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.