Uncovering Student Thinking in Mathematics, Grades 6-12

Informationen zum Autor Cheryl Rose Tobey is the senior program director for mathematics at the Maine Mathematics and Science Alliance (MMSA). Her work at the MMSA is primarily in the areas of leadership, mathematics professional development, and school reform. She is currently the coprincipal investigator of the mathematics section of the NSF-funded project Curriculum Topic Study and principal investigator and project director of a Title IIa State Mathematics and Science Partnership Project, MATHS (Mathematics: Access and Teaching in High School). Prior to working on these projects, Tobey was the coprincipal investigator and project director for MMSA's NSF-funded Local Systemic Change Initiative, BEAMM (Broadening Educational Access to Mathematics in Maine), and was a fellow in the Cohort 4 of the National Academy for Science and Mathematics Education Leadership. Klappentext Discussing standards, research, and more, these 30 probes help secondary teachers assess students' grasp of core mathematics concepts and modify their instruction to improve student achievement. Zusammenfassung Discussing standards, research, and more, these 30 probes help secondary teachers assess students' grasp of core mathematics concepts and modify their instruction to improve student achievement. Inhaltsverzeichnis Foreword by Johnny W. Lott Preface Acknowledgments About the Authors 1. Mathematics Assessment Probes Introduction What Types of Understandings and Misunderstandings Does a Mathematics Assessment Probe Uncover? How Were the Mathematics Assessment Probes Developed? What Is the Structure of a Mathematics Assessment Probe? What Additional Information Is Provided With Each Mathematics Assessment Probe? What Mathematics Assessment Probes Are Included in the Book? 2. Instructional Implications Differentiating Instruction Assessing Points of Entry Analyzing Trends in Student Thinking Giving Student Interviews Promoting Student-to-Student Dialogue Developing Vocabulary Allowing for Individual Think Time Improving Students Process Skills Assessing Effectiveness of Instructional Activities Moving Beyond the Individual Classroom Summary 3. Number and Operations Assessment Probes Probe 1: What Is the Value of the Digit? Teachers Notes: What Is the Value of the Digit? Probe 1a: What Is the Value of the Digit? Variation Probe 2: What Is the Meaning of 2/3? Teachers Notes: What Is the Meaning of 2/3? Probe 2a: What Is the Meaning of 2/3? Variation Probe 3: Is It Equivalent? Teachers Notes: Is It Equivalent? Probe 3a: Is It Equivalent? Variation Probe 4: What s Your Estimate? Teachers Notes: What s Your Estimate? Probe 5: Is It an Estimate? Teachers Notes: Is It an Estimate? Probe 6: Is It Simplified? Teachers Notes: Is It Simplified? Probe 6a: Is It Simplified? Algebraic Variation Probe 7: Where Is a Million? Teachers Notes: Where Is a Million? Probe 8: How Low Can You Go? Teachers' Notes: How Low Can You Go? Probe 8a: How Low Can You Go? Variation Probe 9: What's Your Addition Strategy? Teachers' Notes: What's Your Addition Strategy? Probe 9a: What's Your Addition Strategy? Decimals Variation Probe 9b: What's Your Addition Strategy? Fractions Variation Probe 10: What's Your Subtraction Strategy? Teachers' Notes: What's Your Subtraction Strategy? Probe 10a: What's Your Subtraction Strategy? Decimals Variation Probe 10b: What's Your Subtraction Strategy? Fractions Variation Probe 11: What's Your Multiplication Strategy? Teachers' Notes: What's Your Multiplication Strategy? Probe 11a: What's Your Multiplication Strategy? Decimals Variation Probe 12: What's Your Division Strategy? Teachers' Notes: What's Your Division Strategy? Pr...

Klappentext

Discussing standards, research, and more, these 30 probes help secondary teachers assess students' grasp of core mathematics concepts and modify their instruction to improve student achievement.

Inhalt

Foreword by Johnny W. Lott
Preface
Acknowledgments
About the Authors

1. Mathematics Assessment Probes
   Introduction
   What Types of Understandings and Misunderstandings Does a Mathematics Assessment Probe Uncover?
   How Were the Mathematics Assessment Probes Developed?
   What Is the Structure of a Mathematics Assessment Probe?
   What Additional Information Is Provided With Each Mathematics Assessment Probe?
   What Mathematics Assessment Probes Are Included in the Book?
2. Instructional Implications
   Differentiating Instruction
   Assessing Points of Entry
   Analyzing Trends in Student Thinking
   Giving Student Interviews
   Promoting Student-to-Student Dialogue
   Developing Vocabulary
   Allowing for Individual Think Time
   Improving Students Process Skills
   Assessing Effectiveness of Instructional Activities
   Moving Beyond the Individual Classroom
   Summary
3. Number and Operations Assessment Probes
   Probe 1: What Is the Value of the Digit?
   Teachers Notes: What Is the Value of the Digit?
   Probe 1a: What Is the Value of the Digit? Variation
   Probe 2: What Is the Meaning of 2/3?
   Teachers Notes: What Is the Meaning of 2/3?
   Probe 2a: What Is the Meaning of 2/3? Variation
   Probe 3: Is It Equivalent?
   Teachers Notes: Is It Equivalent?
   Probe 3a: Is It Equivalent? Variation
   Probe 4: What s Your Estimate?
   Teachers Notes: What s Your Estimate?
   Probe 5: Is It an Estimate?
   Teachers Notes: Is It an Estimate?
   Probe 6: Is It Simplified?
   Teachers Notes: Is It Simplified?
   Probe 6a: Is It Simplified? Algebraic Variation
   Probe 7: Where Is a Million?
   Teachers Notes: Where Is a Million?
   Probe 8: How Low Can You Go?
   Teachers' Notes: How Low Can You Go?
   Probe 8a: How Low Can You Go? Variation
   Probe 9: What's Your Addition Strategy?
   Teachers' Notes: What's Your Addition Strategy?
   Probe 9a: What's Your Addition Strategy? Decimals Variation
   Probe 9b: What's Your Addition Strategy? Fractions Variation
   Probe 10: What's Your Subtraction Strategy?
   Teachers' Notes: What's Your Subtraction Strategy?
   Probe 10a: What's Your Subtraction Strategy? Decimals Variation
   Probe 10b: What's Your Subtraction Strategy? Fractions Variation
   Probe 11: What's Your Multiplication Strategy?
   Teachers' Notes: What's Your Multiplication Strategy?
   Probe 11a: What's Your Multiplication Strategy? Decimals Variation
   Probe 12: What's Your Division Strategy?
   Teachers' Notes: What's Your Division Strategy?
   Probe 12a: What's Your Division Strategy? Decimals Variation
4. Geometry, Measurement, and Data Assessment Probes
   Probe 1: What's the Measure?
   Teachers' Notes: What's the Measure?
   Probe 1a: What's the Measure? Variation
   Probe 2: Are Area and Perimeter Related?
   Teachers' Notes: Are Area and Perimeter Related?
   Probe 3: What's the Area?
   Teachers' Notes: What's the Area?
   Probe 4: What's the Capacity?
   Teachers' Notes: What's the Capacity?
   Probe 5: Is It Transformed?
   Teachers' Notes: Is It Transformed?
   Probe 6: Are They Similar?
   Teachers' Notes: Are They Similar?
   Probe 7: What Do You Mean?
   Teachers' Notes: What Do You Mean?
   Probe 7a: What Do You Mean? Variation
   Probe 8: Name of the Graph?
   Teachers' Notes: Name of the Graph?
   Probe 9: Graph Construction?
   Teachers' Notes: Graph Construction?
5. Algebra and Data Assessment Probes
   Probe 1: Equal or Not Equal?
   Teachers' Notes: Equal or Not Equal?
   Probe 2: Is It the Same as a+b?
   Teachers' Notes: Is It the Same as a+b?
   Probe 3: M & N's?
   Teachers' Notes: M & N's?
   Probe 4: What's the Substitute?
   Teachers' Notes: What's the Substitute?
   Probe 5: Is It True?
   Teachers' Notes: Is It True?
   Probe 6: Solving Equations?
   Teachers' Notes: Solving Equations?
   Probe 7: Correct Representation of the Inequality?
   Teachers' Notes: Correct Representation of the Inequality?
   Probe 8: Is It a Variable?
   Teachers' Notes: Is I…