# Intelligent Tutoring Systems and Mathematics

## Mathematics

Artificial Intelligence and Tutoring Systems: Computational and Cognitive Approaches to the Communication of Knowledge by Etienne Wenger, Cognitive Tutoring in Mathematics Based on Assertion Level Reasoning and Proof Strategies by Serge Autexier, Dominik Dietrich and Marvin Schiller, Cognitive Tutor: Applied Research in Mathematics Education by Steven Ritter, John R. Anderson, Kenneth R. Koedinger and Albert Corbett, Adaptation of Problem Presentation and Feedback in an Intelligent Mathematics Tutor by Mia Stern, Joseph Beck and Beverly P. Woolf, Student Modelling by Adaptive Testing: A Knowledge-based Approach by Sophiana C. Abdullah and A Developing Approach to Studying Students’ Learning through Their Mathematical Activity by Martin Simon, Luis Saldanha, Evan McClintock, Gulseren K. Akar, Tad Watanabe and Ismail O. Zembat.

## The Cognitive Neuroscience of Mathematical Reasoning

Neural Foundations of Logical and Mathematical Cognition by Olivier Houdé and Nathalie Tzourio-Mazoyer, The Influence of Cognitive Abilities on Mathematical Problem Solving Performance by Abdulkadir Bahar, Different Components of Working Memory Have Different Relationships with Different Mathematical Skills by Fiona R. Simmons, Catherine Willis, and Anne-Marie Adams, Working Memory and Mathematics: A Review of Developmental, Individual Difference, and Cognitive Approaches by Kimberly P. Raghubar, Marcia A. Barnes, and Steven A. Hecht, Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics by Alan H. Schoenfeld, Metacognition and Mathematics Strategy Use by Martha Carr, Joyce Alexander and Trisha Folds‐Bennett, Working Memory and Children’s Mathematical Skills: Implications for Mathematical Development and Mathematics Curricula by Joni Holmes and John W. Adams, Defining Mathematics Educational Neuroscience by Stephen R. Campbell and Educational Neuroscience: New Horizons for Research in Mathematics Education by Stephen R. Campbell.

## Conceptual Knowledge

Mathematical Concepts, Their Meanings and Understanding by Juan D. Godino, Knowledge Acquisition and Conceptual Change by Stella Vosniadou, Conceptual Structures in Mathematical Problem Solving by Victor Cifarelli, Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process by Bethany Rittle-Johnson, Robert S. Siegler and Martha Wagner Alibali, On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin by Anna Sfard, The Role of Definitions in the Teaching and Learning of Mathematics by Shlomo Vinner, Words, Definitions and Concepts in Discourses of Mathematics, Teaching and Learning by Candia Morgan, Definitions: Dealing with Categories Mathematically by Lara Alcock and Adrian Simpson, Construction of Mathematical Definitions: An Epistemological and Didactical Study by Cécile Ouvrier-Buffet, Definition-construction and Concept Formation by Cécile Ouvrier-Buffet, A Semiotic Model for Analysing the Relationships between Thought, Language and Context in Mathematics Education by Juan D. Godino and Angel M. Redo, Embodied Concept Learning by Benjamin Bergen and Jerome Feldman, Developing Mathematical Knowledge by Lauren B. Resnick, On the Relations between Historical Epistemology and Students’ Conceptual Developments in Mathematics by Kajsa Bråting and Johanna Pejlare, The Role of Conceptual Entities and Their Symbols in Building Advanced Mathematical Concepts by Guershon Harel and James Kaput, Semantics and Comprehension by Herbert H. Clark, Comprehending Complex Concepts by Gregory L. Murphy, The Locus of Knowledge Effects in Concept Learning by Gregory L. Murphy and Paul D. Allopenna and Knowledge and Concept Learning by Evan Heit.

## Procedural Knowledge

Role of Conceptual Knowledge in Mathematical Procedural Learning by James P. Byrnes and Barbara A. Wasik, Conceptual Knowledge as a Foundation for Procedural Knowledge by Thomas P. Carpenter, Conceptual and Procedural Knowledge: The Case of Mathematics edited by James Hiebert, Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process by Bethany Rittle-Johnson, Robert S. Siegler and Martha W. Alibali, On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin by Anna Sfard, Using Conceptual and Procedural Knowledge: A Focus on Relationships by Edward A. Silver, On the Development of Procedural Knowledge by Daniel B. Willingham, Mary J. Nissen and Peter Bullemer, On Learning Complex Procedural Knowledge by Michael A. Stadler and Towards Answering Procedural Questions by Farida Aouladomar.

## Teaching Problem Solving Skills

Human Problem Solving by Allen Newell and Herbert A. Simon, The Role of Tutoring in Problem Solving by David Wood, Jerome S. Bruner and Gail Ross, Teaching Problem-solving Skills by Alan H. Schoenfeld, Problem Solving: A Handbook for Teachers by Stephen Krulik and Jesse A. Rudnick, Problem Solving by Miriam Bassok and Laura R. Novick, Learning to Solve Problems: An Instructional Design Guide by David H. Jonassen, Toward a Design Theory of Problem Solving by David H. Jonassen, Designing Knowledge Scaffolds to Support Mathematical Problem Solving by Bethany Rittle-Johnson and Kenneth R. Koedinger, Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics by Alan H. Schoenfeld, Thinking, Problem Solving, Cognition by Richard E. Mayer, Cognitive Processes in Well‐defined and Ill‐defined Problem Solving by Gregory Schraw, Michael E. Dunkle and Lisa D. Bendixen, Problem Solving and Cognitive Skill Acquisition by Kurt VanLehn, The Development of Problem-solving Strategies by Deanna Kuhn and Erin Phelps, The Importance of Metacognition for Conceptual Change and Strategy Use in Mathematics by Martha Carr, How Children Change Their Minds: Strategy Change Can Be Gradual or Abrupt by Martha W. Alibali, Metacognition and Mathematics Strategy Use by Martha Carr, Joyce Alexander and Trisha Folds‐Bennett, One Problem, Multiple Solutions: How Multiple Proofs can Connect Several Areas of Mathematics by Moshe Stupel and David Ben-Chaim, Moving from Rhetoric to Praxis: Issues Faced by Teachers in Having Students Consider Multiple Solutions for Problems in the Mathematics Classroom by Edward A. Silver, Hala Ghousseini, Dana Gosen, Charalambos Charalambous and Beatriz T. Font Strawhun, Does Comparing Solution Methods Facilitate Conceptual and Procedural Knowledge? An Experimental Study on Learning to Solve Equations by Bethany Rittle-Johnson and Jon R. Star, It Pays to Compare: An Experimental Study on Computational Estimation by Jon R. Star and Bethany Rittle-Johnson, Some Examples of Cognitive Task Analysis with Instructional Implications by James G. Greeno, Implications of Cognitive Theory for Instruction in Problem Solving by Norman Frederiksen, Evidence for Cognitive Load Theory by John Sweller and Paul Chandler, Cognitive Load during Problem Solving: Effects on Learning by John Sweller and Cognitive Load Theory: Instructional Implications of the Interaction between Information Structures and Cognitive Architecture by Fred Paas, Alexander Renkl and John Sweller.

## Mathematical Proof

The Varieties of Mathematical Explanation by Johannes Hafner and Paolo Mancosu, Forms of Proof and Proving in the Classroom by Tommy Dreyfus, Elena Nardi and Roza Leikin, Cognitive Development of Proof by David O. Tall, Oleksiy Yevdokimov, Boris Koichu, Walter Whiteley, Margo Kondratieva and Ying-Hao Cheng, The Long-term Cognitive Development of Different Types of Reasoning and Proof by David O. Tall and Juan Pablo Mejia-Ramos and One Problem, Multiple Solutions: How Multiple Proofs Can Connect Several Areas of Mathematics by Moshe Stupel and David Ben-Chaim.

## Natural Language Generation

Generating Explanatory Discourse by Alison Cawsey, Language Generation and Explanation by Kathleen R. McKeown and William R. Swartout, Generating Explanations in Context: The System Perspective by Vibhu O. Mittal and Cécile L. Paris, An Analysis of Explanation and Its Implications for the Design of Explanation Planners by Daniel D. Suthers, Comprehension Driven Generation of Meta-technical Utterances in Math Tutoring by Ingrid Zukerman and Judea Pearl, Argumentation in Explanations to Logical Problems by Armin Fiedler and Helmut Horacek, Dialog-driven Adaptation of Explanations of Proofs by Armin Fiedler, Adaptation of Problem Presentation and Feedback in an Intelligent Mathematics Tutor by Mia Stern, Joseph Beck and Beverly P. Woolf, Using a Cognitive Architecture to Plan Dialogs for the Adaptive Explanation of Proofs by Armin Fiedler, Macroplanning with a Cognitive Architecture for the Adaptive Explanation of Proofs by Armin Fiedler, Proof Verbalization as an Application of NLG by Xiaorong Huang and Armin Fiedler, The Translation of Formal Proofs into English by Daniel Chester, English Summaries of Mathematical Proofs by Marianthi Alexoudi, Claus Zinn and Alan Bundy, Algebraic Model and Implementation of Translation between Logic and Natural Language by Chen Peng, Computer Presentations of Structure in Algebra by Patrick W. Thompson and Alba G. Thompson, Granularity-adaptive Proof Presentation by Marvin Schiller and Christoph Benzmüller and Representation of Mathematical Concepts for Inferencing and for Presentation Purposes by Helmut Horacek, Armin Fiedler, Andreas Franke, Markus Moschner, Martin Pollet and Volker Sorge.

## Natural Language Understanding

The Role of Conceptual Entities and Their Symbols in Building Advanced Mathematical Concepts by Guershon Harel and James Kaput, Towards Mathematical Expression Understanding by Minh-Quoc Nghiem, Giovanni Yoko, Yuichiroh Matsubayashi and Akiko Aizawa, Unpacking the Logic of Mathematical Statements by John Selden and Annie Selden, The Structure of Mathematical Expressions by Deyan Ginev, A Model of the Cognitive Meaning of Mathematical Expressions by Paul Ernest, The Construction of Mental Representations during Reading edited by Herre Van Oostendorp and Susan R. Goldman, Linguistic Processing in a Mathematics Tutoring System: Cooperative Input Interpretation and Dialogue Modelling by Magdalena Wolska, Mark Buckley, Helmut Horacek, Ivana Kruijff-Korbayová and Manfred Pinkal, Students’ Language in Computer-assisted Tutoring of Mathematical Proofs by Magdalena Wolska, Tutorial Dialogs on Mathematical Proofs by Christoph Benzmüller, Armin Fiedler, Malte Gabsdil, Helmut Horacek, Ivana Kruijff-Korbayová, Manfred Pinkal, Jörg Siekmann, Dimitra Tsovaltzi, Bao Quoc Vo and Magdalena Wolska, Language Phenomena in Tutorial Dialogs on Mathematical Proofs by Ivana Kruijff-Korbayová, Dimitra Tsovaltzi, Bao Quoc Vo and Magdalena Wolska, Interpreting Semi-formal Utterances in Dialogs about Mathematical Proofs by Helmut Horacek and Magdalena Wolska, Understanding Informal Mathematical Discourse by Claus W. Zinn, Investigating Mathematical Cognition Using Distinctive Features of Mathematical Discourse by Donna Kotsopoulos, Joanne Lee and Duane Heide and Theoretical Perspectives for Analyzing Explanation, Justification and Argumentation in Mathematics Classrooms by Erna Yackel.

## Pragmatics

Language in Context: Emergent Features of Word, Sentence, and Narrative Comprehension by Jiang Xu, Stefan Kemeny, Grace Park, Carol Frattali and Allen Braun, Contextual Influences on the Comprehension of Complex Concepts by Richard J. Gerrig and Gregory L. Murphy, Integrating Task Information into the Dialogue Context for Natural Language Mathematics Tutoring by Mark Buckley and Dominik Dietrich, Using Discourse Context to Interpret Object-denoting Mathematical Expressions by Magdalena Wolska, Mihai Grigore and Michael Kohlhase, Modeling Anaphora in Informal Mathematical Dialogue by Magdalena Wolska and Ivanna Kruijff-Korbayová and Context-relative Syntactic Categories and the Formalization of Mathematical Text by Aarne Ranta.

## The Automatic Assessment of Mathematics Exercises and Proofs

Automatic Assessment of Problem-solving Skills in Mathematics by Cliff E. Beevers and Jane S. Paterson, Automatic Assessment in University-level Mathematics by Jarno Ruokokoski, Mathematics Exercise System with Automatic Assessment by Matti Harjula, Automatic Assessment of Mathematics Exercises: Experiences and Future Prospects by Antti Rasila, Matti Harjula and Kai Zenger, Linking On-line Assessment in Mathematics to Cognitive Skills by Jane S. Paterson, Exploring Mathematical Creativity Using Multiple Solution Tasks by Roza Leikin, Multiple Solutions for a Problem: A Tool for Evaluation of Mathematical Thinking in Geometry by Anat Levav-Waynberg and Roza Leikin, Techniques for Plan Recognition by Sandra Carberry, Evaluating E-assessment for Exercises That Require Higher-order Cognitive Skills by Tim A. Majchrzak and Claus A. Usener, An E-assessment System for Mathematical Proofs by Susanne Gruttmann, Herbert Kuchen and Dominik Böhm, Lurch: A Word Processor That Can Grade Students’ Proofs by Nathan C. Carter and Kenneth G. Monks, Computer Aided Assessment of Mathematics by Chris Sangwin, Automatic Assessment of Mathematics Exercises: Experiences and Future Prospects by Antti Rasila, Matti Harjula and Kai Zenger and Automatic Assessment of Problem-solving Skills in Mathematics by Cliff E. Beevers and Jane S. Paterson.