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Children’s Reasoning While Building Fraction Ideas
This book may be used for research, graduate and undergraduate teacher education, and teacher development. It presents an integrated set of studies of a heterogeneously grouped class of twenty-one nine-year olds, engaged in exploring fraction ideas prior to classroom instruction under conditions that supported investigation, collaboration and argumentation. It demonstrates with text and video narrative how young children can reason about mathematics in surprisingly sophisticated ways when provided the opportunity to do so in the proper classroom environment. In this volume, fourth grade students’ reasoning about fraction concepts is described through careful analysis and accompanying video excerpts showcasing the variety and originality of their thinking. These children will serve as an inspiration for educators to encourage the development of reasoning and argumentation in their students as part of a mathematics curriculum designed to produce critical thinkers.
Combinatorics and Reasoning
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level. This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.
Inclusive Access and Open Educational Resources E-text Programs in Higher Education
This volume takes a comprehensive and broad look at e-text programs across a wide spectrum of programs, institutions, and policies in three parts. The first part showcases several policy papers to contextualize the discussion and highlight the reasons for IAE programs’ structure and the obstacles they face for implementation. The second part is an in-depth exploration of various case studies that provide a detailed description of IAE programs, including information about program elements, program structure, program size, and insights into how programs are operationalized, and their shortcomings and benefits to students and stakeholders. The final part is a selection of research papers that...
Jurus Jitu Memahami Ilmu Interaksi Berpikir (Interthinking)
Target utama pencapaian pembelajaran adalah terjadinya perubahan yang lebih baik pada struktur pengetahuan siswa sebagai hasil pengalaman belajarnya. Perubahan struktur pengetahuan siswa ini harus dibantu melalui kegiatan interaksi baik dengan dirinya, siswa lain, guru, maupun dengan lingkungannya. Kegiatan-kegiatan interaksi sangat membantu siswa untuk mengembangkan kemampuan bersama melalui berpikir dan berbicara sehingga terjadi peningkatan prestasi belajarnya. Terdapat tiga interaksi berpikir siswa dalam aktivitas diskusi untuk menyelesaikan masalah statistik yaitu interaksi berpikir produktif, interaksi berpikir statis, dan interaksi berpikir kontraproduktif. Ketiga interaksi berpikir ini terjadi pada setiap kegiatan diskusi selama proses pembelajaran berlangsung. Interaksi berpikir produktif terjadi pada kelompok subjek berkemampuan tinggi dan campuran atau heterogen. Sedangkan interaksi berpikir statis dan kontraproduktif terjadi pada kelompok subjek berkemampuan sedang dan rendah.
Teachable Moments and the Science of Education
This book develops a general theory of autonomous teaching by examining a mysterious educational idea: the teachable moment. By formulating an understanding of the teachable moment as predicated upon ‘educational energy,’ this book takes up John Dewey’s view of teaching to articulate a law-like, scientifically oriented pedagogical theory. By offering a testable hypothesis about effective teaching through an innovative reading of Dewey’s law, this book also provides insights into changes in school practice and schooling policy consonant with an understanding of teaching as a science.
Теорія та методика навчання математики, фізики, інформатики. Випуск XІ
Збірник містить статті з різних аспектів дидактики математики і проблем її викладання у ВНЗ та школі. Значну увагу приділено питанням розвитку методичних систем навчання математики, застосування інноваційних технологій навчання математики, формування предметних математичних компетентностей майбутніх фахівців. Для студентів вищих навчальних закладів, аспірантів, наукових та педагогічних працівників.
Children's Reasoning While Building Fraction Ideas
This book may be used for research, graduate and undergraduate teacher education, and teacher development. It presents an integrated set of studies of a heterogeneously grouped class of twenty-one nine-year olds, engaged in exploring fraction ideas prior to classroom instruction under conditions that supported investigation, collaboration and argumentation. It demonstrates with text and video narrative how young children can reason about mathematics in surprisingly sophisticated ways when provided the opportunity to do so in the proper classroom environment. In this volume, fourth grade students' reasoning about fraction concepts is described through careful analysis and accompanying video excerpts showcasing the variety and originality of their thinking. These children will serve as an inspiration for educators to encourage the development of reasoning and argumentation in their students as part of a mathematics curriculum designed to produce critical thinkers.
Scattered Seeds
Descendants of Rabbi Israel, son of Rabbi Shalom, who was martyred in 1659 in Ruzhany, Lithuania. He had three sons: Menachem Nachum Za'k, Shimon Za'k and Sholem Za'k. Descendants and relatives lived mainly in Lithuania, Poland, Germany, Russia, Israel and New York.
