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Author: John SanGiovanni Publisher: Corwin Press ISBN: 1506375502 Category : Education Languages : en Pages : 385
Book Description
Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.
Author: John SanGiovanni Publisher: Corwin Press ISBN: 1506375502 Category : Education Languages : en Pages : 385
Book Description
Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.
Author: C. Sailaja, Smita Ratish, Lata Wishram Publisher: Vikas Publishing House ISBN: 9352592751 Category : Mathematics Languages : en Pages : 236
Book Description
Understanding Mathematics is a carefully written series of mathematics to help students encourage the study of mathematics in the best interactive form. It contains ample practice material, attractive illustrations and real-life examples for the students to relate the topics with their everyday life. Special care has been taken while teaching topics like geometry and probability to the students. Keeping in mind the development status and comprehension level of students, the text has been presented in a well graded manner.
Author: M.L. Aggarwal Publisher: Arya Publishing Company ISBN: 8182964725 Category : Languages : en Pages : 464
Book Description
Question Bank and Sample Papers in Mathematics for Class XII by Prof. M.L. Aggarwal has been written according to the changed style of question paper relevant for 2015 Board Examinations. The Salient Features of the book are: Latest Sample Papers issued by the CBSE for 2015 Examinations-with solutions Chapterwise Basic Concepts and Important Results Chapterwise Assignments for Practice (1 mark, 4 marks, 6 marks) Chapterwise Questions from Previous Years’ Board Papers Ten Sample Papers for Practice (4 Solved & 6 Unsolved) CBSE Examination Paper 2014 (Fully Solved) (Delhi and Outside Delhi)
Author: John SanGiovanni Publisher: Corwin Press ISBN: 1506382290 Category : Education Languages : en Pages : 385
Book Description
Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our young learners’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 160 high-quality tasks aligned to the standards and big ideas of grades K-2 mathematics, including counting and representing numbers, number relationships and comparison, addition and subtraction within 100 and 1000, money and time, and multiplication and division. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality taskwhat you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.
Author: Derek Haylock Publisher: SAGE ISBN: 152641001X Category : Education Languages : en Pages : 337
Book Description
Having a deep understanding of the mathematical ideas and concepts taught in the classroom is vital as a nursery or primary school teacher. In order for children to get to grips with these concepts, trainee teachers need to be aware of how they come to interpret and understand them. Now in its 5th edition, this essential book helps trainee teachers develop their own knowledge of key mathematical ideas and concepts for the nursery and primary classroom. Now focusing specifically on ages 3-7, it also supports trainees with several age-appropriate classroom activities. As well as updates to further reading suggestions and research focuses, this revised edition includes new content on: Mastery in learning mathematics Simple fractions Roman numerals Money as a form of measurement
Author: Carne Barnett-Clarke Publisher: National Council of Teachers of English ISBN: 9780873536301 Category : Mathematics Languages : en Pages : 83
Book Description
What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know… and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.
Author: Stephen Abbott Publisher: Springer Science & Business Media ISBN: 0387215069 Category : Mathematics Languages : en Pages : 269
Book Description
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
Author: Sean Dineen Publisher: World Scientific Publishing Company ISBN: 9814401404 Category : Mathematics Languages : en Pages : 320
Book Description
This book shows that it is possible to provide a fully rigorous treatment of calculus for those planning a career in an area that uses mathematics regularly (e.g., statistics, mathematics, economics, finance, engineering, etc.). It reveals to students on the ways to approach and understand mathematics. It covers efficiently and rigorously the differential and integral calculus, and its foundations in mathematical analysis. It also aims at a comprehensive, efficient, and rigorous treatment by introducing all the concepts succinctly. Experience has shown that this approach, which treats understanding on par with technical ability, has long term benefits for students.
Author: Keith Kressin Publisher: ISBN: 9780965730013 Category : Mathematics Languages : en Pages : 342
Book Description
A comprehensive overview of elementary, middle, and high-school mathematics. Intended as a supplement to any math program, this book provides additional math explanation from basic to advanced levels. Emphasis is placed on why problems are solved in a certain manner. Tailored for those who need simplified, easy-to-read additional explanations of math concepts.
Author: Jacek Woźny Publisher: Springer ISBN: 3319776886 Category : Mathematics Languages : en Pages : 122
Book Description
This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well.
Author: John SanGiovanni
Author: John SanGiovanni
Author: C. Sailaja, Smita Ratish, Lata Wishram
Author: M.L. Aggarwal
Author: John SanGiovanni
Author: Derek Haylock
Author: Carne Barnett-Clarke
Author: Stephen Abbott
Author: Sean Dineen
Author: Keith Kressin
Author: Jacek Woźny