Mine the Gap for Mathematical Understanding, Grades K-2: Common Holes and Misconceptions and What To Do About Them: Corwin Mathematics Series
Autor John J. SanGiovannien Limba Engleză Paperback – 5 feb 2017
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Specificații
ISBN-10: 1506337686
Pagini: 384
Dimensiuni: 216 x 279 x 13 mm
Greutate: 0.79 kg
Ediția:1
Editura: SAGE Publications
Colecția Corwin
Seria Corwin Mathematics Series
Locul publicării:Thousand Oaks, United States
Recenzii
dozens of great mathematical tasks, but—perhaps more important—it gives teachers the chance
to consider each task; anticipate student responses—a critical first step in formative assessment;
analyze actual student responses; and then consider what they would do in the classroom.
Thoughts about modifying each task provide another option for each task. At a time when teachers
are encouraged to regularly provide students with tasks that promote reasoning and problem
solving, this book will help teachers dig deeper as they mine for understandings.”
“Too often students (and parents and teachers) have the notion that the goal in math should
be to get the right answer. Yet insight into misconceptions and students’ thinking can tell us
much more about what students know (and don’t know) beyond simply a correct or incorrect
answer. SanGiovanni offers teachers a treasure trove of rich tasks and student work on those
tasks. Examples of how to analyze student thinking and next instructional steps make this a volume
that should be on every K–2 math teacher’s desk!”
“This work does what other books only attempt to do. It combines instruction, assessment, and
practice with open-ended and rich tasks that allow for teachers to not only immediately implement
the ideas but also understand the content and pedagogy behind them. The tasks, which are
immediately implementable and customizable, engage each and every learner. They are based on
cutting edge and research-based instructional frameworks and provide countless learning opportunities
for students.”
“Mine the Gap for Mathematical Understanding is a much-needed and anticipated resource for
teachers, mathematics coaches, mathematics specialists, administrators, and other stakeholders.
The easy to follow, teacher-friendly format, the accompanying commentary for each student work
sample, along with the thoughtful reflection questions will quickly make this resource a ‘go-to’
professional development tool.”
“Mine the Gap is a great tool for teachers to use to grow their own understanding of student misconceptions
and incomplete understandings and how to address them. This is an indispensable
resource for all involved in supporting students’ growth in mathematics.”
“More than just a nice collection of problems, this book shares a road map for teachers looking to
enhance the quality of the math tasks they use with students. Teachers will appreciate the examples
of actual student work paired with tips for analysis and instruction.”
“John SanGiovanni continues to provide teacher-friendly, must-have books. They empower teachers
by deepening their understanding of content and teaching.”
Cuprins
Acknowledgments
Publisher’s Acknowledgments
About the Author
Introduction
CHAPTER 1. RICH MATHEMATICS TASKS, STUDENT MISCONCEPTIONS, USING TASKS
CHAPTER 2. COUNTING AND REPRESENTING NUMBERS
BIG IDEAS
1. Counting on From Any Number (0–120)
2. Counting on a Number Line
3. Skip-Counting
4. Representing Numbers
5. Representing Numbers to 1,000 With Models
6. Understanding Relationships Between Numbers
CHAPTER 3. NUMBER RELATIONSHIPS AND COMPARISON
BIG IDEAS
7. Comparing Numbers Within 100
8. Comparing Numbers Within 1,000
9. Comparing Numbers Within 1,000
10. Number Relationships Through Number Lines
11. Decomposing Numbers Less Than 100
12. More Decomposing Numbers
CHAPTER 4. ADDITION AND SUBTRACTION
BIG IDEAS
13. Representing Addition
14. Properties of Addition
15. Reasoning About Addition
16. Representing Subtraction
17. Connecting Addition and Subtraction
18. Reasoning About Subtraction
19. The Meaning of the Equal Sign
20. Problem Solving With Addition and Subtraction
CHAPTER 5. ADDITION AND SUBTRACTION WITHIN 100
BIG IDEAS
21. Addition Within 100
22. More With Addition Within 100
23. Reasoning About Addition Within 100
24. Subtraction Within 100
25. Reasoning About Subtraction Within 100
26. Problem Solving Using Addition and Subtraction Within 100
CHAPTER 6. ADDITION AND SUBTRACTION WITHIN 1,000
BIG IDEAS
27. Adding Within 1,000
28. Reasoning About Addition Within 1,000
29. Subtraction Within 1,000
30. Reasoning About Subtraction Within 1,000
31. Problem Solving Within 1,000
CHAPTER 7. MEASUREMENT WITH MONEY AND TIME
BIG IDEAS
32. Working and Problem Solving With Money
33. Working and Problem Solving With Money
34. Telling Time
35. Elapsed Time
CHAPTER 8. MULTIPLICATION AND DIVISION
BIG IDEAS
36. Representing Multiplication and Division
37. Reasoning About Multiplication
38. Properties of Multiplication
39. Representing Division
40. Problem Solving With Multiplication and Division
CHAPTER 9. WHAT DO WE DO NEXT?
References and Additional Resources
Notă biografică
John J. SanGiovanni is a mathematics coordinator in Howard County, Maryland. There, he leads mathematics curriculum development, digital learning, assessment, and professional development. John is an adjunct professor and coordinator of the Elementary Mathematics Instructional Leadership graduate program at McDaniel College. In addition to this Figuring Out Fluency series, some of his many Corwin books include Daily Routines to Jump-Start Problem Solving, Grades K-8, Answers to Your Biggest Questions about Teaching Elementary Math, the Daily Routines to Jump-Start Math series, and Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance. John is a national mathematics curriculum and professional learning consultant who also speaks frequently at national conferences and institutes. He is active in state and national professional organizations, recently serving on the board of directors for the National Council of Teachers of Mathematics (NCTM) and currently on the board of directors for the National Council of Supervisors of Mathematics (NCSM).