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Integrating Mathematics and Science Curriculum for STEM Students Lifang Tien, Biology Susan Fife, Mathematics Joanne Lin, Chemistry Douglas Bump, Mathematics Aaron Marks, Physics

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2 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. 48 th in quality of mathematics and science education Education is our way to better economy

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3 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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4 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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5 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 teacher- this approach is most effective but also costly and may not sustainable. 4.Semi-Hybrid learning community 5 5

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6 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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7 Courses Targeted College Algebra and General Chemistry Precalculus and College Physics I General Biology and Statistics

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8 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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9 The Mathematics of Biology T ABLE OF C ONTENTS Unit one Science and Scientific methods Unit two Natural Selection Unit three Principle of Inheritance Unit fourPopulation genetics

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10 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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11 AaBbCc + AaBbCc If there is independent assortment, the following gametes will be produced in equal numbers: ABC, ABc, AbC, aBC, abC, aBc, Abc, abc ABCABcAbCaBCAbcaBcabCabc ABCAABCC ABc AbC aBC Abc aBc abC abcaabbcc

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12 Biology survey

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13 The Mathematics of Chemistry T ABLE OF C ONTENTS 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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14 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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15 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) 3H 2 + N 2 ---->2 NH 3 Stoichiometry: A study of quantity relationships in a balanced equation

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16 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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17 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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18 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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19 Unit V: Solving Quadratic Equations Quadratic Formula: If then Applications in solving equilibrium problems

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20 S AMPLE U NIT

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26 S AMPLE U NIT

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27 Basic Layout

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29 Sample Questions

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30 PhysicsPre-Calculus 2-D Kinematics: Velocity and Acceleration Solving Quadratic Equations 3-D Kinematics: Projectile Motion Polar Coordinates, Vectors Newton’s Laws: ForcesSimple Trigonometric functions, Rotation of Coordinates Circular Motion, GravitationParametric 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, StaticsAlgebra with Trigonometric functions

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31 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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32 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 θ

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33 The solution: Free Body Diagram (a picture showing all the forces) mg FNFN x y θ FNFN Use “Rotated” coordinate system to write Newton’s Laws.

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34 m θ FNFN 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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35 The Mathematics: Behavior of the Sine and Cosine functions θ sin(θ) cos(θ) θ Important Limits: 1.θ = 0 o → sin(0 o ) = 0; cos(0 o ) = 1 Flat surface: Acceleration is zero; normal force equals gravitational force. 2.θ = 90 o → sin(90 o ) = 1; cos(90 o ) = 0 Vertical surface: Acceleration is free fall; normal force is zero. 90 o

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36 The Mathematics of Physics T ABLE OF C ONTENTS 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

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Math 0308 Final Exam Review

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Math 0312 Final Exam Review

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Math 1314 Final Exam Review

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High School TAKS Exam

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Eighth Grade TAKS Exam

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56 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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57 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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58 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

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