Concept Mapping in Mathematics: Research into Practice is the first comprehensive book on concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. This collection of research articles examines the usefulness of concept maps in the educational setting, with applications and examples ranging from primary grade classrooms through secondary mathematics to pre-service teacher education, undergraduate mathematics and post-graduate mathematics education. A second meta-cognitive tool, called vee diagrams, is also critically examined by two authors, particularly its value in improving mathematical problem solving. Thematically, the book flows from a historical development overview of concept mapping in the sciences to applications of concept mapping in mathematics by teachers and pre-service teachers as a means of analyzing mathematics topics, planning for instruction and designing assessment tasks including applications by school and university students as learning and review tools. This book provides case studies and resources that have been field tested with school and university students alike. The findings presented have implications for enriching mathematics learning and making problem solving more accessible and meaningful for students. The theoretical underpinnings of concept mapping and of the studies in the book include Ausubel’s cognitive theory of meaningful learning, constructivist and Vygotskian psychology to name a few. There is evidence particularly from international studies such as PISA and TIMSS and mathematics education research, which suggest that students’ mathematical literacy and problem solving skills can be enhanced through students collaborating and interacting as they work, discuss and communicate mathematically. This book proposes the meta-cognitive strategy of concept mapping as one viable means of promoting, communicating and explicating students’ mathematical thinking and reasoning publicly in a social setting (e.g., mathematics classrooms) as they engage in mathematical dialogues and discussions. Concept Mapping in Mathematics: Research into Practice is of interest to researchers, graduate students, teacher educators and professionals in mathematics education.
using and understanding mathematics pdf
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'This book is the ideal way to dispel some of the fears which surround the subject area of mathematics and should be an essential part of the professional development library of every early years setting provider for children aged three and over' - Early Years Update 'A book that is both readable and rigorous. [Its] guidance will help teachers to make mathematics meaningful to young children. Throughout the book connections are made which relate language, symbols, concrete materials and pictures to the key ideas that are central to effective learning for the 21st century. This book will help teachers gain a depth of understanding that will make them confident in engaging children with real mathematical thinking' - Dr J.E. Anghileri, Senior Lecturer in Mathematics and Mathematics Education, Faculty of Education, University of Cambridge 'This is an updated version of a classic text which has been a best -seller among teachers and student teachers for many years. Being always strongly grounded in the classroom, it develops in a non-intimidating way teachers' own understanding of the mathematics they are teaching. Many insightful examples of children's thinking and appropriate activities help to illustrate the points. This is an essential book for teachers of Early Years and Key Stage 1' - Margaret Brown, Professor of Mathematics Education, King's College London, UK This is a fully revised version of the authors' successful and much-used book, Understanding Mathematics in the Lower Primary Years, updated to include the current Foundation Stage Curriculum and the new Primary Framework in England. The authors empower the reader to have a clearer understanding of the mathematical ideas behind the material they use in the classroom. They also show how children can be helped to develop an understanding of mathematics for themselves, rather than just learning recipes and routines with little meaning. Major themes are: - Understanding through making connections - Equivalence and transformation - Using and applying mathematics It is written for teachers and teacher trainees engaged in teaching mathematics to children aged 3 to 8 years. It is an essential student text and professional reference work for all teachers of children aged 3 to 8 years. Dr Derek Haylock is an education consultant and author, working in the field of mathematics education. His book Mathematics Explained for Primary Teachers has been a leader in the field for many years, with a third edition published in 2006. Dr Anne Cockburn is a Reader in the School of Education and Lifelong Learning at the University of East Anglia, Norwich. Watch the authors talking about their book here: YouTube
Written specifically for mathematics teachers at all levels, this resource helps facilitate the understanding and process of writing differentiated lessons to accommodate all levels of learning and learning styles.
A valuable resource for pre-service teachers who wish to integrate contemporary technology into teaching key mathematical concepts.
How can today’s teachers, whose classrooms are more culturally and linguistically diverse than ever before, ensure that their students achieve at high levels? How can they design units and lessons that support English learners in language development and content learning—simultaneously? Authors Amy Heineke and Jay McTighe provide the answers by adding a lens on language to the widely used Understanding by Design® framework (UbD® framework) for curriculum design, which emphasizes teaching for understanding, not rote memorization. Readers will learn * the components of the UbD framework; * the fundamentals of language and language development; * how to use diversity as a valuable resource for instruction by gathering information about students’ background knowledge from home, community, and school; * how to design units and lessons that integrate language development with content learning in the form of essential knowledge and skills; and * how to assess in ways that enable language learners to reveal their academic knowledge. Student profiles, real-life classroom scenarios, and sample units and lessons provide compelling examples of how teachers in all grade levels and content areas use the UbD framework in their culturally and linguistically diverse classrooms. Combining these practical examples with findings from an extensive research base, the authors deliver a useful and authoritative guide for reaching the overarching goal: ensuring that all students have equitable access to high-quality curriculum and instruction.
This book is designed for grades K-2 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-10 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data analysis and probability. 30 Mathematics Lessons Using the TI-10 is correlated to the Common Core State Standards and supports core concepts of STEM instruction. 248pp. plus Teacher Resource CD
The Complete Kit includes 6 copies of each of the 16 Math Readers per grade level (96 books total), Teacher's Resource Guide, Teacher's Resource CD, 16 full-colour problem solving transparencies, and an Interactive Mathematics Activities CD featuring 8 mathematical games.
For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics. T he most successful new calculus text in the last two decades The much-anticipated 3rd Edition of Briggs' Calculus Series retains its hallmark features while introducing important advances and refinements. Briggs, Cochran, Gillett, and Schulz build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor. Examples are stepped out and thoughtfully annotated, and figures are designed to teach rather than simply supplement the narrative. The groundbreaking eBook contains approximately 700 Interactive Figures that can be manipulated to shed light on key concepts. For the 3rd Edition, the authors synthesized feedback on the text and MyLab(tm) Math content from over 140 instructors and an Engineering Review Panel. This thorough and extensive review process, paired with the authors' own teaching experiences, helped create a text that was designed for today's calculus instructors and students. Also available with MyLab Math MyLab Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0134995996 / 9780134995991 Calculus: Early Transcendentals and MyLab Math with Pearson eText - Title-Specific Access Card Package, 3/e Package consists of: 0134763645 / 9780134763644 Calculus: Early Transcendentals 0134856929 / 9780134856926 MyLab Math with Pearson eText - Standalone Access Card - for Calculus: Early Transcendentals
Teaching strategies are grounded in the NCTM standards and illustrated with real student work. In addition, the author provides a full range of concrete developmental activities that encourage future teachers to make math make sense for themselves as well as for their students.Believing that teachers who are comfortable with mathematics develop learners who are comfortable with mathematics, this author empowers preservice preK-4 teachers to teach math confidently by laying a solid foundation of math concepts, and building on that foundation with engaging, meaningful, standards-based teaching methods. Integrated in this unique combined approach to teaching mathematics is a thorough discussion of math manipulatives, as well as the use of technology—computer and otherwise—to assist today's mathematics teacher.For educators, aids, and parents responsible for teaching Pre-K to fourth grade math.