And the Rest is Just Algebra

1. Front Matter

   Pages i-xx

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2. Current State of Students’ Inadequacies, Conceptions and Fluency of Algebra in the US Colleges

   1. Front Matter

      Pages 1-1

      PDF

   2. Algebra Underperformances at College Level: What Are the Consequences?

      • Sepideh Stewart, Stacy Reeder

      Pages 3-18

   3. Examining the Role of Prior Experience in the Learning of Algebra

      • Mercedes McGowen

      Pages 19-39

3. College Algebra in a Broader Context

   1. Front Matter

      Pages 41-41

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   2. Long-Term Effects of Sense Making and Anxiety in Algebra

      • David Tall

      Pages 43-62

   3. Misconceptions and Learning Algebra

      • Julie L. Booth, Kelly M. McGinn, Christina Barbieri, Laura K. Young

      Pages 63-78

   4. A Deep Understanding of Fractions Supports Student Success in Algebra

      • Stacy Reeder

      Pages 79-93

4. Positive Approaches to the Teaching of Algebra

   1. Front Matter

      Pages 95-95

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   2. Overcoming the Algebra Barrier: Being Particular About the General, and Generally Looking Beyond the Particular, in Homage to Mary Boole

      • John Mason

      Pages 97-117

   3. Algebra as Part of an Integrated High School Curriculum

      • James T. Fey, David A. Smith

      Pages 119-129

   4. Teaching and Learning Middle School Algebra: Valuable Lessons from the History of Mathematics

      • Mala S. Nataraj, Mike Thomas

      Pages 131-154

5. Proposed Future Developments

   1. Front Matter

      Pages 155-155

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   2. Cognitive Neuroscience and Algebra: Challenging Some Traditional Beliefs

      • Carolyn Kieran

      Pages 157-172

   3. Rethinking Algebra: A Versatile Approach Integrating Digital Technology

      • Mike Thomas

      Pages 173-201

6. Teaching Higher Algebra

   1. Front Matter

      Pages 203-203

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   2. Why Does Linear Algebra Have to Be So Abstract?

      • John Hannah

      Pages 205-217

   3. School Algebra to Linear Algebra: Advancing Through the Worlds of Mathematical Thinking

      • Sepideh Stewart

      Pages 219-233

7. Back Matter

   Pages 235-238

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This book addresses college students' weak foundation in algebra, its causes, and potential solutions to improve their long-term success and understanding in mathematics as a whole. The authors, who are experts in a wide variety of fields, emphasize that these difficulties are more complex than just forgotten rules, and offer strategic approaches from a number of angles that will increase the chances of student understanding. Instructors who are frustrated with their students’ lack of skills and knowledge at college level will find this volume helpful, as the authors confront the deeper reasons why students have difficulties with Algebra and reveal how to remedy the issue.

• Mathematics education
• College mathematics education
• College algebra
• Neuroscience and mathematics education
• Algebra education
• Learning algebra
• Algebra anxiety
• learning and instruction

“And the Rest is Just Algebra is a book that addresses the increasing weakness in algebra skills among college students. It not only considers the causes of the algebra deficiency but also offers potential solutions for how to improve students’ long-term success and understanding of mathematics. … Instructors who are frustrated with students’ misunderstanding of algebra will find this book most helpful. … I highly recommend this book … .” (Peter T. Olszewski, MAA Reviews, maa.org, April, 2017)

• Department of Mathematics, University of Oklahoma, Norman, USA

  Sepideh Stewart

Sepideh Stewart is an Assistant Professor of Mathematics Education at the Department of Mathematics at the University of Oklahoma. She earned her Ph.D. in Mathematics Education at the University of Auckland.  Her research interests are on the embodied symbolic and formal worlds of mathematical thinking with a particular interest on the pedagogy of linear algebra. Over the past two years she has also been working on several projects investigating the mind of working mathematicians particularly in abstract algebra (formal) and algebraic topology (embodied). She is the author of the book Linear Algebra in Three Worlds of Mathematical Thinking, and has contributed to multiple journals and conference publications.

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