Mathematical and Scientific Cognitive Development
The first half of the workshop focused on the understanding of young children’s learning that has been gained through research. The presenters and discussants were guided by a set of questions, supplied in advance, that were designed to target the most fundamental developments in research on mathematics and science learning in very young children—and those with the greatest potential for informing instructional practice:
How do children’s reasoning capabilities—in mathematics or science—develop across the early childhood years?
How do children’s conceptual “building blocks”—in mathematics and science—develop across these years?
In what ways do mathematical and scientific development in early childhood represent a distinct set of processes? An integrated process? And how do they relate to general development in early childhood?
Presentations by Rochel Gelman and Nora Newcombe addressed the questions in different ways; their presentations were followed by general discussion of the issues raised by the current state of the research.
LEARNING FROM CHILDREN—RESEARCH IN PRESCHOOL SETTINGS
Gelman began by describing research that she has conducted over many years with teachers and children at early childhood centers run by the University
of California at Los Angeles (UCLA) and Rutgers University. Through a prekindergarten program called Preschool Pathways to Science (PrePS), Gelman and her colleagues have found ways to engage young children in complex scientific thinking using a coherent program that is sustained over extended periods of time. The program is designed as a collaboration among researchers and early childhood educators, and it is based on research indicating that young children are capable of building progressively on knowledge they gain in a particular domain (Gelman and Brenneman, 2004). The key finding from Gelman’s work is that children may be capable of scientific thinking far more complex than most casual observers might expect, and than scholars such as Piaget had considered possible.
Gelman illustrated her remarks with examples of children’s complex thinking drawn from her experiences with PrePS. In one example, the children were shown a set of pictures that included both depictions of real animals, though ones likely to be unfamiliar to the children (e.g., an echidna), and depictions of animal-like objects, including fanciful creatures and toys. Using a variety of different questioning strategies, Gelman and her team established that the children could successfully distinguish between the real and nonreal animals and between those that could or could not move on their own power, and they could even identify the features that helped them make these distinctions.
Gelman has drawn several conclusions from her work: perhaps the most important is that providing children with a mental structure to guide their learning is critical. Specifically, Gelman argues, young children have the capacity to build on mental structures, that is, to take new information or observations and link them to concepts they have already thought about. Children can be guided in the development of these cognitive building blocks—concepts such as the general characteristics of a living thing—so that they can develop ways of thinking scientifically or in the intellectual traditions of other domains.
Once a mental structure is in place, she argued, children are much more likely both to notice new data that fit with what they have already learned and to store data in such a way that they can build on it in the future. Conversely, when children lack a mental structure for organizing particular domains of knowledge, the significance of new data is not evident to them and they must either construct a new structure to accommodate it or fail to benefit from it. Gelman also argued that young children need to develop familiarity with the language of science as they are gaining conceptual knowledge. The two go hand in hand and support one another: if children begin learning the correct vocabulary for the scientific work they are doing (observing relevant features, measuring, experimenting, predicting, checking, recording, and the like), it will enhance their conceptual learning.
Throughout her remarks, Gelman stressed that the key to the successes she and her colleagues have had has been the opportunity to work over a long term. The goal for PrePS was, as she put it, to “move children onto relevant learning paths,” and this is done by creating an “environment that is coherent and embed-
ded throughout the year.” Rather than inserting, for example, a week- or even month-long science unit into a curriculum filled with other activities, Gelman and her colleagues were able to incorporate opportunities for scientific thinking into the daily schedule, with tools, such as science notebooks in which the children recorded their observations using drawings, stamps, and other methods, that provide extended opportunities to follow up on patterns of change in the natural world.
The science that the children do throughout the year is designed to be inter-connected and thus to encourage the children to develop conceptually connected knowledge, that is, to build successively on the mental structures they are developing. Thus, a unit on seeds can be used to develop a range of related scientific skills, such as prediction and observation, as the children explore what seeds do, how they can be recognized, and how they can be classified according to various characteristics. At the same time, the exploration of seeds can serve as a building block in a broader exploration of a question such as “how do living things grow and change?” What is learned about seeds and plants can then be compared, contrasted, and connected to findings about other living creatures that the children have studied.
Gelman acknowledged that the time spent on science in these centers came at the expense of time spent on other potentially beneficial enterprises, such as art, music, or other activities that relate to important goals for early learning, but she maintained that the goals they were able to achieve could not be duplicated in an abbreviated format. However, she argued, the lines between key preschool domains such as mathematics, literacy, and science need not be viewed rigidly, nor is the allocation of time a zero-sum game. Science can provide content for math and literacy activities, and math and literacy activities can be incorporated into science activities.
It has taken Gelman and her colleagues a number of years to develop their program and for the teachers to become fully competent at the kinds of practice it requires. Though Gelman believes the program could successfully be duplicated in other settings, she and her colleagues have had little opportunity to test the challenges this would present or to prepare the program to be scaled up so that it could be duplicated in large numbers without direct involvement from those who devised it. Research remains an integral component of the program: discoveries about children give rise to new research questions and paradigms, while collaboration between researchers and practitioners expands the thinking of both.
THEORETICAL EVOLUTION—NEW MODES OF EXPERIMENTATION
Nora Newcombe focused her remarks on the relationship between spatial and mathematical development. Her own research has focused on identifying emerging capabilities in babies and toddlers. She has found that the capacity for
spatial perception is a particularly significant development for mathematics ability not only because of its obvious importance in geometry, but also because of its less obvious role in other kinds of mathematical thinking, such as doing word problems. Newcombe began by setting her research findings and her reactions to the workshop questions in the context of three distinct theoretical perspectives in the study of early learning—Piagetian, nativist, and neoconstructivist.
The work of Jean Piaget, whose work spanned the period from the 1930s to the 1950s, was considered revolutionary when first published and is still very influential in the education of early childhood teachers. Piaget believed that children are born with innate cognitive structures that are programmed to emerge in sequence as the child develops and that cognitive skills require relatively little environmental input in order to emerge (National Research Council and Institute of Medicine, 2000). Thus, as Newcombe explained, Piaget argued that particular cognitive building blocks, such as the ability to measure, will not be evident until their preordained time, at 5-6 years in the case of measurement. However, Newcombe pointed out, researchers since Piaget, including both Gelman and herself, have demonstrated that children can do many things, including measuring, much earlier than Piaget had believed was possible.
Researchers have found that Piaget’s findings can generally be replicated if the questions are asked in the same way that he asked them, but that in many cases the findings look very different if the same question is asked in a different way. For example, Newcombe explained, Piaget assessed children’s capacity to recognize how objects would look if viewed from a different vantage point by showing them photographs of a landscape with clearly identifiable features taken from different perspectives. He found that young children were unsuccessful at this task. However, when Newcombe and her colleagues presented the same task in a different way, by showing children a tableau of objects and asking “If you were sitting over there, what would be closest to you?” they found that children at the same ages Piaget tested were successful. In this context Newcombe noted that she finds the ubiquitous use of the term “developmentally appropriate” very troubling precisely because defining the skills that have developed by a particular age is so difficult.
Piaget’s views were challenged by later researchers known as nativists, who argued, as Newcombe put it, that “there is both metric coding and number sensitivity as early as you can assess it.” In other words, nativists believe that babies are born with significant capacities and that, with appropriate environmental cues, they can function cognitively in much more advanced ways than Piaget had believed.
The theoretical perspective that Newcombe referred to as neoconstructivism borrows from both of these earlier perspectives. In this view, which accords with Newcombe’s, young children are seen as having “much stronger starting points” than Piaget had allowed, but as undergoing many subsequent developmental changes. According to this perspective, the effects of experience on young
children’s cognitive development are very important, and thus what happens in preschool is particularly critical.
Newcombe summarized the key points of difference among these three perspectives—Piaget and his followers, the nativists, and the neoconstructivists:
the age at which competencies emerge;
the degree of subsequent developmental change (i.e., how complete or developed the competencies are when they first emerge);
the existence of initial modularity (i.e., the extent to which cognitive skills are differentiated at early ages); and
the role played by environmental influences.
Newcombe’s research has addressed the first two of these issues in specific ways. She and her colleagues have explored ways of assessing babies’ and toddlers’ thinking, for example, by asking them to find objects hidden in a sandbox or checking their reactions to changes in quantity and number. She has found that there are indeed stronger starting points than Piaget had believed. More specifically, she and other researchers have found that the spatial and quantitative domains seem to share a starting point, that is, to be two components of innate core knowledge, perhaps skills located in particular regions of the brain, and then differentiate at later stages of development (see Newcombe, 2002). Newcombe has also found evidence of developmental change. She noted significant increases in competence on the same task between, for example, 18- and 24-month-olds. She believes that while babies and toddlers are capable of more than Piaget claimed, they are also farther from adult levels of competence than nativists have claimed.
Newcombe noted that her claim about the common starting point for spatial and quantitative thinking remains controversial in the field and used that point to highlight the need for caution in presenting research findings of this kind to the public. As in the public health arena, she explained, new findings can be exciting and seem newsworthy. Practitioners may jump—or be encouraged—to try to incorporate them into their thinking and their practice, only to be disappointed when later findings seem to contradict them. When findings are presented as more certain than they really are, she noted, the result can be that over time the audience for such information becomes increasingly skeptical of new research.
IMPLICATIONS OF CURRENT RESEARCH
Much of the discussion that flowed from the two presentations centered around the question of what framework for understanding mathematical and scientific cognition in young children best fits the available research evidence. Kathleen Metz opened by noting that just as scientists and mathematicians generally operate in parallel spheres with relatively little interaction, cognitive scien-
tists who study mathematics and science learning have tended to follow suit, with the result that there are two disjoint literatures on these topics. She asked whether there is a general theory of cognitive development that accounts for both domains, or whether children’s development occurs in domain-specific ways, and, further, how progress in one domain might feed progress in the other.
Catherine E. Snow touched on the same point and pointed out that the presentations did not seem to have revealed “deep abstract parallel structures underlying mathematical and scientific development.” Other participants identified some points of commonality, noting, for example, that cognitive skills such as sorting and sequencing are components of both domains. However, participants also noted that important differences between these two spheres remain unreconciled. In mathematics the content and skills are closely linked—that is, the capacity to enumerate objects is integrally related to understanding of numbers. In science, by contrast, the cognitive skills to be developed (e.g., observing, predicting, classifying) can be enumerated fairly easily, but the potential content domains in the context of which they might be learned (i.e., any aspect of the natural world that can be made accessible to a preschooler) are essentially limitless.
One participant challenged the notion of a preschool science curriculum by raising the question of whether children might actually be able to learn many science skills in nonscientific contexts, for example, by identifying the characteristics of different literary genres, taking notes, and presenting the results graphically. Nora Newcombe responded by suggesting that the goals for preschool- and elementary-level mathematics education are clearer, or at least more specific, than the goals for preschool- and elementary-level science, precisely because the potential domain of science is so broad.
The challenge of narrowing a science curricula provided one bridge to the discussion of preschool science curricula that dominated the afternoon. Several participants noted that while science and mathematics learning are undeniably important, they are only two on a long list of very important objectives for preschool education. In preschool contexts, it was argued, considerably more attention has been paid to the importance of literacy than to other domains, such as mathematics and science. Possible reasons for this focus were not brought out, but its pervasiveness was acknowledged.
Research on the development of cognitive skills related to mathematics and science has provided fascinating new pictures of what young children can do, but very little guidance for adults about how to use this information in caring for young children. Gregg Solomon highlighted this point by bringing to the discussion the perspective of one who makes decisions about which research to fund. Solomon’s position allows him to observe several research literatures that all pertain to important questions about early learning but seldom benefit from one another. For example, he sees researchers who have developed curricula that seem both creative and effective and yet lack coherent, research-based rationales,
and research into chemistry or physics learning that does not reflect current thinking from the cognitive science literature.
One important problem that results from the fact that so many researchers are not well versed in the developments in other, related, domains, Solomon explained, is that as key findings are summarized and passed on in new contexts, they are often distorted in the process. A single study that suggests an interesting possibility that calls for further investigation is often condensed and described in an oversimplified, exaggerated way. Teachers, the end users of much of this kind of information, are then provided with questionable versions of research findings, or research findings that do not correspond to one another or do not seem to be connected to a set of common ideas. As Newcombe had noted earlier, any over-simplification of research findings only fuels mistrust of future claims.
Noting that the discussion had ranged over a number of issues that call for further investigation, Sharon Lynn Kagan closed the morning discussion by asking the panelists to consider which of the many issues about which more research is needed are the most pressing and important. In response, Newcombe identified a basic research question. For her, the relationship between explicit and implicit knowledge—between action and cognition—is a fundamental issue about which significantly more needs to be known. In other words, while identifying the skills of which young children are capable and pinpointing the stages at which they develop particular skills is very useful, the next logical and necessary step is to understand how children apply these skills. With further insight into the uses children can and do make of the cognitive skills they seem to have at very young ages can come further insight into questions about school readiness and ways that it can be fostered for all racial and socioeconomic groups.
Gelman took a somewhat different tack. She described the additional research that would be needed to scale up her work with preschoolers, that is, to develop it to the point where it could be used effectively in any classroom. For her, however, this need relates to a larger question about the magnitude of the effects that children’s communities, family backgrounds, and social circumstances have on their capacity to benefit from an enriched preschool environment. Her experiences with children from low- and middle-income families has led her to believe that many are being educated in cognitively deprived settings. She believes that because children’s capacities have been consistently underestimated, the importance of enriched learning environments for young children has not been sufficiently recognized. At the same time, better understanding of how children’s educational needs may vary according to the socioeconomic circumstances in which they live will be very useful in developing programs that meet all children’s needs. Gelman hopes that preschool curricula can be developed that work despite inadequate teacher preparation, but she argued that improved preparation and ongoing development for teachers are critical. Research that provides more detailed understanding of children’s capacities can support both of these goals.
As both of these responses to the question about research priorities make evident, the role of practice frequently found its way into the morning’s discussion of research. While Gelman’s research is conducted in a practice setting, Newcombe was also focused on the implications of her findings for the education of young children. The link between the two was the focus of the second half of the workshop.