Math 149. Capstone Mathematics for Teachers. Spring 2010.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Feb 3: | Last day to ADD classes without special permission. Last day to DROP classes without instructor's permission. | ||
| Feb 18: | Last day to DROP classes without a serious and compelling reason. | ||
| Apr 20: | Last day to WITHDRAW from a course for a serious and compelling reason | ||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 26 | - | - | Introduction. Syllabus & Schedule. Field Experience. Single Subject Credential Requirements. Who this class is for (and why to take it), etc. An advanced perspective. (Example: factoring quadratic polynomials.) Integers. Properties and algebraic structure. Decimal (base 10) representation. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields |
| Feb 2 | Construction of the Number Systems: pages 1-3, pages 4-5 (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | Homework 1 (Divisibility tests) | Homework 1 discussion. Axiomatic construction of integers (Peano postulates for N; well-ordering principle; mathematical induction; negative numbers as equivalence classes of differences of natural numbers; properties of integers). Rational numbers. Definition. |
| Feb 9 | The meaning of division by fractions (Liping Ma) | Homework 2 (Rational/irrational numbers) | Homework 2 discussion. Construction and algebraic structure of the set of rational numbers. Teaching multiplication and division of rational numbers. Rational numbers as terminating/repeating decimals. Field experience update: Saturday MFD prep sessions |
| Feb 16 | - | Homework 3 (Real fields) | Homework 3 discussion. Real numbers. Definition and algebraic structure. Complex numbers. Definition and algebraic structure. Rectangular and polar representations and their advantages. Field experience: schedule update |
| Feb 23 | - | Homework 4 (Complex numbers) | Homework 4 discussion. Review: Study Guide and Sample Problems, Spring 09 Test 1 Field experience: schedule update Counting, Binomial Theorem, Probability. Problems and solutions |
| Mar 2 | - | Homework 5 (Polynomials and Binomial Theorem) | Test 1 (Number systems) Test discussion. Homework 5 discussion. Polynomials. Definition. Operations with polynomials. Comparing the algebraic structure of polynomials with that of numbers. Quadratic Polynomials. Graphs of quadratic polynomials. |
| Mar 9 | Homework 6 (Equations and quadratic functions) | Homework 6 discussion. Functions. Definitions of important terms (graph, intercepts, roots, domain, codomain, range, asymptotes). Important classes of functions. Equations. The concept of equation. Quadratic formula. More on graphs of quadratic polynomials. Solving polynomial equations and inequalities. Field experience update: Hoover High materials |
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| Mar 16 | Homework 7 (More equations and inequalities) | Homework 7 discussion.
Problem solving with functions and equations/inequalities using calculators Problems Hoover High Math League topics: Bases other than 10; Counting and probability. |
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| Mar 23 | Homework 8: Problem 4(b,c,d,e) (Polynomial inequalities) | Homework 8 discussion.
Proportional reasoning, ratios, and rates. Problems Discussion of classroom observations and extracurricular activities. |
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| Mar 26 | Spring break | ||
| Apr 6 | - | - | Furlough day (this instructor only). No class. Review: Study Guide and Sample Problems, Answers, Spring 09 Test 2 |
| Apr 13 | - | Homework 9 (Proportional reasoning) | Homework 9 discussion. Test 2 (Functions, equations, proportional reasoning, ratios). Test discussion. |
| Apr 20 | Homework 10 (Optional. Volume of the pyramid) |
Geometry. Length, area, and volume. Approximating the number pi. Proofs of the Pythagorean theorem. Distance formula, equation of circle. |
6:45 PM, S2 109: Integration Bee. Email Dr. Kay Kelm (kbyler@csufresno.edu) to sign up. Must sign up by noon, however, space is limited, so sign up ASAP. Will get extra credit: one point for participation; one more point if make to the second round; third point if win 1st place. |
| Apr 27 | Homework 11 (Approximating the number pi) | Homework 11 discussion. Equations of ellipse and line. Areas and volumes of similar figures/solids. Coordinate geometry problems - do at least first 2 pages Problems on similarity - do all |
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| May 4 | Homework 12 (Similarity) | Homework 12 discussion. Technology. Using technology, such as calculators, Geometer's sketchpad, Mathematica, Maple, etc. in middle and high school. Presentations: Field Experience |
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| May 11 | Homework 13 (Technology) | Presentations: Field Experience (continued). Spring 09 Final Exam |
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| May 13 | Faculty consultation day. Consultation hours: 9:30-12, 12:30-3. | ||
| May 14 | Furlough day: all faculty. No office hours. | ||
| May 18 | - | - | 1:15-3:15 PM: Final Exam (cumilative) |