Using Design Research and History to Tackle a Fundamental Problem with School Algebra

Sinan Kanbir is an Assistant Professor of Mathematics Education, University of Wisconsin-Stevens Point. He received his Ph.D. in mathematics education from Illinois State University, a masters degree in computer and educational technology from Marmara University, and a bachelors degree in mathematics education from Gazi University. Prior to his appointment at UW-Stevens Point, he had taught mathematics at the middle- and high-school levels, and university-level courses for prospective middle- and elementary-school teachers. His main research interests include the development of students' and teachers' algebraic reasoning, particularly in the elementary and middle grades, and the development of pre-service and in-service teachers' mathematical knowledge for teaching. He currently teaches elementary and middle-school mathematics pre-service teacher courses. His main research has been in the areas of algebra education and the history of school mathematics.   Nerida F. Ellerton has been professor in the Department of Mathematics at Illinois State University since 2002. She holds two doctoral degrees-one in Physical Chemistry and the other in Mathematics Education. Between 1997 and 2002 she was Dean of Education at the University of Southern Queensland, Australia. She has taught in schools and at four universities, and has also served as consultant in numerous countries, including Australia, Bangladesh, Brunei Darussalam, China, Malaysia, the Philippines, Thailand, the United States of America, and Vietnam. She has written or edited 18 books and has had more than 150 articles published in refereed journals or edited collections. Between 1993 and 1997 she was editor of the Mathematics Education Research Journal, and between 2011 and 2014 she was Associate Educator of the Journal for Research in Mathematics Education. In 2016 she received an award for top researcher at Illinois State University. M. A. (Ken) Clements 's masters and doctoral degrees were from the University of Melbourne, and at various times in his career he taught, full-time, for a total of 15 years, in primary and secondary schools. He has taught in six universities, located in three nations, and is currently professor in the Department of Mathematics at Illinois State University. He has served as a consultant and as a researcher in Australia, Brunei Darussalam, India, Malaysia, Papua New Guinea, South Africa, Thailand, the United Kingdom, the United States of America, and Vietnam. He served as co-editor of the three International Handbooks of Mathematics Education-published by Springer in 1996, 2003 and 2013-and, with Nerida Ellerton, co-authored a UNESCO book on mathematics education research. He has authored or edited 33 books and over 200 articles on mathematics education, and is honorary life member of both the Mathematical Association of Victoria and the Mathematics Education Research Group of Australasia.