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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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