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This book is based on the belief that, before students can make
sense of any presentation of abstract mathematics, they need to be
engaged in mental activities that will establish an experiential
base for any future verbal explanations and to have the opportunity
to reflect on their activities. This approach is based on extensive
theoretical and empirical studies, as well as on the substantial
experience of the authors in teaching Abstract Algebra. The main
source of activities in this course is computer constructions,
specifically, small programs written in the math-like programming
language ISETL; the main tool for reflection is work in teams of
two to four students, where the activities are discussed and
debated. Because of the similarity of ISETL expressions to standard
written mathematics, there is very little programming overhead:
learning to program is inseparable from learning the mathematics.
Each topic is first introduced through computer activities, which
are then followed by a text section and exercises. The text section
is written in an informal, discursive style, closely relating
definitions and proofs to the constructions in the activities.
Notions such as cosets and quotient groups become much more
meaningful to the students than when they are presented in a
lecture.
Most students in abstract algebra classes have great difficulty
making sense of what the instructor is saying. Moreover, this seems
to remain true almost independently of the quality of the lecture.
This book is based on the constructivist belief that, before
students can make sense of any presentation of abstract
mathematics, they need to be engaged in mental activities which
will establish an experiential base for any future verbal
explanation. No less, they need to have the opportunity to reflect
on their activities. This approach is based on extensive
theoretical and empirical studies as well as on the substantial
experience of the authors in teaching astract algebra. The main
source of activities in this course is computer constructions,
specifically, small programs written in the mathlike programming
language ISETL; the main tool for reflections is work in teams of
2-4 students, where the activities are discussed and debated.
Because of the similarity of ISETL expressions to standard written
mathematics, there is very little programming overhead: learning to
program is inseparable from learning the mathematics. Each topic is
first introduced through computer activities, which are then
followed by a text section and exercises. This text section is
written in an informed, discusive style, closely relating
definitions and proofs to the constructions in the activities.
Notions such as cosets and quotient groups become much more
meaningful to the students than when they are preseted in a
lecture.
Most students in abstract algebra classes have great difficulty
making sense of what the instructor is saying. Moreover, this seems
to remain true almost independently of the quality of the lecture.
This book is based on the constructivist belief that, before
students can make sense of any presentation of abstract
mathematics, they need to be engaged in mental activities which
will establish an experiential base for any future verbal
explanation. No less, they need to have the opportunity to reflect
on their activities. This approach is based on extensive
theoretical and empirical studies as well as on the substantial
experience of the authors in teaching astract algebra. The main
source of activities in this course is computer constructions,
specifically, small programs written in the mathlike programming
language ISETL; the main tool for reflections is work in teams of
2-4 students, where the activities are discussed and debated.
Because of the similarity of ISETL expressions to standard written
mathematics, there is very little programming overhead: learning to
program is inseparable from learning the mathematics. Each topic is
first introduced through computer activities, which are then
followed by a text section and exercises. This text section is
written in an informed, discusive style, closely relating
definitions and proofs to the constructions in the activities.
Notions such as cosets and quotient groups become much more
meaningful to the students than when they are preseted in a
lecture.
Most students in abstract algebra classes have great difficulty
making sense of what the instructor is saying. Moreover, this seems
to remain true almost independently of the quality of the lecture.
This book is based on the constructivist belief that, before
students can make sense of any presentation of abstract
mathematics, they need to be engaged in mental activities which
will establish an experiential base for any future verbal
explanation. No less, they need to have the opportunity to reflect
on their activities. This approach is based on extensive
theoretical and empirical studies as well as on the substantial
experience of the authors in teaching astract algebra. The main
source of activities in this course is computer constructions,
specifically, small programs written in the mathlike programming
language ISETL; the main tool for reflections is work in teams of
2-4 students, where the activities are discussed and debated.
Because of the similarity of ISETL expressions to standard written
mathematics, there is very little programming overhead: learning to
program is inseparable from learning the mathematics. Each topic is
first introduced through computer activities, which are then
followed by a text section and exercises. This text section is
written in an informed, discusive style, closely relating
definitions and proofs to the constructions in the activities.
Notions such as cosets and quotient groups become much more
meaningful to the students than when they are preseted in a
lecture.
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