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Realizing Rigor in the Mathematics Classroom [Pehme köide]

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  • Formaat: Paperback / softback, 192 pages, kõrgus x laius: 279x215 mm, kaal: 460 g
  • Ilmumisaeg: 29-May-2014
  • Kirjastus: Corwin Press Inc
  • ISBN-10: 1452299609
  • ISBN-13: 9781452299600
Teised raamatud teemal:
Realizing Rigor in the Mathematics ClassroomSuurem pilt
  • Formaat: Paperback / softback, 192 pages, kõrgus x laius: 279x215 mm, kaal: 460 g
  • Ilmumisaeg: 29-May-2014
  • Kirjastus: Corwin Press Inc
  • ISBN-10: 1452299609
  • ISBN-13: 9781452299600
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781452299600.html
Märksõnad:
Hull, Miles and Balka help teachers achieve mathematical rigor in the classroom by implementing the Common Core State Standards for Mathematical Practice. They provide a proficiency matrix as a framework for implementation, building lessons, and promoting the strategy sequence of improving mathematical proficiency. They discuss and define rigor and outline the impact and trends associated with the Common Core; examine obstacles to efforts to address the Standards for Mathematical Practice and increase student achievement, such as differentiating instruction, monitoring classrooms, and using data, and how to deal with them; outline a five-step solution process for implementing and sustaining the standards and providing a rigorous math class; and detail the roles of teachers, coaches, and leaders, and how to sustain momentum. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

Rigor put within reach!

Rigor: The Common Core has made it policy—and this first-of-its-kind guide takes math teachers and leaders through the process of making it reality. Using the Proficiency Matrix as a framework, the authors offer proven strategies and practical tools for successful implementation of the CCSS mathematical practices—with rigor as a central objective. You’ll learn how to

  • Define rigor in the context of each mathematical practice
  • Identify and overcome potential issues, including differentiating instruction and using data
  • Relate specific roles and goals for all stakeholders
  • Use assessment tools to guide work and monitor progress

Arvustused

"This comprehensive, step-by-step guide for enhancing student thinking and reasoning through rigor is yet another major contribution to the field of mathematics education by this outstanding author trio! Hull, Balka, and Harbin Miles tackle the challenges related to rigor head-on, providing support for teachers and teacher leaders through well over a dozen new tools geared toward engaging teacher teams in the work of enhancing student thinking and reasoning through mathematical rigor." -- Jon Wray, Mathematics Instructional Facilitator "The value of this book is in its capacity to explain rigor in the context of teach­ing and learning mathematics. The authors have succeeded in presenting the case for rigor by developing definitions and tools that can be used to find evidence of stu­dent learning including a deep understanding of mathematics as well as the ability to transfer learning into new and challenging situations." -- From the Foreword by Suzanne Mitchell

Foreword xi
About the Authors xiii
Introduction 1(6)
CCSS Content and Practices
2(1)
A Clue to Rigor
3(1)
Outline of the Book
4(1)
How to Use This Book
5(2)
Part I The Foundation
7(62)
1 Understanding and Meeting the Challenge of Rigor
8(6)
National Assessments
8(1)
Teacher Evaluation
9(1)
Learning Shifts
10(1)
Meeting the Challenges
10(1)
Looking at Assessments
11(2)
Rigor as a Common Factor
13(1)
2 Defining and Instituting Rigor
14(13)
Searching for Evidence
15(1)
Dictionary and Thesaurus
16(1)
Professional Opinions
16(2)
Powerful Mathematics Instruction
17(1)
Rigor and Relevance
17(1)
Depth of Knowledge
18(1)
Indicators of Rigor
18(1)
Drawing Conclusions
19(1)
Decision Point
20(3)
Contrasting Lessons Examples
23(1)
Problem 1
23(1)
Problem 2
23(1)
Problem Analysis
23(3)
Problem 1
23(1)
Problem 2
24(1)
Problem Usage
25(1)
Transforming Classrooms to Support Rigor
26(1)
Having Productive Conversations
26(1)
3 Building Team Leadership to Support Rigor
27(6)
Role of a Steering Committee
29(1)
Role of the Leadership Team
30(1)
Role of the Principal
30(1)
Developing Learning Communities
31(1)
A Principal's Story
31(1)
Having Productive Conversations
32(1)
4 Rigor and the Standards for Practice
33(13)
Standards for Mathematical Practice
33(1)
Practice 1a Make Sense of Problems
34(1)
Defining the Practice
34(1)
Recognizing the Practice in Action
34(1)
Practice 1b Persevere in Solving Them
35(1)
Defining the Practice
35(1)
Recognizing the Practice in Action
35(1)
Practice 2 Reason Abstractly and Quantitatively
36(1)
Defining the Practice
36(1)
Recognizing the Practice in Action
37(1)
Practice 3 Construct Viable Arguments and Critique the Reasoning of Others
37(1)
Practice 3a Construct Viable Arguments
37(1)
Defining the Practice
38(1)
Recognizing the Practice in Action
38(1)
Practice 3b Critique the Reasoning of Others
38(1)
Defining the Practice
39(1)
Recognizing the Practice in Action
39(1)
Practice 4 Model With Mathematics
39(1)
Defining the Practice
39(1)
Recognizing the Practice in Action
40(1)
Practice 5 Use Appropriate Tools Strategically
40(1)
Defining the Practice
40(1)
Recognizing the Practice in Action
41(1)
Practice 6 Attend to Precision
41(1)
Defining the Practice
41(1)
Recognizing the Practice in Action
42(1)
Practice 7 Look for and Make Use of Structure
42(1)
Defining the Practice
42(1)
Recognizing the Practice in Action
43(1)
Practice 8 Look for and Express Regularity in Repeated Reasoning
43(1)
Defining the Practice
43(1)
Recognizing the Practice in Action
44(1)
Rigor and Practices
44(1)
A Principal's Story (Continued)
45(1)
Having Productive Conversations
45(1)
5 Rigor Related to Classroom Formative Assessment
46(13)
Assessment Types
47(1)
Classroom Formative Assessment: The Missing Instructional Element
48(1)
Refining Formative Assessment
49(1)
Classroom Formative Assessment
50(1)
Formative Assessment and Intervention
51(1)
Current Learning
51(1)
Effective Intervention
52(2)
Instructional Research
54(2)
Synergy
56(1)
A Principal's Story (Continued)
57(1)
Having Productive Conversations
58(1)
6 Rigor and the Proficiency Matrix
59(10)
Organization
59(1)
Initial
60(1)
Intermediate
60(1)
Advanced
60(1)
Progress Toward Rigor
60(1)
Strategy Relationship in the Matrix
61(1)
Classroom Formative Assessment and the Matrix
62(5)
Lesson Example: Using the Matrix to Select Strategies and Student Actions While Planning
62(4)
Domain: Geometry
66(1)
Problem
66(1)
A Principal's Story (Continued)
67(1)
Having Productive Conversations
67(2)
Part II Issues and Obstacles
69(20)
7 Issues to Resolve
70(10)
Issue: Teaching the Identified Content
70(1)
Issue: Deepening Mathematical Understandings
71(2)
Making Connections
71(1)
Creating Meaning
72(1)
Using Learning Research
72(1)
Issue: Reaching All Students
73(6)
Learning Opportunities
73(3)
Using the Strategy Sequence to Address Issues
76(3)
Using the Matrix
79(1)
Having Productive Conversations
79(1)
8 Obstacles to Success
80(9)
Obstacle: Working in Isolation
80(1)
Obstacle: Attempting to Evaluate People to Change
81(1)
Obstacle: Failing to Monitor Student Actions
82(1)
Obstacle: Overadoption
82(1)
Obstacle: Mistaken Efforts
82(1)
Mathematics Adoption Analysis Tool
83(4)
Understanding Maat
87(1)
Having Productive Conversations
87(2)
Part III Solutions
89(58)
9 Solution Step 1: Monitoring Student Actions Related to the Practices
90(11)
Opening Classroom Doors
90(1)
Nonevaluative Monitoring
91(1)
Starting With Students
91(2)
Classroom Visit Types
92(1)
Classroom Visit Tally-Students
93(1)
Teacher Self-Assessment of Student Actions
93(5)
Math Coach Scenario
98(2)
Having Productive Conversations
100(1)
10 Solution Step 2: Using Classroom Visit Data---Assessment of Student Actions
101(11)
Conducting Productive Conversations
101(2)
Understanding Change Process
103(1)
Levels of Adoption
104(1)
Intervention as Support
105(1)
Building a Critical Mass
105(1)
Changing the Culture
106(1)
Connecting Actions Chart
106(2)
Math Coach Scenario (Continued)
108(3)
Meeting 2
110(1)
Having Productive Conversations
111(1)
11 Solution Step 3: Monitoring Teacher Actions Related to the Practices
112(10)
Using the Classroom Visit Tally--Teachers Form
114(1)
Conversations About the Data
115(1)
Working on Individual Needs
115(4)
Experimenting, Using, Integrating
119(1)
Mathematics Collaborative Log
119(1)
Teacher Planning Guide
119(1)
Having Productive Conversations
119(3)
12 Solution Step 4: Gathering and Using Additional Data
122(10)
Assessments Collectively
122(1)
Achievement Data
122(1)
Data From Classrooms
123(1)
Specified Classroom Visits
123(1)
Validity Visits
124(1)
Reverse Visits
124(1)
Teacher-Requested Visits
125(1)
Supporting Teachers' Change Efforts
125(1)
Experimenting
125(1)
Using
126(1)
Integrating
126(1)
Adoption Stages
126(1)
Documenting Progress
127(1)
Completing the Form
127(4)
Having Productive Conversations
131(1)
13 Solution Step 5: Maintaining Progress Toward Rigor
132(15)
Background
132(1)
Relating Mathematical Rigor and the Practices
133(1)
Inferences From the Standards for Mathematical Practice
134(3)
Inferences on Content
135(1)
Inferences on Instruction
135(1)
Inferences on Assessment
136(1)
Inferences on Climate
137(1)
Rigor as an Outcome
137(1)
Categories
138(1)
Content
138(1)
Instruction
138(1)
Assessment
138(1)
Climate
138(1)
Rigor Analysis Form
139(1)
Explanation
139(1)
Directions
139(3)
Guiding the Work
142(1)
Having Productive Conversations
142(5)
Part IV Inputs and Outcomes
147(12)
14 Teaching for Rigor
148(3)
Inputs
148(1)
Curriculum
148(1)
Classrooms
148(1)
Outcomes
149(1)
Communication
149(1)
Culture
150(1)
Teaching for Progress in Rigor
150(1)
Having Productive Conversations
150(1)
15 Coaching for Rigor
151(4)
Inputs
151(2)
Curriculum
151(1)
Classrooms
152(1)
Outcomes
153(1)
Communication
153(1)
Culture
153(1)
Coaching for Progress in Rigor
154(1)
Having Productive Conversations
154(1)
16 Leading for Rigor
155(4)
Inputs
155(1)
Curriculum
155(1)
Classroom
156(1)
Outcomes
156(1)
Communication
156(1)
Culture
157(1)
Leading for Progress in Rigor
157(1)
Having Productive Conversations
158(1)
Part V Momentum
159(7)
17 Linking Responsibilities--Assessing Progress
160(6)
Professional Trust
161(1)
Professional Conversations
161(1)
Supporting Teacher Change
162(1)
Working to Improve
162(1)
Documenting Change
163(1)
Using the Form
163(1)
Conclusion
163(2)
Having Productive Conversations
165(1)
Appendix A Standards of Student Practice Mathematics Proficiency Matrix 166(2)
Appendix B Instructional Implementation Sequence 168(2)
References 170(3)
Index 173
Consulting Description

Ted H. Hull completed 32 years of service in public education before retiring and opening Hull Educational Consulting. He served as a mathematics teacher, K-12 mathematics coordinator, middle school principal, director of curriculum and instruction, and a project director for the Charles A. Dana Center at the University of Texas in Austin. While at the University of Texas, 2001 to 2005, he directed the research project Transforming Schools: Moving from Low-Achieving to High Performing Learning Communities. As part of the project, Hull worked directly with district leaders, school administrators, and teachers in Arkansas, Oklahoma, Louisiana, and Texas to develop instructional leadership skills and implement effective mathematics instruction. Hull is a regular presenter at local, state, and national meetings. He has written numerous articles for the NCSM Newsletter, including "Understanding the Six Steps of Implementation: Engagement by an Internal or External Facilitator" (2005) and "Leadership Equity: Moving Professional Development into the Classroom" (2005), as well as "Manager to Instructional Leader" (2007) for the NCSM Journal of Mathematics Education Leadership. He has been published in the Texas Mathematics Teacher (2006), Teacher Input Into Classroom Visits: Customized Classroom Visit Form. Hull was also a contributing author for publications from the Charles A. Dana Center: Mathematics Standards in the Classroom: Resources for Grades 68 (2002) and Middle School Mathematics Assessments: Proportional Reasoning (2004). He is an active member of Texas Association of Supervisors of Mathematics (TASM) and served on the NCSM Board of Directors as regional director for Southern 2.

 

Ruth Harbin Miles coaches rural, suburban, and inner-city school mathematics teachers.  Her professional experiences include coordinating the K-12 Mathematics Teaching and Learning Program for the Olathe, Kansas, Public Schools for more than 25 years; teaching mathematics methods courses at Virginias Mary Baldwin College; and serving on the Board of Directors for the National Council of Teachers of Mathematics, the National Council of Supervisors of Mathematic, and both the Virginia Council of Teachers of Mathematics and the Kansas Association of Teachers of Mathematics.  Ruth is a co-author of five Corwin books including A Guide to Mathematics Coaching, A Guide to Mathematics Leadership, Visible Thinking in the K-8 Mathematics Classroom, The Common Core Mathematics Standards, and Realizing Rigor in the Mathematics Classroom.  As co-owner of Happy Mountain Learning, Ruth specializes in developing teachers content knowledge and strategies for engaging students to achieve high standards in mathematics.

Consulting Description

Don S. Balka, Ph.D., is a noted mathematics educator who has presented more than 2,000 workshops on the use of math manipulatives with PK-12 students at national and regional conferences of the National Council of Teachers of Mathematics and at in-service trainings in school districts throughout the United States and the world.

 

He is Professor Emeritus in the Mathematics Department at Saint Marys College, Notre Dame, Indiana. He is the author or co-author of numerous books for K-12 teachers, including Developing Algebraic Thinking with Number Tiles, Hands-On Math and Literature with Math Start, Exploring Geometry with Geofix, Working with Algebra Tiles, and Mathematics with Unifix Cubes. Balka is also a co-author on the Macmillan K-5 series, Math Connects and co-author with Ted Hull and Ruth Harbin Miles on four books published by Corwin Press.

He has served as a director of the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics. In addition, he is president of TODOS: Mathematics for All and president of the School Science and Mathematics Association.