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ABSTRACT
Mathematics is often taught by explaining an idea, then giving students practice in applying it. Tutoring systems can increase the effectiveness of this method by monitoring the students’ practice and giving feedback. However, math can also be taught by having students work collaboratively on problems that lead them to discover the idea. Here, teachers spend the bulk of their time orchestrating collaborations and supporting students in building productively on each other’s contributions. Our research question is: Can tutoring technology somehow make teaching-by-eliciting more effective? Using tutoring technology, we developed an intelligent orchestration system named FACT. While students solve problems in small groups, it makes recommendations to the teacher about which groups to visit and what to say. Data from over 50 iterative development trials (study 1) suggest that FACT increased neither the collaboration nor productivity of the students’ struggle compared to paper-based classes. However, the data also suggest that when there is just one teacher in the classroom, then only a few of the groups that need a visit can get one. We modified FACT to directly send students the provocative questions that it formerly sent only to teachers. A pilot test (study 2) suggests that this version may increase productive struggle, but increasing collaboration remains an unsolved problem.
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No potential conflict of interest was reported by the authors.
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Notes on contributors
Kurt VanLehn
Kurt VanLehn is the Diane and Gary Tooker Chair for Effective Education in Science, Technology, Engineering and Math in the Ira Fulton Schools of Engineering at Arizona State University. He has published over 125 peer-reviewed publications, is a fellow in the Cognitive Science Society, and is on the editorial boards of Cognition and Instruction and the International Journal of Artificial Intelligence in Education. Dr. VanLehn's research focuses on intelligent tutoring systems, classroom orchestration systems, and other intelligent interactive instructional technology.
Hugh Burkhardt
Hugh Burkhardt was Director of the Shell Centre for Mathematical Education and Professor in the Department of Mathematics at Nottingham from 1976-92. Since then he has led a series of impact-focused research and development projects. His work has been recognised by an ISDDE Prize for Lifetime Achievement and, with Malcolm Swan, as first recipients of the Emma Castelnuovo Prize of the International Commission on Mathematical Instruction.
Salman Cheema
Salman Cheema is a research scientist at Microsoft. His 2014 Computer Science PhD was from University of Florida. He has published 8 refereed publications and secured 1 patent. He was won first prize at 3 software competitions and was awarded a Provost’s Fellowship in 2007.
Seokmin Kang
Seokmin Kang is a Postdoctoral Research Associate in the Ira Fulton Schools of Engineering at Arizona State University. His 2012 PhD in Human Cognition and Learning was from Columbia University. He has published 9 journal articles and 22 refereed conference papers. His 2016 article was selected a “featured article” by the Psychonomics Society.
Daniel Pead
Daniel Pead has contributed to the design of computer-based learning and teaching materials in many Shell Centre Projects since the early 1980s, becoming IT director for the Shell Centre and MARS. He research work includes the strengths and limitations of computers in assessing complex student performances.
Alan Schoenfeld
Alan Schoenfeld is the Elizabeth and Edward Conner Professor of Education and Affiliated Professor of Mathematics at the University of California at Berkeley, and Honorary Professor in the School of Education at the University of Nottingham. His research has been recognized with, among many honors, the Presidency of the American Educational Research Association and the Felix Klein Prize of the International Commission on Mathematical Instruction.
Jon Wetzel
Jon Wetzel is an Assistant Research Scientist in the Ira Fulton Schools of Engineering at Arizona State University. His 2014 PhD from Northwestern University was in Computer Science with Specialization in Cognitive Science. He has published 7 journal articles and 13 refereed conference publications, and secured 1 patent.