Dialogue on Early Childhood Science, Mathematics, and Technology Education

First Experiences in Science, Mathematics, and Technology

Young Children and Technology

Douglas Clements

Computers are increasingly present in early childhood education settings. Toward the end of the 1980s, only one-fourth of licensed preschools had computers. Today almost every preschool has a computer, with the ratio of computers to students changing from 1:125 in 1984 to 1:22 in 1990 to 1:10 in 1997. This last ratio matches the minimum ratio that is favorable to social interaction (Clements and Nastasi 1993; Coley et al. 1997). During the last 13 years, perspectives on the principle of developmental appropriateness have become more sophisticated. Researchers have extended these perspectives to include such dimensions as cultural paradigms and multiple intelligences (Bowman and Beyer 1994; Spodek and Brown 1993).

Research on young children and technology similarly has moved beyond simple questions to consider the implications of these changing perspectives for the use of technology in early childhood education. For example, we no longer need to ask whether the use of technology is “developmentally appropriate.” Very young children have shown comfort and confidence in using software. They can follow pictorial directions and use situational and visual cues to understand and think about their activity (Clements and Nastasi 1993). Typing on the keyboard does not seem to cause them any trouble; if anything, it is a source of pride.

With the increasing availability of hardware and software adaptations, children with physical and emotional disabilities can also use the computer with ease. Besides enhancing their mobility and sense of control, computers can help improve their self-esteem. One totally mute four-year-old with diagnoses of retardation and autism began to echo words for the first time while working at a computer (Schery and O’Connor 1992). However, such access is not always equitable across our society. For example, children attending low-income and high-minority schools have less access to most types of technology (Coley et al. 1997).

Research has also moved beyond the simple question of whether computers can help young children learn. They can. What we need to understand is how best to aid learning, what types of learning we should facilitate, and how to serve the needs of diverse populations. In some innovative projects, computers are more than tools for bringing efficiency to traditional approaches. Instead, they open new and unforeseen avenues for learning. They allow children to interact with vast amounts of information from within their classrooms and homes. They tie children from across the world together (Riel 1994).

Not every use of technology, however, is appropriate or beneficial. The design of the curriculum and social setting are critical. This paper reviews the research in three broad areas: social interaction, teaching with computers, and curriculum and computers. Finally, it describes a new project that illustrates innovative, technology-based curriculum for early childhood education.

Social Interaction

clements1.jpg (10961 bytes)An early concern, that computers will isolate children, was alleviated by research. In contrast, computers serve as catalysts for social interaction. The findings are wide-ranging and impressive. Children at the computer spent nine times as much time talking to peers while on the computer than while doing puzzles (Muller and Perlmutter 1985). Researchers observe that 95 percent of children’s talking during Logo work is related to their work (Genishi et al. 1985). (Logo is a computer programming language designed to promote learning. Even young children can use it to direct the movements of an on-screen “turtle.”) Children prefer to work with a friend rather than alone. They foster new friendships in the presence of the computer. There is greater and more spontaneous peer teaching and helping when children are using computers (Clements and Nastasi 1992).

The software they use affects children’s social interactions. For example, open-ended programs such as Logo foster collaboration. Drill-and-practice software, on the other hand, can encourage turn-taking but also competition. Similarly, video games with aggressive content can engender competitiveness and aggression in children. Used differently, however, computers can have the opposite effect (Clements and Nastasi 1992). In one study, a computer simulation of the playhouse from the animated t.v. series The Smurfs attenuated the themes of territoriality and aggression that emerged with a real playhouse version of the Smurf environment (Forman 1986).

The physical environment also affects children’s interactions (Davidson and Wright 1994). Placing two seats in front of the computer and one at the side for the teacher can encourage positive social interaction. Placing computers close to each other can facilitate the sharing of ideas among children. Centrally located computers invite other children to pause and participate in the computer activity. Such an arrangement also helps to keep teacher participation at an optimum level. Teachers are nearby to provide supervision and assistance as needed, but they are not constantly so close as to inhibit the children (Clements 1991).

Teaching with Computers

The computer offers unique advantages in teaching. Opportunities to aid learning are addressed in the following section. Technology also offers unique ways to assess children. Observing the child at the computer provides teachers with a “window into a child’s thinking process” (Weir et al. 1982). Research has also warned us not to curtail observations after a few months. Sometimes, beneficial effects appear only after a year. Ongoing observations also help us chart children’s learning progress (Cochran-Smith et al 1988).

Differences in learning styles are more readily visible at the computer, where children have the freedom to follow diverse paths towards a goal (Wright 1994). This flexibility is particularly valuable with special children, as the computer seems to reveal their hidden strengths. Different advantages emerge for other groups of children. For example, researchers have found differences in Logo programming between African-American and Caucasian children. The visual nature of Logo purportedly was suited to the thinking style of African-American children’s thinking style (Emihovich and Miller 1988).

Gender differences also emerge when children engage in programming. In one study, a post-test-only assessment seemed to indicate that boys performed better. However, assessment of the children’s interactions revealed that the boys took greater risks and thereby reached the goal. In comparison, girls were more keen on accuracy; they meticulously planned and reflected on every step (Yelland 1994). Again, the implication for teaching is the need for consistent, long-term observation.

Yet another opportunity offered us by technology is to become pioneers ourselves. Because we know our children best, we can best create the program that will help them. Frustrated by the lack of good computer software, Tom Snyder started using the computer to support his classroom simulations of history. Mike Gralish, a first-grade teacher, used several computer devices and programs to link the base-10 blocks and the number system for his children. Today, both of these gentlemen are leading educational innovators (Riel 1994).

To be innovators and to keep up with the growing changes in technology, teachers need in-service training. Research has established that less than 10 hours of training can have a negative impact (Ryan 1993). Others have emphasized the importance of hands-on experience and warned against brief exposure to a variety of software programs, encouraging an in-depth knowledge of one program (Wright 1994).

Curriculum and Computers

The computer also offers unique opportunities for learning through exploration, creative problem solving, and self-guided instruction. Realizing this potential demands a simultaneous focus on curriculum and technology innovations (Hohmann 1994). Effectively integrating technology into the curriculum demands effort, time, commitment, and, sometimes, even a change in one’s beliefs.

We begin with several overarching issues. What type of computer software should be used? Drill-and-practice software leads to gains in certain rote skills. However, it has not been as effective in improving the conceptual skills of children (Clements and Nastasi 1993). Discovery-based software that encourages and allows ample room for free exploration is more valuable in this regard. However, research has shown that children work best with this type of software when they are assigned to open-ended projects rather than asked merely to “free explore” (Lemerise 1993). They spend more time and actively search for diverse ways to solve the task. The group of children who were allowed to free explore grew disinterested quite soon.

clements2.jpg (11214 bytes)Another concern was that computers would replace other early childhood activities. Research shows that computer activities yield the best results when coupled with suitable off-computer activities. For example, children who are exposed to developmental software alone—the on-computer group—show gains in intelligence, non-verbal skills, long-term memory, and manual dexterity. Those who also worked with supplemental activities, in comparison—the off-computer group—gained in all of these areas and improved their scores in verbal, problem-solving, and conceptual skills (Haugland 1992). In addition, these children spent the least amount of time using the computers. A control group that used drill-and-practice software spent three times as long on the computer but showed less than half of the gains that the on- and off-computer groups did. Given these capabilities of the computer, how has it affected children’s learning?

In mathematics specifically, the computer can provide practice on arithmetic processes and foster deeper conceptual thinking. Drill-and-practice software can help young children develop competence in counting and sorting (Clements and Nastasi 1993). However, it is questionable if the exclusive use of such drill-and-practice software would subscribe to the vision of the National Council of Teachers of Mathematics (NCTM) (1989): Children should be “mathematically literate” in a world where the use of mathematics is becoming more and more pervasive. NCTM recommends that we “create a coherent vision of what it means to be mathematically literate both in a world that relies on calculators and computers to carry out mathematical procedures and in a world where mathematics is rapidly growing and is extensively being applied in diverse fields” (National Council of Teachers of Mathematics 1989). This vision de-emphasizes rote practice on isolated facts. It emphasizes discussing and solving problems in geometry, number sense, and patterns with the help of manipulatives and computers.

For example, using software programs that allow the creation of pictures with geometric shapes, children have demonstrated growing knowledge and competence in working with concepts such as symmetry, patterns, and spatial order. Tammy overlaid two overlapping triangles on one square and colored select parts of this figure to create a third triangle that did not exist in the program! Not only did this preschooler exhibit an awareness of how she had made this figure, but she also showed awareness of the challenge it would be to others (Wright 1994). Using a graphics program with three primary colors, young children combined these colors to create three secondary colors (Wright 1994). Such complex combinatorial abilities are often thought to be out of the reach of young children. The computer experience led the children to explorations that expanded their boundaries.

Young children can also explore simple “turtle geometry.” They direct the movements of a robot or screen “turtle” to draw different shapes. One group of five-year-olds was constructing rectangles. “I wonder if I can tilt one,” mused one boy. He turned the turtle with a simple mathematical command, “L 1” (turn left one unit), drew the first side, then was unsure about what to do next. He finally figured out that he must use the same turn command as before. He hesitated again. “How far now? Oh, it must be the same as its partner!” He easily completed his rectangle. The instructions he should give the turtle at this new heading were, at first, not obvious. He analyzed the situation and reflected on the properties of a rectangle. Perhaps most important, he posed the problem for himself (Clements and Battista 1992).

This boy had walked rectangular paths, drawn rectangles with pencils, and built them on geo-boards and pegboards. What did the computer experience add? It helped him link his previous experiences to more explicit mathematical ideas. It helped him connect visual shapes with abstract numbers. It encouraged him to wonder about mathematics and pose problems in an environment in which he could create, experiment, and receive feedback about his own ideas.

Such discoveries happen frequently. One preschooler made the discovery that reversing the turtle’s orientation and moving it backwards had the same effect as merely moving it forwards. The significance the child attached to this discovery and his overt awareness of it was striking. Although the child had done this previously with toy cars, Logo helped him abstract a new and exciting idea (Tan 1985).

Building Blocks©: An Innovative Technology-Based Curriculum

At present, Julie Sarama and I are developing innovative pre-K to grade 2 curriculum materials. The project, “Building Blocks—Foundations for Mathematical Thinking, Pre-Kindergarten to Grade 2: Research-based Materials Development,” is funded by a grant from the National Science Foundation. It is designed to enable all young children to build solid content knowledge and develop higher-order thinking. The program’s design is based on current theory and research and represents a state-of-the-art technology curriculum for young children in the area of mathematics. It is discussed in this paper in that light. The reader might notice that our description does not begin with a listing of its technologically sophisticated elements, including multimedia features. This strategy is deliberate. We emphasize the art and science of teaching and learning, in contrast to many early childhood software programs, which use technologically advanced bells and whistles to disguise ordinary activities.

The design of a state-of-the-art curriculum must begin with audience considerations. The demographics of this age range imply that materials should be designed for home, daycare, and classroom environments and for children who have various backgrounds, interests, and ability levels. To reach this broad audience, the curriculum materials will be progressively layered: Users will be able to “dig deeper” into them to reach increasingly rich, but demanding, pedagogical and mathematical levels. The materials should not rely on technology alone. They should integrate three types of media: computers, manipulatives (and everyday objects), and print.

clements3.jpg (10492 bytes)The project’s basic educational approach is finding the mathematics in children’s activities and developing mathematics from them. We focus on helping children extend and find mathematics in their everyday activities, from building blocks to art to songs to puzzles. Thus, we will design activities based on children’s experiences and interests, with an emphasis on supporting the development of mathematical activity. This process emphasizes representation: using mathematical objects and actions that relate to children’s everyday activities. Our materials will embody these actions-on-objects in a way that mirrors the theory of and research on children’s cognitive building blocks—creating, copying, uniting, and dis-embedding both units and composite units.

Perhaps the most important aspect of the project’s material design is our model for the design process. Curriculum and software design can and should have an explicit theoretical and empirical foundation, beyond its genesis in someone’s intuitive grasp of children’s learning. It should also interact with the ongoing development of theory and research, reaching toward the ideal of testing a theory by testing the software and the curriculum in which it is embedded. In this model, one conducts research at multiple aggregate levels, making the research relevant to educators in many positions. We have cognitive models with sufficient explanatory power to permit the design to grow co-jointly with the refinement of these cognitive models (Biddlecomb 1994; Clements and Sarama 1995; Fuson 1992; Hennessy 1995).

The phases of our nine-step design process model follow.

  1. Draft curriculum goals.
  2. Build an explicit model of children’s knowledge and learning in the goal domain.
  3. Create an initial design.
  4. Investigate components.
  5. Assess prototypes and curriculum.
  6. Conduct pilot tests.
  7. Conduct field tests in multiple settings.
  8. Recurse.
  9. Publish and disseminate.

These phases include a close interaction between materials development and a variety of research methodologies, from clinical interviews to teaching experiments to ethnographic participant observation.

A new technology permits the reflective consideration of objects, actions, and activities, which can help developers re-conceptualize the nature and content of mathematics that might be learned. The developer can also conceive new designs by reflecting on how software might provide tools that enhance students’ actions and imagination or that suggest an encapsulation of a process or obstacles that force students to grapple with an important idea or issue. Finally, the flexibility of computer technologies allows the creation of a vision less hampered by the limitations of traditional materials and pedagogical approaches (cf. Confrey, in press). For example, computer-based communication can extend the model for mathematical learning beyond the classroom. Computers can allow representations and actions not possible with other media. The materials in Building Blocks will not only ensure that computerized actions-on-objects mirror the goal concepts and procedures, but also that they are embedded in tasks and developmentally appropriate settings (e.g., narratives, fantasy worlds, building projects).

The materials will emphasize the development of basic mathematical building blocks—ways of knowing the world mathematically. These building blocks will be organized into two areas: (1) spatial and geometric competencies and concepts; and (2) numeric and quantitative concepts, based on the considerable research in that domain. Three mathematical sub-themes will be woven through both main areas: (1) patterns and functions; (2) data; and (3) discrete mathematics (e.g., classifying, sorting, sequencing). Most important will be the synthesis of these domains, each to the benefit of the other. The building blocks of the structure are not elementary school topics “pushed down” to younger ages; they are developmentally appropriate domains, that is, topics that are meaningful and interesting to children. Access to topics such as large numbers or geometric ideas such as depth, however, are not restricted. In fact, research indicates that these concepts are both interesting and accessible to young children.

By presenting concrete ideas in a symbolic medium, for example, the computer can help bridge these two concepts for young children. But are these manipulatives still “concrete” on the computer screen? One has to examine what concrete means. Sensory characteristics do not adequately define it (Clements and McMillen 1996; Wilensky 1991). First, it cannot be assumed that children’s conceptions of the manipulatives are similar to those of adults (Clements and McMillen 1996). Second, physical actions with certain manipulatives may suggest different mental actions than those we wish students to learn. For example, researchers found a mismatch among students using the number line to perform addition. When adding five and four, the students located the number 5, counted “one, two, three, four” and read the answer. This action did not help them solve the problem mentally, for to do so they have to count “six, seven, eight, nine” and at the same time count the counts—6 is 1, 7 is 2, and so on. These actions are quite different (Gravemeijer 1991).

Thus, manipulatives do not always carry the meaning of the mathematical idea. Students must use these manipulatives in the context of well-planned activities and ultimately reflect on their actions in order to grasp the idea. Later, we expect them to have a “concrete” understanding that goes beyond these physical manipulatives.

It appears that there are different ways to define concrete (Clements and McMillen 1996). We define sensory-concrete knowledge as that in which students must use sensory material to make sense of an idea. For example, at early stages, children cannot count, add, or subtract meaningfully unless they have actual objects to aid in those functions. They build integrated-concrete knowledge as they learn. Such knowledge is connected in special ways. (The root of the word concrete is “to grow together.”) What gives sidewalk concrete its strength is the combination of separate particles in an interconnected mass. What gives integrated-concrete thinking its strength is the combination of many separate ideas in an interconnected structure of knowledge (Clements and McMillen 1996).

For example, computer programs may allow children to manipulate on-screen “building blocks.” These blocks are not physically concrete. However, no base-10 blocks “contain” place-value ideas (Kamii 1986). Students must build these ideas from working with the blocks and thinking about their actions. Furthermore, research indicates that physical base-10 blocks can be so clumsy and the manipulations so disconnected from each other that students see only the trees (manipulations of many pieces) and miss the forest (place-value ideas). Computer blocks can be more manageable and “clean” (Thompson and Thompson 1990). Students can break computer base-10 blocks into single blocks, or glue these blocks together to form 10s. These actions are more in line with the mental actions that we want students to learn: They are children’s cognitive building blocks.

One essential cognitive “building block” of place value is children’s ability to count by 10 from any number, thus constructing composite units of 10 (Steffe and Meinster 1997). The computer helps students make sense of their activity and the numbers by linking the blocks to symbols. For example, the number represented by the base-10 blocks is usually linked dynamically to the students’ actions with the blocks, automatically changing the number spoken and displayed by the computer when the student changes the blocks. As a simple example, a child who has 16 single blocks might glue 10 together and then repeatedly duplicate this “10.” In counting along with the computer, “26, 36, 46,” and so on, the child constructs composite units of 10.

Computers encourage students to make their knowledge explicit, which helps them build integrated-concrete knowledge. Specific theoretically and empirically grounded advantages of using computer manipulatives follow (Clements and McMillen 1996).:

Of course, multimedia and other computer capabilities should, and will, be used when they serve educational purposes. Features such as animation, music, surprise elements, and especially consistent interaction get and hold children’s interest (Escobedo and Evans 1997). They can also aid learning, if they are designed to support and be consistent with the pedagogical goals. In addition, access to technology is an important equity issue. Much of our material will be available on the Internet.

In summary, the Building Blocks project is designed to combine the art and science of teaching and learning with the science of technology, with the latter serving the former. Such synthesis of curriculum and technology development as a scientific enterprise with mathematics education research will reduce the separation of research and practice in mathematics and technology education. Materials based on research can then be produced, and research can be based on effective and ecologically sound learning situations. Moreover, these results will be immediately applicable by practitioners (parents, teachers, and teacher educators); administrators and policy makers; and curriculum and software developers.

Final Words

One can use technology to teach the same old stuff in the same way. Integrated computer activities can increase achievement. Children who use practice software 10 minutes per day increase their scores on achievement tests. However,

if the gadgets are computers, the same old teaching becomes incredibly more expensive and biased towards its dullest parts, namely the kind of rote learning in which measurable results can be obtained by treating the children like pigeons in a Skinner box….I believe with Dewey, Montessori, and Piaget that children learn by doing and by thinking about what they do. And so the fundamental ingredients of educational innovation must be better things to do and better ways to think about oneself doing these things. (Papert 1980)

We believe, with Papert, that computers can be a rich source of these ingredients. We believe that having children use computers in new ways—to solve problems, manipulate mathematical objects, create, draw, and write simple computer programs—can be a catalyst for positive school change.

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Douglas Clements is a professor in the department of learning and instruction in the graduate school of education at the SUNY-Buffalo.

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