWB, and even higher at SSC.
Different subsets of the above courses were used in the three different
parts of the study described below; Table 1 shows which courses were used in
which parts. In order to maximize narrative clarity, the study’s parts are not
presented in a strictly chronological order.
Song development. Five to nine physiology songs were incorporated
into each of the above courses; 26 different songs were used in all. Songs were
generally written specifically for the above courses by the lead author. The
songs were intended to cover material central to many physiology courses, and
to present information as well as possible within the constraints of musical
rhythms and rhymes. Seven of the songs covered mathematical relationships,
as discussed below.
Song implementation in the classroom. Songs were generally
performed live by the instructor in the classroom a cappella (without
instruments), though karaoke backing tracks were used occasionally. Each song
was performed once. Lyrics were simultaneously provided to students via
PowerPoint slides. Students were sometimes encouraged to sing along and/or
make gestures illustrating the meaning of the lyrics. Lyrics and sheet music
were also available to students outside of class via the instructor’s website, but
links to these files were not always included on the slides.
Ethical treatment of human subjects. No personally identifiable
information was collected in this study. Because this study’s surveys were
originally created and administered primarily for purposes of course
development, they were not prospectively reviewed by an Institutional Review
Board (IRB). However, the subsequent decision to publish the data was
approved by the Human Subjects Division of the University of Washington.
Researcher positionality. The lead author taught all of the students
surveyed in this study. In presiding over the classes listed above, he made no
attempt to hide his enthusiasm for science-based music, and may have given
students the impression that he expected them to enjoy it as well. Thus, it is
possible that the lead author’s position of authority over the students influenced
Crowther et al. 59
the students’ responses even though the responses were collected anonymously.
The other authors had no relationship with the lead author’s students.
Table 1
Timeline of Study
Part 1: Students’ overall
reactions to physiology
Bio 241
Bio 241
& 352
Part 2: Students’ detailed
reactions to physiology
Bio 220
Part 3: Development of a
suite of math -themed
physiology jingles
Bio 220
Bio 352
Bio 352
Bio 242
Part 1: Students’ Overall Reactions to Physiology Songs
All SSC and UWB students completed Likert-style survey questions of
the following format: “To what degree did [course component] help you learn
the material? (A) very helpful, (B) helpful, (C) neither helpful nor unhelpful,
(D) unhelpful, (E) very unhelpful.” Course components that we asked about
included songs as well as (depending on the quarter) in-class discussions, in-
class worksheets, kinesthetic movements, laboratory exercises, and study
guides/practice tests. These surveys were completed by >90% of enrolled
students. To simplify analysis, the categorical responses above were converted
to numbers between 0 (very unhelpful) and 4 (very helpful).
Part 2: Students’ Detailed Reactions to Physiology Songs
General UW student evaluations of teaching. UWS students
completed standard anonymous end-of-quarter course evaluations administered
by UW’s Office of Educational Assessment. These evaluations asked students
to rate many aspects of the course and the instructor on a 0-to-5 scale, and also
to answer the following open-ended questions: Was this class intellectually
stimulating? Did it stretch your thinking? Why or why not? What aspects of this
class contributed most to your learning? What aspects of this class detracted
from your learning? What suggestions do you have for improving the class?
These optional evaluations were completed (either online or in person,
depending on the quarter) by 59% to 76% of enrolled students (depending on
the quarter).
To classify students’ song-related comments, the following categories
were created post hoc. (A) Songs were a positive aspect of the course, without
specific mention of themes C, D, or E below. (B) Songs were a negative aspect
of the course, without specific mention of themes C, D, or E below. (C) Songs’
60 Math Jingles in Physiology Courses
length and/or class time devoted to discussing them were excessive. (D)
Connections between song lyrics and lectures were not always clear or strong.
(E) Songs would be more beneficial if heard or sung multiple times (i.e., more
than the one time each was presented in class).
Song-specific survey. After one quarter, Biology 220 students at UWS
were invited to complete a survey about the six specific songs used during that
quarter: “Erythropoietin,” “Fick’s Law of Diffusion,” “Meet My Threshold,”
“Surface Area-to-Volume Ratio,” “The Sodium Jeer,” and “Where Is That
Sound?” (“Fick’s Law of Diffusion” and “Surface Area-to-Volume Ratio”
focused on mathematical relationships; the others did not.) Performance and
discussion of these songs which varied greatly in style and length
collectively filled 24 minutes of class time, spread over 17 hours of animal
physiology lectures. (An additional 17 hours of plant physiology lectures did
not include songs and were not covered by this survey.) Students were asked to
rate each song as a very poor use of class time, poor use of class time, okay use
of class time, good use of class time, or very good use of class time. To simplify
the analysis, these categorical responses were converted to numbers between 0
(very poor use of class time) and 4 (very good use of class time). Students were
also asked whether the maximum amount of class time that should be devoted
to a content-rich song should be 0 minutes, 1-2 minutes, 3-4 minutes, 5-6
minutes, 7-10 minutes, 10-20 minutes, or more than 20 minutes. This survey
was completed by only 15% of enrolled students, probably reflecting the
delayed timing of the survey and the limited motivation of students to complete
it at that point.
Part 3: Development of a Suite of Math-Themed Physiology Jingles
In reflecting on Part 2 of this study, the lead author decided to
expand his repertoire of math-related songs beyond “Fick’s Law of Diffusion”
and “Surface Area-to-Volume Ratio.” He identified additional mathematical
relationships that seemed sufficiently important to merit inclusion in most
physiology survey courses. He then wrote out key phrases about each
relationship and tried to find rhythms and melodies that suited these phrases.
For example, the central lesson of Poiseuille’s Law is that flow is proportional
to vessel radius raised to the 4th power. The idea arose that this relationship
could be captured in the phrase “r times r times r times r, with the repetition of
the key variable providing appropriate emphasis. The song was then built
around this phrase, with a verse to introduce the topic and a chorus to deliver
the equation itself (Figure 1).
In this manner, over several quarters, the lead author created five
additional math-themed songs for his physiology courses. Songs were intended
to be brief and thus may be considered “jingles” rather than full songs as
well as clear, pleasant, and easy to sing. These goals were not 100% compatible
with each other; for example, changing the above-mentioned phrase to “radius
times radius times radius times radius” would improve its clarity but would
Crowther et al. 61
compromise its musicality. Since some ambiguities are unavoidable, we use
them to spark class discussions, as exemplified by the questions provided in the
Results and Discussion
Part 1: Students’ overall reactions to physiology songs
As part of the lead author’s teaching, he routinely inserts content-rich
songs into lectures. Our initial assessments of this approach were usually
limited to multiple-choice surveys asking students whether they liked the songs
and/or whether the songs helped them learn. Data from three different classes
of physiology students are shown in Figure 2. These data suggest that most
students (60 to 67%, depending on the course) find the songs helpful or very
helpful, as opposed to neutral (18% to 37%) or unhelpful or very unhelpful (0%
to 12%).
Additional analysis of surveys from these courses suggested an
important caveat regarding the Figure 2 data: students’ ratings of the songs
might reflect their overall satisfaction with the course content and/or instructor
as much as or moreso than their specific opinions of the songs per se. That is,
the more the students like the course content and/or instructor, the more highly
they will tend to rate songs (and other tools), irrespective of the specific merits
of the songs (or other tools). This possibility first occurred to us when we found
strong correlations between SSC Biology 241 students’ ratings of the songs and
their ratings of other teaching tools, with R2 values of 0.88 (songs vs. kinesthetic
movements), 0.39 (songs vs. worksheets), and 0.48 (songs vs. labs). We had
previously assumed that students’ reactions to songs would be independent of
their reactions to other course tools because, for example, the songs were
written by the course instructor (G.J.C.), whereas the lab exercises were taken
from a standard mass-published lab manual.
62 Math Jingles in Physiology Courses
Figure 1. Sheet music for the jingle “Poiseuille’s Law of Laminar Flow.”
Having noticed these correlations retrospectively at SSC, we then
prospectively tested their occurrence in two physiology courses (Biology 241
and Biology 352) at a different institution (UWB). These courses used
somewhat different teaching tools and multiple lab instructors, but the same
classroom lecturer (G.J.C.). We again found highly significant correlations
between students’ perceived usefulness of the songs and their perceived
usefulness of other tools (songs vs. in-class discussions: R2 = 0.16, p=0.002;
songs vs. study guides: R2 = 0.16, p=0.003). Thus, “bleed-over” of overall
satisfaction into ratings of songs (or any specific course component) likely
biases the latter. Additional support for this interpretation comes from surveys
from the same course (Biology 220) taught by G.J.C. two consecutive quarters
in a row at the same institution (UWS). From the first quarter to the second
quarter, students’ ratings of the course content rose from 3.2 to 3.8 on a 5-point
scale, and their ratings of the instructor’s contribution to the course rose from
3.0 to 4.0; likewise, the percentage of music-related survey comments that were
positive (as opposed to mixed or negative) climbed from 33% (46 of 140) to
61% (11 of 18). While other explanations for these quarter-to-quarter changes
cannot be ruled out, the data are consistent with the idea that students’ ratings
of specific instructional features (such as music, in our case) are biased by their
overall opinion of the course content and/or instructor. This argument has
previously been advanced (though not about music in particular) by others such
as d’Apollonia & Abrami (1997) and Young (2006). A practical implication is
that any class’s ratings of songs should be interpreted in the context of its
overall “baseline” satisfaction with the course. Several previous studies of
educational STEM songs (McLachlin, 2009; Grossman & Watson, 2015;
Weinhaus & Massey, 2015; Yee Pinn Tsin, 2015), including our own (Crowther
& Davis, 2013), have omitted this important context. Future studies could
address this issue by reporting students’ ratings of music alongside their ratings
of other aspects of the course. Students who give a course’s music a 4 on a 1-
to-5 scale might be considered pro-music if they give 3s to most other parts of
a course, but perhaps not if they give 4.5s to most other parts.
Crowther et al. 63
Figure 2. Responses of three different physiology classes to the question
“To what degree did the songs used in class help you learn the class
material?” Possible answers were: very unhelpful (red), unhelpful (orange),
neither unhelpful nor helpful (yellow), helpful (light green), and very helpful
(dark green).
Part 2: Students’ detailed reactions to physiology songs
Having noticed the limitations of typical survey results like those
presented above, we desired more extensive and therefore more valuable
feedback to inform our development of songs as biology teaching tools.
Fortunately, such feedback was available via generic end-of-course evaluations
completed by 433 of the 573 UWS students enrolled in Biology 220 in the
spring quarter of 2014. Of these 433 students, 348 answered one or more of the
open-ended questions following the multiple-choice questions (see Methods);
of these 348, 140 students (40%) commented specifically on the songs used
during lectures despite the lack of a song-related prompt and the limited class
time devoted to the songs (2% of total lecture time). A summary of these song-
specific comments is given in Figure 3. Remarkably, despite the lack of a song-
related prompt, many students made specific suggestions for improving the
songs’ usefulness. The three most common suggestions (explicit or implied)
were (C) class time devoted to songs should be carefully limited (13% of
students commenting on the songs), (D) connections between song lyrics and
lectures should be made more obvious (10% of students), and (E) songs should
be repeated for maximum impact (6% of students). Examples of each type of
comment are given in Figure 3.
A song-specific survey completed by 85 students in this same class (see
Methods) resulted in two additional findings of note. First, 84% of these
students said that any in-class musical exercises should be limited to 6 minutes
or less, thus confirming the prevalence of theme C above (Figure 4). Second,
64 Math Jingles in Physiology Courses
among the six featured songs, the two mathematical songs (“Surface Area to
Volume Ratio” and “Fick’s Law of Diffusion”) received the highest and 3rd-
highest ratings, respectively (Figure 5).
Part 3: Development of a suite of math-themed physiology jingles
Intrigued by the studentspossible preference for math-themed songs,
and now recognizing the need for clearer songs that reinforce key course
content in more obvious ways (theme D above), the lead author developed
additional songs covering mathematical relationships central to animal
physiology (Table 2). Each song lasts less than one minute, perhaps qualifying
it as a “jingle” rather than a full song; this brevity enables concise in-class
interludes (theme C). Lyrics, sheet music, and simple online recordings are all
now publicly available (at the URLs listed in Table 2) to facilitate subsequent
recall and practice (theme E). Thus, the development of these jingles has been
informed by students’ feedback, as well as checked for accuracy and clarity by
a second physiologist (J.L.B.). Brief notes on each jingle are included below;
possible questions to ask students about each jingle are included in the
Cardiac Output and Pulmonary Ventilation. This jingle compares
the analogous equations for calculating cardiac output and calculating
pulmonary ventilation. Parallels in the two equations are emphasized by the
parallels in the verses, with only a few words changed between the cardiac
output verse and the pulmonary ventilation verse. For cardiac output: “Volume
moved per beat/Times number of beats per minute/Equals volume of blood per
minute;/That’s all this equation has in it!” For pulmonary ventilation: “Volume
moved per breath/Times number of breaths per minute/Equals volume of air per
minute;/That’s all this equation has in it!” Our hope is that if a student can recall
either one of the two equations, the other will be easy to retrieve.
Crowther et al. 65
Figure 3: Comments about physiology songs from UWS Biology 220
students. (140 students who commented specifically on songs used in class
were classified as shown. Percentages sum to >100% because five students fit
into two categories).
66 Math Jingles in Physiology Courses
Figure 4. Responses of UWS Biology 220 students (N=85) to a question on
the maximum amount of class time that should be devoted to a content-
based song.
Figure 5. Ratings of UWS Biology 220 students (N=82) of six songs on a 0-
to-4 scale. Error bars represent standard errors of the mean (SEM). Means
with different letters are significantly different from each other (p < 0.01)
according to paired t-tests with a Bonferroni correction for multiple
comparisons. SA/V and Fick are the two song topics on mathematical
Crowther et al. 67
Table 2
Math-Themed Physiology Jingles Developed During This Study
Output and
(~50 sec)
  
  
Cardiac output (CO) and pulmonary ventilation (PV)
are both calculated in the same way: the volume pumped
(stroke volume [SV] or tidal volume [TV]) is multiplied
by the frequency of pumping (heart rate [HR] or
respiratory rate [RR]).
Fick’s Law
of Diffusion
(~40 sec)
  
Diffusion rate is directly proportional to the
concentration gradient (∆P, for partial pressures of
gases) and surface area (A), and is inversely
proportional to diffusion barrier thickness (D).
(~50 sec)
For loads moved by muscles, the mechanical advantage
(MA) equals the length of the in-lever (Li) divided by
the length of the out-lever (Lo).
The Nernst
(~40 sec)
 
An ion’s equilibrium potential (Eion) can be calculated
from its concentrations outside and inside the cell
([ion]out and [ion]in) and its electrical charge (z).
Pee Values
(~40 sec)
      
In the kidney, a substance’s excretion rate (E) equals its
filtration rate (F) plus its secretion rate (S), minus its
reabsorption rate (R).
Law of
Flow (~40
  
The rate of blood flow through a blood vessel (Q)
depends most strongly on the radius of the blood vessel
(r). Q also depends on the hydrostatic pressure gradient
(∆P), blood vessel length (L), and fluid viscosity (η).
(~55 sec)
Animals’ metabolic rates reflect a balance between
intake of nutrients via their surface area (SA) and the
use of these nutrients by their internal volume (V). For
a hypothetical cube-shaped animal, as body length (L)
increases, V increases more rapidly than SA.
68 Math Jingles in Physiology Courses
“Fick’s Law of Diffusion.” When equations are expressed concisely,
the meaning of the abbreviations may be forgotten (Watkins & Elby, 2013).
“Fick’s Law of Diffusion” addresses this issue by presenting the abbreviations
in the first half of the jingle, then spelling out the full terms (in the same order)
in the second half. Thus, “delta P” corresponds to “pressure difference,” “A”
corresponds to “surface area,” “k” corresponds to “the constant k,” and “D”
corresponds to “diffusion barrier.”
“In-Lever, Out-Lever.” Students generally remember that mechanical
advantage (MA) is equal to a ratio involving the in-lever (Li) and the out-lever
(Lo), but they often flip the numerator and denominator. This jingle helps them
remember that MA equals Li divided by Lo and points out that a change in either
one can improve the mechanical advantage: “Elongate the in-lever, shorten up
the out.”
“The Nernst Equation.” This jingle does not present the terms of the
equation as one would write them out from left to right; rather, it starts with the
ratio of extracellular and intracellular ion concentrations because this is the core
of the equation an ion’s equilibrium potential (E) reflects its relative
concentrations outside and inside the cell and the other terms should not
distract from that.
“Pee Values.” In studying the kidney, many students struggle with the
terms filtration, reabsorption and secretion. In particular, they often do not
know whether each of these processes moves substances from the blood to the
pre-urine or vice versa. They will keep these straight if they understand the
jingle’s equation, which conveys that filtration and secretion move substances
into the pre-urine (for excretion) while reabsorption does the opposite.
“Poiseuille’s Law of Laminar Flow” (Figure 1). The repetition of r
times r times r times remphasizes the surprising fact that blood flow rate is
proportional to vessel radius (r) raised to the 4th power. (In addition, the rhyme
with “employ” helps students pronounce the French surname “Poiseuille.)
Surface Area-to-Volume Ratio. This jingle references the formulas
for the surface area and volume of a cube: 6L2 and L3, respectively, where L is
the length of a side of the cube. These formulas should be written out explicitly
to avoid confusion (e.g., “Six L to the two” might not otherwise be understood
as 6L2). Also, the alliteration of “large” and “low” in the line “If you’re large,
it’s low” reminds students to group these two adjectives together: a large body
size implies a low surface area-to-volume ratio.
Advice on Implementation
Based on the data presented in Part 2 and past experience deploying
music in the classroom, we recommend that physiology instructors who wish
to use a jingle should consider the following. Though some instructors consider
music to be a fun way of introducing new topics (Crowther et al., 2016), we
usually use songs as recaps or extensions of already-covered topics, so that
students have some context in which to interpret the song lyrics (theme D
Crowther et al. 69
above). Instructors should facilitate multiple passes through a jingle (theme E),
perhaps by using it in class and also encouraging out-of-class, web-aided
practice. Non-singing instructors may wish to recruit musically inclined
colleagues, teaching assistants, or student volunteers. In addition, rather than
assuming that a jingle “speaks for itself,” instructors should help students
unpack the highly compact lyrics (theme D). Finally, as with any other aspect
of a lecture, advance rehearsal of jingles will help ensure that valuable class
time is used efficiently (theme C).
Obviously, further evaluation will be necessary to assess the
effectiveness of the seven jingles listed in Table 2. These jingles are now being
evaluated by hundreds of students NOT taught by the lead author; we look
forward to reporting these results in a future publication.
While this study focused on college physiology courses due to our
expertise and current teaching assignments, our work may be informative to any
high school or college-level efforts (e.g., in a math class) to teach math with
content-rich music. In particular, we believe that college students’ apparently
strong preference for very short jingles is an important finding, partly because
it contrasts with the extended length of most commercially available math songs
for this age group, as catalogued at (Crowther, 2012b).
Indeed, it is notable that two of the only studies to demonstrate a positive impact
of content-rich math music on test performance (VanVoorhis, 2002; Lesser et
al., 2014) used jingles rather than full-length songs as their intervention.
In summary, while math remains a considerable challenge for many
biology students, brief content-rich jingles may render it less dreary and more
accessible. The examples presented here may, at the very least, provide
engaging interludes that are minimally disruptive to existing curricula.
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72 Math Jingles in Physiology Courses
Sample Questions to Ask Students about the Physiology Jingles
“Cardiac Output and Pulmonary Ventilation”
Questions: (1) The terms cardiac output, stroke volume, heart rate,
pulmonary ventilation, tidal volume, and respiration rate are not included in the
jingle’s lyrics, but their definitions ARE included. Which definitions go with
which terms? (2) How do these variables change when you start performing
aerobic exercise?
Answers: (1) “Volume of blood per minute” is cardiac output. “Volume
moved per beat” is stroke volume. “Number of beats per minute” is heart rate.
“Volume of air per minute” is pulmonary ventilation. “Volume moved per
breath” is tidal volume. “Number of breaths per minute” is respiration rate. (2)
All of these values increase during aerobic exercise.
“Fick’s Law of Diffusion”
Questions: (1) Which term of the equation reflects a concentration
gradient, which is necessary for diffusion? (2) What does the constant k
depend on?
Answers: (1) Pressure difference (delta P) refers to a difference in the
partial pressures of a gas, and thus reflects a concentration gradient. (2)
“Constant” k depends on the temperature, the size of the molecule that is
diffusing, the specific medium through which it is diffusing (water? air?), etc.
“In-Lever, Out-Lever”
Questions: (1) What units does Mechanical Advantage (MA) have? (2)
What range of values can a Mechanical Advantage have? (3) Mechanical
Advantage can also be calculated from the force in (Fi) and force out (Fo), or
from the velocity in (Vi) and velocity out (Vo). How do those formulas compare
to the one presented in the jingle?
Answers: (1) MA is unitless; the units of the numerator and denominator
cancel. (2) In theory, mechanical advantage can be anywhere from just above 0
to far above 1. (3) MA is also equal to Fo divided by Fi and to Vi divided by Vo.
“The Nernst Equation”
Questions: (1) What is ion valence? (2) What units are carried by the
equilibrium potential (E)? (3) What does the value of E mean?
Answers: (1) Ion valence is the charge carried by an ion, such as minus-
1 or plus-2. (2) E, an electrical potential, generally is reported in units of
millivolts. (3) E is the electrical gradient across the membrane needed to
perfectly counterbalance any concentration gradient, such that there is no net
movement of the given ion from one side of the membrane to the other.
Crowther et al. 73
“Pee Values”
Questions: (1) Does secretion of a solute by the kidney increase or
decrease the rate at which it is excreted? (2) Is it possible for the excretion rate
of a solute to be 0? If so, how?
Answers: (1) Secretion of a solute increases the solute’s excretion rate.
(2) Yes, this is possible. If the filtration, secretion, and reabsorption rates are all
0, then the excretion rate will be 0 as well. (This is generally true for proteins
in the blood.) Alternatively, if the reabsorption rate is equal to the sum of the
filtration rate and the secretion rate, the excretion rate will be 0. (This is
generally true for glucose in the blood.)
“Poiseuille’s Law of Laminar Flow”
Questions: (1) How does vessel radius (the r in the song) relate to
resistance to blood flow? (2) What is delta P here? Is this the same delta P that
is in Fick’s Law of Diffusion? (3) Can you rearrange the equation so that pi is
in the numerator?
Answers: (1) Resistance to flow (often abbreviated with a capital R) is
proportional to radius to the 4th power. (2) Here delta P refers to a difference in
hydrostatic pressure over the length of the vessel. It is not the same as the delta
P in Fick’s Law of Diffusion. (3) The equation can be rewritten as: Flow =
“Surface Area-to-Volume Ratio”
Question: (1) If we were to assume that an animal were spherical, rather
than cube-shaped, would SA/V be similarly affected by body size?
Answer: (1) Yes. The surface area of a sphere equals 4*π*r2, where r is
the radius. The volume of a sphere equals (4/3)* π*r3. The surface area-to-
volume ratio is 3/r, which decreases as r increases. Thus this ratio decreases
with increasing size, regardless of whether the object is cube-shaped or
Gregory J. Crowther
University of Washington, Bothell
Lekelia D. Jenkins
Arizona State University
Katie Davis
University of Washington, Seattle
Jennifer L. Breckler
San Francisco State University
... The mathematical physiology theme was pursued for two reasons. First, this study expanded on a previous study of songs on that topic (8), which, in turn, was based on the first and last authors' experience that students often struggle with mathematical aspects of physiology and could use extra help in this area. Second, we thought that using songs about equations would help students grasp the point of each song without a lot of additional explanation. ...
... Song length. The songs used in phase 1 were all between 36 and 46 s long, in line with previous recommendations to keep them short (8,17). For the 14 comments classified by both coders as being positive regarding song length, all 14 praised the song's conciseness. ...
... Regarding song length, our evidence that students prefer songs to be as short as possible, perhaps Ͻ30 s, corroborates and extends previous data on this point (8), but seems to be in conflict with the lengths of most educational STEM songs used in high school and college. In a national curated database of 178 songs about statistics (19,21,28), the median song length was found to be 1 min 55 s, i.e., over twice as long as the longest song in the present study, whereas in a database of 191 physics songs (32), the median song length was 2 min 7 s (Fig. 3). ...
The possible benefits of using music to enhance learning of STEM content are numerous, diverse, and largely unproven. We sought to determine which (if any) of these possible benefits are commonly experienced by undergraduate students and are thus especially worthy of further investigation. Four hundred ninety-three students in nine physiology courses at two midsized American universities rated the usefulness of short instructor-penned mathematical physiology songs and explained in their own words why each song would or would not be a useful study aid. The students collectively perceived the usefulness of each song to depend on both academic factors (e.g., the lyrics' clarity or relevance to the course) and aesthetic values (e.g., the appeal of the rhythm or the quality of the singing). Most strikingly, although students' free responses were brief (median length: 18 words in study phase 1, 16 words in study phase 2), nearly one-half of them (1,039 of 2,191) concerned memory, suggesting that many students see educational songs primarily as mnemonic devices. A second major theme of students' comments concerned the conciseness and information density of the songs. Though all 10 songs were brief, lasting 17-54 s, students seemed to prefer shorter songs (perhaps better called "jingles"). This first-of-its-kind data set on student perceptions of educational songs should inform the creation and usage of such songs, as well as further research on their possible value.
... Despite these caveats, we were pleased that our intervention went smoothly and led to positive student responses. Based on that and other relevant experience (12,21,22), we can offer practical encouragement to other instructors who may be tempted to try something similar. The following vignettes illustrate additional ways to incorporate music into a biology course with the aid of a remote guest speaker. ...
... As a counterweight to our enthusiasm for musical interventions, we should admit that such interventions do come with several possible pitfalls, which we have enumerated previously (21,22). These include perceptions that musical activities are a waste of time in a biology class, unclear connections between song lyrics and course content, and unrealistic expectations that a single pass through a song is sufficient for memorization and recall. ...
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As most instruction has been forced online, biology instructors have become acutely aware of the many advantages and limitations of online teaching. Here, we investigate one possible advantage of online education: the ease of allowing remote guest speakers to interact with students in real time. In particular, we piloted a model in which guest speakers could facilitate direct music-related interactions with students, possibly benefiting students' content knowledge and sense of community. In the context of an undergraduate animal physiology course, face-to-face lessons on arterial blood gases and the renal system were supplemented with videoconferences with a guest speaker who presented relevant content-rich songs and led class discussions of the lyrics. Survey and test data suggested that, after each of the lessons, the students (i) had increased confidence in their understanding of the material, (ii) performed better on objective test questions, and (iii) attributed their learning chiefly to the musical intervention. While our approach awaits further exploration and testing, this report provides preliminary evidence of its feasibility and offers practical suggestions for others who may wish to give it a try.
... Lyrics may be cryptic due to length constraints and/or artistic flourishes, but wellcrafted study questions can help listeners unpack these lines to make their meanings and implications clearer (47). However, with some exceptions (63)(64)(65), most STEM songs do not come with such study questions, potentially propagating the fallacies that songs speak for themselves or are only for rote memorization. Instructors who use model 2 should therefore spend time creating or finding study questions that help students connect the musical content with the course content. ...
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The idea of teaching science through music has undeniable appeal in implying that learning can be engaging and fun while also covering content efficiently. Indeed, there is little doubt that songs can be uniquely memorable, suggesting mnemonic options for core content. However, many classroom implementations of science music have limitations such as an overemphasis on rote memorization, rather than a constructivist building of understanding. In this brief review we ask how music might facilitate learning of science content in a manner consistent with the well-known pedagogical framework of Universal Design for Learning (UDL). In our view, UDL suggests certain distinct possible benefits of incorporating music into curricula, leading us to propose four models of practice. These four models are: (1) students enjoy music together, (2) students critically analyze songs as texts, (3) students creatively augment existing songs, and (4) students create new songs. Model 1 can contribute to an inclusive learning environment, while Models 2-4 can encourage cognitively rich active learning, and Models 3-4 can additionally help students channel scientific understanding into the creation of authentic products. We conclude with comments on logistical issues that arise in implementing these four models, including the use of appropriate rubrics and the prioritization of artistic quality.
... One of us (GJC) regularly uses music in teaching anatomy and physiology courses (Crowther et al. 2015), including Biology 241-242 (human anatomy and physiology for pre-nursing students) and Biology 351-352 (comparative anatomy and physiology for biology majors) at a Primarily Undergraduate Institution in the state of Washington. We assess this integration of music into the curriculum in part by distributing IRB-approved surveys to students after obtaining the students' informed consent. ...
... One of us (GJC) regularly uses music in teaching anatomy and physiology courses (Crowther et al. 2015), including Biology 241-242 (human anatomy and physiology for pre-nursing students) and Biology 351-352 (comparative anatomy and physiology for biology majors) at a Primarily Undergraduate Institution in the state of Washington. We assess this integration of music into the curriculum in part by distributing IRB-approved surveys to students after obtaining the students' informed consent. ...
... One of us (GJC) regularly uses music in teaching anatomy and physiology courses (Crowther et al. 2015), including Biology 241-242 (human anatomy and physiology for pre-nursing students) and Biology 351-352 (comparative anatomy and physiology for biology majors) at a Primarily Undergraduate Institution in the state of Washington. We assess this integration of music into the curriculum in part by distributing IRB-approved surveys to students after obtaining the students' informed consent. ...
Full-text available
Writing To Learn (WTL) is a promising pedagogical approach by which students can process scientific content. However, much remains unsettled regarding WTL's likely mechanisms of action and corresponding best practices, particularly for nontraditional forms of writing, such as the writing of song lyrics about disciplinary content. Here we present pilot data suggesting that, when given music assignments, some anatomy and physiology students are resistant to what we term " Songwriting To Learn " (STL), while others see its potential as a catalyst for learning. We offer recommendations on implementing STL in science courses. Our emphasis is on facilitating and tracking the learning that occurs during the song-writing process, rather than focusing on the final song. Our key recommendations are encapsulated in a template for documenting this along-the-way learning and, in doing so, guiding students through science song-writing assignments that might otherwise seem difficult. We welcome feedback on this template.
One STEAM (STEM + Arts) strategy is to supplement traditional STEM instruction with music. Using music could provide the dual benefits of (1) making STEM content more accessible and (2) enhancing students’ engagement in the learning process. Here we explore the extent to which music-oriented high school students achieve these two benefits when they participate in ‘Songwriting To Learn’, a possible variation on the Writing To Learn (WTL) model of instruction. We analysed 81 artist statements, collected over 12 years at an annual science fair, in which students described their music compositions and the compositions’ connections to science. Rather than simply reporting scientific facts in song lyrics, these students used an impressive variety of musical elements (Genre, Instruments, Lyrics, and Structure [i.e. chords, dynamics, melody, rhythm]) as metaphors or symbols for science-related elements (Scientific Topic, Conveying Information, Affect, Personal Story, Scientific Story). Many students demonstrated a sophisticated attention to musical details and nuances, consistent with their frequent self-identification as musicians and/or music fans. Moreover, in composing and performing songs, these students fulfilled some of the key criteria by which scientific identities are developed, including the forging of personal connections to science. By writing songs about science, students may use their practice-linked identities in the domain of music to express their growing understanding in the domain of science.
This chapter surveys interdisciplinary pedagogy that emphasizes the connections between mathematics and music by contextualizing the mathematics learning process within musical experiences. Both empirical research and international practice have demonstrated a variety of opportunities for music-themed mathematics teaching methods to be developed and implemented across all grade levels, from kindergarten to college. This chapter, which summarizes the current state of research and practice for music-themed interdisciplinary mathematics education, is divided into three main sections: (1) the overview of connection between mathematics and music, (2) theoretical perspectives on music and mathematics learning, and (3) a description of pedagogical approaches appropriate for supporting music-mathematics interdisciplinary lessons. Regarding the overview, the chapter discusses research studies that have investigated the mathematics present within music and the application of mathematics to improving musical composition and musical instrument design. Regarding the theoretical perspectives, the chapter discusses research studies that have investigated passive musical immersion as well as more active musical learning processes and their comparative impacts upon learners’ mathematical cognitive processes and capabilities within informal learning settings. Regarding the pedagogical approaches, the chapter presents and evaluates the prevalent mathematics-music-integrated teaching strategies about how student-centered musical activities (i.e., listening and singing, composing and performing, musical notating, and musical instrument design) can be utilized to teach specific mathematics topics.
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Many colleges and universities have adopted the use of student ratings of instruction as one (often the most influential) measure of instructional effectiveness. In this article, the authors present evidence that although effective instruction may be multidimensional, student ratings of instruction measure general instructional skill, which is a composite of 3 subskills: delivering instruction, facilitating interactions, and evaluating student learning. The authors subsequently report the results of a meta-analysis of the multisection validity studies that indicate that student ratings are moderately valid; however, administrative, instructor, and course characteristics influence student ratings of instruction. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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Music can be used in lectures to increase student engagement and help students retain information. In this paper, I describe my use of biochemistry-related lyrics written to the tune of the theme to the television show, The Flintstones, in a large class setting (400-800 students). To determine student perceptions, the class was surveyed several weeks after the song was used. Students reported a high level of engagement and enjoyment during the song. Many students found the song to be a helpful study tool. To guide future song selection, the students were also asked to indicate their familiarity with 30 popular songs from the past 50+ years. The songs that were least familiar to the students were all released before 1980, but some older songs were well known. The results support the use of content-specific lyrics set to familiar tunes as an educational tool, and provides information about specific songs that would or would not be suitable for this purpose.
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We describe the use of original music videos as instructional aides for a large non-science major course in natural history. The course meets university general education requirements for life sciences and environmental literacy. Over two class years (Fall 2012 and 2013), the senior author wrote and recorded five music videos to reinforce class lecture materials including songs on: (1) conceptual topics, (2) important habitats, and (3) important species. The purpose of the videos was to utilize a multimodal form of instruction in a format (music videos) commonly used and appreciated by university students. The videos were uploaded to YouTube between 18 August 2012 and 13 November 2013. Anonymous, voluntary questionnaires in both years indicated that students' perceived that videos improved their learning and attitudes towards both class and studying. We assume that a portion of the positive responses was due to the fact that the class instructor generally created and sang the songs in the videos, rather than employ materials from other sources. The results reveal potential for measuring actual gains in learning and retention and an investigation of their correlation with different video content (e.g., natural history concepts, habitat types, and species information) is ongoing.
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Full report is available here:
Next Generation Science Standards identifies the science all K-12 students should know. These new standards are based on the National Research Council's A Framework for K-12 Science Education. The National Research Council, the National Science Teachers Association, the American Association for the Advancement of Science, and Achieve have partnered to create standards through a collaborative state-led process. The standards are rich in content and practice and arranged in a coherent manner across disciplines and grades to provide all students an internationally benchmarked science education. The print version of Next Generation Science Standards complements the website and: Provides an authoritative offline reference to the standards when creating lesson plans. Arranged by grade level and by core discipline, making information quick and easy to find. Printed in full color with a lay-flat spiral binding. Allows for bookmarking, highlighting, and annotating.
Mathematical lyrics are song lyrics connected to, or inspired by, mathematics or statistics. This paper explores various types of mathematical lyrics and their roles in mathematics education. In particular, the paper contains many examples of my own lyrics as well as an extensive bibliography of lyrics composed by others. It also provides resources and strategies for creating such lyrics and for using them in an educational setting.
Potential benefits of incorporating music into science and math curricula include enhanced recall of information, counteraction of perceptions that the material is dull or impenetrable, and opportunities for active student engagement and creativity. To help instructors and others find songs suited to their needs, I created the “Math And Science Song Information, Viewable Everywhere” database in March of 2004. Recently rebranded as the database, it now covers >5,500 songs varying widely in topic and grade level. Website visitors may search the database using such criteria as keywords from lyrics, performer/songwriter names, and age ranges targeted by songs. Changes in the database's contents over the past 7 years suggest that the online availability of educational songs has increased greatly during this period. College biochemistry and molecular biology instructors can use the database to find songs covering core concepts for majors and nonmajors as well as relevant material from related subjects, such as physics and mathematics. In offering teachers and students a menu of existing scientific songs, the database may inspire some of them to create additional content-rich music.
Music is not typically used in teaching high school- and college-level chemistry. This may be attributable to instructors’ perceptions of educational music as being solely for memorization, their uncertainty about how to incorporate music effectively, or because of a limited number of suitable songs in which the music and words reinforce each other. To address these issues by way of a biochemistry example, we created Amino Acid Jazz, a sing-along exercise in which students synthesize a musical polypeptide from amino acid building blocks. Along the way, musical elements indicate key points about protein chemistry and structure. This exercise is an example of how the music of a song can amplify (rather than distract from) the content of the lyrics, and can thus promote knowledge acquisition that goes beyond rote memorization. Furthermore, it may be extended to incorporate students’ own creative ideas. Most initial feedback from students and other teachers has been positive.