Integrating Mathematics and Science Curriculum for STEM Students

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

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

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

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.

5. Implementation Development of individual and interdisciplinary workbooks Problems and study questions are selected from faculty input. A common portal to the workbook will be accessible for all students within the district 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. Semi-Hybrid learning community 5

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

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

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

9. 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

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".

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

12. Biology survey

13. 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

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

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) 3H2 + N2 ---->2 NH3 • Stoichiometry: A study of quantity relationships in a balanced equation

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

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

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 = hx frequency En = - Rh ( 1/nf2 – 1/ni2)

19. Unit V: Solving Quadratic Equations • Unit V: Solving Quadratic Equations • Quadratic Formula: If then • Applications in solving equilibrium problems

20. Sample Unit

27. 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

28. m θ 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.

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

30. FN m θ The physics: Acceleration of the crate down the ramp Normal (Contact) force of the ramp • Conclusions: • The steeper the slope (increasing θ), the greater the acceleration of the crate. • The shallower the slope (decreasing θ), the greater the contact force between the crate and slope.

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

32. 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

38. Internet Mathematics Videos

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