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The textbook for the course is Algebra by I. M. Gelfand and A. Shen, ISBN # 0-8176-3677-3. This is a terrific text by superior mathematicians, with excellent exposition and nice applications. We will use it primarily to supplement the lectures, and in general, the homework will be based more on the classroom discussion. Everyone should also have at least one developmental algebra textbook for reference. This can be a textbook that you have used in your own classroom, or you can use the text Integrated Arithmetic & Basic Algebra by Bill E. Jordan and William P. Palow.
Homework
Homework will be assigned daily and will be due at the start of the next class. Problems will come in four distinct flavors: computational, exploratory, theoretical, and discussion, each with a different purpose. Computational exercises are meant to strengthen fundamental understanding. Exploratory problems are meant to engage creativity to solve open-ended problems. Theoretical problems address the underpinnings of computations and techniques. Discussions will focus on how students learn the subject matter and what techniques are most likely to be useful in the classroom.
Homework will be corrected and returned at the next session.
You are encouraged to work with classmates on all of the homework assignments. Please note any close collaborators on your homework, and if you receive substantial assistance from any textbook or individual, be sure to credit that person for their contribution.
Class Notes
Each class session, a pair of students will be responsible for taking notes and writing them up. These notes will corrected, and then the pair of students will revise them and distribute them to the rest of the class.
Lesson Plan Project
In small groups, students will plan a lesson in algebra. These lessons will be presented, discussed, and revised during the second and third weeks of class. The lesson should be abbreviated, 30 minutes long, in order to leave time for discussion afterward. After the lesson has been presented, the students will write up the lesson, including what they learned from the presentation and discussions and how they would revise the lesson before using it with their classes.
Grades
Grades will be based on homework performance (40%), final exam (30%), lesson plan (15%), class notes (10%), and classroom participation (5%).
Tentative Schedule
Number Systems and Algebra |
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| July 5 | First class: Introduction and numbers. What is algebra? Why do we teach it? Start talking about numbers and arithmetic. |
| July 6 | Integer arithmetic the ordering of the integers. Mathematical induction. Deductive reasoning and proofs. |
| July 7 | Number bases, division, and rational numbers. |
| July 8 | Real numbers and modular arithmetic. |
Functions and Algebra |
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| July 11 | The strange letter x: Variables in algebra. Historical perspective. Use of variables in functions, equations, and rule patterns. Modeling using variables. |
| July 12 | Functions, graphing, bottle calibration problem. |
| July 13 | Linear functions, change, modeling using linear functions. |
| July 14 | Exponential and logarithmic functions. Lesson presentation #2. |
Polynomials and Algebra |
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| July 15 | Polynomials: definition and terminology. Is a polynomial a function? Algebra with polynomials. |
| July 18 | FOIL and the binomial theorem. Pascal's triangle. |
| July 19 | Factoring polynomials. Zeros of polynomials, solving polynomial equations. |
| July 20 | Solving equations and inequalities (including non-polynomial equations). |
| July 21 | Algebra of polynomials. Graphing polynomials. Course wrap-up. Lesson presentation #4. |
| July 22 | Final exam. |