Published research comes in a variety of forms, ranging from erudite scientific studies to popular trade books written by leading math educators. We read it all. Here are some sample books, white papers, and journals that have molded our thinking a great deal:

Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement, by Steven Leinwand. This is a stunning book about sensible and effective ways to teach mathematics. We are profoundly influenced by this work, and through our ongoing discussions with Steven Leinwand. From our CEO, Arjan Khalsa: “Steven spends more time observing and analyzing math education in classrooms than anyone I know, and he is lucid in sharing his understandings. If schools can step up to the plate and follow the suggestions in this book, the results will be wonderful. We strive to be part of this shift.”

Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense, Grades 3-5, by Julie McNamara & Meghan M. Shaughnessy. This excellent instructional resource with its 10 Essential Strategies offers a unique and insightful approach to helping teachers excel at teaching fractions. We have collaborated with Julie McNamara to support the strategies in the book with our dynamic software tools. Dr. McNamara has been consulting on instructional design for our tools and is a valuable content partner.

Learn more about our connection to this book >

Teaching Fractions and Ratios for Understanding, by Susan J. Lamon. From our CEO, Arjan Khalsa: “When I first read this book, it was an emotional experience. I realized how complicated it is to teach proportional reasoning. She presents problems that are so provocative and so challenging. And it makes me think that rational numbers are closely related to rational thinking. The book got my blood flowing. We owe it to the kids to make this content come alive.”

Karen Fuson’s work. We read a piece by Dr. Fuson in a compilation called Engaging Young Children in Mathematics (Chapter 5), and we were taken by her careful attention to pedagogical sequence. We saw her speak a few times at conferences, read more papers, and then recently studied NCTM’s Focus on Grade 5, which she co-authored. Dr. Fuson’s work has influenced our strong emphasis on a careful sequence of skills and the specific models we deploy to support fractions topics.

Singapore Math Publications. We have been studying the work of Yeap Ban Har, the Marshall Cavendish International group in Singapore, Char Forsten, and others who are leaders in Singapore Math. We are grateful for support we have received from Staff Development for Educators, Inc. (sde.com) and Singaporemath.com. Educators who spend time in workshops with Yeap Ban Har or Char Forsten will find sensible ways to teach, and will appreciate what we at Conceptua Math are trying to accomplish.

Direct work with Barbara Dougherty, Ph.D., Nora Ramirez, Julie McNamara, Ph.D., Nadine Bezuk, Ph.D., Steven Leinwand, Susan Midlarsky, Ann Lawrence, Judith Sowder, Ph.D., Jay Sivin-Kachala, Ph.D. and Mari Cary, Ph.D. These people, along with others, have been giving of their time and spirit in helping us to understand the topics we must teach, the models we need to use, the proper pace for student learning, the way that teachers learn, and the structure of research. We have not sought formal endorsements from any of these folks, but we are indebted to all of them.

We have received awards for our own research. The entire Conceptua Math team enjoyed many wonderful years at IntelliTools, Inc., where we were involved in a number of research and development projects funded through grants from the NSF and the NIH, most of which were through the Small Business Innovation Research or SBIR program. Arjan Khalsa served as Principal Investigator on several of these projects. While still with IntelliTools, our team received SBIR's annual “Tibbetts Award” for exemplary recipients in 1996 and again in 2002. In 2009, Conceptua Math received a Phase I research grant* from SBIR to support the development and study of our fractions software.

*Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD): Grant # 1R43HD061108-01.