Integrating Mathematics and
Science Curriculum for STEM
Students
Lifang Tien, Biology
Susan Fife, Mathematics
Joanne Lin, Chemistry
Douglas Bump, Mathematics
Aaron Marks, Physics
The need for the project
• Students don’t see the relevance of math within
their math class.
• When they enroll in science, they are unable to
understand the math behind the science and
struggle with the exercise problems.
• A result is that fewer students enrolled and
completed in STEM majors in our country.
• World Economic Forum now ranks U.S. 48th in
quality of mathematics and science education
• Education is our way to better economy
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Chancellor’s Innovation Fund
• The intent of the Chancellor’s Innovation Fund
Awards is to provide the resources for
members of the college family to conduct
demonstration or research projects that
ultimately result in practices or institutional
self-knowledge that when operationalized,
will benefit and improve the institution.
• 1 of 4 awards received for 2010 – 2011 School
Year
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The Strategy
• Mastery of the concept through practice
• Promote problem-solving based learning
communities to enhance students’ critical
thinking ability
• Ultimately, to increase student enrollment
and completion rate.
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Implementation
1. Development of individual and interdisciplinary
workbooks
Problems and study questions are selected from faculty
input.
2. A common portal to the workbook will be
accessible for all students within the district
3. On-campus learning community: paired classes
taught by one math and one science teacherthis approach is most effective but also costly
and may not sustainable.
4. Semi-Hybrid learning community
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Project Goals
• To implement a shared curriculum for math/science
classes
• Creation of an environment where students will
develop the necessary critical thinking skills desired for
students to succeed in science careers
• For students to recognize the mathematics behind
physical situations
• Production and distribution of supplemental materials
that can be used in any introductory college or
advanced high school level science or math class
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Courses Targeted
• College Algebra and General Chemistry
• Precalculus and College Physics I
• General Biology and Statistics
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Results
• Students showed positive attitude toward the
newly created integrated workbooks
• No significant grade change between
experimental group and control group
• On-campus learning community approach was
effective but had limitations
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The Mathematics of
Biology
TABLE OF CONTENTS
Unit one Science and Scientific methods
Unit two Natural Selection
Unit three Principle of Inheritance
Unit four Population genetics
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Mathematics in Polygenic Inheritance
• A polygenic trait is due to more than one gene locus. It involves
active and inactive alleles.
• Active alleles function additively. Height (tallness) in humans is
polygenic but the mechanism of gene function or the number of
genes involved is unknown.
• Suppose that there are 3 loci with 2 alleles per locus (A, a, B, b, C,
c).
• Assume that:
• Each active allele (upper case letters: A, B, or C) adds 3 inches of
height.
• The effect of each active allele is equal, A = B = C.
• Males (aabbcc) are 5' tall.
• Females (aabbcc) are 4'7".
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AaBbCc + AaBbCc
• If there is independent assortment, the
following gametes will be produced in equal
numbers:
• ABC, ABc, AbC, aBC, abC, aBc, Abc, abc
ABC
ABC
ABc
AbC
aBC
Abc
aBc
abC
abc
AABCC
ABc
AbC
aBC
Abc
aBc
abC
abc
aabbcc
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Biology survey
Biology survey results
I will recommend my friends/family/fellow students to try this
workbook
Since the project is critical thinking, I will spend more time on the
material
Following the examples in the project makes biology easier to
study
No effect
Agree
This project is a very good supplemental resource for science
classes
Strongly agree
The project makes the subject more interesting to learn
Practicing the project of biology workbook help me to understand
the material better
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1
2
3
4
5
6
7
8
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The Mathematics of
Chemistry
TABLE OF CONTENTS
UNIT I: MEASUREMENT IN CHEMISTRY
UNIT II: MASS RELATIONSHIPS IN CHEMICAL REACTIONS
UNIT III: GRAPHING EQUATIONS
UNIT IV: SOLVING EQUATIONS
UNIT V: SOLVING QUADRATIC EQUATIONS
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Unit I: Measurements in Chemistry
• Reinforces concepts of dimensional analysis
and significant figures
– Zeros, exact numbers and rounding in measured
numbers
– Significant digits for addition, subtraction,
multiplication and division
– Scientific notation and addition, subtraction,
multiplication, division
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Unit II: Mass Relationship in Chemical
Reactions
•
•
•
•
Moles to Grams Conversions
Moles: from Concentrations and Volume
Gas Laws: n = PV/RT
Balanced Chemical Equations (work as the
cooking recipes)
3H2 + N2 ---->2 NH3
• Stoichiometry: A study of quantity
relationships in a balanced equation
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Unit II: Mass Relationship in Chemical
Reactions
• Dimensional Analysis: Using units of each
measurement to derive the final answer in the
correct units
• Application of dimensional analysis in solving
stoichiometry problems
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Unit III: pH, pOH and pKw
•
•
•
•
•
LOG (base 10 log) and LN (base e)
Definition of pH: pH = -log [H]
pOH = -log[OH]
pKw = -log[Kw] = pH + pOH = 14
Scale and range of pH: usually falls between 0
to 14 with 0 being very acidic and 14 being
very basic
• Anti- log calculations
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Unit IV: Solving Linear Equations
• Density
d = m/v; m = dv; v = m/d
• Various Temperature Scales
F = 1.8C + 32; C = (F – 32)/1.8
• Ideal Gas Equation
PV = nRT; n = PV/RT
• Moles = MV; M = moles /V
• Solving light wave related equations
C = wave length x frequency;
E = h x frequency
En = - Rh ( 1/nf2 – 1/ni2)
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
Unit V: Solving Quadratic Equations
• Unit V: Solving Quadratic Equations
• Quadratic Formula:
2
b

b
 4ac
2
If ax  bx  c  0 then x 
2a
• Applications in solving equilibrium problems

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SAMPLE UNIT
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Physics
Pre-Calculus
2-D Kinematics: Velocity and
Acceleration
Solving Quadratic Equations
3-D Kinematics: Projectile
Motion
Polar Coordinates, Vectors
Newton’s Laws: Forces
Simple Trigonometric
functions, Rotation of
Coordinates
Circular Motion, Gravitation
Parametric Equations, Ellipses,
Conic Sections
Conservation of Mechanical
Energy and Momentum
Solving Equations, Systems of
Equations
Simple Harmonic Motion,
Oscillations and Waves
Trigonometric Identities
Rotation, Torque, Statics
Algebra with Trigonometric
functions
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Current Implementation:
•Semi-linked class with 8 shared students
•Workbook with example walkthrough problems and additional
practice problems for students to try on their own
•Online workbook with supplemental materials including video
solutions of walkthrough problems
•Coordinated instruction of problems in both Physics and PreCalculus classes
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Sample Problem
Mathematics Objective: Understanding the behavior of simple
trigonometric functions, using a nonstandard coordinate system
Physics Objective: Using Newton’s Laws to solve force problems.
The problem: A mass slides down an inclined plane.
m

a
θ
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The solution: Free Body Diagram (a picture showing all the forces)
y
FN
FN

a
x
mg
θ mg
Use “Rotated” coordinate system to write Newton’s Laws.
F
 ma  mg sin  
F
 0  FN  mg cos 
x
y
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FN
The physics:
m
Acceleration of the crate
down the ramp

a
Normal (Contact) force of
the ramp
a  g sin  
FN  mg cos 
θ
Conclusions:
1. The steeper the slope (increasing θ), the greater the acceleration of the crate.
2. The shallower the slope (decreasing θ), the greater the contact force between
the crate and slope.
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The Mathematics:
Behavior of the Sine and Cosine functions
sin(θ)
90o
a  g sin  
cos(θ)
FN  mg cos 
θ
θ
90o
Important Limits:
1. θ = 0o → sin(0o) = 0; cos(0o) = 1
Flat surface: Acceleration is zero; normal force equals gravitational force.
2. θ = 90o → sin(90o) = 1; cos(90o) = 0
Vertical surface: Acceleration is free fall; normal force is zero.
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The Mathematics of
Physics
TABLE OF CONTENTS
HTTP://SOPHIA.HCCS.EDU/~MATH.REVIEW/LC/PHYS1401/WEBSITE/INDEX.HTML
UNIT I: KINEMATICS
UNIT II: NEWTON’S LAWS
UNIT III: CIRCULAR MOTION
UNIT IV: CONSERVATION OF (MECHANICAL) ENERGY
UNIT V: CONSERVATION OF MOMENTUM
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Math 0306 Final Exam Review
Math 0308 Final Exam Review
Math 0312 Final Exam Review
Math 1314 Final Exam Review
High School TAKS Exam
Eighth Grade TAKS Exam
What is a successful project?
• 1. Effective-enhance SLO
• 2. Reduce cost –at least do not increase
budget
• 3. Easy adaptable-no extra working load to
faculty
• 4. Sustainable
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Future Plans
Fall 2011:
•Continue Physics/Pre-Calculus linked class
•Comparison of test scores from linked/non-linked classes
•Expansion of Workbook and shared class materials
Beyond:
•Multiple linked classes
•Recruit STEM students into an AS degree plan involving multiple linked
classes
•Development of Physics/Calculus class pairing
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Questions?
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Contact Information
Lifang Tien, Biology lifang.tien@hccs.edu
Susan Fife, Mathematics susan.fife@hccs.edu
Joanne Lin, Chemistry joanne.lin@hccs.edu
Douglas Bump, Mathematics douglas.bump@hccs.edu
Aaron Marks, Physics aaron.marks@hccs.edu