Learning with Digital Manipulatives

New Frameworks to Help Elementary-School Students
Explore "Advanced" Mathematical and Scientific Concepts

Mitchel Resnick, MIT Media Lab
Michael Eisenberg, Department of Computer Science, University of Colorado
Robbie Berg, Department of Physics, Wellesley College
Bakhtiar Mikhak, MIT Media Lab
Diane Willow, MIT Media Lab

Things before words, concrete before abstract.

– Johann Heinrich Pestalozzi (1803)

Introduction

In 1837, Friedrich Fröbel created the world’s first kindergarten in Germany. Fröbel’s school was an important departure from previous educational institutions not only in the age of its students, but in its educational approach. In sharp contrast with previous schools, Fröbel put physical objects and physical activity at the core of his kindergarten. He developed a set of 20 so-called "gifts" – objects such as balls, blocks, and sticks – for children to use in the kindergarten. Fröbel carefully designed these gifts (two of which are shown below) to help children recognize and appreciate common patterns and forms found in nature. Fröbel’s gifts and ideas were eventually distributed throughout the world, influencing the development of generations of young children. Some historians argue that Fröbel’s gifts have had a significant impact on the course of 20th century art; indeed, Frank Lloyd Wright credited his boyhood experiences with Fröbel’s gifts as the foundation of his architecture (Brosterman, 1997).

Many of today’s kindergartens and early-elementary classrooms are still full of physical objects and physical activity. Walk into a classroom, and you are likely to see a diverse collection of "manipulative materials" such as Cuisenaire Rods and Pattern Blocks. As children build and experiment with these materials, they develop deeper understandings of mathematical concepts such as number, size, and shape. As children play with Cuisenaire Rods, for example, they discover that one brown rod is the same length as two purple rods (or four red ones) – and, in the process, they begin to develop a framework for thinking about fractions and proportions.

But the use of manipulative materials in schools has been limited, focused especially on the early grades and on a relatively narrow range of concepts. Many important mathematical and scientific concepts are very difficult (if not impossible) to explore with traditional manipulative materials. For example, traditional manipulatives do not help children learn about dynamic processes – how things change over time, how patterns form, and how behaviors arise. Such concepts are typically taught through more formal methods, involving abstract mathematical formalisms such as differential equations – certainly not accessible to young children.

But, in our view, these "advanced" concepts are not inherently too complex for young children. Rather, the core problem is that traditional representations of these concepts are inaccessible. The challenge is to create new representations that make these concepts more "manipulable" by young children. It is here that computational technologies can play a major role. By adding computational capabilities to manipulative materials, we believe we can greatly expand the range of concepts that children can explore through direct interaction with physical objects. We believe these new "digital manipulatives" will enable young children to learn concepts that were previously viewed as too advanced. At the same time, these new manipulatives will provide older students (in middle school and beyond) new ways of exploring and understanding concepts that they previously studied only through more abstract formalisms.

Imagine, for example, a set of computationally-enhanced beads, which communicate with neighboring beads and turn different colors based on the interactions. By playing with these beads, children could begin to gain an understanding of how large-scale dynamic patterns can "emerge" from local interactions – an idea traditionally not studied until college.

We believe that these new manipulatives can combine the best of the physical and digital worlds, drawing on children’s passions and intuitions about physical objects, but extending those objects to allow new types of explorations. In this way, digital manipulatives are starkly different from traditional uses of computers in education, which tend to draw children away from physical-world interactions. An important aspect of our research will involve the development of principles to guide the design of digital manipulatives – and, just as important, the design of the surrounding environments in which the manipulatives are used. One design goal, of course, is to make mathematical and scientific concepts salient and manipulable, in the spirit of Cuisenaire Rods. At the same time, we believe that digital manipulatives should enable children to engage in personally-meaningful design activities, in the spirit of LEGO bricks.

Project Goals

In this project, we propose to develop a collection of new "digital manipulatives" by embedding computational power in traditional children’s toys such as blocks, beads, and balls. The core of our research will involve the study of children using our manipulatives in a collection of schools and informal-learning settings (focusing especially on underserved communities), with the larger goals of:

- Extending theories on the role of manipulatives in children’s learning – and developing principles for the design and assessment of digital manipulatives
. Key issues include: What affordances are provided by physical objects (in comparison with "virtual objects" and symbolic representations)? In what ways can manipulative materials become "social objects" (facilitating collaboration, sharing, and trading)? What types of relationships and affective associations do children form with manipulative materials, and what role do those relationships play in children’s learning? How can we describe and assess children’s "fluency" with manipulative materials? Our evolving understanding of the role of manipulatives in children’s learning (along with our previous research on the role of design activities in children’s learning) will guide us in the development of principles for the design of new digital manipulatives. In particular, we will examine how to combine the affordances of the digital world with the affordances of the physical world.

- Rethinking elementary math-science curricula to place greater emphasis on concepts related to dynamic processes – and developing a deeper understanding of children’s mental models of these knowledge domains
. As new technologies and materials become available, it is important to rethink what elementary-school children can and should learn. Our hypothesis is that digital manipulatives will help elementary children learn important mathematical and scientific concepts that were previously considered "too advanced." In particular, we expect that these new manipulatives will help children explore concepts related to dynamic processes, patterns, and behaviors – concepts that previously were taught primarily in later grades, through manipulation of abstract, symbolic representations. To make these concepts more accessible, we need to develop new representations that are suitable for manipulation by young children. As part of this effort, we need to develop a deeper understanding of children’s intuitions and mental models of these concepts. Our understanding of children’s mental models will, in turn, guide our design of new digital manipulatives (and activities using the manipulatives).

Theoretical Frameworks

Our proposed research builds on the long tradition of manipulative materials in education, drawing on ideas of educational pioneers such as Pestalozzi (1803), Fröbel, and Montessori (1912). In recent times, mathematics educators have continued to embrace the idea of manipulatives. The NCTM document (1989, p. 17), for instance, recommends their use in K-4 classrooms; and traditional objects such as geoboards, balance beams, tangrams, and pattern blocks have retained their popularity.

At least some recent research supports this general tone of optimism. Serbin and Connor (1979) found a positive correlation between play with various manipulative toys (blocks, Lincoln Logs, etc.) and visual-spatial performance. Similarly, Mitchelmore (1980), in a cross-cultural study, found British students to be developmentally ahead of their American counterparts in certain spatial abilities by three years and suggested that at least part of this observed gap was due to the prevalence of manipulatives in British classrooms (and their relative scarcity in American classrooms). But there have also been cautionary notes: Resnick and Omanson (1987) observed that children, in arithmetic classes, do not always succeed in linking the use of manipulatives to the mathematical concepts or operations that these objects are supposed to illuminate, while Ball (1992) laments that "[t]here is little open, principled debate about the purposes of using manipulatives and their appropriate role in helping students learn."

Our research is intended to invigorate the type of debate advocated by Ball. We believe that the landscape of mathematical manipulatives can be vastly enriched by the ongoing explosion of powerful, portable, and expressive computational media. But at the same time, this renewed interest in manipulative design must be accompanied by greater insight into the mechanisms – cognitive, affective, and social – by which manipulatives contribute (or fail to contribute) to children’s learning. Creating new manipulatives affords the opportunity for conducting integrative research in all the various dimensions of design – the mathematical dimension (identifying concepts that are both powerful and generative); the cognitive dimension (identifying what aspects of these powerful concepts prove most resistant to visual or tangible understanding); the dimension of play (asking what elements of manipulative design can make these new objects creative, expressive, and inspiring); and the technological dimension (finding new ways of exploiting computational and material technology in the service of manipulative design).

In that final (technological) dimension, our work relates to current research on ubiquitous computing (Weiser, 1991; Tinker, 1997). That research, like our own, aims to extend computation beyond the desktop, integrating digital technology into everyday objects and putting computation at people’s fingertips. But while most educational applications of ubiquitous computing aim to provide students with anywhere-anytime access to information, we take a much more design-oriented approach, aiming to provide students with new types of objects for building and constructing. We view our digital manipulatives as building blocks with which students can compose in many different ways. Our approach grows out of a constructionist philosophy of education (Papert, 1994), emphasizing the importance of enabling children to create their own personalized, meaningful, and sharable artifacts.

Our proposed research grows most directly out of our own NSF-sponsored Beyond Black Boxes project (Resnick, Berg, & Eisenberg, 2000). In that project, we have developed new technologies and project materials that enable children to build their own scientific instruments – enabling today’s children, like scientists of earlier eras, to become engaged in scientific inquiry not only through observing and measuring but also through designing and building. For this and other related projects, we have developed a family of programmable bricks that children can use to add dynamics and behaviors to their constructions (Martin, 1994; Resnick, Martin, Sargent, & Silverman, 1996). These programmable bricks, which led to the introduction of a commercial product (called LEGO MindStorms) in 1998, can be viewed as the technological forerunners of our proposed digital manipulatives. We designed our programmable bricks primarily for children in grades 6-12. Our new digital-manipulatives research grows out of our interest in making these types of ideas and technologies accessible to younger children.

Learning About (and Through) Dynamic Processes

Children are naturally curious about the dynamics of the world – how things change over time, how patterns form, how behaviors arise. And these ideas are clearly important for understanding the workings of the world. The NCTM standards (1989) call for an increased focus on dynamic processes (and concepts relating to "change over time") from the earliest grades. Yet ideas related to dynamic processes are under-represented in elementary and middle schools, in part because a lack of tools and materials that enable children to manipulate and explore dynamic processes.

We believe that new computational media (and, in particular, digital manipulatives) provide an unprecedented opportunity to elevate the role of dynamic processes in elementary math and science education. We envision introducing dynamic processes in two ways. First, we aim to help children learn about dynamic processes, to help them explore and understand the key concepts underlying the behavior of dynamic systems. At the same time, we aim to help children learn through dynamic processes, enabling them to create and use dynamic representations to explore a wide range of mathematical and scientific concepts that have traditionally been studied through static representations.

In this section, we present two extended examples. In one, we describe how children might use digital manipulatives to learn about dynamic processes, focusing particularly on the concept of emergence, which underlies the workings of many dynamic systems. In the other, we describe how children can learn through dynamic processes, proposing a dynamic-process approach to the concept of functions, focusing on the ways that "outputs" vary dynamically as "inputs" change.

Clearly, these two examples are just a first step in the full integration of dynamic processes into elementary mathematics and science education. We believe that these two areas represent a good place to start, and will lay the foundation for future research efforts. In the course of this project, we expect to broaden both the conceptual areas that we explore and the technologies that we employ.

Emergence

In the past few years, a growing number of researchers have begun to study how people make sense of systems with lots of interacting parts (Chi, 2000, Perkins and Grotzer, 2000; Resnick, 1994, 1999). In our own research, we have found that students tend to have what we call a "centralized mindset": they assume that all dynamic patterns arise from centralized causes when, in fact, many dynamic patterns "emerge" from simple interactions among the component parts. For example, most students assume that the birds in a flock are all following a single leader. In fact, orderly flock patterns arise from simple, local interactions: each bird follows a set of simple rules, reacting to the movements of neighboring birds.

Many systems in the world work the same way. Market economies, highway traffic, ant colonies, immune systems – in all of these systems, patterns are determined not by some centralized authority but by local interactions among decentralized components. Indeed, decentralized systems play an important role in all of the sciences and social sciences, yet most people have great difficulty understanding the workings of such systems.

We believe that this difficulty arises, in part, from the lack of tools that enable people to create, explore, and "play with" decentralized systems. In previous research, we developed a programmable on-screen environment, called StarLogo, that enables people to build their own models of bird flocks, market economies, and other decentralized systems. We found that students, by building such systems, developed much better understandings of the concept of "emergence." But StarLogo was designed primarily for high-school students: it requires users to master a formal programming language. We believe that new digital manipulatives could make the concept of emergence accessible to much younger students.

For example, we plan to develop a set of "digital beads" with which children can create (and play with) emergent patterns. In recent years, beads have become increasingly popular among children, especially young girls. There are entire stores with nothing but bins of beads of varying colors and sizes. Children string beads together to create colorful necklaces and bracelets. With traditional beads, children create colorful but static patterns. With our new digital beads, children will create dynamic patterns.

We have already created an initial prototype: each bead has a built-in microprocessor and small light, and it communicates with neighboring beads by simple inductive coupling. Different beads can have different programs or rules. Some beads pass the light to the next bead along the string, other beads reflect the light back, still others "swallow" the light. Imagine a necklace made of "passing beads," with "reflector beads" at the ends. If we start a light on one of the beads, it will travel from one end of the necklace to the other, bouncing back and forth.

Imagine we introduce lights of two different colors: red and blue. Let’s say that the passing beads have the following rule to handle "colliding lights": if two lights arrive at a passing bead at the same time, each light is reflected back. So what happens to the red and blue lights? If they happen to collide at the center, each light will "own" half of the necklace, each bouncing back and forth within its own half. But what if they collide elsewhere along the necklace? Then you will get two different collision points, with collisions alternating between them. Now imagine that the red light travels twice as fast as the blue light. What pattern will emerge?

We believe that digital beads can also provide a meaningful and motivating context for children to begin thinking about probabilistic behaviors. What if each bead passes the light to the next bead half of the time but reflects the light back to the previous bead the other half of the time? By stringing a set of these beads together, children can explore random-walk behaviors. If the string has ten beads, and the light starts in the middle, how long will it take to reach the ends? What if you then add a bead that passes the light three-quarters of the time and reflects it just one-quarter of the time? How will that change the overall dynamic pattern? Most children (indeed, most people) have poor intuitions about such systems (Wilensky, 1993). Our hypothesis is that children who grow up playing with digital beads will develop much richer intuitions about probabilistic behaviors.

It is clear that even very simple rules for the beads can lead to interesting (and unexpected) patterns along the necklace. And slight changes in the behavior or placement of one of the beads can lead to the emergence of an entirely different pattern in the overall collection.

Of course, the beads are not nearly as versatile as StarLogo for creating and exploring emergent phenomena. But we expect that children, by playing with the beads, will begin to develop some of the conceptual "building blocks" for understanding emergence, developing an initial fluency with the ideas of rules, local interaction, and dynamic patterns. Obviously, a child’s understanding of these concepts will not be the same as a scientist’s understanding. In our study of children using the digital beads, we will examine what it means for young students to "understand" the concept of emergence – and how can this "kid-level understanding" provide a basis for a more sophisticated understanding over time.

Functions

When the concept of a "function" is introduced in school, generally at the middle-school level, the initial focus is on functions as collections of "ordered pairs." These pairs are sometimes represented in a table, sometimes as a line graph. But there is another way of thinking about functions which has a stronger connection to children’s everyday experiences, drawing on their intuitions about cause and effect. This alternative formulation offers a more dynamic conception of functions, focusing on the ways that "outputs" vary dynamically as "inputs" change. (For an overview of approaches of teaching and learning about functions, see Harel & Dubinsky, 1992.)

Why has the ordered-pair approach become much more common in schools? In part because it is better suited to the media that have been most prevalent in schools over the past 100 years: paper and pencil, blackboard and chalk. In contrast, the dynamics-oriented approach is particularly well-suited to computational media. Thus, there is now an opportunity to rethink the ways that children are introduced to the concept of functions.

We plan to develop a new set of "digital blocks" that embody this more dynamics-oriented approach to functions – and, we hope, make the concept of functions accessible to younger children than was possible in the past. Imagine three of these blocks on a tabletop. On the left is a block with a crank; on the right is a "music block." In the middle is a "function block" that represents a monotonically-increasing function. When you turn the crank, music starts playing. The faster you turn the crank, the louder the music.

You can replace the middle block with a new block representing a monotonically decreasing function. Now, when you turn the crank faster, the music becomes quieter. If you replace the crank-block with a light-sensor block, you can control the music with a flashlight, or by casting shadows with your hand. The less light that hits the sensor block, the louder the music. Replace the music block with a motion block, and the motion block will speed up when you cast a shadow on the sensor block.

There will be three categories of digital blocks: sensor blocks, function blocks, and action blocks. The digital blocks will look and feel like traditional building blocks, but each will have a tiny computer embedded inside. The blocks will communicate with their neighbors via infrared light. The sensor blocks send signals to the function blocks, which in turn send modified signals to the action blocks. We plan to create a variety of all three types of blocks. For example, there will be a function block representing a step function, a sensor block that reacts to your clapping, an action block with a collection of lights.

In the spirit of previous research in which children created graphical representations of functions through their own motions (Mokros & Tinker, 1987), the digital blocks help reify the concept of a function, providing a much more concrete and accessible introduction to the concept. We believe the digital blocks will enable children to form a more personal connection to the concept. When children turn the crank block, they can literally feel their input to the function. And by designing their own action blocks (for example, a moving-sculpture block), they can personalize the outputs.

Empirical Studies and Evaluation

We will pursue our project goals through an iterative design process, in the spirit of design experiments (Brown, 1992). Throughout the course of the project, we will continually design not only new artifacts but also new educational environments and supports. We will systematically study the evolution of student thinking and activity within these environments, then adapt and modify the artifacts and environments based on our observations. Through this cyclical process, we expect to develop a stronger framework for both the theory and practice of children’s learning with digital manipulatives.

We will assess our ideas and technologies in a variety of different educational settings. The PIs will work most closely with sites in Boston and Colorado, working with children of elementary school age (K-6) in both school and non-school settings, with special focus on children from underserved communities. In Colorado, we will work closely with the Collage Children’s Museum in Boulder, a museum with which we have established a long-term working relationship. In Boston, we will work closely with Alma Wright, a member of our Board of Advisors (see below), with whom we have collaborated for more than a decade. Wright teaches a multi-grade first/second grade class at a Boston public elementary school, and she is a recipient of the prestigious Milken Educator Award. We will work with older children (upper elementary and middle-school ages) at Computer Clubhouses, a network of after-school learning centers for inner-city youth (Resnick, Rusk, and Cooke, 1998). Some members of our Board of Advisors also plan to use the digital manipulatives within their own research projects. For example, Rich Lehrer and Leona Schauble, educational psychologists at University of Wisconsin, will use the manipulatives as part of their longitudinal investigation of young elementary students’ scientific reasoning about central themes in science. During the course of the project, we will hold regular sessions with teachers from our local sites, to introduce them to new materials, work with them in organizing classroom activities, and get feedback from their classroom experiences. We will also organize annual workshops to bring together researchers and teachers from all of the research sites.

Our strategy for evaluating both children’s work with our manipulatives and our design of the manipulatives will employ a variety of techniques. Members from our research team will work directly with children at the local sites, to trace the evolution of children’s thinking and activity. We will rely primarily on an in-context interviewing approach a variant of Piagetian interviewing in which we help children in their ongoing work but also ask questions to probe their thinking and understanding. In addition, we will conduct structured interviews with children. All interview sessions will be audiotaped and/or videotaped for later analysis.

There are several major research themes that will underlie our evaluative work. These themes are summarized below:

The cognitive role of manipulatives

. As suggested earlier by the quote from Ball, there is still a great deal of mystery and speculation about how (and whether) manipulatives "work" educationally. A recurring theme in much work on mathematical cognition is the role played by visual imagery and spatial visualization in mathematical and scientific problem-solving and creativity (Miller, 1984; Ferguson, 1992; Sutherland and Mason 1995). It is plausible that traditional manipulatives play a role in providing and exercising a repertoire of "standard images" for notions such as number and place notation, and we expect that digital manipulatives will play a similar role in providing images for concepts related to dynamic processes. We believe that previous research on mathematical and physical imagery can be incorporated into, and extended by, design investigations of digital manipulatives. For example, we plan to explore whether a child who has played extensively with digital blocks resorts to those blocks for imagery in solving problems that involve functions, or in encountering a novel concept such as the composition of functions. In a similar vein, we plan to compare that child’s visual (and physical) associations with functions with those of a student who had not worked with the manipulatives.

One of our major goals is to develop a richer understanding of how children make sense of dynamic processes, and how their models of these processes evolve through their interactions with the digital manipulatives. Our research will be in the spirit of diSessa’s work (1983) on phenomenological primitives (or "p-prims"), which he sees as basic cognitive building blocks (possibly associated with abstract visual imagery) that people rely for constructing explanations. For example, people rely on the "Ohm’s Law" p-prim ("more effort begets more results") to build up models of "agency" and "resistance." We plan to do similar analyses of children’s understanding of concepts related to "emergence" and "function." What are the cognitive building blocks that children use to construct explanations of these concepts? Note that we are not starting with a preconceived notion of what it means for children to "understand" these concepts. Developing a better understanding of what it means for children to understand these concepts is part of our research agenda – and will certainly influence the design of future manipulatives and activities.

A typical element of many such cognitive studies involves the (often thorny and controversial) notion of cognitive transfer. If manipulatives – whether digital or not – do indeed play a role in fostering or exercising mathematical imagery, then ideally the visual representations that they provide will transfer to more symbolic or abstract problem-solving. We will vigorously investigate this question for our own designs, with an eye toward comparing the possibilities of cognitive transfer in digital manipulatives to those associated with more traditional objects.

Fluency and expertise with manipulatives

. The paragraphs above focused on the "interior" cognitive role of manipulatives – i.e., how a child’s construction of mental models of mathematical and scientific concepts is shaped by experiences with manipulatives. A related, but not quite identical, issue focuses on "exterior" measures of progress: what does it mean for a child to become a fluent, creative, or productive user of manipulatives? This is a particularly interesting question for the types of digital manipulatives that we have in mind, as many of these (such as the beads and blocks) are intended for creative, open-ended, and long-term play.

We believe that assessment of the educational role of digital manipulatives must include attention to the ways in which children’s vocabulary, language, and (where applicable) personal "notations" develop in the course of use. How, for instance, would a child describe a particular bead pattern after one, three, or six months of experience with the materials? Or, how do the notations developed by children when describing ideas related to mathematical functions compare to conventional notations? Can we use insights gained from studying these notations to identify effective strategies for making connections to more abstract representations? What are the metrics by which we can identify growth of expertise, or obstacles to understanding? How do children communicate their ideas and insights about the behavior of the manipulatives? Investigating questions such as these will be particularly useful in designing educational environments and supports in addition to the manipulatives themselves.

The social dimension

. Historically, mathematical manipulatives have been seen as tools for early education (and very young children) exclusively; older students and adults often feel a mild sense of embarrassment at the suggestion that they might employ tangible materials to aid or motivate abstract understanding. This cultural state of affairs is reinforced by subtle (and not-so-subtle) design decisions: for many traditional manipulatives the bold primary colors, sturdy materials, and oversized fumble-proof dimensions are clear indicators of a youthful target audience. Nonetheless, there are also objects that might be seen as "advanced manipulatives" for older students and adults. For example, Rubik’s Cube could well be interpreted as a manipulative for the basic concepts of group theory; and the long-term popularity of the Cube (and similar mathematical puzzles) suggests that there is indeed a receptive older audience for well-designed manipulatives. One of our research themes, then, will be to investigate (through the techniques discussed above) the ways in which students at different ages interact with our manipulatives. An important element of these investigations will be a look at the social role played by manipulatives in group and classroom settings: how are these objects shared, how (if at all) are collaborative projects undertaken, how are insights exchanged, how (when applicable) are creations put on display? These explorations will in turn inform our design principles for future generations of manipulatives; our goal is to develop heuristics that could "tune" a particular manipulative design toward older or younger children, individual or collaborative work, short-term or long-term use, and so forth.

Implementation Plan and Dissemination

Year 1

. During the first six months, we will focus primarily on development of technologies and activities. We will adopt a highly iterative approach to the design process, making use of regular pilot studies with a small numbers of participants at our local sites to guide the development. We will start by developing initial versions of the digital beads and digital blocks discussed earlier in the proposal. In our initial work with children, we will set up open-ended activities to see how children play with these new objects, what difficulties they have, what goals they set for themselves, and what language they use to describe their interactions. Based on these initial observations, we will develop more structured activities, designed to probe children’s thinking about the concepts of emergence and functions. In summer 2001, we will hold the first of our annual workshops with our collaborating teachers and educators.

Year 2

. During the second year, we will expand our pilot studies, working with larger number of children at our local sites. We will continue to revise the designs of the beads and blocks, based on our classroom experiences. And we will begin deeper and more textured evaluation studies, focusing on issues of children’s cognitive development and fluency with manipulatives (as described in the Empirical Studies and Evaluation section). During this year, we will also examine how our activities with beads and blocks (and the concepts associated with the activities) could be integrated into the elementary and middle school curricula. Our goal is to build a compelling case to expand the mathematics and science standards for elementary-school to place greater emphasis on concepts associated with dynamic processes. Based on our classroom studies, we expect to expand the scope of our study beyond the initial focus on "emergence" and "functions," developing other manipulatives to help children explore other concepts related to dynamic processes.

Year 3

. We expect some of our digital manipulatives to move into regular use in some of our research sites (while our "second generation" manipulatives, initiated during Year 2, move into pilot studies). In our evaluation studies of classroom use, we will focus especially on the "social dimension": how the new manipulatives fit into (and influence) the culture of the classroom. We will also continue to work on the development of support and curricular materials. By the end of Year 3, we expect that technologies and activities will be ready for widespread dissemination, and we will begin discussions with commercial developers to arrange for dissemination.

Throughout the project, we will disseminate our ideas through traditional academic channels: by publishing in major research journals, participating in major conferences, and advising organizations that develop curriculum standards. Many educational-research projects never move beyond the prototype stage. But we have strong reason to believe that our technologies and activities will eventually be used in large numbers of classrooms (and other educational settings). Our research team has a very strong track record for disseminating educational-technology innovations. More than a decade ago, members of our research team developed the first computerized construction kit, called LEGO/Logo. This technology, commercialized by the LEGO company, has been used in more than one-third of all K-12 schools in the United States, reaching millions of children. Our group also developed the technologies and ideas underlying the LEGO MindStorms "programmable brick" product. The LEGO company released this product for both home and school markets in 1998, and sold nearly 100,000 units in the first three months. We expect that our digital manipulatives to follow the same path toward widespread use in classrooms and homes.

Project Team

Principal Investigators Mitchel Resnick, Mike Eisenberg, Robbie Berg, and Bakhtiar Mikhak will lead teams of graduate-student researchers and undergraduates at their respective institutions. The PIs each blend together backgrounds in scientific disciplines and computer science, with extensive experience in educational research and cognitive science. Their research combines the design of new computational technologies with analysis of how and what students learn through the use of those technologies. They are regular contributors at major educational-research and cognitive-science conferences, and have published extensively in educational-research journals.

Diane Willow will serve as Education Director of the project, coordinating observations and evaluations of children’s learning experiences with digital manipulatives, and also contributing to the design of new manipulatives. With a background in child development and early-childhood education, Willow has extensive experience working with preschool and elementary-school children, parents, care givers and educators. She worked for 14 years as a developer of educational programs and exhibits at the Boston Children’s Museum, developing materials and environments for scientific inquiry and artistic expression. She currently serves as Artist-in-Residence at MIT.

In support of our observations and evaluation studies, we will also hire a post-doctoral researcher who will focus on analysis of children’s evolving conceptions and understandings.