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Integrating Mathematics and Science Curriculum for STEM Students
Lifang Tien, BiologySusan Fife, Mathematics
Joanne Lin, ChemistryDouglas Bump, Mathematics
Aaron Marks, Physics
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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 workbooksProblems 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 teacher- this 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
Practicing the project of biology workbook help me to understand the material bet-ter
The project makes the subject more interesting to learn
This project is a very good supplemental resource for science classes
Following the examples in the project makes biology easier to study
Since the project is critical thinking, I will spend more time on the material
I will recommend my friends/family/fellow students to try this workbook
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Biology survey results
No effectAgreeStrongly agree
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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 EquationPV = nRT; n = PV/RT
• Moles = MV; M = moles /V• Solving light wave related equations
C = wave length x frequency;E = h x frequencyEn = - Rh ( 1/nf2 – 1/ni2)
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Unit V: Solving Quadratic Equations
• Unit V: Solving Quadratic Equations
• Quadratic Formula:If then
• Applications in solving equilibrium problems
ax 2 bx c 0
x b b2 4ac
2a
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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 Pre-Calculus classes
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Sample Problem
Mathematics Objective: Understanding the behavior of simple trigonometric functions, using a non- standard 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)
mg
FN
x
y
θ
a
FN
mg
Use “Rotated” coordinate system to write Newton’s Laws.
cos0
sin
mgFF
mgmaF
Ny
x
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singa
cosmgFN
m
a
θ
FN The physics:
Acceleration of the crate down the ramp
Normal (Contact) force of the ramp
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
θ
sin(θ) cos(θ)
θ
singa cosmgFN
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.
90o
90o
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The Mathematics of Physics
TABLE OF CONTENTSHTTP://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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INTERNETMATHEMATICS
VIDEOS
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
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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 PlansFall 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 InformationLifang Tien, Biology [email protected] Fife, Mathematics [email protected] Lin, Chemistry [email protected] Bump, Mathematics [email protected] Marks, Physics [email protected]
