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The experience and knowledge acquired in teacher education courses
should build important fundamentals for the future teaching of
mathematics. In particular, experience in mathematical problem
solving, and in planning lessons devoted to problem solving, is an
essential component of teacher preparation. This book develops a
problem solving approach and is intended to be a text used in
mathematics education courses (or professional development) for
pre-service or in-service middle and secondary school teachers. It
can be used both in graduate and undergraduate courses, in
accordance with the focus of teacher preparation programs. The
content of the book is suited especially for those students who are
further along in their mathematics education preparation, as the
text is more involved with mathematical ideas and problem solving,
and discusses some of the intricate pedagogical considerations that
arise in teaching. The text is written not as an introduction to
mathematics education (a first course), but rather as a second, or
probably, third course. The book deals both with general
methodology issues in mathematics education incorporating a problem
solving approach (Chapters 1-6) and with more concrete applications
within the context of specific topics - algebra, geometry, and
discrete mathematics (Chapters 7-13). The book provides
opportunities for teachers to engage in authentic mathematical
thinking. The mathematical ideas under consideration build on
specific middle and secondary school content while simultaneously
pushing the teacher to consider more advanced topics, as well as
various connections across mathematical domains. The book strives
to preserve the spirit of discussion, and at times even argument,
typical of collaborative work on a lesson plan. Based on the
accumulated experience of work with future and current teachers,
the book assumes that students have some background in lesson
planning, and extends their thinking further. Specifically, this
book aims to provide a discussion of how a lesson plan is
constructed, including the ways in which problems are selected or
invented, rather than the compilation of prepared lesson plans.
This approach reflects the authors' view that the process of
searching for an answer is often more important than the formal
result.
The experience and knowledge acquired in teacher education courses
should build important fundamentals for the future teaching of
mathematics. In particular, experience in mathematical problem
solving, and in planning lessons devoted to problem solving, is an
essential component of teacher preparation. This book develops a
problem solving approach and is intended to be a text used in
mathematics education courses (or professional development) for
pre-service or in-service middle and secondary school teachers. It
can be used both in graduate and undergraduate courses, in
accordance with the focus of teacher preparation programs. The
content of the book is suited especially for those students who are
further along in their mathematics education preparation, as the
text is more involved with mathematical ideas and problem solving,
and discusses some of the intricate pedagogical considerations that
arise in teaching. The text is written not as an introduction to
mathematics education (a first course), but rather as a second, or
probably, third course. The book deals both with general
methodology issues in mathematics education incorporating a problem
solving approach (Chapters 1-6) and with more concrete applications
within the context of specific topics - algebra, geometry, and
discrete mathematics (Chapters 7-13). The book provides
opportunities for teachers to engage in authentic mathematical
thinking. The mathematical ideas under consideration build on
specific middle and secondary school content while simultaneously
pushing the teacher to consider more advanced topics, as well as
various connections across mathematical domains. The book strives
to preserve the spirit of discussion, and at times even argument,
typical of collaborative work on a lesson plan. Based on the
accumulated experience of work with future and current teachers,
the book assumes that students have some background in lesson
planning, and extends their thinking further. Specifically, this
book aims to provide a discussion of how a lesson plan is
constructed, including the ways in which problems are selected or
invented, rather than the compilation of prepared lesson plans.
This approach reflects the authors' view that the process of
searching for an answer is often more important than the formal
result.
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