Improving the Mathematics and Science Achievement of American Children:
Psychology's Role

David C. Geary and Carmen O. Hamson


University of Missouri-Columbia

Cognitive, educational, and developmental psychologists have considerable expertise in the understanding of how children think, learn, and remember, and, at the same time, cognitive neuroscientists are advancing our knowledge of the brain systems that support these cognitive activities. Research on children's thinking, learning, and the associated brain systems is not enough, however. We must also come to better understand the individual and cultural influences on children's motivation to learn in school. Research in social psychology and social development are aimed at just these goals. All of these different facets of psychology hold great potential for improving the mathematics and science-related achievement of America's children and this document provides a framework for considering the many ways in which psychological research can help to foster the goal of developing a world-class educational system for mathematics and science in the United States.

The Importance of Mathematics and Science Education


Although the economic benefits of a good education fluctuate somewhat from one decade to the next, it is generally the case that higher levels of education result in a higher likelihood of employability and higher wages once employed. Moreover, the benefits associated with education tend to increase with increases in the technical complexity of the associated school-taught competencies. In technologically complex societies, such as the United States, there is a particular premium associated with math-intensive, science-related skills.

Strong quantitative competencies influence employability and productivity in many blue collar and white collar jobs, above and beyond the influence of intelligence, reading ability, years of schooling, race, and gender. Poor mathematical competencies restrict college major and later career choices for individuals pursuing post-secondary education. Moreover, the more math-intensive the occupation, the higher the entry-level and subsequent wages. These relatively high-paying occupations include engineering and the math-intensive physical sciences (e.g., physics). In contrast, there is little relation between the language-related demands of different occupations and the wages associated with those occupations. It is not that mathematical and science-related competencies are inherently better than language-related competencies, it is simply that they are in shorter supply and therefore garner greater economic benefits.

Strong academic competencies in mathematics and science improve the chances of employment and result in higher wages and higher on-the-job productivity once employed.

Not only do strong mathematical and science-related competencies influence the economic well-being of individuals, through their relation to employability and wages, they also have wider social consequences, as noted above. For instance, it has been estimated that the poor numeracy and literacy of the workforce will cost the U.S. economy nearly 170 billion dollars each year by the year 2000.

Thus, a first-rate educational system provides individual and general social benefits and educational outcomes in mathematics and science would appear to be especially important and beneficial in societies, such as the United States, where many jobs require some level of technical sophistication. With this in mind, it is important to consider how the mathematics and science education of our children rate in terms of international standards.

Mathematics and Science Education in the United States

and the Rest of the World

The most recent cross-national study--conducted in 1994 and 1995--compared primary-, middle-, and high-school students in mathematics and science achievement across 45 nations. The results are not yet available for primary- and high-school students, but preliminary findings for middle-school students indicated that U.S. students ranked 28th out of 41 nations in 8th grade and 24th out of 39 nations in 7th grade. The assessment of 8th graders included 8 of the 12 nations that participated in the first multi-national assessment. Of these, U.S. 8th graders ranked 7th, although the gap between the U.S. 8th graders and 8th graders in several of these other nations (e.g., England and Germany) did not appear to be as large as was found in the 1960s. Either way, in both 7th and 8th grade, the performance of U.S. students was far below that of their same-age peers in the top ranked nations (i.e., Singapore, Korea, and Japan).

American children and adolescents have scored below the international average in mathematics achievement for more than 30 years.

The relative ranking of American students in these international comparisons is disturbing but actually belies the real significance of these differences. A more substantive issue is What is the magnitude of the gap in the mathematical competencies of American students relative to the international average and relative to the world's best educated students? For the first cross-national comparison, about 4 out of 5 of American 17-year-olds scored below the overall international average in mathematics. Results for the second cross-national assessment of mathematical competencies, conducted in the early 1980s, showed a similar pattern. Here, 17-year-olds who were enrolled in college-preparatory mathematics courses--this includes about 13% of American high-school seniors--from 22 educational systems were compared. The results indicated that the top 5% of these elite American students had only average scores, in relation to international standards, in algebra and functions and calculus and slightly above average scores in geometry.

In the most recent study, about 3 out of 5 U.S. 7th and 8th graders scored below the international average in mathematics. Or, stated differently, just over 2 out of 5 U.S. students scored above the international average. However, only about 1 out of 100 U.S. students scored as well as the average student in the top-ranked nation, Singapore. Thus, while this most recent study indicates that U.S. middle-school students are not substantially below the international average, they are far from being the best in the world.

A series of cross-national studies conducted in the 1980s and 1990s indicated that American students do somewhat better in science, but they still do not perform as well as students in the highest ranked nations. The first of these studies was conducted between 1983 and 1986 and included 5th, 9th, and 12th graders from 23 countries. The countries participating in this study included both developed and developing nations in all regions of the world. The overall results revealed that American 5th graders ranked 9th out of the 17 countries that participated in the assessment of 5th graders, while the American 9th graders ranked 19th out of 23 countries. This pattern suggests a decline in the relative performance of American students from elementary school to the end of junior high school, and the decline appears to continue through 12th grade.

As with the mathematics comparisons of 17-year-olds (12th graders), the cross-national comparisons of the science-related competencies of 12th graders included only students who were enrolled in an academic high school and enrolled in sciences courses. In the United States, participants were selected from those students enrolled in their second year of high school science and were tested only on their knowledge of the specific science field (biology, chemistry, or physics) in which they were enrolled--clearly a select group of American high school seniors. Similar criteria were used for selecting participants from other countries, although larger percentages of students in other countries were enrolled in science courses--a bias that would favor the United States. Despite the elite nature of the American 12th graders, out of 17 participating nations, they ranked last in biology, 15th in chemistry, and 11th in physics.

A smaller study conducted in 1989 compared the science knowledge of 13 year olds from 6 nations, including subassessments of several Canadian providences: Once again the U.S. students did not do well, ranking 5th. Moreover, only about 1 out of 4 U.S. 13 year olds scored above the average student in the top ranked educational systems (i.e., British Columbia and Korea). A more recent cross-national comparison of science achievement, conducted in 1991, revealed a similar pattern of results. This much larger study included 9- and 13-year-olds from 19 countries. In keeping with the earlier described study, the younger U.S. students did well, ranking 4th out of the 14 countries that participated in the study of 9-year-olds. However, the performance of the 13 year olds was again poor, tying for 14th out of 19 countries. The one bright spot was the finding that some American 13 year olds did about as well as the top students in other countries, with the top 1% scoring at about the 95th percentile of the top three countries (Korea, Taiwan, & Switzerland).

The most recent science assessment, which, as noted above, included 7th and 8th graders, also indicated relatively good science performance for U.S. students, at least in comparison to mathematics. In this study, the U.S. 7th and 8th graders ranked 13th and 17th out of 39 and 41 nations, respectively. Stated otherwise, nearly 3 out of 4 U.S. 7th graders and 2 out of 3 U.S. 8th graders scored above the overall international average in science. However, less than 1 out of 4 7th graders and 1 out of 10 8th graders scored above the average score of students in the top-ranked nation, which was again Singapore.

In all, while the rank of American children and adolescents is disturbingly low in mathematics, the real significance of these studies is found in the large gap between the mathematical competencies of America's students and their peers in most other nations. The mathematical competencies of the typical American student are below international standards and even the best educated mathematics students in the United States are, in most comparisons, no match for the best educated students in many other industrialized nations. The picture is somewhat better for science, at least for 5th graders (i.e., 9 year olds) and, in the most recent study, 7th and 8th graders. At these grade levels, U.S. students tend to score at about or somewhat better than the international average. However, the relative science-related competencies of American students appears to decline after this point. By the end of high school, the performance of American students mirrors that found in mathematics--it is at or near the bottom.

Why Psychology Is Important to Mathematics and Science Achievement

Psychological scientists are uniquely positioned to provide the foundation of basic and applied research that will be essential to the development of a world-class mathematical and science-related educational system in the United States. The basic research tells us how children naturally learn about and understand numerical, biological, and physical phenomena and applied research uses this foundation in an attempt to facilitate children's school-based learning. This section highlights such basic and applied research in psychology and illustrates how it is directly related to the goal of developing an internationally competitive educational system in mathematics and the sciences.

Basic psychological research related to mathematics and science education includes studies of the brain mechanisms that underlie basic numerical and arithmetical competencies; studies of the apparently inherent numerical abilities of human infants and their relation to the numerical abilities of primates and other species of animal; the cognitive processes that govern problem solving in arithmetic, mathematics and our understanding of the biological and physical world; and people?s naive understanding of biological and physical phenomena.

Research in these basic science areas, among others, has provided a solid foundation for a growing body of research on the teaching and learning of mathematics and science. Psychologists throughout the country, indeed the world, are currently studying such things as how the representation of scientific information can influence learning in the biological and physical sciences (See Psychological Science and the Teaching of Scientific Concepts section); the use of multi-media presentations for facilitating the solving of mathematical word problems; the teaching practices that facilitate the learning and long-term retention of mathematical and scientific concepts; the ways in which anxiety about mathematics can disrupt problem solving; the cognitive, environmental, and genetic factors that contribute to the development of arithmetical learning disabilities; the development of children's valuation and beliefs about the importance of academic competencies, including mathematics; and the wider cultural and even evolutionary factors that influence children's motivation in learn in school, among many other topics.

Psychological scientists focus on many issues related to mathematics and science education, ranging from the genetics of learning disabilities in arithmetic to cultural influences on children's motivation to learn in school.

Some of this research is highlighted in the sections below. At the same time, these sections are focused around broader themes that should provide an important conceptual frame for understanding how psychological research can be used to improve the mathematical and science-related competencies of American children. These frames include a contrast of natural learning and school learning, children's motivation to learn in school, and more specific research on children's learning and understanding of mathematical and scientific principles.

Natural learning. One exciting area of psychological research involves studies of people?s natural modes of reasoning and problem solving and how these natural modes of understanding the world facilitate or impede school learning. Research in this area has shown that nature has provided human beings with a desire to control or influence their social and physical environments. Effective control requires both motivational processes and the development of mental models of how the social, biological, and physical worlds operate, as well as skills and competencies needed to achieve control. These models appear to develop through children's play and exploration, along with maturation, and allow us to predict the behavior of other people and make judgments about the biological (e.g., behavior of animals) and physical environment within which we live. However, at times, these mental models are inaccurate when compared with our scientific understanding of the same phenomena.

For instance, people often make judgments about the relative risk of various activities (e.g., flying in an airplane) based, in part, on how easily they can remember examples of mishaps associated with those activities (e.g., plane crashes). This memory-based method for determining risk often leads to poor probability and risk judgments. This is because mass media coverage of rare events produces an inaccurate picture of the actual risk associated with various activities. Most people, for example, greatly overestimate the risk associated with flying, because they can remember many spectacular and disturbing examples of plane crashes. Most people have not personally experienced these crashes but were exposed to them through television.

The use of this memory-based assessment of relative risk probably worked rather well in the types of environments in which human beings evolved, but it not only leads to poor risk assessment in modern societies, it appears to interfere with the understanding and use of formal school-taught probability. In an analogous fashion, it also appears that our natural modes of understanding quantity and the biological and physical world often interfere with the learning of many of the school-taught competencies associated with mathematics and the biological and physical sciences. Yet, in other areas our natural knowledge might actually facilitate learning in school.

For instance, human beings, and even the common chimpanzee, appear to have a natural understanding of simple counting and arithmetic. At this point, it is not clear exactly how infants or chimpanzees count or solve simple addition or subtraction problems, although these types of problems appear to be solved with the use of some type of preverbal counting, that is, counting without number words or language. However it works, this preverbal counting system provides the scaffolding on which many later school-taught counting and arithmetic skills develop. This natural understanding of simple arithmetic and counting makes learning some, but not all, features of formal counting and more complex arithmetic easier than would otherwise be the case. At the same time, children's natural understanding of counting--that quantity increases with each successive count--interferes with their understanding of fractions: Children's conceptual understanding of counting leads them to conclude that because 4>3, 1/4>1/3. Thus, children's natural understanding of counting makes fractions difficult to learn and difficult to teach.

In the same manner, people's intuitive understanding of how the physical world works often interferes with learning many basic concepts associated with the physical sciences. As an example, imagine the trajectory of a thrown baseball, a ball that rolls off the edge of a table, and a package dropped from a moving airplane. Psychological research has shown that both children and adults have natural but often times inaccurate conceptions about motion in these situations. The case of an object being dropped by another moving object, such as an airplane, presents a particular challenge; even adults often do not realize that the dropped object continues to move forward, rather than straight down. This and other naive conceptions about the workings of the physical world often interfere with learning the scientific principles associated with mechanics, as well as many other scientific principles, such as those that represent centrifugal force and velocity.

Similarly, children and adults develop mental models of biological phenomena, for example, that animals eat, have internal structures, and reproduce offspring that share characteristics with their parents. At the same time, many people do not readily grasp the mechanism of natural selection.

Research in this area indicates that an important task for psychological scientists is to better understand how students? intuitive understanding of the numerical, biological, and physical features of the world impedes or facilitates learning in school. This is particularly true in technical areas, such as mathematics and science, where much of what needs to be learned in school is unnatural, that is, in areas where the development of world-class academic competencies requires engaging in activities that nature has not prepared us to engage in or learning to think about the world in ways that contradict our natural mental models of quantitative, biological, and physical phenomena.

School learning. The consideration of learning in terms of what is natural and what is unnatural provides an explanation for why children learn some things, such as language, with little effort and then, many years later, struggle to learn other things, such as reading. Learning to read, learning algebra, or learning the principles represented by Newton's laws will not occur as automatically and effortlessly as language acquisition, because the former represent unnatural domains for human beings while the latter--language--is a natural domain and its acquisition represents a natural form of learning. Given these differences, basic psychological research on the factors that influence the acquisition of school-taught and largely unnatural mathematical and science-related competencies is essential to the development of a world-class educational system in mathematics and science--without such research, and the associated instructional techniques, most students will not grasp complex mathematical and scientific concepts.

The ways in which children think and learn outside of school are best understood in terms of living in environments that are more natural than the environment we currently live in. Children's learning in these more natural environments almost certainly involved learning about the behaviors and intentions of other people, learning about where and how to get food, and about the characteristics of the biological and physical environment within which they lived. Indeed, children appear to be prepared by nature to automatically and effortlessly learn, for example through play, about people and their environment. Moreover, nature has made play fun, which motivates children to engage in all sorts of learning activities. In other words, children learn, often without being aware of this learning, about the rules of social behavior and about their environment while engaging in play and exploration. While children's play results in natural learning, much of what needs to be learned in school is unnatural, that is, children are not prepared by nature to learn much of what they need to learn in school in order to function as adults in modern societies.

There are several important implications of this view of schooling for mathematics and science education. The first is that children are more motivated to learn some things than others. For instance, curiosity about other people's intentions and the desire to seek out relationships with other people appears to be a natural and near universal goal. A burning desire to master algebra or Newtonian physics is not so universal. There are, of course, many individuals who do pursue learning in these areas on their own initiative. However, it must be remembered that the goal in contemporary American society is near universal education, that is, that nearly everyone learn many unnatural school-taught competencies. With the exception of recent industrialized societies, this goal is unprecedented in human history!

children's natural ways of thinking and learning might not be sufficient for learning complex mathematical and scientific principles.

The second implication is that children's natural modes of learning, such as play and social discourse, might not be sufficient for learning in many unnatural, school-taught domains. Indeed, as noted above, children's natural understanding of some phenomena actually impede the learning of some related school-taught competencies. The next two subsections deal directly with these issues; the contributions of psychological research to understanding children's motivation to learn in school and psychological research that is focused on school-based, or unnatural learning in mathematics and science.

Motivation to learn in school. It was noted earlier that nature has provided people with a desire to exert some influence or level of control in their social and physical environments. At the same time, people's attempts to achieve some level of influence often fail--this is where motivational processes come into play. Motivational processes help people cope with failure and keep their behavior directed toward achieving important goals. These processes include the extent to which various goals (e.g., being with other people) are valued, the extent to which one believes the goal can be achieved, and interpretations of why goals were not achieved (e.g., bad luck or personal incompetence). As noted above, nearly all individuals naturally seek out some social affiliations and motivational mechanisms are likely to be more or less automatically and universally triggered with social failures. Even with such failures, these motivational mechanisms will ensure that nearly everyone will continue to seek social affiliations.

Living in modern societies, in contrast, requires most people to develop competencies that all human beings are not universally motivated to develop. These appear to include many school-taught or work-related competencies, including much of mathematics and science. Nevertheless, psychological research has discovered that children's beliefs about learning can influence the acquisition of school-taught competencies. Beliefs in and of themselves will not result in learning mathematics or science, but will affect the motivation to continue to stick with it once the material becomes difficult. For instance, it has been shown that, across cultures, children come to understand that learning in school is related to both effort and ability, but the relative emphasis on effort or ability affects the persistence with which students pursue learning in difficult areas, such as mathematics and science; an emphasis on effort rather than ability is associated with greater persistence. Research has also shown that East Asian culture emphasizes the importance of effort for school learning, while American culture places more of an emphasis on ability.

Moreover, cross-national research suggests that wider cultural values influence these school-related motivational processes, which, in turn, likely contribute to the earlier described cross-national differences in mathematics and science achievement. The cultural valuation of competencies in one area or another is important because it influences how motivated students are to achieve in one area or another, how much the society invests in teacher training in one area or another, and how much parents are willing to invest in their children's education in one area or another. For instance, East Asian culture gives priority to achievement in mathematics, whereas American culture does not. In fact, American children value achievement in sports much more than achievement in mathematics, or any other academic area for that matter. As a result, East Asian nations invest much more in mathematics education, such as in the training of elementary-school mathematics teachers, than the United States. In China, for example, elementary mathematics teachers are specialists, only teaching mathematics, much like art teachers are specialists in the United States. Moreover, East Asian parents support the learning of mathematics (e.g., through help with homework) much more than American parents.

We cannot assume that all children will be inherently motivated to learn everything they need to learn in school in order to be a productive adult.

Psychological studies have provided both insights and interventions related to the motivation to learn in school. For instance, interventions that make the importance of mathematics clear, in terms of later career options, increase participation in advanced mathematics classes in high school. But there is still much to be learned: Psychological models of motivational processes and research on how personal, family, and society-level factors influence children's motivation to learn in school will provide an essential element for the development and maintenance of a world-class educational system in mathematics and science.

Learning and cognition. A considerable amount of psychological research has focused on the factors that influence the acquisition of academic competencies, as well as the underlying architecture of these competencies. This research is important because the motivation to learn is necessary but will not in and of itself actually produce academic competencies in mathematics and science. The acquisition of mathematical and science-related competencies requires engaging in activities that are specifically designed to foster their development. This section provides a brief introduction to psychologists? understanding of the architecture of children's cognition and then highlights some of the ways in which the understanding of this architecture can be used to facilitate children's learning of mathematics and science.

Cognitive abilities, such as counting, involve both knowing and doing, as well as an understanding of why this knowledge is important and where and when it should be used. Cognitive psychologists refer to the knowing aspect of cognitive abilities as conceptual competence, the doing aspect as procedural competence, and the where and when aspect as utilization competence. Conceptual, procedural, and utilization competencies are linked together because they are designed to achieve the same goal; goals represent the why of knowledge, as shown in Figure 1. Conceptual competencies refer to knowledge associated with the domain. Procedures are behaviors that act on the environment in order to achieve the associated goal and their use is constrained by conceptual knowledge. Utilization competence is reflected in the use of procedures in appropriate contexts and in ways that are most adaptive (e.g., balancing the speed and accuracy features of one problem-solving approach or another).

The goal of counting, for instance, is to determine the number of items in a group of items. The procedure associated with natural counting, for children and chimps, typically involves pointing at objects as they are counted; pointing helps the child, and presumably the chimp, keep track of which items have been counted and which still need to be counted. The use of counting procedures, in turn, appears to be constrained by an implicit conceptual understanding of several basic features of counting. For instance, the counting behavior of children and chimps is constrained by an implicit understanding that correct counting involves tagging, for example through pointing, each counted item once and only once. Utilization competence is reflected by the fact that counting procedures are only used in contexts where the goal is to enumerate a set of objects.

The three-part goal-related architecture of cognitive abilities appears to effectively capture the essential features of learning and problem solving in both natural and unnatural domains. However, there are a number of important differences between the acquisition of these competencies in natural as opposed to unnatural domains. First, the basic goals associated with natural learning appear to be provided by nature, whereas the goals associated with unnatural domains largely reflect the demands of the wider society. Second, children appear to be biologically prepared to acquire the conceptual, procedural, and utilization competencies associated with natural goals, such as affiliating with people, and the associated natural abilities, such as language--biologically prepared means that these competencies will emerge with experiences that are sought by the child (e.g., play). In contrast, learning in unnatural domains is not biologically prepared. As noted earlier, these differences between natural and unnatural domains create differences in the degree to which children are motivated to learn in one domain (e.g., about people) or another (e.g., about algebra), and differences in the ease with which learning occurs in natural and unnatural domains.

Thus, in addition to research on how children's natural ways of understanding numerical, biological, and physical phenomena can facilitate or impede learning associated concepts in school, cognitive research can contribute to the goal of developing a world-class educational system for mathematics and science by focusing on the factors that influence the acquisition of conceptual, procedural, and utilization competencies in unnatural school-taught mathematical and science domains. These factors include motivational influences, noted above, instruction in school, as well as research on the more basic cognitive and brain processes that support these three competencies.

Understanding the architecture of cognition also provides an important organizing framework for understanding the cross-national differences in mathematics and science-related competencies. For instance, studies of East Asian and American children suggest that the achievement gap in mathematics is largely due to an East Asian advantage in conceptual and procedural competencies, rather than utilization competencies. Moreover, the East Asian advantage in conceptual and procedural competencies is found only for unnatural, school-taught mathematical domains and not on tests that assess children's natural understanding number, counting, and simple arithmetic. The implications are clear: Changes in mathematics education in this country should focus on fostering conceptual and procedural competencies in unnatural, school-taught mathematical domains.

As another example of the usefulness of this approach to the architecture of thinking and problem solving and related psychological research, consider a series of studies on the acquisition of the conceptual and procedural competencies associated with the solving of simple kinematics problems in physics (e.g., finding the final velocity of a moving object) and the solving of algebra and geometry problems. Research in this area focuses on the factors that facilitate students? conceptual understanding of problems within these domains and factors that result in the automatic use of the mathematical procedures used to actually solve the problems; automatically means that the procedures are used without having to consciously think about what to do. These studies revealed that the processes underlying the acquisition of conceptual and procedural competencies, as well as the amount of experience needed for skill development, are largely independent.

The acquisition of procedural competencies, such as learning the rules for adding or subtracting variables from each side of algebraic equations, occurs only with extensive practice. Research indicates that this practice should involve using the procedure to solve all of the different types of problems on which the procedure might be used and practice should occur with sets of problems that require different procedures (e.g., practicing addition and subtraction together). After extensive practice, the procedure will be used automatically, which makes the overall processing of the problem less cognitively demanding. This in turn appears to make the processing of other problem features easier and increases the chances that the procedure will be appropriately used to solve, or transfer to, novel problems.

Unlike the acquisition of procedural competencies, it appears that the learning of conceptual principles can occur rather quickly, that is, without extensive practice. Generally, the learning of conceptual principles is more dependent on how the problem is presented than on how frequently it is presented. For instance, psychological research has shown that asking students to simply solve for X, as is done in most classrooms in the United States, does not greatly influence their problem-solving approaches--problem-solving approaches will be influenced by the students? conceptual understanding of the class of problems. Even after extensive practice, students still use problem-solving approaches that are commonly used by novices. However, providing more general goals, such as asking students to find different ways to solve the same problem, does lead to the use of problem-solving approaches typically used by experts, suggesting that this approach fosters the conceptual understanding of the problem.

In science, and to a lesser degree in mathematics, much of the conceptual information that is to be learned consists of such things as terms and definitions, categorical relationships, characteristics of various types of things, and sequences of steps in events, rather than problem-solving principles. These have typically been approached in a traditional lecture/textbook style of teaching. One criticism of this style is that it encourages a "rote rehearsal" approach to learning, which has been characterized as memorization rather than understanding. While some students are able to learn and understand with this approach, many do not. A long history of psychological research on memory has shown that a simple, repetitive, "rote", type of rehearsal is most useful for maintaining information in working memory (i.e., keeping something in mind for a short period of time), but is less effective in transferring information to long-term memory. In contrast, research has shown that in order to transfer information to long-term memory, with the best chance for later retrieval, some type of "deep processing" must be done with this information. New information must be richly connected with existing knowledge, which is accomplished by actively seeking to understand the important elements of the new information, and how they relate to each other and to existing knowledge. This process can be enhanced through multiple exposures to the new information, in somewhat different contexts and formats.

Psychological Science and the Teaching of Scientific Concepts

The research of psychologist Richard Mayer and his associates illustrates how basic research can address teaching issues in science. Among other things, they have been studying the ways in which traditional textbook presentations of science material can be modified and supplemented in order to enhance learning and understanding. Their work has focused on explanations of scientific processes that involve sequences of cause and effect relationships. They have created what they call "multimedia summaries", which are sequences of drawings, each illustrating a step in the process and each accompanied by a caption that explains that step, as shown in Figure 2. In the laboratory, Mayer and his associates ask college students to learn these scientific explanations by studying textbook passages, the multimedia summaries alone, or both the passages and the summaries. Learning is measured by both recall of facts and by transfer to related situations. They found that traditional passages alone did little to enhance learning, while the summaries (alone or with the passages) did enhance learning. They have also found that both the verbal and visual aspects of the summaries are important, that either one alone is not sufficient to promote learning.

In all, theoretical and empirical research on children's learning and cognition has many implications for educational practices in mathematics and science. Theoretically, the understanding of the architecture of cognition provides an important framework for dissecting mathematical and science-related abilities into their component conceptual, procedural, and utilization competencies. Once dissected, it can be shown that, at least in mathematics, American children perform particularly poorly, relative to their peers in other nations, on tests that assess school-taught conceptual and procedural competencies. At the same time, empirical research in psychology is resulting in a more complete understanding of the factors that influence the acquisition of conceptual and procedural competencies in mathematics and the sciences and the development of the more basic cognitive and memory systems that support these competencies. Continued basic research in these areas, and supporting areas in the cognitive neurosciences, will be an essential component to the development of a world-class educational system in mathematics and science.

Applications of Psychological Science to Mathematics and Science Education


In addition to laboratory-based research on learning and cognition, psychologists are also conducting research on the effectiveness of different ways of presenting mathematical and science-related material in classroom-like settings. The research conducted by the Cognition and Technology Group at Vanderbilt University provides one example for mathematics.

Here, the focus is on the usefulness of video-based presentations of realistic problems for facilitating students? ability to solve simple and complex algebraic word problems. The first 15 minute video is Journey to Cedar Creek, which presents the following scenario: