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The purpose of this module is to familiarize
mathematics teachers at the high school and lower division college
level with the content and teaching strategies for a promising new
approach to teaching advanced algebra.
This approach stresses modeling and solving real world problems and
develops skills and concepts of algebra as needed for this modeling
process. In this course, the students work in a collaborative
learning environment and make extensive use of a graphing calculator
with data analysis and sequence capabilities such as those found on
the TI-82, TI-83, TI-83+ and TI-83+ Silver Edition
After completing this module, a teacher will know the details of
this approach and will be prepared to use or adapt the course or
some topics of the course to his or her own instructional setting.
This course, which has been used at the University of Illinois
quite successfully for six years, was based on preliminary editions
of the text, 'Functioning in the Real World', by Sheldon Gordon and
Ben Fusaro which was published by Addison-Wesley Publishing Company
in November, 1996 and in a second edition in 2004. [See the Required
Materials button at the bottom of the Module 5 home page for a
detailed description of the text and ordering information.] This
text presents algebra, trigonometry and other topics from a
non-traditional perspective that emphasizes the use of the basic
algebraic and trigonometric functions to model interesting and
current real-world problems. Data analysis is used to develop and
test these models and to draw inferences from them. Manipulative
skills are taught "as needed" for the model development and analysis
and not as "stand alone" topics as is typical in traditional algebra
texts and courses.
The Illinois version of the course is taught using the following
teaching strategies and tools:
1) The Small-Group Instruction (or Collaborative
Learning) Method
2) Mastery Testing of Algebraic Skills
3) Graphing calculators with data analysis and
sequence capabilities (for example, any member of the TI-83 family
of graphing calculators).
The use of the graphing calculator is an essential requirement of
the text. We believe that the use of the Collaborative Learning
Method has been absolutely crucial to the success of our course at
Illinois. Although we believe that the use of Mastery Testing has
also been helpful, we have not discussed that aspect of this course
in this module because it is rather independent of the other two
strategies. Thus, this module will focus on features 1)
and 3) of the Illinois course. This module will
prepare you to implement and adapt this course or aspects of this
course for your school if you choose to do so.
Although it is certainly possible to use other graphing calculators
for this course, the TI-83 family of graphing calculator have
features that are especially well suited to the required tasks.
Consequently, we have used it throughout this module. If you or your
students are not familiar with the operation of the TI-83 family of
calculators, there are interactive tutorials available at the bottom
of the MTL Course Modules home page. These tutorials are tailored to
the needs of this course module.
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