ICUE Scope and Sequence

Improving Children's Understanding of Equivalence (ICUE) was developed by Prof. Nicole McNeil, Prof. Caroline Byrd Hornburg, Ms. Julia Matthews, and Ms. Heather Brletic-Shipley with additional contributions from undergraduates and staff in the Cognition, Learning, and Development Lab (CLAD Lab) at Notre Dame, especially Alex Boehm, Stephanie Borjas, Cristina Carrazza, Erin Celeste, Brianna Devlin, April Dunwiddie, Emily Fyfe, Casey Hall, and Marissa Veiga (née Rieber). The iterative development process was guided by McNeil and Alibali’s (2005) change-resistance account of children’s difficulties with mathematical equivalence, and it incorporated activities and instructional practices that prior research had shown to decrease children’s activation of and reliance on operational ways of thinking about mathematical equations. Please see the research tab for a list of references. We are grateful for the advice and feedback of Prof. Martha Alibali, Prof. Arthur Baroody, Prof. Lynn Fuchs, Prof. Eric Knuth, and Prof. Analucia Schliemann during the early stages of the development process. The original artwork in an earlier version of the workbook was created by Notre Dame undergraduate Katie Veasey Gillette.

We especially appreciate the contribution of the teachers who field-tested the curriculum and participated in our research studies. Their feedback and insights shaped the development of these materials every step of the way.

Camera-Ready Version of ICUE Materials

Staff at WestEd contributed to the final development of the materials. Jodi Davenport and Yvonne Kao led the research study to test the efficacy of this curriculum. We would also like to recognize Lisa Couper for her illustrations, Anita Moorjani for creating the design template and layout, and Jacklyn Yani and Kristen Johannes for copyediting, proofreading, and quality assurance.

Dr. Martha Alibali, Dr. Maria Blanton, and Dr. Herb Ginsburg served as external advisors for the development of these materials, providing valuable feedback that improved the final products.


The videos of the ICUE components were created by Steven McClure, Audrey Scott, and Timothy Will from the Institute of Educational Initiatives Communications Team at the University of Notre Dame. Special thanks to the narrator, Lindsay Will, and to the members of the IEI/ACE family who helped by being teacher and student hands in the videos (Video 1: Naji A. and Tim W.; Video 2: Emerson H. and Itzxul M.; Video 3: Tripp M. and Jodene M.; Video 4: James W. and Sam A.).

Grant Funding

This research was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A150088 to WestEd (PI: Davenport, co-PIs: McNeil, Kao, Johannes), and Grants R305B070297 and R305A110198 to the University of Notre Dame (PI: McNeil) and by the National Science Foundation, through CAREER Grant DRL-1054467 (PI: McNeil) and Graduate Research Fellowship DGE-1313583 (Hornburg while at the University of Notre Dame). The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education or the National Science Foundation.