Category Archives: Mathematics

Thought Experiments

Publications pertinent to thought experiments include: Thought Experiments in Methodological and Historical Contexts edited by Katerina Ierodiakonou and Sophie Roux, Thought Experiments by Roy A. Sorensen, Thought Experiments by James Robert Brown and Yiftach Fehige, Thought Experiments by Tamar S. Gendler, Thought Experiments: Determining their Meaning by Igal Galili, Thought Experiments in Science and Philosophy by Tamara Horowitz and Gerald Massey and Thought Experiments in Science, Philosophy, and Mathematics by James R. Brown.

Publications pertinent to thought experiments, epistemology and imagination include: An Epistemological Role for Thought Experiments by Michael Bishop, Imagination and Epistemology by Jonathan Ichikawa, Imagination and Insight: A New Account of the Content of Thought Experiments by Letitia Meynell, When an Image Turns Into Knowledge: The Role of Visualization in Thought Experimentation by Miriam Reiner and John Gilbert, Interrogation of a Dynamic Visualization During Learning by Richard K. Lowe, Imagery and Mental Processes by Allan Paivio, Dynamics of Brain Processing During Mental Imagery by Livia Tomova, Voluntary and Automatic Attentional Control of Visual Working Memory by Brandon K. Schmidt, Geoffrey F. Woodman, Edward K. Vogel and Steven J. Luck, Perceptual Simulation in Conceptual Tasks by Lawrence W. Barsalou, Karen O. Solomon and Ling-Ling Wu, Situated Simulation in the Human Conceptual System by Lawrence W. Barsalou, Using Imagination to Understand the Neural Basis of Episodic Memory by Demis Hassabis, Dharshan Kumaran and Eleanor A. Maguire and Episodic and Semantic Memory by Endel Tulving.

Publications pertinent to thought experiments and argumentation include: Why Thought Experiments are not Arguments by Michael A. Bishop, On Thought Experiments: Is There More to the Argument? by John D. Norton and Intuition Pumps and the Proper Use of Thought Experiments by Elke Brendel.

Publications pertinent to mathematical thought experiments, argumentation and creativity include: Deiknymi by Jan Gonda, On the First Greek Mathematical Proof by Vassilis Karasmanis, On Mathematical Thought Experiments by Marco Buzzoni, Thought Experimentation and Mathematical Innovation by Eduard Glas, The Varieties of Mathematical Explanation by Paolo Mancosu and Johannes Hafner, The Meaning of Proof in Mathematics Education by David A. Reid, Proof and Proving in Mathematics Education by Maria A. Mariotti, The Role of Mental Argumentation in Mathematics Vis-à-vis Property Perception and the Operational Mode by Joanna Mamona-Downs, Necessary Realignments from Mental Argumentation to Proof Presentation by Joanna Mamona-Downs and Martin Downs, Representation of Mathematical Concepts for Inferencing and for Presentation Purposes by Martin Pollet, Andreas Franke, Armin Fiedler, Helmut Horacek, Markus Moschner and Volker Sorge, Making Actions in the Proving Process Explicit, Visible, and “Reflectable” by Kerry McKee, Milos Savic, John Selden and Annie Selden, Granularity-adaptive Proof Presentation by Christoph Benzmüller and Marvin Schiller and Interpretation of Scientific or Mathematical Concepts: Cognitive Issues and Instructional Implications by Frederick Reif.

Publications pertinent to thought experiments and science include: Tracing the Development of Thought Experiments in the Philosophy of the Natural Sciences by Aspasia S. Moue, Kyriakos A. Masavetas and Haido Karayianni, Thought Experiment in the Natural Sciences by Marco Buzzoni, Galileo and the Indispensability of Scientific Thought Experiment by Tamar S. Gendler, Thought Experiments Since the Scientific Revolution by James R. Brown, Thought Experiments in Scientific Reasoning by Andrew D. Irvine, The Role of Imagistic Simulation in Scientific Thought Experiments by John J. Clement, The Nature and Role of Thought Experiments in Solving Conceptual Physics Problems by Şule Dönertaş Kösem and Ömer Faruk Özdemir, The Evidential Significance of Thought Experiment in Science by James W. McAllister, Why Thought Experiments do not Transcend Empiricism by John D. Norton, Experimentation and the Meaning of Scientific Concepts by Theodore Arabatzis, Thought Experiments and Physics Education by Hugh Helm, John Gilbert and D. Michael Watts, The Context of Thought Experiments in Physics Learning by Miriam Reiner, Thought Experiments in Science and in Science Education by Mervi A. Asikainen and Pekka E. Hirvonen, Thought Experiments in Science Education: Potential and Current Realization by John K. Gilbert and Miriam Reiner, Understanding and Teaching Important Scientific Thought Processes by Frederick Reif, Visualization: A Metacognitive Skill in Science and Science Education by John K. Gilbert, Prospects for Scientific Visualization as an Educational Technology by Douglas N. Gordin and Roy D. Pea and Mental Models: Theoretical Issues for Visualizations in Science Education by David N. Rapp.

Publications pertinent to thought experiments and mental models: Mental Models and Thought Experiments by Nenad Miščević, Thought Experiments and Conceptual Revision by Ian Winchester, Mental Models, Conceptual Models, and Modelling by Ileana M. Greca and Marco A. Moreira, Model Building for Conceptual Change by David Jonassen, Johannes Strobel and Joshua Gottdenker, Model-based Reasoning in Conceptual Change by Nancy J. Nersessian, Mental Modeling in Conceptual Change by Nancy J. Nersessian and Thought Experiments and the Belief in Phenomena by James W. McAllister.

Publications pertinent to thought experiments, linguistics and pragmatics include: Thought Experiments in Linguistics by Sarah G. Thomason, Data and Evidence in Linguistics: A Plausible Argumentation Model by András Kertész and Csilla R. Kosi, From Thought Experiments to Real Experiments in Pragmatics by András Kertész and Ferenc Kiefer, The Puzzle of Thought Experiments in Conceptual Metaphor Research by András Kertész and Pragmatic Evidence, Context, and Story Design: An Essay on Recent Developments in Experimental Pragmatics by Jörg Meibauer.

Publications pertinent to thought experiments and philosophy include: Thought Experiments in Philosophy by Soren Haggqvist, Philosophical Thought Experiments, Intuitions, and Cognitive Equilibrium by Tamar S. Gendler, Intuition, Imagination, and Philosophical Methodology by Tamar S. Gendler and Philosophical Thought Experiments as Excercises in Conceptual Analysis by Christian Nimtz.

Publications pertinent to thought experiments and ethics include: The Gedankenexperiment Method of Ethics by Michael W. Jackson, The Role of Imaginary Cases in Ethics by Jonathan Dancy and Variations in Ethical Intuitions by Jennifer L. Zamzow and Shaun Nichols.

Publications pertinent to thought experiments and narrative include: Thought Experiments, Hypotheses, and Cognitive Dimension of Literary Fiction by Iris Vidmar, Thought Experiments and Fictional Narratives by David Davies, Fiction as Thought Experiment by Catherine Z. Elgin, Narrative Experiments and Imaginative Inquiry by Noel Gough and The Call of Stories: Teaching and the Moral Imagination by Robert Coles.

Natural Language Understanding and Education Technology

Publications pertinent to language technologies and education include: Language Technologies for Enhancement of Teaching and Learning in Writing by Tak P. Lau, Shuai Wang, Yuanyuan Man, Chi Fai Yuen and Irwin King, Automated Writing Assessment in the Classroom by Mark Warschauer and Douglas Grimes, Handbook of Automated Essay Evaluation: Current Applications and New Directions edited by Mark D. Shermis and Jill Burstein, Computer‐assisted Language Testing by Ruslan Suvorov and Volker Hegelheimer, Technologies That Support Students’ Literacy Development by Carol M. Connor, Susan R. Goldman and Barry Fishman and Writeability: The Principles of Writing for Increased Comprehension by Edward B. Fry.

Publications pertinent to readability, rhetorical structure and cognitive linguistics include: Readability: A View from Cognitive Psychology by Walter Kintsch and James R. Miller, Coh-Metrix: Automated Cohesion and Coherence Scores to Predict Text Readability and Facilitate Comprehension by Danielle S. McNamara, Max M. Louwerse and Arthur C. Graesser, Coherence and Cohesion for the Assessment of Text Readability by Amalia Todirascu, Thomas François, Nuria Gala, Cédrick Fairon, Anne-Laure Ligozat and Delphine Bernhard, Variation in Language and Cohesion across Written and Spoken Registers by Max M. Louwerse, Philip M. McCarthy, Danielle S. McNamara and Arthur C. Graesser and Measuring the Inference Load of a Text by Susan Kemper.

Publications pertinent to the automatic assessment of mathematics exercises and proofs include: Automatic Assessment of Mathematics Exercises: Experiences and Future Prospects by Antti Rasila, Matti Harjula and Kai Zenger, Automatic Assessment of Problem-solving Skills in Mathematics by Cliff E. Beevers and Jane S. Paterson, Computer Aided Assessment of Mathematics by Chris Sangwin and Lurch: A Word Processor that Can Grade Students’ Proofs by Nathan C. Carter and Kenneth G. Monks.

Publications pertinent to the automatic assessment of argumentation include: Towards Automated Analysis of Student Arguments by Nancy L. Green, Foundations of Argumentative Text Processing by Pierre Coirier and Jerry Andriessen and Educational Technologies for Teaching Argumentation Skills by Niels Pinkwart and Bruce M. MacLaren.

Publications pertinent to evaluating the outputs of natural language generation include: Towards Evaluation in Natural Language Generation by Robert Dale and Chris Mellish, Evaluation in the Context of Natural Language Generation by Chris Mellish and Robert Dale and Comparing Automatic and Human Evaluation of NLG Systems by Anja Belz and Ehud Reiter.

Language and Mathematics

Publications pertinent to language and mathematics education include: Language and Mathematical Education by John L. Austin and Albert G. Howson, Language in Mathematics Teaching and Learning by Mary J. Schleppegrell, A Morphology of Teacher Discourse in the Mathematics Classroom by Libby Knott, Bharath Sriraman and Irv Jacob, The Teacher’s Discourse Moves: A Framework for Analyzing Discourse in Mathematics Classrooms by Libby Krussel, Barbara Edwards and G. T. Springer, Stance and Engagement in Pure Mathematics Research Articles: Linking Discourse Features to Disciplinary Practices by Lisa McGrath and Maria Kuteeva, University Language: A Corpus-based Study of Spoken and Written Registers by Douglas Biber and Relations between Text and Mathematics across Disciplines by Philip Shaw.

Publications pertinent to language and mathematics tutoring include: 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 and Students’ Language in Computer-assisted Tutoring of Mathematical Proofs by Magdalena Wolska.

Publications pertinent to written mathematical language include: Mathematical Discourse: Language, Symbolism and Visual Images by Kay O’Halloran, Reading Mathematical Exposition by Regina B. Brunner, The Effect of the Symbols and Structures of Mathematical English on the Reading Comprehension of College Students by Ann E. Watkins, Reading Comprehension in Mathematics by Peter Fuentes and Characterizing Reading Comprehension of Mathematical Texts by Magnus Österholm.

Publications pertinent to symbolic declarations, linguistic precedents, lexical entrainment and differentiation include: Symbol Declarations in Mathematical Writing: A Corpus Study by Magdalena Wolska and Mihai Grigore, Directives: Argument and Engagement in Academic Writing by Ken Hyland, Conceptual Pacts and Lexical Choice in Conversation by Susan E. Brennan and Herbert H. Clark, Anchoring Comprehension in Linguistic Precedents by Dale J. Barr and Boaz Keysar, Lexical Entrainment in Spontaneous Dialog by Susan E. Brennan and Lexical Entrainment and Lexical Differentiation in Reference Phrase Choice by Mija M. Van der Wege.

Publications pertinent to vocabulary learning and mathematical vocabulary learning include: Learning Vocabulary through Reading by Joseph R Jenkins, Marcy L Stein and Katherine Wysocki, Learning Word Meanings from Context during Normal Reading by William E. Nagy, Richard C. Anderson and Patricia A. Herman, Most Vocabulary is Learned from Context by Robert J. Sternberg, The Acquisition of Word Meanings: A Developmental Study by Heinz Werner and Edith Kaplan, Definition and Specification of Meaning by Abraham Kaplan, 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 and Definition-construction and Concept Formation by Cécile Ouvrier-Buffet.

Publications pertinent to understanding mathematical expressions include: 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 and The Role of Conceptual Entities and their Symbols in Building Advanced Mathematical Concepts by Guershon Harel and James Kaput.

Publications pertinent to context and the understanding of mathematical language include: Participating in Explanatory Dialogues: Interpreting and Responding to Questions in Context by Johanna D. Moore and Joanna D. Moore, Integrating Task Information into the Dialogue Context for Natural Language Mathematics Tutoring by Mark Buckley and Dominik Dietrich, Towards Context-based Disambiguation of Mathematical Expressions by Mihai Grigore, Magdalena Wolska and Michael Kohlhase, 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 Korbayová, Lexical Disambiguation in a Discourse Context by Nicholas Asher and Alex Lascaridesy, Discourse Pragmatics and Semantic Categorization by Ellen Contini-Morava, The Effect of Context on the Structure of Categories by Emilie M. Roth and Edward J. Shoben, Inferences about Contextually Defined Categories by Gail McKoon and Roger Ratcliff, Context-relative Syntactic Categories and the Formalization of Mathematical Text by Aarne Ranta, Context and Structure in Conceptual Combination by Douglas L. Medin and Edward J. Shoben, Wayne Cowart and Ann D. Jablon, Contextually Relevant Aspects of Meaning Gail McKoon and Roger Ratcliff and Effects of Prior Context upon the Integration of Lexical Information during Sentence Processing by Helen S. Cairns.

Publications pertinent to text inferencing and reading comprehension include: Inference during Reading by Gail McKoon and Roger Ratcliff, A Theory of Inference Generation during Text Comprehension by Arthur C. Graesser and Roger J. Kreuz, Computing Presuppositions and Implicatures in Mathematical Discourse by Claus Zinn, An Experimental Study on Pragmatic Inferences: Processing Implicatures and Presuppositions by Napoleon Katsos and Automaticity and Inference Generation during Reading Comprehension by Richard Thurlow and Paul van den Broek.

Publications pertinent to generating natural language from mathematics include: The Translation of Formal Proofs into English by Daniel Chester, English Summaries of Mathematical Proofs by Marianthi Alexoudi, Claus Zinn and Alan Bundy and Generating Arguments in Natural Language by Chris Reed, Algebraic Model and Implementation of Translation between Logic and Natural Language by Chen Peng and Proof Verbalization as an Application of NLG by Xiaorong Huang and Armin Fiedler.

Publications pertinent to natural language generation macroplanning and mathematics include: 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, Planning Reference Choices for Argumentative Texts by Xiaorong Huang, Granularity-adaptive Proof Presentation by Marvin Schiller and Christoph Benzmüller and An Algorithm for Generating Document-deictic References by Ivandré Paraboni.

Publications pertinent to generating referring expressions include: Managing Lexical Ambiguity in the Generation of Referring Expressions by Imtiaz H. Khan and Muhammad Haleem, Alignment in Interactive Reference Production: Content Planning, Modifier Ordering, and Referential Overspecification by Martijn Goudbeek and Emiel Krahmer, Generation of Repeated References to Discourse Entities by Anja Belz and Sebastian Varges and Contextual Influences on Attribute Selection for Repeated Descriptions by Pamela W. Jordan.

Publications pertinent to lexical selection include: Concept-based Lexical Selection by Bonnie Dorr, Clare Voss, Eric Peterson and Michael Kiker, From Concepts to Lexical Items by Manfred Bierwisch and Robert Schreuder, A Theory of Lexical Access in Speech Production by Willem J. Levelt, Lexicalization Patterns: Semantic Structure in Lexical Forms by Leonard Talmy and Vocabulary Choice as an Indicator of Perspective by Beata Beigman Klebanov, Eyal Beigman and Daniel Diermeier.

Publications pertinent to generating mathematical expressions for inferencing and presentation include: Computer Presentations of Structure in Algebra by Patrick W. Thompson and Alba G. Thompson 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.

Mathematics Educational Technology and Multimodal User Interfaces

Publications pertinent to multimodal input and mathematics include: Semi-synchronous Speech and Pen Input by Yasushi Watanabe, Kenji Iwata, Ryuta Nakagawa, Koichi Shinoda and Sadaoki Furui, Hamex – A Handwritten and Audio Dataset of Mathematical Expressions by Solen Quiniou, Harold Mouchère, Sebastián Peña Saldarriaga, Christian Viard-Gaudin, Emmanuel Morin, Simon Petitrenaud and Sofiane Medjkoune, Multimodal Mathematical Expressions Recognition: Case of Speech and Handwriting by Sofiane Medjkoune, Harold Mouchere, Simon Petitrenaud and Christian Viard-Gaudin, Multimodal Interfaces That Process What Comes Naturally by Sharon Oviatt and Philip Cohen, Developing Handwriting-based Intelligent Tutors to Enhance Mathematics Learning by Lisa Anthony, Analysis of Mixed Natural and Symbolic Language Input in Mathematical Dialogs by Magdalena Wolska and Ivana Kruijff-Korbayová and Interpretation of Mixed Language Input in a Mathematics Tutoring System by Helmut Horacek and Magdalena Wolska.

Publications pertinent to mathematical sketches and diagrams include: Mathematical Sketching: An Approach to Making Dynamic Illustrations by Joseph J. LaViola Jr, A Sketch-based System for Teaching Geometry by Gennaro Costagliola, Salvatore Cuomo, Vittorio Fuccella, Aniello Murano and Via Ponte Don Melillo, Intelligent Understanding of Handwritten Geometry Theorem Proving by Yingying Jiang, Feng Tian, Hongan Wang, Xiaolong Zhang, Xugang Wang and Guozhong Dai, Hierarchical Parsing and Recognition of Hand-sketched Diagrams by Levent Burak Kara and Thomas F. Stahovich, Combining Geometry and Domain Knowledge to Interpret Hand-drawn Diagrams by Leslie Gennari, Levent Burak Kara, Thomas F. Stahovich and Kenji Shimada and Multi-domain Sketch Understanding by Christine Alvarado.

Publications pertinent to multimodal input, note-taking and context include: Speech Pen: Predictive Handwriting based on Ambient Multimodal Recognition by Kazutaka Kurihara, Masataka Goto, Jun Ogata and Takeo Igarashi, Development of Note-taking Support System with Speech Interface by Kohei Ota, Hiromitsu Nishizaki and Yoshihiro Sekiguchi, Unsupervised Vocabulary Selection for Real-time Speech Recognition of Lectures by Paul Maergner, Alex Waibel and Ian Lane, Dynamic Language Model Adaptation Using Presentation Slides for Lecture Speech Recognition by Hiroki Yamazaki, Koji Iwano, Koichi Shinoda, Sadaoki Furui and Haruo Yokota, Rhetorical Structure Modeling for Lecture Speech Summarization by Pascale Fung, Justin Jian Zhang, Ricky Ho Yin Chan and Shilei Huang and Topic Segmentation and Retrieval System for Lecture Videos based on Spontaneous Speech Recognition by Natsuo Yamamoto, Jun Ogata and Yasuo Ariki.

Planning and Generating Sequences of Exercises for the Assessment and Development of Mathematical Knowledge and Proficiency

Publications pertinent to teaching problem solving skills include: 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, 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, Problem Solving and Cognitive Skill Acquisition by Kurt VanLehn, The Development of Problem-solving Strategies by Deanna Kuhn and Erin Phelps, How Children Change Their Minds: Strategy Change Can Be Gradual or Abrupt by Martha W. Alibali, The Importance of Metacognition for Conceptual Change and Strategy Use in Mathematics by Martha Carr, Metacognition and Mathematics Strategy Use by Martha Carr, Joyce Alexander and Trisha Folds‐Bennett, 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.

Publications pertinent to generating mathematical examples include: Learning Mathematics from Examples and by Doing by Xinming Zhu and Herbert A. Simon, Learning from Examples: Instructional Principles from the Worked Examples Research by Robert K. Atkinson, Sharon J. Derry, Alexander Renkl and Donald Wortham, Sequencing Examples and Nonexamples to Facilitate Concept Attainment by Osmond S. Petty and Lars C. Jansson, Worked Examples and Concept Example Usage in Understanding Mathematical Concepts and Proofs by Keith Weber, Mary Porter and David Housman, Structuring Effective Worked Examples by Mark Ward and John Sweller, Teaching by Examples: Implications for the Process of Category Acquisition by Judith Avrahami, Yaakov Kareev, Yonatan Bogot, Ruth Caspi, Salomka Dunaevsky and Sharon Lerner, The Subgoal Learning Model: Creating Better Examples so That Students Can Solve Novel Problems by Richard Catrambone, Increasing Mathematics Confidence by Using Worked Examples by William M. Carroll, Generalizing Solution Procedures Learned from Examples by Richard Catrambone, Generalizing from the Use of Earlier Examples in Problem Solving by Brian H. Ross and Patrick T. Kennedy, Generating Tailored Worked-out Problem Solutions to Help Students Learn from Examples by Giuseppe Carenini and Cristina Conati, Facilitating Learning Events through Example Generation by Randall P. Dahlberg and David L. Housman, Dialog-driven Adaptation of Explanations of Proofs by Armin Fiedler, English Summaries of Mathematical Proofs by Marianthi Alexoudi, Claus Zinn and Alan Bundy, Argumentation in Explanations to Logical Problems by Armin Fiedler and Helmut Horacek, 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 and An Analysis of Explanation and its Implications for the Design of Explanation Planners by Daniel D. Suthers.

Publications pertinent to transitioning from studying examples to problem solving exercises include: Structuring the Transition from Example Study to Problem Solving in Cognitive Skill Acquisition: A Cognitive Load Perspective by Alexander Renkl and Robert K. Atkinson, Towards Adaptive Generation of Faded Examples by Erica Melis and Giorgi Goguadze, Transitioning From Studying Examples to Solving Problems: Effects of Self-Explanation Prompts and Fading Worked-Out Steps by Robert K. Atkinson, Alexander Renkl and Mary Margaret Merrill and From Example Study to Problem Solving: Smooth Transitions Help Learning by Alexander Renkl, Robert K. Atkinson, Uwe H. Maier and Richard Staley.

Publications pertinent to generating mathematical exercises and sequences of exercises include: What is a Mathematical Question? by Christopher J. Sangwin, Mathematical Question Spaces by Christopher J. Sangwin, The Exercise as Mathematical Object: Dimensions of Possible Variation in Practice by Anne Watson and John Mason, What Do Students Learn While Solving Mathematics Problems? by Elizabeth Owen and John Sweller, Students’ Mathematical Reasoning in University Textbook Exercises by Johan Lithner, Designing Problems to Promote Higher-order Thinking by Renee E. Weiss, Writing Problems for Deeper Understanding by Barbara J. Duch, Inquiring Systems and Problem Structure: Implications for Cognitive Development by Phillip K. Wood, Automatic Creation of Exercises in Adaptive Hypermedia Learning Systems by Stephan Fischer and Ralf Steinmetz, Automatically Generating Algebra Problems by Rohit Singh, Sumit Gulwani and Sriram K. Rajamani, Automatic Exercise Generation in Euclidean Geometry by Andreas Papasalouros, Generating Mathematical Word Problems by Sandra Williams, Content Effects in Problem Categorization and Problem Solving by Stephen B. Blessing and Brian H. Ross, Problem Content Affects the Categorization and Solutions of Problems by Stephen B. Blessing and Brian H. Ross, Effects of Semantic Cues on Mathematical Modeling: Evidence from Word-problem Solving and Equation Construction Tasks by Shirley A. Martin and Miriam Bassok, Influence of Rewording Verbal Problems on Children’s Problem Representations and Solutions by Erik De Corte, Lieven Verschaffel and Luc De Win, Using Students’ Representations Constructed during Problem Solving To Infer Conceptual Understanding by Daniel Domin and George Bodner, This Is like That: The Use of Earlier Problems and the Separation of Similarity Effects by Brian H. Ross, Towards a Formalization of the Automatic Generation of Exercises by Sergio Gutiérrez, Francisco J. Losa and Carlos Delgado Kloos, Using AI Planning to Enhance E-Learning Processes by Antonio Garrido, Lluvia Morales and Ivan Serina and Modeling E-Learning Activities in Automated Planning by Antonio Garrido, Eva Onaindia, Lluvia Morales, Luis Castillo, Susana Fernández and Daniel Borrajo.

Publications pertinent to the aesthetic properties of mathematical exercises include: What Makes a Good Problem? An Aesthetic Lens by Nathalie Sinclair and Sandra Crespo, The Roles of the Aesthetic in Mathematical Inquiry by Nathalie Sinclair, Aesthetic Influences on Expert Mathematical Problem Solving by Edward A. Silver and Wendy Metzger, Which Problems do Teachers Consider Beautiful? A Comparative Study by Alexander Karp and Mathematical Beauty and its Characteristics. A Study of the Students’ Points of View by Astrid Brinkmann.

Publications pertinent to generalizing, comparing and selecting strategies include: Generalizing Solution Procedures Learned from Examples by Richard Catrambone, The Effects of Information Order and Learning Mode on Schema Abstraction by Renee Elio and John R. Anderson, The Effects of Category Generalizations and Instance Similarity on Schema Abstraction by Renee Elio and John R. Anderson, Principle Explanation and Strategic Schema Abstraction in Problem Solving by Allan B. Bernardo, The Importance of Prior Knowledge When Comparing Examples: Influences on Conceptual and Procedural Knowledge of Equation Solving by Bethany Rittle-Johnson, Jon R. Star and Kelley Durkin, 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, The Benefits of Comparing Solution Methods in Solving Equations by Zuya Habila Elisha, Learning through Case Comparisons: A Meta-analytic Review by Louis Alfieri, Timothy J. Nokes-Malach and Christian D. Schunn and Strategy Selection in Question Answering by Lynne M. Reder.

Publications pertinent to analogical reasoning, priming and context include: Mathematical Problem Solving by Analogy by Laura R. Novick and Keith J. Holyoak, Exploring the Relationship between Similar Solution Strategies and Analogical Reasoning by Peter Liljedah, Role of Analogical Reasoning in the Induction of Problem Categories by Denise D. Cummins, Learning by Analogy: Discriminating between Potential Analogs by Lindsey E. Richland and Ian M. McDonough, Analogical Problem Construction and Transfer in Mathematical Problem Solving by Allan B. Bernardo, Priming, Analogy, and Awareness in Complex Reasoning by Christian D. Schunn and Kevin Dunbar, Conceptual Priming in a Generative Problem-solving Task by Richard L. Marsh, Martin L. Bink and Jason L. Hicks, Analogy as Relational Priming: A Developmental and Computational Perspective on the Origins of a Complex Cognitive Skill by Robert Leech, Denis Mareschal and Richard P. Cooper, Analogical Priming via Semantic Relations by Barbara A. Spellman, Keith J. Holyoak and Robert G. Morrison, Relational Processing in Conceptual Combination and Analogy by Zachary Estes, Lara L. Jones, Robert Leech, Denis Mareschal and Richard P. Cooper, Surface and Structural Similarity in Analogical Transfer by Keith J. Holyoak and Kyunghee Koh, Context-dependent Effects on Analogical Transfer by R. Mason Spencer and Robert W. Weisberg and Analogy in Context by Brian Falkenhainer.

Publications pertinent to sequences of exercises and context include: Context in Problem Solving: A Survey by Patrick Brézillon, The Role of Situational Context in Solving Word Problems by Elisabeth Stern and Anne Lehrndorfer, Effects of Problem Context on Strategy Use within Functional Thinking by Katherine L. McEldoon, Caroline Cochrane-Braswell and Bethany Rittle-Johnson, Making Connections in Math: Activating a Prior Knowledge Analogue Matters for Learning by Pooja G. Sidney and Martha W. Alibali, The Effect of Context on the Structure of Categories by Emilie M. Roth and Edward J. Shoben, Context-independent and Context-dependent Information in Concepts by Lawrence W. Barsalou, Feature Availability in Conceptual Combination by Ken Springer and Gregory L. Murphy, Feature Accessibility in Conceptual Combination: Effects of Context-induced Relevance by Sam Glucksberg and Achary Estes, Memory in Context: Context in Memory by Graham M. Davies and Donald M. Thomson, Feeling of Knowing in Memory and Problem Solving by Janet Metcalfe, The Combined Contributions of the Cue-familiarity and Accessibility Heuristics to Feelings of Knowing by Asher Koriat and Ravit Levy-Sadot, Context and Structure in Conceptual Combination by Douglas L. Medin and Edward J. Shoben and Contextual Influences on the Comprehension of Complex Concepts by Richard J. Gerrig and Gregory L. Murphy.

Publications pertinent to multitasking and task switching include: Toward a Unified Theory of the Multitasking Continuum: From Concurrent Performance to Task Switching, Interruption, and Resumption by Dario D. Salvucci, Niels A. Taatgen and Jelmer P. Borst, Creativity under Concurrent and Sequential Task Conditions by Deepika Rastogi and Narendra K. Sharma, Task Switching by Stephen Monsell, The Effects of Recent Practice on Task Switching by Nick Yeung and Stephen Monsell, The Strategic Use of Preparation Cues in the Task Switching Paradigm by Mike Wendt, Aquiles Luna-Rodriguez, Renate Reisenauer and Gesine Dreisbach, Intuition, Incubation, and Insight: Implicit Cognition in Problem Solving by Jennifer Dorfman, Victor A. Shames and John F. Kihlstrom, Modeling the Aha! Moment: A Computational Mechanism for Structuring and Incubation in Creative Problem Solving by Zhao Cheng, Laura Ray, Ha T. Nguyen and Jerald D. Kralik, Cues to Solution, Restructuring Patterns, and Reports of Insight in Creative Problem Solving by Patrick J. Cushen and Jennifer Wiley and Investigating the Effect of Mental Set on Insight Problem Solving by Michael Öllinger, Gary Jones and Günther Knoblich.

Publications pertinent to mathematical discovery include: Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving by George Polya, How Children Discover New Strategies by Robert S. Siegler and Eric Jenkins, The “AHA moment”: Students Insights in Learning Mathematics by Peter Liljedahl, Mathematical Discovery and Concept Formation by Charles S. Chihara, A Theory of the Discovery and Predication of Relational Concepts by Leonidas A. Doumas, John E. Hummel and Catherine M. Sandhofer, On the Spontaneous Discovery of a Mathematical Relation during Problem Solving by James A. Dixon and Ashley S. Bangert, Investigating Insight as Sudden Learning by Ivan K. Ash, Benjamin D. Jee and Jennifer Wiley, A Computational Model of Conscious and Unconscious Strategy Discovery by Robert Siegler and Roberto Araya, Visualizing as a Means of Geometrical Discovery by Marcus Giaquinto and Creativity: Flow and the Psychology of Discovery and Invention by Mihaly Csiksentmihalyi.

Publications pertinent to the phenomenological aesthetics of mathematical thought, reasoning and of proof, pertinent to the enjoyment of mathematical exercises, include: The Mathematical Experience by Philip J. Davis and Reuben Hersh, On the Aesthetics of Mathematical Thought by Tommy Dreyfus and Theodore Eisenberg, The Phenomenology of Mathematical Beauty by Gian-Carlo Rota, The Phenomenology of Mathematical Proof by Gian-Carlo Rota, Mathematics as Story by George Gadanidis and Cornelia Hoogland, The Aesthetic in Mathematics as Story by George Gadanidis and Cornelia Hoogland, Mathematical Beauty and the Evolution of the Standards of Mathematical Proof by James W. McAllister, Syntax and Meaning as Sensuous, Visual, Historical Forms of Algebraic Thinking by Luis Radford and Luis Puig, Can a Computer Proof be Elegant? by Steve Seiden, Granularity by Jerry R. Hobbs, Granularity-adaptive Proof Presentation by Marvin Schiller and Christoph Benzmüller, Representation of Mathematical Concepts for Inferencing and for Presentation Purposes by Helmut Horacek, Armin Fiedler, Andreas Franke, Markus Moschner, Martin Pollet and Volker Sorge, Visual Salience of Algebraic Transformations by David Kirshner and Thomas Awtry, Computer Presentations of Structure in Algebra by Patrick W. Thompson and Alba G. Thompson and Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics by Ulianov Montano.

Publications pertinent to motivation and affect during problem solving activities include: Cognitive, Metacognitive, and Motivational Aspects of Problem Solving by Richard E. Mayer, Motivation and Ability as Factors in Mathematics Experience and Achievement by Ulrich Schiefele and Mihaly Csikszentmihalyi, The Concept of Flow by Jeanne Nakamura and Mihaly Csikszentmihalyi, Arousal of Flow Experience in a Learning Setting and its Effects on Exam Performance and Affect by Julia Schüler, The Intricate Dance between Cognition and Emotion during Expert Tutoring by Blair Lehman, Sidney D’Mello and Natalie Person, Emotions During the Learning of Difficult Material by Arthur C. Graesser and Sidney D’Mello, The Effect of Perceived Challenges and Skills on the Quality of Subjective Experience by Giovanni B. Moneta and Mihaly Csikszentmihalyi, Affect and Mathematics Learning by Gilah C. Leder, Positive Affect Facilitates Creative Problem Solving by Alice M. Isen, Kimberly A. Daubman and Gary P. Nowicki, Positive Affect Increases the Breadth of Attentional Selection by Gillian Rowe, Jacob B. Hirsh and Adam K. Anderson and Positive Emotions Broaden the Scope of Attention and Thought-action Repertoires by Barbara L. Fredrickson and Christine Branigan.

Publications pertinent to the automatic assessment of mathematical exercises include: 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 and An E-Assessment System for Mathematical Proofs by Susanne Gruttmann, Herbert Kuchen and Dominik Böhm.

Publications pertinent to modeling students and student problem solving include: Modelling Student’s Problem Solving by Derek H. Sleeman and Michael J. Smith, A Review of Student Models Used in Intelligent Tutoring Systems by Philip I. Pavlik Jr, Keith Brawner, Andrew Olney and Antonija Mitrovic and Student Modeling: Supporting Personalized Instruction, from Problem Solving to Exploratory Open-ended Activities by Cristina Conati and Samad Kardan.

The Cognitive Neuroscience and Development of Mathematical Reasoning

Publications pertinent to the cognitive neuroscience of mathematical reasoning include: 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.

Mathematical Creativity, Analogical Reasoning and Visualization

Publications pertinent to mathematical creativity include: Mathematical Creation by Henri Poincaré, An Essay on the Psychology of Invention in the Mathematical Field by Jacques Hadamard, The State of Art in Mathematical Creativity by Erkki Pehkonen, The Characteristics of Mathematical Creativity by Bharath Sriraman, Creativity, Cognitive Mechanisms, and Logic by Ahmed Abdel-Fattah, Tarek Besold and Kai-Uwe Kühnberger, What is Mathematical Thinking by Robert J. Sternberg, Mathematical Thinking and Learning by Herbert P. Ginsburg, Joanna Cannon, Janet Eisenband and Sandra Pappas, Creativity in Mathematics Education by Hartwig Meissner, Metaphor in Educational Discourse by Lynne Cameron and Analogy, Explanation, and Education by Paul Thagard.

Publications pertinent to mathematical metaphor, analogy and blending include: The Cognitive Foundations of Mathematics: The Role of Conceptual Metaphor by Rafael Núñez and George Lakoff, A Formal Cognitive Model of Mathematical Metaphors by Markus Guhe, Alan Smaill and Alison Pease, Using Information Flow for Modelling Mathematical Metaphors by Markus Guhe, Alan Smaill and Alison Pease, Metaphoric and Metonymic Signification in Mathematics by Norma C. Presmeg, Mathematics and Plausible Reasoning: Induction and Analogy in Mathematics by George Pólya, Analogical Reasoning and the Development of Algebraic Abstraction by Lyn D. English and Patrick V. Sharry, Using Analogies to Find and Evaluate Mathematical Conjectures by Alison Pease, Markus Guhe and Alan Smaill, Blending and Other Conceptual Operations in the Interpretation of Mathematical Proofs by Adrian Robert, Mathematical Blending by James C. Alexander, Material Anchors for Conceptual Blends by Edwin Hutchins, Mathematical Symbols as Epistemic Actions by Helen De Cruz and Johan De Smedt and A Theoretical Taxonomy of External Systems of Representation in the Learning and Understanding of Mathematics by Andri Marcou and Athanasios Gagatsis.

Publications pertinent to mathematical visualization include: Creativity, Visualization Abilities, and Visual Cognitive Style by Maria Kozhevnikov, Michael Kozhevnikov, Chen Jiao Yu and Olesya Blazhenkova, Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning by Raymond Duval, Image – Metaphor – Diagram: Visualization in Learning Mathematics by Gert Kadunz and Rudolf Sträßer, The Role of Visual Representations in the Learning of Mathematics by Abraham Arcavi, Research on Visualization in Learning and Teaching Mathematics by Norma C. Presmeg, Geometry and the Imagination by David Hilbert and Stephan Cohn-Vossen, Geometry and Spatial Reasoning by Douglas H. Clements and Michael T. Battista, The Nature of Spatial Ability and its Relationship to Mathematical Problem Solving by Barbara Elaine Moses and Spatial Ability, Visual Imagery, and Mathematical Performance by Glen Lean and M. A. (Ken) Clements.