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Applications of Simulated Students: An Exploration
 JOURNAL OF ARTIFICIAL INTELLIGENCE IN EDUCATION
, 1996
"... It is now possible to build machine learning systems whose behavior is consistent with data from human students. How can education use such simulated students? Applications that help three user groups are discussed. Teachers can practice the art of tutoring byhaving them teach a simulated student ..."
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Cited by 47 (1 self)
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It is now possible to build machine learning systems whose behavior is consistent with data from human students. How can education use such simulated students? Applications that help three user groups are discussed. Teachers can practice the art of tutoring byhaving them teach a simulated student. Using a simulation instead of a real student allows teachers to see how their actions affect that student's knowledge, to undo their actions, and to try their skills on students with varying prior knowledge and learning strategies. Students can learn in collaboration with a simulated student. Because the simulated student can be simultaneously an expert and a colearner, it can scaffold and guide the human's learning in subtle ways. Instructional developers can test their instruction on simulated students. Unlike formativeevaluations with real students, a simulationbased evaluation can indicate exactly what piece of the instruction caused which pieces of knowledge, and thus help developers troubleshoot their instructional designs early in the design process. For each of these three areas of application, inherent technical limitations, existing systems and prospective systems are discussed.
The Transfer of Scientific Principles Using Concrete and Idealized Simulations
 THE JOURNAL OF THE LEARNING SCIENCES
, 2005
"... ..."
Manipulatives as symbols: a new perspective on the use of concrete objects to teach mathematics
, 1997
"... This article offers a new perspective on the use of concrete objects to teach mathematics. It is commonly assumed that concrete manipulatives are effective because they allow children to perform mathematics without understanding arbitrary, written mathematical symbols. We argue that the sharp distin ..."
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Cited by 14 (0 self)
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This article offers a new perspective on the use of concrete objects to teach mathematics. It is commonly assumed that concrete manipulatives are effective because they allow children to perform mathematics without understanding arbitrary, written mathematical symbols. We argue that the sharp distinction between concrete and abstract forms of mathematical expression may not be justified. We believe instead that manipulatives are also symbols; teachers intend for them to stand for or represent a concept or written symbol. Consequently, research on how young children comprehend symbolic relations is relevant to studying their comprehension of manipulatives. We review evidence that many of the problems that children encounter when using manipulatives are very similar to problems that they have using other symbol systems such as scale models. Successful use of manipulatives depends on treating them as symbols rather than as substitutes for symbols. A persistent dilemma for teachers of mathematics concerns how to help children understand abstract concepts, such as addition and multiplication, and the symbols that are used to represent these concepts (Hiebert & Carpenter, 1992; Resnick & Ford, 1984). Teachers face a double challenge. Symbols may be difficult to teach to children who have not yet grasped the concepts that they represent. At the same time, the concepts may be difficult to teach to children who have not yet mastered the symbols. Not surprisingly, both teachers and mathematics researchers have called for better techniques to help children learn mathematical concepts and symbols.
Organizing Instruction and Study to Improve Student Learning IES Practice Guide
, 2007
"... The opinions and positions expressed in this practice guide are the authors ’ and do not necessarily represent the opinions and positions of the Institute of Education Sciences or the U.S. Department of Education. This practice guide should be reviewed and applied according to the specific needs of ..."
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Cited by 13 (6 self)
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The opinions and positions expressed in this practice guide are the authors ’ and do not necessarily represent the opinions and positions of the Institute of Education Sciences or the U.S. Department of Education. This practice guide should be reviewed and applied according to the specific needs of the educators and education agencies using it and with full realization that it represents only one approach that might be taken, based on the research that was available at the time of publication. This practice guide should be used as a tool to assist in decisionmaking rather than as a “cookbook.” Any references within the document to specific education products are illustrative and do not imply endorsement of these products to the exclusion of other products that are not referenced. U.S. Department of Education
Playing linear number board games—but not circular ones —improves lowincome preschoolers’ numerical understanding
 Journal of Educational Psychology
, 2009
"... A theoretical analysis of the development of numerical representations indicated that playing linear number board games should enhance preschoolers ’ numerical knowledge and ability to acquire new numerical knowledge. The effect on knowledge of numerical magnitudes was predicted to be larger when th ..."
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Cited by 8 (2 self)
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A theoretical analysis of the development of numerical representations indicated that playing linear number board games should enhance preschoolers ’ numerical knowledge and ability to acquire new numerical knowledge. The effect on knowledge of numerical magnitudes was predicted to be larger when the game was played with a linear board than with a circular board because of a more direct mapping between the linear board and the desired mental representation. As predicted, playing the linear board game for roughly 1 hr increased lowincome preschoolers ’ proficiency on the 2 tasks that directly measured understanding of numerical magnitudes—numerical magnitude comparison and number line estimation—more than playing the game with a circular board or engaging in other numerical activities. Also as predicted, children who had played the linear number board game generated more correct answers and better quality errors in response to subsequent training on arithmetic problems, a task hypothesized to be influenced by knowledge of numerical magnitudes. Thus, playing linear number board games not only increases preschoolers ’ numerical knowledge but also helps them learn from future numerical experiences.
Rexible execution of cognitive procedures
 Department of Psychology, CarnegieMellon University
, 1987
"... Many current theories of human problem solving and skill acquisition assume that people work only on the unsatisfied goal that was created most recently. That is, the architecture obeys a lastinfirstout (LIFO) constraint on the selection of goals. This restriction seems necessary for the proper f ..."
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Cited by 7 (2 self)
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Many current theories of human problem solving and skill acquisition assume that people work only on the unsatisfied goal that was created most recently. That is, the architecture obeys a lastinfirstout (LIFO) constraint on the selection of goals. This restriction seems necessary for the proper functioning of automatic learning mechanisms, such as production compilation and chunking. It is argued that this restriction is violated by some subjects on some tasks. In particular, 8 subiects (from a sample of 26) execute subtraction procedures in a way that violates the LIFO constraint. Although there is a great deal of between and withinsubject strategy variation in the 8 subjects ’ behavior, it can be simply exploined by hypothesizing that (1) the goal selection is not necessarily LIFO, (2) goal selection knowledge is represented by explicit preferences, and (3) the 8 subjects have just a few preferences that are overgeneralized, overspecialized, or missing. The rest of their preferences ore correct. On the other hand, LIFObosed models seem unable to explain the strategy variations in any simple way. Thus, it seems that port of the flexibility in humon problem solving comes from having a choice of which goal to work on next. Fortunately, it is simple to ammend automatic learning mechanisms so thot they will function correctly in a nonLIFO architecture. 1.
Designing effective multirepresentational learning environments
, 1999
"... For learning with multiple external representations (MERs) to be successful, the design of a learning environment must take advantage of the properties of different representations without overwhelming a leaner with their associated costs. This paper presents an analytic framework that consists of a ..."
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Cited by 5 (0 self)
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For learning with multiple external representations (MERs) to be successful, the design of a learning environment must take advantage of the properties of different representations without overwhelming a leaner with their associated costs. This paper presents an analytic framework that consists of a description of the functions of MERS, an analysis of the learning demands of using MERs and consideration of the design decisions that uniquely apply to multirepresentational learning environments. These are integrated to propose a set of idealised designs for each function of MERs. This framework was constructed for two purposes. Firstly, it can be used to compare existing learning environments and so allow more accurate generalisations from previous empirical work. Secondly, it is intended to provide the basis for further experimentation in order to develop
Representations of the magnitudes of fractions
 Journal of Experimental Psychology: Human Perception and Performance
, 2010
"... We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and den ..."
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Cited by 4 (0 self)
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We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However, atypical characteristics of the presented fractions might have provoked the use of atypical comparison strategies in that study. In our 3 experiments, university and community college students compared more balanced sets of singledigit and multidigit fractions and consistently exhibited a logarithmic distance effect. Thus, adults used integrated, analog representations, akin to a mental number line, to compare fraction magnitudes. We interpret differences between the past and present findings in terms of different stimuli eliciting different solution strategies.
Output Devices, Computation, and the Future of Mathematical Crafts
 International Journal of Computers in Mathematical Learning
, 2002
"... As I write this sentence, I am glancing over at the color printer sitting beside my screen. In the popular jargon of the computer industry, that printer is called a "peripheral"—which, upon reflection, is a rather odd way to describe it. What, precisely, is it peripheral to? If the ultimat ..."
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Cited by 3 (1 self)
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As I write this sentence, I am glancing over at the color printer sitting beside my screen. In the popular jargon of the computer industry, that printer is called a "peripheral"—which, upon reflection, is a rather odd way to describe it. What, precisely, is it peripheral to? If the ultimate
Shop Class for the Next Millennium: Education Through ComputerEnriched
, 1998
"... Abstract: In this paper we use our experiences with the HyperGami program as a springboard for a broader look at the future of computationallyenriched handicrafts. HyperGami is an educational application for the design and construction of mathematical models and sculptures in paper; as such, it ser ..."
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Cited by 2 (0 self)
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Abstract: In this paper we use our experiences with the HyperGami program as a springboard for a broader look at the future of computationallyenriched handicrafts. HyperGami is an educational application for the design and construction of mathematical models and sculptures in paper; as such, it serves as a source of examples and insights for the more general problem of how to integrate the “hightech ” features of computation with the “lowtech ” features of traditional craft materials in education. We begin by describing the HyperGami program, focusing on those features that were designed in response to problems encountered by papercrafters; we illustrate the program’s capabilities by presenting some of our own and our students ’ papercraft designs; and we describe our initial steps in implementing elements of HyperGami on the World Wide Web. In the closing sections of the paper, we explore the broader educational issues involved in integrating computation and handicrafts; and we conclude with a discussion of how physical objects could play a role in a future “educational object economy.”