National Academies Summer Institutes for Undergraduate Education in Biology
Teachable Unit Framework
Title of Unit
Date and
Location of SI
Unit Developers &
Contact
Information
Mathematical Modeling in Developmental Biology
NESI2013 Aug4-11th
Stony Brook University
Add names, emails, institutional affiliations of developers
New Jersey City University
Benjamin Griffel benjamin.griffel@gmail.com
Freda Wasserstein-Robbins frobbins@njcu.edu
St. John’s University
Xingguo Cheng chengx@stjohns.edu
Diane Hardej hardejd@stjohns.edu
Stony Brook University
David Green david.green@stonybrook.edu
Benjamin Martin benjamin.martin@stonybrook.edu
What kind of course is unit designed for?
 Undergraduate STEM Juniors and Seniors
Context
How long is unit?
 6 lecture hours
When will the unit be used in the course?
 Last half of the course
Abstract A 15-minute teachable tidbit was developed on the application of the clock-wavefront
(< 200 words) model in predicting somite patterning in vertebrate embryos. The tidbit includes a brief
review of the model, followed up with short “clicker” questions to assess student
understanding. The core activity involves students being given graphs displaying
quantitative changes to the model (clock frequency or steepness of wavefrontgenerating gradient) and working to predict how the pattern of developing somites
would differ from a reference embryo. Students work in pairs to solve the problem,
and then enter a group discussion to develop a consistent prediction. Groups then
present their predictions, and the instructor leads a discussion of common
misconceptions. To reinforce the concepts, students would be given a homework
assignment involving predictions of difference in the model based on embryo
phenotype. The learning objective of the tidbit is aimed at a high level of cognition:
Students will be able to predict changes in phenotype from quantitative changes to an
underlying mathematical model. The exercise is focused on graphical analysis of the
model, and thus could be applied within either a traditional Developmental Biology
course or in a class that delves more deeply into the underlying mathematics of the
model.
Rationale How did the idea for the unit arise?
 brainstorming
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National Academies Summer Institutes for Undergraduate Education in Biology
Teachable Unit Framework
Why was this topic chosen?
 Pattern formation in development is a fundamental problem in biology. It is a
topic where math has provided deep insight. Extensive modeling has been done
in this area.
What misconceptions or difficult topics are addressed?
Misconceptions:
 Mathematical models are perfect
 Mathematical models are useless
Difficult Topics:
 Translation of Descriptive biology into a quantitative model
Learning Goals: Students will understand…
what students will
 Factors that affect the process of somitogenesis
know, understand,
 the interrelatedness of Math and Bio in the process of somitogenesis
and be able to do;
 how chemical agents can disrupt the process of somitogenesis
includes content
knowledge,
attitudes, & skills
Learning Students will be able to…
Outcomes:
 students will be able to predict changes phenotype from a quantitative change
Student behaviors
in a model
or performances
 define somitogenesis
that will indicate
 define an ordinary differential equation
they have
 understand the three control elements
successfully
 use mathematical models to determine oscillations in the genes responsible for
accomplished the
somitigenesis
goals
 explain communication through Notch leads to synchronization within the
segment
 understand how signaling gradients position somite borders
 understand how chemical agents can disrupt genes in somitogenesis
 Predict using a mathematical model, the process of somitogenesis in the
absence and presence of a chemical agent
 Choose an appropriate biostatistical test to analyze data in the absence and
presence of the chemical agents
 Explain the limitations of the model
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National Academies Summer Institutes for Undergraduate Education in Biology
Teachable Unit Framework
Incorporation of Scientific Teaching Themes
Active Learning
How students will engage actively
in learning the concepts
Activities outside of class:
 Homework
 Reading assignments
 Reading primary literature
Assessment
How teachers will measure
learning; how students will selfevaluate learning
Diversity
How the unit is designed to
include participants with a variety
of experiences, abilities, and
characteristics
Pre-assessments:
Post-tidbit assessments:
Activities in class:



Principles and applications
of mathematical modeling
in developmental biology
Using and graphing of
differential equations
involving trig functions,
exponentials and
thresholds
Students learn biological
processes of
somitogenesis
(tempospacial gene
regulation, gradient
diffusion and threshold)

Given changes in
phenotype, students are
asked to predict changes
in the clock and wavefront
models (reverse of tidbit
activity which would
represent a higher Bloom
level activity)

Activities during tidbit:
1) Clicker questions to assess
understanding of clock and
wavefront model video
2) Group pair share. Groups of 4-6
students are given a graph
showing a quantitative
variation in either the clock or
wavefront. Students spend 3
minutes in pairs discussing how
the variations will affect somite
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National Academies Summer Institutes for Undergraduate Education in Biology
Teachable Unit Framework
patterning. Pairs of students
then discuss their answers with
their group for 2 minutes and
draw somite patterning
changes with respect to wildtype somites. Groups present
their answer and the instructor
leads a discussion about the
interpretation of the graphs.
Sample Presentation Plan (general schedule with approximate timing for unit)
Session 1
Time (min) Learning Outcome(s)
Preclass
Read Cook and
Zeeman, 1976. A
clock and
wavefront model
for control of the
number of
repeated
structures during
animal
morphogenesis
Understand the roles of
Her and FGF in the clock
and wavefront models
Teachable Unit Framework
Activity/assessment
The reading will be
assessed with a “ clicker
question”
Explanation, notes, suggestions,
tips
The tidbit is mostly focused on
the dynamic properties of the
model itself, but not the relevant
biochemistry. The preclass
assessment and reading provides
students with the biochemistry
context and the clicker
assessment determines if this
information was read.
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National Academies Summer Institutes for Undergraduate Education in Biology
Teachable Unit Framework
Enter approx.
class time for
learning activity
preparatory
material
presentation
approxi. 3 min
Intro/Somitogenesis
Need to be familiar with clicker
system
Choose appropriate slides and
video
Prepare the handout for the
student activity
Enter approx.
class time for
learning activity
#1
3 min
Clicker/Video
Video helps to clarify the clock
and wavefront models and
correlate the two models
2 min
Explanation of activity
6 min
Group activities
3 min
Reporting/Wrap up
Enter
approximate time
for additional
learning activities
and associated
class
Work/preparatory
materials
Given 4 different
mutations/changes in clock gene
and Fgf threshold, predict the
changes on phenotype
Approximately 3
minutes
Enter
approximate time
Approximately 3
for post-activity minutes
summing up or
transition
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National Academies Summer Institutes for Undergraduate Education in Biology
Teachable Unit Framework
Add additional activities information as needed for the unit.
Resources for Teaching the Unit
(other files and information needed/helpful to teach the unit, including files for papers from which original data
for class activities is taken, supporting information for the instructor, handouts, in class activities materials,
assessments with answer keys, homework assignments, etc.)
Effectiveness of unit (if you have used it in your own teaching)
N/A
Acknowledgements
Peter Mirabito and Rona Ramos
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