DOCSLIB.ORG

Problem Solving and Situated Cognition." in Robbins, P., & Aydede, M

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Problem Solving and Situated Cognition. Kirsh, David. "Problem solving and situated cognition." In Robbins, P., & Aydede, M. (Eds.). (2009). The Cambridge handbook of situated cognition (pp. 264-306). Cambridge: Cambridge University Press. CHAPTER I 5 Problem Solving and Situated Cognition David Kirsh Introduction exploratory process is not well understood, as it is not always systematic, but various In the course of daily life we solve prob- heuristic search algorithms have been pro- lems often enough that there is a special posed and some experimental support has term to characterize the activity and the been provided for them. right to expect a scientific theory to explain Situated cognition, by contrast, does not its dynamics. The classical view in psychol- have a theory of problem solving to compete ogy is that to solve a problem a subject with the classical view. It offers no com- must frame it by creating an internal rep- putational, neuropsychological, or mathe- resentation of the problem's structure, usu- matical account of the internal processes ally called a problem space. This space is underlying problem cognition. Nor does it an internally generable representation that explain the nature of the control of exter- is mathematically identical to a graph struc- nal processes related to problem solving. ture with nodes and links. The nodes can Partly this is a matter of definition. Prob- be annotated with useful information, and lems are not regarded to be a distinct cate- the whole representation can be distributed gory for empirical and computational analy- over internal and external structures such sis because what counts as a problem varies as symbolic notations on paper or diagrams. from activity to activity. Problems do arise If the representation is distributed across all the time, no matter what we are doing. internal and external structures the sub- But from a situated cognition perspective ject must be able to keep track of activ- these problems should not be understood ity in the distributed structure. Problem as abstractions with a formal structure that solving proceeds as the subject works from may be the same across different activities. an initial state in this mentally supported Each problem is tied to a concrete setting space, actively constructing possible solu- and is resolved by reasoning in situation- tion paths, evaluating them and heuristi- specific ways, making use of the material and cally choosing the best. Control of this cultural resources locally available. What is 264 177 problem sol ving and situated cognition called a problem, therefore, depends on the explain how people solve problems that are discourse of that activity, and so in a sense, is ill defined, which they recognized a large socially constructed. There is no natural kind class of problems to be. called "problem" and no natural kind process To develop their theory they presented called "problem solving" for psychologists to subjects with a collection of games and puz- study. Problem solving is merely a form of zles with unique solutions or solution sets. reasoning that, like all reasoning, is deeply Having a correct answer - a solution set - bound up with the activities and context in is the hallmark of a problem being well which it takes place. Accordingly, the situ- defined. Problems were posed in contexts ational approach highlights those aspects of in which the experimenter could be sure problem solving that reveal how much the subjects had a clear understanding of what machinery of inference, computation, and they had to solve. Games and puzzles were representation is embedded in the social, chosen because they are self-contained; it is cultural, and material aspects of situations. assumed that no special knowledge outside This critical approach to problem solving of what is provided is needed to solve them. is what I shall present first. In Part 11 discuss These sorts of problems have a strict defi- the assumptions behind the classical psycho- nition of allowable actions (you move your logical theory. In Part 2 I present the major pawn like this), the states these actions cause objections raised by those believing that cog- (the board enters this configuration), and a nition must be understood in an embodied, strict definition of when the game or puzzle interactive, and situated way, and not pri- has been solved, won, or successfully com- marily as a cognitive process of searching pleted (opponent's king is captured). It was through mental or abstract representations. assumed that subjects who read the prob- There is a tendency in the situated cogni- lem would be able to understand these ele- tion literature to be dismissive of the clas- ments and create their internal representa- sical view without first acknowledging its tion. Such problems are both well defined flexibility and sophistication. Accordingly, I and knowledge lean, as "everything that the present the classical account in its best form subject needs to know to perform the task in an effort to appreciate what parts may be is presented in the instructions" (VanLehn, useful in a more situated theory. In Part 3 I 1989, p. 528). No special training or back- collect pieces from both accounts, situated ground knowledge is required. and classical, to move on to sketch a more positive theory - or at least provide desider- ata for such a theory - though only frag- 2. Task Environment ments of such a view can be presented here. In the classical theory, the terms problem and task are interchangeable. Newell and PART 1: THE CLASSICAL THEORY Simon introduced the expression task envi- ronment to designate an abstract structure 1. Newell and Simon's Theory that corresponds to a problem. It is called an environment because subjects who improve In an extensive collection of papers and task performance are assumed to be adapt- books, Herbert Simon, often with Allen ing their behavior to some sort of environ- Newell, presented a clear statement of the mental constraints, the fundamental struc- now-classical approach to problem solv- ture of the problem. It is abstract because ing (see, among others, Newell & Simon, the same task environment can be instan- 1972). Mindful that science regularly pro- tiated in very different ways. In chess, for ceeds from idealization, Simon and Newell example, the task environment is the same worked from the assumption that a the- whether the pieces are made of wood or sil- ory based on how people solve well-defined ver or are displayed on a computer screen. problems can be stretched or augmented to Any differences arising because agents need DAVID KIRSH to interact differently in different physical nomenon. The same would apply to other contexts are irrelevant. It does not matter things nonexperts do when they play, SUcj1 whether an agent moves pieces by hand, as putting a finger on a piece, trying |f by mouse movements, by requesting some- possible actions on the board, using pencil one else to make the move for them, or and paper, talking to oneself, or consulting by writing down symbols and sending a a book (if allowed at all). All are assumed description of their move by mail. Issues irrelevant to task performance. They may associated with solving these movement or occur while a subject is working on a prob- communication subtasks belong to a differ- lem, or while playing chess, but, according ent problem. to the classical account, they are not liter- A task environment, accordingly, delin- ally part of problem-solving activity. This is eates the core task. It specifies an under- obviously a point of dispute for situation- alists, as many of these actions are regularly lying structure that determines the rele- observed during play, and they may critically vant effects of every relevant action that a affect the success of an agent. given agent can perform. This has the effect that if two agents have different capacities for action they face different task environ- ments. When four-legged creatures confront 3. Problem Space an obstacle, they face a different locomo- tion problem than two-legged creatures, and Task environments are differentiated from both problems are different from the loco- problem spaces, the representation sub- motion problem the obstruction poses to jects are assumed to mentally construct a snake. Thus, two agents operating in the when they understand a task correctly. This same physical environment, each facing the problem-space representation might be dis- same objective - get from atob- may face tributed over external resources. It encodes different task environments because of their the following: different capacities. Their optimal path may be different. Moreover, of all the actions a | The current state of the problem. At the creature or subject can perform, the only beginning this is the initial state. ones that count as task relevant are the ones • A representation of the goal state or con- that can, in principle, bring it closer to or far- dition - though this might be a procedure ther from an environmental state meeting or test for recognizing when the goal has the goal condition. It is assumed that dif- been reached, rather than a declarative ferences in expertise and intellectual ability statement of the goal. affect search and reasoning rather than the I Constraints determining allowable moves definition of the task itself. and states, hence the nodes and allow- Task environments are theoretical projec- able links of the space I these too tions that let researchers interpret problem- may be specified implicitly in procedures solving activity in concrete situations. They for generating all and only legal moves identify what counts as a move in a problem rather than explicitly in declarative state- (for a given agent). As such, they impose ments. a powerful filter over the way a researcher • Optionally, other representations that interprets subjects' actions.
Load more

Recommended publications
  • Compare and Contrast Two Models Or Theories of One Cognitive Process with Reference to Research Studies
    ! The following sample is for the learning objective: Compare and contrast two models or theories of one cognitive process with reference to research studies. What is the question asking for? * A clear outline of two models of one cognitive process. The cognitive process may be memory, perception, decision-making, language or thinking. * Research is used to support the models as described. The research does not need to be outlined in a lot of detail, but underatanding of the role of research in supporting the models should be apparent.. * Both similarities and differences of the two models should be clearly outlined. Sample response The theory of memory is studied scientifically and several models have been developed to help The cognitive process describe and potentially explain how memory works. Two models that attempt to describe how (memory) and two models are memory works are the Multi-Store Model of Memory, developed by Atkinson & Shiffrin (1968), clearly identified. and the Working Memory Model of Memory, developed by Baddeley & Hitch (1974). The Multi-store model model explains that all memory is taken in through our senses; this is called sensory input. This information is enters our sensory memory, where if it is attended to, it will pass to short-term memory. If not attention is paid to it, it is displaced. Short-term memory Research. is limited in duration and capacity. According to Miller, STM can hold only 7 plus or minus 2 pieces of information. Short-term memory memory lasts for six to twelve seconds. When information in the short-term memory is rehearsed, it enters the long-term memory store in a process called “encoding.” When we recall information, it is retrieved from LTM and moved A satisfactory description of back into STM.
    [Show full text]
  • 13. Mathematics University of Central Oklahoma
    Southwestern Oklahoma State University SWOSU Digital Commons Oklahoma Research Day Abstracts 2013 Oklahoma Research Day Jan 10th, 12:00 AM 13. Mathematics University of Central Oklahoma Follow this and additional works at: https://dc.swosu.edu/ordabstracts Part of the Animal Sciences Commons, Biology Commons, Chemistry Commons, Computer Sciences Commons, Environmental Sciences Commons, Mathematics Commons, and the Physics Commons University of Central Oklahoma, "13. Mathematics" (2013). Oklahoma Research Day Abstracts. 12. https://dc.swosu.edu/ordabstracts/2013oklahomaresearchday/mathematicsandscience/12 This Event is brought to you for free and open access by the Oklahoma Research Day at SWOSU Digital Commons. It has been accepted for inclusion in Oklahoma Research Day Abstracts by an authorized administrator of SWOSU Digital Commons. An ADA compliant document is available upon request. For more information, please contact [email protected]. Abstracts from the 2013 Oklahoma Research Day Held at the University of Central Oklahoma 05. Mathematics and Science 13. Mathematics 05.13.01 A simplified proof of the Kantorovich theorem for solving equations using scalar telescopic series Ioannis Argyros, Cameron University The Kantorovich theorem is an important tool in Mathematical Analysis for solving nonlinear equations in abstract spaces by approximating a locally unique solution using the popular Newton-Kantorovich method.Many proofs have been given for this theorem using techniques such as the contraction mapping principle,majorizing sequences, recurrent functions and other techniques.These methods are rather long,complicated and not very easy to understand in general by undergraduate students.In the present paper we present a proof using simple telescopic series studied first in a Calculus II class.
    [Show full text]
  • Simple Variations on the Tower of Hanoi to Guide the Study Of
    Simple Variations on the Tower of Hanoi to Guide the Study of Recurrences and Proofs by Induction Saad Mneimneh Department of Computer Science Hunter College, The City University of New York 695 Park Avenue, New York, NY 10065 USA [email protected] Abstract— Background: The Tower of Hanoi problem was The classical solution for the Tower of Hanoi is recursive in formulated in 1883 by mathematician Edouard Lucas. For over nature and proceeds to first transfer the top n − 1 disks from a century, this problem has become familiar to many of us peg x to peg y via peg z, then move disk n from peg x to peg in disciplines such as computer programming, data structures, algorithms, and discrete mathematics. Several variations to Lu- z, and finally transfer disks 1; : : : ; n − 1 from peg y to peg z cas’ original problem exist today, and interestingly some remain via peg x. Here’s the (pretty standard) algorithm: unsolved and continue to ignite research questions. Research Question: Can this richness of the Tower of Hanoi be Hanoi(n; x; y; z) explored beyond the classical setting to create opportunities for if n > 0 learning about recurrences and proofs by induction? then Hanoi(n − 1; x; z; y) Contribution: We describe several simple variations on the Tower Move(1; x; z) of Hanoi that can guide the study and illuminate/clarify the Hanoi(n − 1; y; x; z) pitfalls of recurrences and proofs by induction, both of which are an essential component of any typical introduction to discrete In general, we will have a procedure mathematics and/or algorithms.
    [Show full text]
  • Cognition, Affect, and Learning —The Role of Emotions in Learning
    How People Learn: Cognition, Affect, and Learning —The Role of Emotions in Learning Barry Kort Ph.D. and Robert Reilly Ed.D. {kort, reilly}@media.mit.edu formerly MIT Media Lab Draft as of date January 2, 2019 Learning is the quintessential emotional experience. Our species, Homo Sapiens, are the beings who think. We are also the beings who learn, and the beings who simultaneously experience a rich spectrum of affective emotional states, including a selected suite of emotional states specifically and directly related to learning. This proposal reviews previously published research and theoretical models relating emotions to learning and cognition and presents ideas and proposals for extending that research and reducing it to practice. Our perspective The concept of affect in learning (i.e., emotions in learning) is the same pedagogy applied by an athletic coach at a sporting event. A coach recognizes the affective state of an athlete, and, for example, exhorts that athlete toward increased performance (e.g., raises the level of enthusiasm), or, redirects a frustrated athlete to a productive affective state (e.g., instills confidence, or pride). A coach recognizes that an athlete’s affective state is a critical factor during performance; and, when appropriate, a coach will intervene with a meaningful strategy or tactic. Athletic coaches are skilled at recognizing affective states and intervening appropriately. Educators can have the same impact on a learner by understanding a learner’s affective state and intervening with appropriate strategies or tactics that will meaningfully manage and guide a person’s learning journey. There are several learning theories and a great deal of neuroscience/affective research.
    [Show full text]
  • Chapter 14: Individual Differences in Cognition 369 Copyright ©2018 by SAGE Publications, Inc
    INDIVIDUAL 14 DIFFERENCES IN COGNITION CHAPTER OUTLINE Setting the Stage Individual Differences in Cognition Ability Differences distribute Cognitive Styles Learning Styles Expert/Novice Differences or The Effects of Aging on Cognition Gender Differences in Cognition Gender Differences in Skills and Abilities Verbal Abilities Visuospatial Abilities post, Quantitative and Reasoning Abilities Gender Differences in Learning and Cognitive Styles Motivation for Cognitive Tasks Connected Learning copy, not SETTING THE STAGE .................................................................. y son and daughter share many characteristics, but when it comes Do to school they really show different aptitudes. My son adores - Mliterature, history, and social sciences. He ceremoniously handed over his calculator to me after taking his one and only college math course, noting, “I won’t ever be needing this again.” He has a fantastic memory for all things theatrical, and he amazes his fellow cast members and directors with how quickly he can learn lines and be “off book.” In contrast, my daughter is really adept at noticing patterns and problem solving, and she Proof is enjoying an honors science course this year while hoping that at least one day in the lab they will get to “blow something up.” She’s a talented dancer and picks up new choreography seemingly without much effort. These differences really don’t seem to be about ability; Tim can do statis- tics competently, if forced, and did dance a little in some performances, Draft and Kimmie can read and analyze novels or learn about historical topics and has acted competently in some school plays. What I’m talking about here is more differences in their interests, their preferred way of learning, maybe even their style of learning.
    [Show full text]
  • Cognitive Retention of Generation Y Students Through the Use of Games
    11 COGNITNE RETENTION OF GENERATION Y STUDENTS THROUGH THE USE OF GAMES AND SIMULATIONS A Dissertation Submitted to the Faculty of Argosy University - Sarasota In partial fulfillment of The requirements for the degree of Doctorate of Business Administration Accounting Major by Melanie A. Hicks Argosy University - Sarasota August 2007 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. III Abstract A new generation of students has begun to proliferate colleges and universities. Unlike previous generations, Generation Y students have been exposed to a variety of technological advancements, have different behaviors towards learning, and have been raised in a different environment. These differences may be causing conflict with traditional pedagogy in educational institutions, thereby creating, while it may be unintentional, an inability for Generation Y students to learn under the standard educational method of lecture presented to previous generations. The literature supports the position that additional teaching methods are needed in order to effectively educate Generation Y students (Prensky, 2001; Brozik & Zapalska, 1999; Albrecht, 1995). Consequently, the primary goal of this dissertation is to examine the ability of Generation Y students to achieve greater cognitive retention when the instructional material is conveyed with the assistance of or through the use of games andlor simulations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV © Copyright 2007 by Melanie A. Hicks Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. v ACKNOWLEDGEMENTS This dissertation is dedicated to my husband, Scott Hicks, who has encouraged me and constantly pushed me to "seek first to understand, then to be understood".
    [Show full text]
  • Arxiv:0905.0015V3 [Math.CO] 20 Mar 2021
    The Tower of Hanoi and Finite Automata Jean-Paul Allouche and Jeff Shallit Abstract Some of the algorithms for solving the Tower of Hanoi puzzle can be applied “with eyes closed” or “without memory”. Here we survey the solution for the classical Tower of Hanoi that uses finite automata, as well as some variations on the original puzzle. In passing, we obtain a new result on morphisms generating the classical and the lazy Tower of Hanoi. 1 Introduction A huge literature in mathematics and theoretical computer science deals with the Tower of Hanoi and generalizations. The reader can look at the references given in the bibliography of the present paper, but also at the papers cited in these references (in particular in [5, 13]). A very large bibliography was provided by Stockmeyer [27]. Here we present a survey of the relations between the Tower of Hanoi and monoid morphisms or finite automata. We also give a new result on morphisms generating the classical and the lazy Tower of Hanoi (Theorem 4). Recall that the Tower of Hanoi puzzle has three pegs, labeled I, II,III,and N disks of radii 1,2,...,N. At the beginning the disks are placed on peg I, in decreasing order of size (the smallest disk on top). A move consists of taking the topmost disk from one peg and moving it to another peg, with the condition that no disk should cover a smaller one. The purpose is to transfer all disks from the initial peg arXiv:0905.0015v3 [math.CO] 20 Mar 2021 to another one (where they are thus in decreasing order as well).
    [Show full text]
  • Graphs, Random Walks, and the Tower of Hanoi
    Rose-Hulman Undergraduate Mathematics Journal Volume 20 Issue 1 Article 6 Graphs, Random Walks, and the Tower of Hanoi Stephanie Egler Baldwin Wallace University, Berea, [email protected] Follow this and additional works at: https://scholar.rose-hulman.edu/rhumj Part of the Discrete Mathematics and Combinatorics Commons Recommended Citation Egler, Stephanie (2019) "Graphs, Random Walks, and the Tower of Hanoi," Rose-Hulman Undergraduate Mathematics Journal: Vol. 20 : Iss. 1 , Article 6. Available at: https://scholar.rose-hulman.edu/rhumj/vol20/iss1/6 Rose-Hulman Undergraduate Mathematics Journal VOLUME 20, ISSUE 1, 2019 Graphs, Random Walks, and the Tower of Hanoi By Stephanie Egler Abstract. The Tower of Hanoi puzzle with its disks and poles is familiar to students in mathematics and computing. Typically used as a classroom example of the important phenomenon of recursion, the puzzle has also been intensively studied its own right, using graph theory, probability, and other tools. The subject of this paper is “Hanoi graphs”,that is, graphs that portray all the possible arrangements of the puzzle, together with all the possible moves from one arrangement to another. These graphs are not only fascinating in their own right, but they shed considerable light on the nature of the puzzle itself. We will illustrate these graphs for different versions of the puzzle, as well as describe some important properties, such as planarity, of Hanoi graphs. Finally, we will also discuss random walks on Hanoi graphs. 1 The Tower of Hanoi The Tower of Hanoi is a famous puzzle originally introduced by a “Professor Claus” in 1883.
    [Show full text]
  • Rethinking Co-Cognition Contents 1. Introduction
    This paper was published in Mind & Language, 13, 1998, 499-512. Archived at Website for the Rutgers University Research Group on Evolution and Higher Cognition. Rethinking Co-cognition Shaun Nichols Department of Philosophy College of Charleston Charleston, SC 29424 [email protected] and Stephen Stich Department of Philosophy and Center for Cognitive Science Rutgers University New Brunswick, NJ 08901 [email protected] Contents 1. Introduction 2. Points of Agreement 3. The Co-Cognition Thesis and a Friendly Amendment 4. A Critique of the Co-Cognition Thesis 1. Introduction In cognitive science and philosophy of mind, there has been a wealth of fascinating work trying to tease out the cognitive mechanisms that are involved in understanding other minds or "mindreading" (e.g., Baron-Cohen, 1995; Bartsch & Wellman, 1995; Fodor, 1995; Goldman, 1992; Gopnik, 1993; Harris, 1991; Leslie, 1991; Perner, 1991). This research has focused on evaluating the empirical evidence for various accounts of mindreading, predicting the results of future experiments, and carrying out experiments that might distinguish between the available theories. Our own previous work adopted this naturalistic approach (Stich & Nichols, 1992, 1995, 1997; Nichols et al., 1996; Nichols et al., 1995). In contrast to the naturalistic exploration of mindreading, Jane Heal has argued that simulation theorists have discovered an a priori truth about mindreading (Heal, 1994, 1995). In Heal's most recent paper (this issue), which is largely a response to an earlier paper of ours (Stich & Nichols, 1997), she maintains that we are committed to a view that conflicts with a simulationist thesis which is a priori true.
    [Show full text]
  • Memory & Cognition
    / Memory & Cognition Volume 47 · Number 4 · May 2019 Special Issue: Recognizing Five Decades of Cumulative The role of control processes in temporal Progress in Understanding Human Memory and semantic contiguity and its Control Processes Inspired by Atkinson M.K. Healey · M.G. Uitvlugt 719 and Shiffrin (1968) Auditory distraction does more than disrupt rehearsal Guest Editors: Kenneth J. Malmberg· processes in children's serial recall Jeroen G. W. Raaijmakers ·Richard M. Shiffrin A.M. AuBuchon · C.l. McGill · E.M. Elliott 738 50 years of research sparked by Atkinson The effect of working memory maintenance and Shiffrin (1968) on long-term memory K.J. Malmberg · J.G.W. Raaijmakers · R.M. Shiffrin 561 J.K. Hartshorne· T. Makovski 749 · From ·short-term store to multicomponent working List-strength effects in older adults in recognition memory: The role of the modal model and free recall A.D. Baddeley · G.J. Hitch · R.J. Allen 575 L. Sahakyan 764 Central tendency representation and exemplar Verbal and spatial acquisition as a function of distributed matching in visual short-term memory practice and code-specific interference C. Dube 589 A.P. Young· A.F. Healy· M. Jones· L.E. Bourne Jr. 779 Item repetition and retrieval processes in cued recall: Dissociating visuo-spatial and verbal working memory: Analysis of recall-latency distributions It's all in the features Y. Jang · H. Lee 792 ~1 . Poirier· J.M. Yearsley · J. Saint-Aubin· C. Fortin· G. Gallant · D. Guitard 603 Testing the primary and convergent retrieval model of recall: Recall practice produces faster recall Interpolated retrieval effects on list isolation: success but also faster recall failure IndiYiduaLdifferences in working memory capacity W.J.
    [Show full text]
  • I Note on the Cyclic Towers of Hanoi
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Theoretical Computer Science 123 (1994) 3-7 Elsevier I Note on the cyclic towers of Hanoi Jean-Paul Allouche CNRS Mathkmatiques et Informatique. lJniversit& Bordeaux I. 351 cows de la Lib&ration, 33405 Talence Cedex, France Abstract Allouche, J.-P., Note on the cyclic towers of Hanoi, Theoretical Computer Science 123 (1994) 3-7. Atkinson gave an algorithm for moving N disks from a peg to another one in the cyclic towers of Hanoi. We prove that the resulting infinite sequence obtained as N goes to infinity is not k-automatic for any k>2. 0. Introduction The well-known tower of Hanoi puzzle consists of three pegs and N disks of radius 1,2, I.. ) N. At the beginning, all the disks are stacked on the first peg in decreasing order (1 being the topmost disk). At each step one is allowed to pick up the topmost disk of a peg and to put it on another peg, provided a disk is never on a smaller one. The game is ended when all disks are on the same (new) peg. The classical (recursive) algorithm for solving this problem provides us with an infinite sequence of moves (with values in the set of the 6 possible moves), whose prefixes of length 2N - 1 give the moves which carry N disks from the first peg to the second one (if N is odd) or to the third one (if N is even).
    [Show full text]
  • Models of Memory
    To be published in H. Pashler & D. Medin (Eds.), Stevens’ Handbook of Experimental Psychology, Third Edition, Volume 2: Memory and Cognitive Processes. New York: John Wiley & Sons, Inc.. MODELS OF MEMORY Jeroen G.W. Raaijmakers Richard M. Shiffrin University of Amsterdam Indiana University Introduction Sciences tend to evolve in a direction that introduces greater emphasis on formal theorizing. Psychology generally, and the study of memory in particular, have followed this prescription: The memory field has seen a continuing introduction of mathematical and formal computer simulation models, today reaching the point where modeling is an integral part of the field rather than an esoteric newcomer. Thus anything resembling a comprehensive treatment of memory models would in effect turn into a review of the field of memory research, and considerably exceed the scope of this chapter. We shall deal with this problem by covering selected approaches that introduce some of the main themes that have characterized model development. This selective coverage will emphasize our own work perhaps somewhat more than would have been the case for other authors, but we are far more familiar with our models than some of the alternatives, and we believe they provide good examples of the themes that we wish to highlight. The earliest attempts to apply mathematical modeling to memory probably date back to the late 19th century when pioneers such as Ebbinghaus and Thorndike started to collect empirical data on learning and memory. Given the obvious regularities of learning and forgetting curves, it is not surprising that the question was asked whether these regularities could be captured by mathematical functions.
    [Show full text]