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Beginning Algebra - Textbook Preface
Beginning Algebra, an Individualized Approach is designed to
aid the student in learning its material.
The text possesses strong teaching qualities that virtually
assure the conscientious student of steady, confident progress. At the same time,
the text’s interactive processes assure the student of continuous opportunities
to get help where and when it is needed. Solid mathematics, quality instruction,
and personal assistance are the hallmark of this series of texts.
The text is designed in a format that constantly creates an
interaction between the student, the mathematics to be learned, and an experienced
teacher either in a classroom or in cyberspace. The majority of the book is a
series of questions/answers that achieves a true dialogue with its student reader.
Most of the time, the dialogue teaches the mathematics effectively, and students
learn easily without benefit of outside assistance. Sometimes, however, the dialogue
may be insufficient; it is in such cases where the student can find extra, personal
assistance through conversation with a friend or teacher. These helpful conversations
can occur in person, but also are available with a cyberspace instructor who is
always as close as the nearest computer.The quality of the mathematical content
and instructional use of this text have been thoroughly documented in a wide range
of situations and with great numbers of students. Specifically, there are no units
or chapters where common difficulties can be expected. When a student has a problem
understanding the material, the difficulties will be unique to that student. Something
of importance was overlooked, misunderstood, etc. That is the reason for providing
personal assistance in those instances and getting the student back into the flow
of the book’s dialogue. The personal assistance will both answer the questions
of individual students and give guidance in the best ways to study mathematics.
Because of the design of this book, the student can expect other
dramatic improvements in the study and learning of mathematics. One of those advantages
is the student’s ability to vary the pace of instruction to match their ability
to learn. At times, a student needs to work slowly through the instruction and
carefully ponder each new concept. At other times, the student grasps the material
quickly and can accelerate their learning rapidly through the material. As a result,
most students will move through this material more quickly than in a regular class
situation.
Another great advantage of this book is the fact that students
have an opportunity to learn to ask intelligent, specific questions about the
mathematics in a context that encourages and does not threaten the student. Study
skill deficiencies can be corrected within the context of these materials while
maintaining traditional levels of achievement and rigor.
The content of this book is comparable to a first semester of
Algebra as it is normally taught in high school. Chapters 1-3 deal only with the
counting numbers so that the first concepts of Algebra can be introduced in a
simple, already known context. Chapter 1 teaches the generalizations of arithmetic
that need to be understood. In Chapter 2, the first skills of algebra, including
the simplification of open expressions, are taught. Chapter 3 teaches the basic
skills and concepts of solving equations. Chapters 4-6 repeat the concepts of
Chapters 1-3, but apply this learning to the integers. Then Chapters 7-9 repeat
the cycle for the rational numbers. The spiraling effect on learning is obvious
in the treatment of the counting numbers, integers, and rational numbers. Each
chapter ends with an Application Unit teaching word problem-solving processes.
Unlike most text presentations of word problems, the student is taught a process
for breaking down the information of a word problem and developing methods for
extending these processes to more difficult problems to be encountered later.
The book contains many opportunities for the student to make
wise decisions about the level of understanding achieved. Each chapter begins
with an Objectives Test that illustrates, by example, all of the concepts and
skills which are to be presented. Each problem is accompanied by a designation
showing where it will be taught in the chapter. Each chapter is broken into units
in a way that divides the content into topics of such length that it gives the
student a way of organizing their own studying to make it most effective. Most
units are designed to be completed in a single study session and, for best results,
should be handled in that way. The unit ends with a Feedback which is an opportunity
for the student to test the level of understanding achieved. It is strongly suggested
that the Feedback be taken at the beginning of the next study session so that
some time intervenes between the learning and assessment. The chapter ends with
a Mastery Test that is similar to the Objectives Test. When a student can do all
the problems correctly on a Mastery Test, it indicates a complete understanding
of all the material in the chapter. Again, each problem is accompanied by a designation
showing where it was taught in the chapter. Answers for all problems in the Tests
and Feedbacks are included at the back of the book. Good learning can occur only
when the student is aware of what is known and what still needs to be learned.
We are greatly indebted to thousands of teachers and hundreds
of thousands of students who have successfully used our previous materials and
given us the benefit of their own experiences and ideas. The strength of this
new book is a result of that special kind of study of the work and challenges
we face in teaching mathematics to students — some in desperate need for
overcoming past experiences that were markedly unsuccessful and have interfered
with motivations to try again.
Robert H. Alwin
Robert D. Hackworth
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