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Uncovering Student Thinking in Mathematics, Grades 6-12

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

Edited by:

Foreword by Johnny W. Lott

June 2008 | 248 pages | Corwin

"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 probes—brief, easily administered activities targeting specific mathematics ideas—to 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!

Foreword by Johnny W. Lott
About the Authors
1. Mathematics Assessment Probes

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


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 It a Variable?

Probe 9: Binomial Expansion?

Teachers’ Notes: Binomial Expansion?

Probe 10: Is It Quadratic?

Teachers’ Notes: Is It Quadratic?

Resource A: Note Template for QUEST Cycle

"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
University of Minnesota, Minneapolis

"The book is timely. The probes will be beneficial to teachers and very useful to districts developing local assessments."

Debra Scarpelli, Mathematics Teacher
Slater Junior High School, North Smithfield, RI

"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
Springfield Public Schools, MO

"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
New Hampshire Department of Education

"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
Kenilworth Middle School, Baton Rouge, LA

"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
Key features
  • Probes and teacher guides cover grades 6-12
  • Student examples show readers the typical obstacles and faulty thinking they are likely to encounter
  • Combines standards, educational research findings, and practical craft knowledge
  • Linked to NCTM standards

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