Course Schedule for Teaching Secondary Mathematics | MATH 4417, Exams of Elementary Mathematics

Download Course Schedule for Teaching Secondary Mathematics | MATH 4417 and more Exams Elementary Mathematics in PDF only on Docsity! Fall 2007 Math 4417 Teaching of Secondary Mathematics Schedule: 3:45 – 5:05 p.m. Tuesdays and Thursdays Instructor: Michel Helfgott Office: 308G Gilbreath Hall Telephone/Email: (423) 439-6977 helfgott@etsu.edu Office Hours: T-R 2-3 p.m. or by appointment Course Description: Math 4417 is a course on Secondary School mathematics from a higher point of view. We will deal both with methods and content areas, trying to reach a balance between conceptual and computational aspects of mathematics. Textbook: “Teaching Secondary Mathematics”, 7th edition, by A.S. Posamentier and J. Stepelman. Merrill Prentice Hall, 2006. References: ● Principles and Standards for School Mathematics, NCTM. ● Polya, G., Mathematical Discovery. John Wiley&Sons, New York 1962. ● S.F. Taback, Coordinate Geometry: A powerful tool for solving problems. The Mathematics Teacher, April 1990, pp. 264-268. ● R. Newburgh, Real, Imaginary, and Complex Numbers: Where does the physics hide? The Physics Teacher, Vol. 34, January 1996, pp. 23-25. ● M. Helfgott, Computer Technologies and the Phenomenon of Refraction, The Physics Teacher, Vol. 36, April 1998, pp. 236-238. Technology Recommended: TI-83 , or similar graphing calculators. Secondary Mathematics Competency: At the beginning of the academic semester students will have to take a test to demonstrate proficiency in High School Mathematics (Algebra II, Geometry, and Trigonometry). Lesson Presentation: The first part of the textbook on methods of teaching secondary mathematics (pp. 1-230) will help students deliver one lesson, which should be appropriate for a High School class. Everyone is advised to read the textbook carefully, striving for understanding. Moreover, students are expected to write a lesson plan, related to the above-mentioned lesson, which should be submitted for grading. Grading Procedure: Secondary Mathematics Competency Test 25% Lesson Presentation 15% Test 1 (parts I and II of content area) 20% Test 2 (parts III and IV of content area) 20% Final Test (comprehensive) 20% Grading Scale: A (93 and above), A- ( 90-92), B+ (87-89), B (83-86), B- (80-82), C+ (77-79), C(73-76), C- (70-72), D+ (67-69), D (60-66), F (below 60). Content Area: Part I 1. Linear equations in one and two variables. Assorted real-life problems that lead to linear equations. Basic linear programming. 2. Non-linear equations involving exponentials and logarithms. Annuities. 3. Quadratic equations. Quadratic formula. Justification by “completion of squares”. Equations that can be reduced to quadratics by a suitable transformation. 4. Diverse applications to physics ( a boat going upstream and downstream, depth of a well and speed of sound, and the like) 5. Complex numbers. Use of the complex field to solve problems in the real domain, especially in the areas of number theory and geometry. Roots of cubics and quartics (comparison between Ferrari’s and Descartes’ method). Examples from geometry and physics that lead to polynomial equations of third or fourth degree. Part II 1. Cartesian approach to parabolas and other conics. 2. Maxima and minima of quadratic and biquadratic functions. Solution of optimization problems in plane and solid geometry. 3. Equation of the tangent to a parabola, ellipse, and hyperbola. Parabolic telescopes. 4. Basic kinematics and parabolas. Range of a projectile. Lambert W function and closed solution of equations of the type debxa cx  )( 5. Area of a segment of a parabola through a limit process. 6. Comparison between Euclidean and Cartesian methods in geometry. Part III 1. Geometry of the circle. 2. Justification of the fact that for any circles with perimeters pp , and radii rr , the equality rprp  is true. Definition of  . Radian measure of angles. 3. Approximation of  through Archimedes method and by simulation. How to avoid the phenomenon of “cancellation”. 4. Area of a circle through a limit process. 5. Proof of an important equality: orp 3602   . The conical hat problem. 6. Basic plane trigonometry. Ptolemy’s theorem. Sine and cosine of the sum and difference of two angles (different proofs). Law of sines and cosines. Proof of Heron’s formula using the law of cosines (comparison with a purely algebraic approach). Application problems (building a tunnel, two-islands, antenna, et cetera). Huygens and the phenomenon of refraction of light. 7. Volume of a pyramid, cone, and sphere. Alternative use of Cavalieri’s principle.