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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 ..."
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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 &quot;peripheral&quot;—which, upon reflection, is a rather odd way to describe it. What, precisely, is it peripheral to? If the ultimate
Point and Click or Grab and Heft: Comparing the Influence of Physical and Virtual Instructional Materials on Elementary School Students’Ability to Design Experiments
"... The widespread availability of computers in elementary schools makes them an appealing option for presenting instructional materials in laboratory science. However, there are neither theoretical nor empirical grounds for predicting whether virtual or physical presentation of instructional materials ..."
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The widespread availability of computers in elementary schools makes them an appealing option for presenting instructional materials in laboratory science. However, there are neither theoretical nor empirical grounds for predicting whether virtual or physical presentation of instructional materials will be more effective. The definition of “active manipulation ” is poorly specified and there are few studies that directly compare the two approaches unaccompanied by other potential confounds. In this study, 4th and 5thgrade children were taught how to design simple unconfounded experiments using 1 of 2 instructional methods differing only in whether children manipulated physical or virtual materials. The 2 types of materials were equally effective in achieving several instructional objectives, including the design of unconfounded experiments, the derivation of correct predictions from them, and explicit reference to the need for experiments to be unconfounded. The increasingly widespread availability of computers in elementary schools makes them an appealing option for presenting instructional materials in laboratory science. U.S. public schools have an average of one instructional computer for every four students (Education Week, 2002). Of the more than 700 instructional software titles recommended by Technology and Learning (2002), hundreds are oriented specifically toward science education. There are many obvious advantages to the use of computerbased instructional materials, especially for
On the relation between play and symbolic thought: The case of mathematics manipulatives
 In O. Saracho and B. Spodek (Eds), Contemporary perspectives in early childhood
, 2003
"... Most develop~~ental psychologists and early childhood educators agree that young children learn best through play and exploration. As the chapters in this volume suggest, play and learning are intertwined for young children. Indeed, a focus on natural, playbased activities lies at the core of deve ..."
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Most develop~~ental psychologists and early childhood educators agree that young children learn best through play and exploration. As the chapters in this volume suggest, play and learning are intertwined for young children. Indeed, a focus on natural, playbased activities lies at the core of developmentally appropriate curricula. Organizations such as the National Association for the Education of Young Children (NAEYC) and the National Council for Teachers of Mathematics (NCTYM) stress that children's natural play should be the focus of preschool, kindergarten education, and (to a lesser extent) early elementary education (Uttal, Scudder, & DeLoache, 1997). As used here, the term "play " does not mean only free play that lacks direction or purpose. Instead, I also use the term play to refer to structured
Research Article It Works Both Ways: Transfer Difficulties between Manipulatives and Written Subtraction Solutions
"... Copyright © 2013 David H. Uttal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Three experiments compared performance and tra ..."
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Copyright © 2013 David H. Uttal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Three experiments compared performance and transfer among children aged 83–94 months after written or manipulatives instruction on twodigit subtraction. In Experiment 1a, children learned with manipulatives or with traditional written numerals. All children then completed a written posttest. Experiment 1b investigated whether salient or perceptually attractive manipulatives affected transfer. Experiment 2 investigated whether instruction with writing would transfer to a manipulativesbased posttest. Children demonstrated performance gains when the posttest format was identical to the instructed format but failed to demonstrate transfer from the instructed format to an incongruent posttest. The results indicate that the problem in transferring from manipulatives instruction to written assessments stems from a general difficulty in using knowledge gained in one format (e.g., manipulatives) in another format (e.g., writing). Taken together, the results have important implications for research and teaching in early mathematics. Teachers should consider making specific links and alignments between written and manipulativesbased representations of the same problems. 1.
Touching Points on a Numeral as a Means of Early Calculation: Does this Method Inhibit Progression to Abstraction and Fact Recall?
, 2005
"... Throughout the years, several teachers have noticed that although some students are taught TouchMath at an early age, and seem to benefit from it, they continue to count on the TouchPoints in their middle and high school years. It is important to note that these teachers are referring to a small por ..."
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Throughout the years, several teachers have noticed that although some students are taught TouchMath at an early age, and seem to benefit from it, they continue to count on the TouchPoints in their middle and high school years. It is important to note that these teachers are referring to a small portion of the student population. However, to these teachers, and to Innovative Learning Concepts, Inc., the developers of TouchMath, addressing these concerns is essential. Therefore, this paper will briefly describe the TouchMath process, as well as provide sample research involving students’ understandings of mathematical concepts, as supported by research and developed through the TouchMath program. The TouchMath program will be demonstrated as a scaffold or instructional support that students can move away from when, and if, ready. Research involving the importance of visualizing numbers in predictable and structured ways, as well as developing and using counting procedures, will be presented as a way for teachers to modify their view of counting as a primitive, and unwanted skill. Finally, research involving 722 adult respondents, who are successful at higher
Physically Distributed Learning: Adapting and Reinterpreting Physical Environments in the Development of Fraction Concepts
, 2004
"... Five studies examined how interacting with the physical environment can support the development of fraction concepts. Nine and 10yearold children worked on fraction problems they could not complete mentally. Experiments 1 and 2 showed that manipulating physical pieces facilitated children’s abili ..."
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Five studies examined how interacting with the physical environment can support the development of fraction concepts. Nine and 10yearold children worked on fraction problems they could not complete mentally. Experiments 1 and 2 showed that manipulating physical pieces facilitated children’s ability to develop an interpretation of fractions. Experiment 3 demonstrated that when children understood a content area well, they used their interpretations to repurpose many environments to support problem solving, whereas when they needed to learn, they were prone to the structure of the environment. Experiments 4 and 5 examined transfer after children had learned by manipulating physical pieces. Children who learned by adapting relatively unstructured environments transferred to new materials better than children who learned with “wellstructured ” environments that did not require equivalent adaptation. Together, the findings reveal that during physically distributed learning, the opportunity to adapt an environment permits the development of new interpretations that can advance learning.
Running head: PHYSICALLY DISTRIBUTED LEARNING Physically Distributed Learning: Adapting and Reinterpreting Physical Environments in the Development of Fraction Concepts
"... Five studies examined how interacting with the physical environment can support the development of fraction concepts. Nine and 10yearold children worked on fraction problems they could not complete mentally. Experiments 1 and 2 showed that manipulating physical pieces facilitated children’s abili ..."
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Five studies examined how interacting with the physical environment can support the development of fraction concepts. Nine and 10yearold children worked on fraction problems they could not complete mentally. Experiments 1 and 2 showed that manipulating physical pieces facilitated children’s abilities to develop an interpretation of fractions. Experiment 3 demonstrated that when children understood a content area well, they used their interpretations to repurpose many environments to support problem solving, whereas when they needed to learn, they were prone to the structure of the environment. Experiments 4 and 5 examined transfer after children had learned by manipulating physical pieces. Children who learned by adapting relatively unstructured environments transferred to new materials better than children who learned with “wellstructured ” environments that did not require equivalent adaptation. Together, the findings reveal that during physically distributed learning, the opportunity to adapt an environment permits the development of new interpretations that can advance learning.
Learning Math 1 Running head: LEARNING MATH WITH MANIPULATIVES Learning Math with Manipulatives
"... A standard set of variables is extracted from a set of studies with different perspectives and different findings involving learning aids in the classroom. The variables are then used to analyze the studies in order to draw conclusions about learning aids in general and manipulatives in particular. ..."
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A standard set of variables is extracted from a set of studies with different perspectives and different findings involving learning aids in the classroom. The variables are then used to analyze the studies in order to draw conclusions about learning aids in general and manipulatives in particular. Learning Math 3 Learning Math with Manipulatives Manipulatives are a widely used part of the mathematics curriculum. The National Council for Teachers of Mathematics includes the use of manipulatives in its Principles and Standards for School Mathematics (NCTM, 2000), a document that has been used nationally for developing local mathematics standards. According to the National Center for Educational Statistics (NCES, 1993), during the 19921993 school year manipulatives were used every day for math or science in fortynine percent of all public kindergarten classrooms. In the 19941995 school year, manipulatives were used in sixteen percent of all math lessons in US public eighth grade classrooms and in thirtyfour percent of all math lessons in Japanese eighth grade classrooms (NCES, 1999). Research with manipulatives such as base ten blocks have been