Mathematics in Middle and Secondary School

The experience and knowledge acquired in teacher education courses should build important fundamentalsfor the future teaching of mathematics. In particular experience in mathematical problem solving and inplanning lessons devoted to problem solving is an essential component of teacher preparation. This bookdevelops a problem solving approach and is intended to be a text used in mathematics education courses (orprofessional development) for pre-service or in-service middle and secondary school teachers. It can be usedboth 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 mathematicseducation preparation as the text is more involved with mathematical ideas and problem solving anddiscusses some of the intricate pedagogical considerations that arise in teaching. The text is written not as anintroduction to mathematics education (a first course) but rather as a second or probably third course. Thebook deals both with general methodology issues in mathematics education incorporating a problem solvingapproach (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 onspecific middle and secondary school content while simultaneously pushing the teacher to consider more advanced topics as well as variousconnections across mathematical domains. The book strives to preserve the spirit of discussion and at times even argument typical of collaborativework on a lesson plan. Based on the accumulated experience of work with future and current teachers the book assumes that students have somebackground in lesson planning and extends their thinking further. Specifically this book aims to provide a discussion of how a lesson plan isconstructed including the ways in which problems are selected or invented rather than thecompilation of prepared lesson plans. This approach reflects the authors' view that the process ofsearching for an answer is often more important than the formal result.