Cognitive Demand of Model Tracing Tutor Tasks: Conceptualizing and Predicting How Deeply Students Engage

Abstract Model tracing tutors represent a technology designed to mimic key elements of one-on-one human tutoring. We examine the situations in which such supportive computer technologies may devolve into mindless student work with little conceptual understanding or student development. To analyze the support of student intellectual work in the model tracing tutor case, we adapt a cognitive demand framework that has been previously applied with success to teacher-guided mathematics classrooms. This framework is then tested against think-aloud data from students using a model tracing tutor designed to teach proportional reasoning skills in the context of robotics movement planning problems. Individual tutor tasks are coded for designed level of cognitive demand and compared to students’ enacted level of cognitive demand. In general, designed levels predicted how students enacted the tasks. However, just as in classrooms, student enactment was often at lower levels of demand than designed. Several contextual design features were associated with this decline. Implications for intelligent tutoring system design and research are discussed.

[1]  E. Jablonka International group for the psychology of mathematics education , 2008 .

[2]  John Seely Brown,et al.  Intelligent Tutoring Systems , 2016, Lecture Notes in Computer Science.

[3]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[4]  Olusola O. Adesope,et al.  Intelligent tutoring systems and learning outcomes: A meta-analysis , 2014 .

[5]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[6]  T. P. Carpenter,et al.  Learning and teaching with understanding. , 1992 .

[7]  Mitchell J. Nathan,et al.  Embodiment in Mathematics Teaching and Learning: Evidence From Learners' and Teachers' Gestures , 2012 .

[8]  James Hiebert Missing Links@@@Conceptual and Procedural Knowledge: The Case of Mathematics , 1987 .

[9]  Margaret S. Smith,et al.  Transforming secondary mathematics teaching: increasing the cognitive demands of instructional tasks used in teachers' classrooms , 2009 .

[10]  W. Doyle Academic Work , 1983 .

[11]  Kurt VanLehn,et al.  The Andes Physics Tutoring System: Lessons Learned , 2005, Int. J. Artif. Intell. Educ..

[12]  Mary Catherine O'Connor,et al.  “Can any Fraction be Turned into a Decimal?” A Case Study of a Mathematical Group Discussion , 2002 .

[13]  T. Seidel,et al.  Teaching Effectiveness Research in the Past Decade: The Role of Theory and Research Design in Disentangling Meta-Analysis Results , 2007 .

[14]  J. Boaler,et al.  Creating Mathematical Futures through an Equitable Teaching Approach: The Case of Railside School , 2008, Teachers College Record: The Voice of Scholarship in Education.

[15]  Margaret S. Smith Balancing Old and New: An Experienced Middle School Teacher's Learning in the Context of Mathematics Instructional Reform , 2000, The Elementary School Journal.

[16]  Jere Confrey,et al.  On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations. , 2004 .

[17]  B. Rittle-Johnson,et al.  Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process. , 2001 .

[18]  John Sweller,et al.  Cognitive Load Theory: Instructional Implications of the Interaction between Information Structures and Cognitive Architecture , 2004 .

[19]  M. Stein,et al.  Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning. , 1997 .

[20]  J. Sweller,et al.  Cognitive Load Theory and Complex Learning: Recent Developments and Future Directions , 2005 .

[21]  P. Thompson,et al.  Fractions and multiplicative reasoning , 2003 .

[22]  Robert E. Reys,et al.  The Impact of Middle-Grades Mathematics Curricula and the Classroom Learning Environment on Student Achievement. , 2008 .

[23]  Christian D. Schunn,et al.  Resources for Robot Competition Success: Assessing Math Use in Grade-School-Level Engineering Design , 2011 .

[24]  A. Michael Huberman,et al.  An expanded sourcebook qualitative data analysis , 1994 .

[25]  Jooyoung Jang,et al.  A framework for unpacking cognitive benefits of distributed complex visual displays. , 2014, Journal of experimental psychology. Applied.

[26]  M. Stein,et al.  Instructional Tasks and the Development of Student Capacity to Think and Reason: An Analysis of the Relationship between Teaching and Learning in a Reform Mathematics Project , 1996 .

[27]  Vicki L. Wilkins,et al.  Teaching , 2001, Transcultural Graffiti.

[28]  Christian D. Schunn,et al.  Spatially Distributed Instructions Improve Learning Outcomes and Efficiency. , 2011 .

[29]  Carolyn Penstein Rosé,et al.  Fading and Deepening: The Next Steps for Andes and other Model-Tracing Tutors , 2000, Intelligent Tutoring Systems.

[30]  R. Sawyer The Cambridge Handbook of the Learning Sciences: Introduction , 2014 .

[31]  J. Fey,et al.  Effects of Standards-Based Mathematics Education: A Study of the Core-plus Mathematics Project Algebra and Functions Strand , 2000 .

[32]  Christian D. Schunn,et al.  Applying Math onto Mechanism: Investigating the Relationship Between Mechanistic and Mathematical Understanding , 2014, CogSci.

[33]  Rose Mary Zbiek,et al.  Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics: Grades 6-8 , 2010 .

[34]  Eli Silk Calculational versus mechanistic mathematics in propelling the development of physical knowledge , 2011 .

[35]  D. Schifter,et al.  A research companion to Principles and standards for school mathematics , 2003 .

[36]  K. A. Ericsson,et al.  Protocol Analysis: Verbal Reports as Data , 1984 .

[37]  J. Hiebert,et al.  THE EFFECTS OF CLASSROOM MATHEMATICS TEACHING ON STUDENTS ’ LEARNING , 2006 .

[38]  Charleen M. DeRidder Standards-Based School Mathematics Curricula: What Are They? What Do Students Learn? (Book) , 2004 .

[39]  Mary Kay Stein,et al.  Selecting and Supporting the Use of Mathematics Curricula at Scale , 2010 .

[40]  Denisse R. Thompson,et al.  Standards-based school mathematics curricula : What are they? What do students learn? , 2004 .

[41]  B. Rittle-Johnson,et al.  Conceptual and procedural knowledge of mathematics: Does one lead to the other? , 1999 .

[42]  Gwendolyn M. Lloyd,et al.  Sharing Mathematical Authority with Students: The Challenge for High School Teachers. , 2000 .

[43]  B MilesMatthew,et al.  Qualitative Data Analysis , 2009, Approaches and Processes of Social Science Research.

[44]  K. VanLehn The Relative Effectiveness of Human Tutoring, Intelligent Tutoring Systems, and Other Tutoring Systems , 2011 .

[45]  Hsinchun Chen,et al.  Browsing in hypertext: a cognitive study , 1992, IEEE Trans. Syst. Man Cybern..

[46]  Albert T. Corbett,et al.  Cognitive Tutor: Applied research in mathematics education , 2007, Psychonomic bulletin & review.

[47]  THE CASE OF CHILDREN'S ANTICIPATORY SCHEME FOR CONSTANCY OF TASTE , 2016 .

[48]  J. Stigler,et al.  Improving Mathematics Teaching. , 2004 .

[49]  Edward A. Silver,et al.  Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development , 2009 .

[50]  Peter Maurer,et al.  The Cambridge Handbook of the Learning Sciences , 2022 .

[51]  S. Krauss,et al.  Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress , 2010 .

[52]  C. Hirsch Curriculum and Evaluation Standards for School Mathematics , 1988 .

[53]  David L. Elliott,et al.  Textbooks in School and Society: An Annotated Bibliography & Guide to Research , 1988 .

[54]  John R. Anderson ACT: A simple theory of complex cognition. , 1996 .

[55]  Mary Kay Stein,et al.  Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms , 1996 .

[56]  J. Hiebert,et al.  Instructional Tasks, Classroom Discourse, and Students’ Learning in Second-Grade Arithmetic , 1993 .

[57]  Brian W. Junker,et al.  Model Specification for Cognitive Assessment of Proportional Reasoning , 2004 .