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El. knyga: Uncovering Student Thinking in Mathematics, Grades 6-12: 30 Formative Assessment Probes for the Secondary Classroom

  • Formatas: EPUB+DRM
  • Išleidimo metai: 27-Jun-2008
  • Leidėjas: Corwin Press Inc
  • Kalba: eng
  • ISBN-13: 9781452295565
Kitos knygos pagal šią temą:
  • Formatas: EPUB+DRM
  • Išleidimo metai: 27-Jun-2008
  • Leidėjas: Corwin Press Inc
  • Kalba: eng
  • ISBN-13: 9781452295565
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"Cheryl Rose and Carolyn Arline provide a valuable resource to teachers who are interested in determining how their students think and answer questions in mathematics classes." From the Foreword by Johnny W. Lott Director, Center for Excellence in Teaching and Learning University of Mississippi

Use these targeted probes to assess secondary students grasp of key mathematics concepts!

Research findings show that formative assessment is an important strategy for improving student achievement in mathematics. This practical resource by best-selling authors Cheryl M. Rose and Carolyn B. Arline provides tools and examples that allow middle and high school teachers to gauge students knowledge of core mathematics concepts and strengthen their ability to teach effectively.

The authors provide 30 formative assessment probesbrief, easily administered activities targeting specific mathematics ideasto reveal common understandings and misunderstandings in student thinking. Field-tested with teachers and students at various grade levels, these powerful diagnostic tools help teachers modify their teaching and identify areas that require more instruction. Written in accessible language, this invaluable book:





Discusses standards, research results, and practical craft knowledge Describes the purpose, structure, and development of mathematics assessment probes Helps teachers build on students current understandings while addressing their identified difficulties Offers examples of the faulty thinking students are likely to exhibit and typical obstacles they may encounter

These assessment probes will help teachers can make sound instructional choices and increase the mathematics knowledge of all their students!

Recenzijos

"Cheryl Rose and Carolyn Arline provide a valuable resource to teachers who are interested in determining how their students think and answer questions in mathematics classes." -- From the Foreword by Johnny W. Lott "The authors contribute to the field by answering the question: How do I help my struggling students who hold a variety of misconceptions or have limited prior knowledge of the content?" -- Lesa M. Covington Clarkson, Assistant Professor "The book is timely. The probes will be beneficial to teachers and very useful to districts developing local assessments." -- Debra Scarpelli, Mathematics Teacher "An efficient teaching tool to uncover and correct misconceptions students have across all mathematics strands. This book provides numerous opportunities for increased student achievement that are both powerful and exciting for educators." -- Jennifer Petersen, K-12 Math Curriculum Facilitator "A tool for middle school and high school mathematics teachers that combines the effective use of research, formative assessment, and ready-to-go student tasks. This resource belongs int he hands of any mathematics educator who seeks to balance procedural knowledge, conceptual understanding, and skills for each student." -- Christine Downing, Mathematics School Improvement Coach and Educational Consultant "Using probes with my students has helped me plan and modify my instruction. The range of student explanations elicit rich mathematical discourse." -- Johnette R. Winfrey, Math Specialist "One of the most effective tools for teachers to gather valuable formative assessment data. This resource provides an easily accessible, yet powerful way for teachers to elicit and analyze student work that truly reflects student thinking. The probes are targeted to specific concept areas that are easily connected to daily lesson plans and curriculum materials." -- Michelle Parks, Educational Consultant

Foreword ix
Johnny W. Lott
Preface xi
Acknowledgments xiii
About the Authors xv
Mathematics Assessment Probes
1(21)
What Types of Understandings and Misunderstandings Does a Mathematics Assessment Probe Uncover?
2(5)
How Were the Mathematics Assessment Probes Developed?
7(3)
What Is the Structure of a Mathematics Assessment Probe?
10(5)
What Additional Information Is Provided With Each Mathematics Assessment Probe?
15(5)
What Mathematics Assessment Probes Are Included in the Book?
20(2)
Instructional Implications
22(10)
Differentiating Instruction
23(1)
Assessing Point of Entry
24(1)
Analyzing Trends in Student Thinking
24(1)
Giving Student Interviews
25(1)
Promoting Student-to-Student Dialogue
26(1)
Developing Vocabulary
26(2)
Allowing for Individual Think Time
28(1)
Improving Students' Processing Skills
29(1)
Assessing Effectiveness of Instructional Activities
29(1)
Moving Beyond the Individual Classroom
30(1)
Summary
31(1)
Number and Operations Assessment Probes
32(74)
What Is the Value of the Digit?
33(5)
Teachers' Notes: What Is the Value of the Digit?
34(3)
Student Responses to ``What Is the Value of the Digit?'' Probe
37(1)
Variation: What Is the Value of the Digit? Card Sort
38(1)
What Is the Meaning of 2/3?
39(5)
Teachers' Notes: What Is the Meaning of 2/3?
40(3)
Student Responses to ``What Is the Meaning of 2/3?''
43(1)
Variation: What Is the Meaning of 2/3? Card Sort
44(1)
Is It Equivalent?
45(5)
Teachers' Notes: Is It Equivalent?
46(3)
Student Responses to ``Is It Equivalent?''
49(1)
Variation: Is It Equivalent? Card Sort
50(1)
What's Your Estimate?
51(5)
Teachers' Notes: What's Your Estimate?
52(3)
Student Responses to ``What's Your Estimate?''
55(1)
Is It an Estimate?
56(5)
Teachers' Notes: Is It an Estimate?
57(2)
Student Responses to ``Is It an Estimate?''
59(2)
Is It Simplified?
61(4)
Teachers' Notes: Is It Simplified?
62(2)
Student Responses to ``Is It Simplified?''
64(1)
Is It Simplified? Algebraic Variation
65(1)
Where Is One Million?
66(5)
Teachers' Notes: Where Is One Million?
67(2)
Student Responses to ``Where Is One Million?''
69(2)
How Low Can You Go?
71(4)
Teachers' Notes: How Low Can You Go?
72(2)
Student Responses to ``How Low Can You Go?''
74(1)
Variation: How Low Can You Go?
75(1)
What's Your Addition Strategy?
76(6)
Teachers' Notes: What's Your Addition Strategy?
77(4)
Student Responses to ``What's Your Addition Strategy?''
81(1)
Variation: What's Your Addition Strategy? Decimals
82(1)
Variation: What's Your Addition Strategy? Fractions
83(1)
What's Your Subtraction Strategy?
84(6)
Teachers' Notes: What's Your Subtraction Strategy?
85(4)
Student Responses to ``What's Your Subtraction Strategy?''
89(1)
Variation: What's Your Subtraction Strategy? Decimals
90(1)
Variation: What's Your Subtraction Strategy? Fractions
91(1)
What's Your Multiplication Strategy?
92(6)
Teachers' Notes: What's Your Multiplication Strategy?
93(3)
Student Responses to ``What's Your Multiplication Strategy?''
96(2)
Variation: What's Your Multiplication Strategy? Decimals
98(1)
What's Your Division Strategy?
99(6)
Teachers' Notes: What's Your Division Strategy?
100(3)
Student Responses to ``What's Your Division Strategy?''
103(2)
Variation: What's Your Division Strategy? Decimals
105(1)
Geometry, Measurement, and Data Assessment Probes
106(51)
What's the Measure?
107(4)
Teachers' Notes: What's the Measure?
108(2)
Student Responses to ``What's the Measure?''
110(1)
Variation: What's the Measure?
111(1)
Are Area and Perimeter Related?
112(5)
Teachers' Notes: Are Area and Perimeter Related?
113(2)
Student Responses to ``Are Area and Perimeter Related?''
115(2)
What's the Area?
117(5)
Teachers' Notes: What's the Area?
118(2)
Student Responses to ``What's the Area?''
120(2)
What's the Capacity?
122(4)
Teachers' Notes: What's the Capacity?
123(2)
Student Responses to ``What's the Capacity?''
125(1)
Is It Transformed?
126(5)
Teachers' Notes: Is It Transformed?
127(3)
Student Responses to ``Is It Transformed?''
130(1)
Are They Similar?
131(5)
Teachers' Notes: Are They Similar?
132(2)
Student Responses to ``Are They Similar?''
134(2)
What Do You Mean?
136(8)
Teachers' Notes: What Do You Mean?
137(5)
Student Responses to ``What Do You Mean?''
142(2)
Variation: What Do You Mean?
144(1)
Name of the Graph?
145(6)
Teachers' Notes: Name of the Graph?
146(3)
Student Responses to ``Name of the Graph?''
149(2)
Graph Construction
151(6)
Teachers' Notes: Graph Construction
152(3)
Student Responses to ``Graph Construction''
155(2)
Algebra Assessment Probes
157(63)
Expressions: Equal or Not Equal?
158(7)
Teachers' Notes: Expressions: Equal or Not Equal?
159(4)
Student Responses to ``Expressions: Equal or Not Equal?''
163(2)
Is It the Same as a + b?
165(5)
Teachers' Notes: Is It the Same as a + b?
166(2)
Student Responses to ``Is It the Same as a + b?''
168(2)
M & N's?
170(5)
Teachers' Notes: M & N's?
171(2)
Student Responses to ``M & N's?''
173(2)
What's the Substitute?
175(5)
Teachers' Notes: What's the Substitute?
176(3)
Student Responses to ``What's the Substitute?''
179(1)
Is It True?
180(7)
Teachers' Notes: Is It True?
181(4)
Student Responses to ``Is It True?''
185(2)
Solving Equations
187(7)
Teachers' Notes: Solving Equations
188(4)
Student Responses to ``Solving Equations''
192(2)
Correct Representation of the Inequality?
194(6)
Teachers' Notes: Correct Representation of the Inequality?
195(4)
Student Responses to ``Correct Representation of the Inequality?''
199(1)
Is It a Variable?
200(7)
Teachers' Notes: Is It a Variable?
201(4)
Student Responses to ``Is It a Variable?''
205(2)
Binomial Expansion
207(6)
Teachers' Notes: Binomial Expansion
208(3)
Student Responses to ``Binomial Expansion''
211(2)
Is It Quadratic?
213(7)
Teachers' Notes: Is It Quadratic?
214(4)
Student Responses to ``Is It Quadratic?''
218(2)
Resource A: Note Template 220(2)
References 222(3)
Index 225
Cheryl Rose Tobey is a senior mathematics associate at Education Development Center (EDC) in Massachusetts. She is the project director for Formative Assessment in the Mathematics Classroom: Engaging Teachers and Students (FACETS) and a mathematics specialist for Differentiated Professional Development: Building Mathematics Knowledge for Teaching Struggling Students (DPD); both projects are funded by the National Science Foundation (NSF). She also serves as a director of development for an Institute for Educational Science (IES) project, Eliciting Mathematics Misconceptions (EM2). Her work is primarily in the areas of formative assessment and professional development.

Prior to joining EDC, Tobey was the senior program director for mathematics at the Maine Mathematics and Science Alliance (MMSA), where she served as the coprincipal investigator of the mathematics section of the NSF-funded Curriculum Topic Study, and principal investigator and project director of two Title IIa state Mathematics and Science Partnership projects. Prior to working on these projects, Tobey was the coprincipal investigator and project director for MMSAs NSF-funded Local Systemic Change Initiative, Broadening Educational Access to Mathematics in Maine (BEAMM), and she was a fellow in Cohort 4 of the National Academy for Science and Mathematics Education Leadership. She is the coauthor of six published Corwin books, including seven books in the Uncovering Student Thinking series (2007, 2009, 2011, 2013, 2014), two Mathematics Curriculum Topic Study resources (2006, 2012), and Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction and Learning (2011). Before joining MMSA in 2001 to begin working with teachers, Tobey was a high school and middle school mathematics educator for ten years. She received her BS in secondary mathematics education from the University of Maine at Farmington and her MEd from City University in Seattle. She currently lives in Maine with her husband and blended family of five children.

Carolyn B. Arline is a secondary mathematics educator, currently teaching high school students in Maine. Carolyn also works as a teacher leader in the areas of mathematics professional development, learning communities, assessment, systematic school reform, standards-based teaching, learning and grading, student-centered classrooms, and technology.  She has previously worked as a mathematics specialist at the Maine Mathematics and Science Alliance (MMSA) and continues her work with them as a consultant. Carolyn is a fellow of the second cohort group of the Governors Academy for Science and Mathematics Educators and serves as a mentor teacher with the current cohort. She participated as a mathematics mentor in the NSF-funded Northern New England Co-Mentoring Network (NNECN) and continues her role as a mentor teacher. She serves as a board member of the Association of Teachers of Mathematics in Maine (ATOMIM) and on local curriculum committees.  Carolyn received her B.S. in secondary mathematics education from the University of Maine.