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Course Description This course develops basic algebraic skills: factoring, exponents, rational expressions, linear equations and inequalities, systems of equations, quadratic equations, and an introduction to functions. This course is not a terminal course for any of the majors on campus, but a prerequisite to the courses they need. Students lacking in high school mathematics skills from all majors across campus take this course to get into the math classes they need for their majors. Class sizes are 36 students maximum. They are conducted in a networked classroom, and all students have laptop computers. It is a hybrid class; the lecture/discussion is given for the first part of the 55 minute period, then students begin work on their homework assignment. All assignments, tests and quizzes are completed online. This lesson comes about 2 months into the course. By this time, students have learned to factor polynomials. In the previous lesson, students learned to multiply and divide rational expressions.
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Executive Summary Learning Goals. The overall learning goal is to have students be able to add and subtract rational expressions. Students will first combine expressions with common denominators, then find a common denominator to combine expressions with unlike denominators. Long-term goals not directly assessed by the lesson are to ease anxiety when dealing with fractions and to have students realize the connection between adding/subtracting rational numbers and adding/subtracting rational expressions. Lesson Design. The lesson reviewed addition and subtraction of fractions, demonstrated addition and subtraction of simple rational expressions, and worked up to difficult examples. The lesson began with three examples of rational numbers, one with common denominators and two with un-like denominators, followed by rational expressions with common denominators. Examples of rational expressions with un-like denominators started out simple and increased in difficulty level. The number of expressions to be added increased along with the difficulty in the factorization of the denominators. The examples were chosen so that the answers could be rewritten in reduced forms at the end to remind students to check that final step in their answers. Due to the anxiety that this lesson has caused in the past, hard examples were presented by the end so that students could be exposed to more difficult problems. Major findings about student learning. The findings showed that even though students were successful at the beginning problems in the homework, they were intimidated by the "difficult look" of the later homework problems and simply did not attempt them. This was evident in the analysis of the homework where the amount of incomplete problems drastically increased at a certain problem when the difficulty level was higher. In the revised lesson, more difficult examples were used, and it was stressed that the steps remain the same even though it looked much harder than previous examples. Several days later when the students had to use the lesson to solve equations involving rational expressions their confidence level was greater and the majority of students got the correct answers.
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