ALGEBRAIC FUNCTIONS

**Subject Areas**: First year algebra with a focus on functions
and applications for problem solving.

**Topics**: Operations with signed numbers, expressions, operations
with monomials, first degree equations, patterns, function tables and their
relationship to first and second degree equations, graphing first and second
degree equations, problem solving using algebra as a strategy.

**Skills**: In order to learn the topics, students practice
operating with whole numbers and fractions, taking notes, writing solution strategies,
discussion, organizing material for use in open notebook exams, cooperative
learning, close reading of mathematical problems, making class presentations
and teaching others the mechanics of algebraic manipulations.

Assessment Used: Six open notebook exams are given during the semester. These are graded numerically based on the percentage of correct answers. The final grade for the students' work is most dependent on those scores. Notes taken from the board are checked twice during the semester for completeness and organization. They are assigned a "check plus", "check", or "check minus". Approximately twenty homework assignments are given and are simply noted as having been done, not for correctness but for effort. I usually indicate on the returned assignment any problems (or no problems) that I've noticed. All students are required to make a presentation as "teacher" at the board near the end of class, especially during the earlier developmental part of the semester. This is usually simply noted as having been done, along with the date. Each student must keep track of his/her daily attendance with a cumulative bar graph. One is done the first half of the semester, the other the second half. These are evaluated using the check system. When working in groups for the problem solving activities, the check system is used to assess how well each group worked as a unit.

Instructional Material: An evolved, personal adaptation of __INTEGRATED
MATHEMATICS: COURSE 1; ALGEBRA FOR EVERYONE__, published by The National Council
of Teachers of Mathematics; Logic Algebra Problems, published by Dale Seymore
Publications;__ PROBLEM SOLVING STRATEGIES - CROSSING THE RIVER WITH DOGS__,
published by Key Curriculum Press.

Instructional Strategies: This is largely a teacher centered course. When at the board reviewing the previous day's work, students are always called upon to either explain the problem from their seats or to come up front and show the class their interpretation. When developing the lesson, especially during the first half of the semester, I do most of the talking, requesting that any and all questions be voiced as I proceed. Usually, after completing a daily worksheet, a different student every day comes up to the board and "teaches" the material. What they actually do is what I did at the beginning of class. They call on different students to explain how each problem was done. Again, all students are expected to ask questions at this time if they have any. This daily procedure becomes much more student centered later in the semester as more complex problem solving assignments are introduced. These problems require an understanding of the content that has been developed so far as well as knowing what strategy and content to apply. At this point, the class is broken up into small groups and I become more of a facilitator.