Running head: KNOWLEDGE DOMAINS AND DOMAIN LEARNING

Knowledge Domains and Domain Learning
Liliana Maggioni and Patricia A. Alexander
University of Maryland

In press

Keywords: discipline, domain, learning, history, knowledge, mathematics, reading, science, writing.
Abstract
The roots of current disciplines and domains of study reach well back in history. An exploration of their development shows that these areas of knowledge have not only reflected cultural changes but have also influenced societies, especially through formal educational systems. Besides being characterized by their focus on a particular part of the world, disciplines are also distinguished by a specific way of thinking about their respective domains of study. Psychological research has identified several features of these pathways to knowledge (e.g., reading, writing, history, mathematics, and science) that generally define the landscape of academic practice.
Although educational psychologists’ interest in how knowledge develops within specific domains has fluctuated across time, formal education throughout the world is organized around particular fields of studies and students soon come to characterize their experience of school in terms of subject matters. Thus, in education, domains seem to make a difference. The term knowledge domain refers to the part of the world investigated by a specific discipline. In other words, the domain can be characterized as the object (e.g., plants, numbers, or the past) of a specific body of knowledge (e.g., botany, mathematics, or history). Herein, we offer a survey of the development of increasingly specialized disciplines and of the corresponding identification of ever narrower knowledge domains. In particular, we consider the cultural trends that accompanied these changes and the major influences on the structure of formal education. Then, we turn to consider the characteristics of learning and generating knowledge within specific domains. Specifically, we consider the findings of educational research in understanding the processes of learning and teaching in history, mathematics, and science. We also include contributions regarding the processes of reading and writing, given their relevance in the school curriculum and the tendency in educational research to conceptualize these activities as domains of learning in their own right.
The Development of Disciplines Besides being characterized by its systematic knowledge of a particular domain, each discipline is also distinguished by a specific way of thinking about associated phenomena. Thus, disciplinary knowledge includes a specific taxonomy, vocabulary, concepts, theories, research methods, and standards of justification. Histories of science, such as those offered by Noah Edward Fehl (1966), A. Rupert Hall and Marie Boas Hall (1988), and Walter Libby (1917) illustrate that disciplines developed over the centuries as privileged pathways toward understanding of almost any topic. The reciprocal influences between the prevalent cultural climate, disciplinary developments, and formal education are well exemplified by cultural histories of Western education, such as the one composed by Freeman Butt (1955). These studies concur in affirming that organized bodies of knowledge arose in conjunction with the human needs of gaining understanding of the world, establishing some control on the physical environment, and organizing social life. In ancient Egypt, for example, efforts at controlling and predicting the floods of the Nile fostered remarkable advances in geometry and astronomy. However, it was in the Greek cities of Asia Minor and later in Athens that the investigation of philosophers into the nature and origin of the universe introduced the method of rational inquiry that so deeply influenced the development of knowledge in Western civilization. In fact, Western thought owes much of its systematization of knowledge to the Greeks and to their reliance on critical reason in speculating about the origin and nature of the universe. The Greeks came to regard rationality as the human faculty allowing the acquisition of knowledge and truth; hence, the intellectual formation afforded by mathematics and philosophy was considered a privileged road to knowledge and learning and acquired centrality in education. In time, increased complexity in the knowledge and skills characterizing competence in specific areas fostered the development of formal instruction and the establishment of schools as separate institutions. The process of organization of knowledge was greatly favored by reliance on the written form, a practice relatively soon adopted by the liberal arts, but not by the practical arts. In the practical arts, informal apprenticeship remained the prevalent way of passing technical skills from one generation to the next. On the other hand, formal education tended to focus on those bodies of knowledge that were systematically organized in written form. The importance of accurate definitions in furthering thoughts and the power accorded in Athenian life to those who could speak effectively prompted the development of grammar and rhetoric. The need to think clearly encouraged the development of logic or dialectics. In addition, Greek philosophy began to organize into bodies of knowledge studies regarding the ultimate reality of things (metaphysics), the theory of knowledge (epistemology), human nature and human conduct (ethics, political science, economics, sociology, and psychology), the physical world (astronomy, geography, physics, mechanics, hydraulics, mineralogy, botany), and the living world (zoology, physiology, anatomy). The search for intellectual discipline and the problems investigated by the developing sciences favored the progress in the field of mathematics and the refinement and systematization of theories and concepts in arithmetic, geometry, and trigonometry. In addition, Greek inquiry extended to the human past, investigating the causes of historical events and thus laying the foundation of history. Finally, although the fine arts were not organized into systematic bodies of knowledge, the Greeks cultivated several forms of literary criticism, thus giving systematic organization to the theory of art and aesthetics. Roman culture widely drew from Greek thought, furthering the systematization of knowledge and its organization in forms suitable for teaching. By the end of the fourth century, the liberal arts had been circumscribed to the study of compendia (written in Latin) of those Greek works deemed suitable to the spiritual and intellectual development of the pupils. Specifically, the Trivium, that is, the elementary liberal art curriculum included grammar, rhetoric, and logic. The higher liberal arts, or Quadrivium, incorporated mainly mathematical studies and comprehended arithmetic, geometry, astronomy, and music. The boundaries of these disciplines did not necessarily include the same content that they comprise in modern times. For example, grammar also involved the study of poetry and literature. In addition, the content reflected changes in the Roman intellectual climate. For instance, the purpose of rhetoric changed from preparation to active participation in the debates over public policies to the study of elegant language to be employed in public celebrations. At the same time, the Romans did not tend to value the sciences for their own sake, but applied the theoretical knowledge gained from the Greeks in geometry, astronomy, and natural philosophy to the solution of practical problems. The disciplines included in the Trivium and the Quadrivium continued to constitute the backbone of knowledge during the Middle Ages. However, many changes were made in each of the seven disciplines in response to the varying needs and interests of the time. Latin increasingly became the language of educated people; hence, grammar gained preponderance among the elementary liberal arts during the Early Middle Ages when the non-Latin people began to take part in the intellectual life of Europe. Nonetheless, Medieval Latin became increasingly different from classical Latin, reflecting the influence of the various languages spoken by the European peoples. Rhetoric lost most of its celebratory purpose and focused on the use of the written language for drawing up legal and feudal documents. Logic was increasingly identified with the rules of deductive thinking and, as such, became distinguished from philosophy. Arithmetic, geometry, and astronomy saw important developments during the Middle Ages. The cultural exchanges with the Arab world and the translation into Latin of the most important Greek, Arabs, and Hindus works laid the foundations for the scientific and mathematical investigations of later centuries. Within the Quadrivium, music retained its theoretical nature, even if its performance gained importance in medieval life. Although knowledge of the Greek tradition was praised by Christian philosophers for the contribution it gave to truth, and thus as an aid to the understanding of God and the soul, the intellectualism of pursuing knowledge for knowledge’s sake was rejected. In the Benedictine tradition, where the monastery became the home of practical agriculturalists, as well as of religious, artists, and scholars, the alliance between learning and concrete reality foreshadowed the importance of factual knowledge and the relation between science and technology that came to characterize modern science. Beginning in the twelfth century, teachers and students began to organize themselves into guilds for protections against the king, the bishop, or anyone else who tried to control them. In time, the term universitas began to refer specifically to guilds of teachers (faculties) and students. Reflecting the articulation of knowledge of the time, the typical guilds of teachers were the faculties of liberal arts, law, medicine, and theology. Specific universities became famous for one specific faculty, thus deeply influencing the development of a particular discipline. In addition, the university system fostered an expansion of the liberal arts curriculum, adding the works of Aristotle on the physical sciences, ethics, politics, and metaphysics. The system also promoted the institutionalization of the educational curriculum (with its degrees, licenses to teach, exams, and titles) and thus the grouping of studies into separate faculties. The Renaissance celebrated the return to the classics (Latin, Greeks, and Hebrew) and highly regarded rhetoric as a way to cultivate polite letters and expression. Logic fell in disrepute due to the humanist opposition to scholasticism. However, these changes had a deeper effect on the content of the Trivium and Quadrivium than on the disciplines taught in the universities, where medieval philosophy conserved its predominance. In the sciences, humanists turned away from the deductive methods of argumentation and advocated the use of the inductive method (observations of facts and generalization). The belief that the method of induction is the proper method to gain scientific knowledge is at the root of the classification of human knowledge provided by Francis Bacon in the seventeenth century. Here the disciplines came to be characterized mainly as “histories” of nature, collections of descriptions regarding a vast array of natural phenomena. At the same time, a method common to all sciences began to take shape. The scientist should observe nature, collect facts, identify their common qualities, and express these similarities in general formulas. Empiricism highlighted the patient work of scientists in acquiring facts. However, empiricism dismissed the guiding role of theory in deciding observations and experiments. Although the almost exclusive reliance on induction disappeared in later work on method by Descartes, the uniqueness of the scientific method to gain knowledge was not challenged. Actually, the certitude granted by mathematics was upheld as the goal of scientific knowledge, and the scientific method was considered applicable and appropriate to all fields of human thought. Whereas in the physical sciences this new method of gaining knowledge proved compatible with the emergence of a unitary principle of explanation, i.e., the mechanism, a close relation between abstract thought and scientific investigation failed to surface in the biological sciences. The complexities involved in studying living things and the philosophical impossibility of reconciling the existence of human soul with a completely mechanistic physiology supported the specificity of different bodies of knowledge. The search for natural laws was extended to the study of society and political economy during the era of Enlightenment. The rules for scientific data gathering began to be applied also in the field of the social sciences and historians began to identify progress as the fundamental law of history. This process was furthered by the role played by Darwinism in the biological science, where the process of change assumed a central explanatory role. From biology, the idea that change is an inherent part of natural and human development influenced the social sciences and their methodological approach, which increasingly tried to emulate the scientific approach of the natural sciences. In the nineteenth century, the rise of positivism in philosophy further promoted the assumption that reality obeys general and universal laws. The purpose of the disciplines became to discover by observation and experimentation relationships able to explain nature, the universe, human nature, and social institutions. Psychology, anthropology, and scientific medicine were all deeply influenced by this way of thinking. In the nineteenth century, the effect on education of the increasingly important role attributed to the sciences in the overall knowledge landscape was delayed by the lingering humanist belief that a truly liberal education has to be strongly based on a deep acquaintance with the classics. Secondary instruction was particularly successful in protecting this view; in contrast, in the universities, and especially in Germany where professors and students were recognized a remarkable degree of independence and freedom, mathematics and science became the dominant studies during the second half of the nineteenth century. In the American colleges and universities, the attempt to extend to all fields of knowledge the application of the scientific method and the rise of professional organizations of scholars and specialists in various fields encouraged the subdivision of traditional bodies of knowledge into specialized “subjects.” What at the beginning of the century was studied under the label of “natural history” was by the end of the century subdivided into the various biological and natural sciences, thus including botany, zoology, physiology, psychology, paleontology, ornithology, entomology, and anthropology. Natural philosophy was articulated into specialized physical sciences (astronomy, physics, chemistry, mineralogy, geology, meteorology, and physical geography); similarly, history, economics, political sciences, sociology, and anthropology acquired their own specificity within the field of moral philosophy. The scientific discoveries of the twentieth centuries in astronomy and physics challenged the positivistic assumptions of a rigid and indestructible matter, obedient to rigid laws. More generally, these new insights questioned the close correspondence between what the universe is really like and the picture rendered by science at a certain point in time and brought the debate about the epistemic status of scientific knowledge to the forefront. At the same time, and almost paradoxically, the process of disciplinary subdivision went even further as scholars tended to specialize in ever narrower aspects of one discipline. However, as noted by David Easton and Corinne S. Schelling (1991), real world problems are rarely confined to a specific knowledge domain and the parceled understandings afforded by the increasing specialization do not easily reassemble into a unitary view of the issue at hand. Proposed solutions include interdisciplinary training and teamwork within specific research topics, although the point of departure for these attempts at integration tends to remain the specialized knowledge granted by the various disciplines. On one hand, the overview of the development of disciplinary knowledge showed that a certain partition of the world in different domains reflects broad cultural and institutional trends. On the other hand, the nature of the object investigated makes specific methodological choices more effective and fruitful than others, thus characterizing each discipline as a specific way of knowing. In the next section, we turn to consider the influence that these differences in thinking have on learning and teaching.
Domain Learning Do teaching and learning differ across domains? As documented by Lee S. Shulman and Kathleen M. Quinlan (1996), educational psychologists’ answer to this question has changed considerably across time. During the first two decades of the twentieth century, the answer has been mainly in the affirmative. In particular, John Dewey (1902/1916) advocated the need to psychologize the subject matter of the studies by making explicit the research work that generated knowledge in a specific domain and by referring it to the present experience of the child. His experimental research was thus located within the naturalistic setting of the laboratory school. In the next decades, following the lead of researchers such as Thorndike, educational psychologists’ interest shifted toward the search for general theories of learning. Even when their research was nested within a particular subject matter, the general theoretical framework constrained the analysis of the disciplinary tasks. In addition, the controlled experiment in laboratory setting became the preferred methodological approach, further detaching psychological research from the educational setting. Beginning in the 80s, subject matters regained centrality. For instance, studies on classroom teaching increased understanding of the importance of pedagogical content knowledge. Further, comparisons between novices and experts uncovered the role played by heuristics typical of a certain discipline in the performance on domain specific tasks. Moreover, the classroom with its complexities came to be considered a viable and preferred setting for studying these issues. Overall, researchers found that performance of domain specific tasks calls for particular psychological processes. These findings spurred investigations of what pedagogical practices can best favor the development of these processes and thus improve students’ learning. In the ensuing sections, we consider some of the outcome of this research for the domains of reading, writing, history, mathematics, and science. Traditionally, these domains occupy a large portion of the educational curriculum, especially in the early years. Thus, it is not by chance that a large body of research about domain learning focused on these areas. We also mention a few controversial issues regarding the translation of research results into pedagogical practice. A general review of the work of educational psychologists in regard to learning within these specific domains may be found in the relevant chapters of the first and second editions of the Handbook of Educational Psychology (Alexander & Winne, 2006; Berliner & Calfee, 1996). Alexander (2006) offers an introductory overview of these topics.
Reading
Theories of learning have played a critical role in identifying what is meant by reading and writing, and more generally by literacy. Thus, definitions of readings span from the ability to decode (i.e., breaking the linguistic code) and to encode (i.e., convert written signs fluently into meaning), to being well-learned in a variety of topics, to a set of cultural practices (with more or less emphasis on the power structure engrained in them). The method chosen to study the process of reading and writing contributed to influence the definition of literacy, too. For example, the exclusive focus on observable behavior characterizing research in the behaviorist tradition precluded the possibility to study understanding. Thus, these researchers focused mainly on handwriting, grammar, word recognition, and perception of print. Further, assuming that meaning is inherent in the text and the individual’s role consists in uncovering it, understanding was mainly studied by observing vocabulary and recall. The pedagogical implications of this approach, still present in current curricula, include the suggestion to break the reading process into steps and to teach reading as a series of skills and subskills. As well exemplified by Jerome Bruner (1990), the cognitive revolution focused on explaining mental processes; thus, understanding how meaning was generated became crucial. However, within the cognitive tradition, researchers conceived meaning in different terms. Specifically, those researchers working within the framework of information-processing theory assumed that meaning is transported from the author to the readers, while constructivists posited that meaning is constructed by the readers on the basis of information provided by the author. This difference notwithstanding, cognitive psychologists fostered understanding of how individuals make sense of information conveyed by texts. By investigating the nature of readers’ schemata and how information was organized in memory, researchers studied the role of background knowledge (Anderson & Pearson, 1984). Other studies focused on how different texts work, paying attention to their various structures (e.g., narrative or expository; Alexander & Kulikowich, 1994). Finally, research on the control that individuals maintain during meaning-making has explored individuals’ knowledge of their own cognitive processes (i.e., metacognition). In particular, researchers investigated individuals’ knowledge of the tasks and goals required by reading or writing (i.e., declarative knowledge), of the strategies that allow one to pursue these goals (i.e., procedural knowledge), and individuals’ awareness of how, when, and where to use a specific strategy (i.e., conditional knowledge; Garner, 1987). This work provided the background for research in strategy instruction and, limits notwithstanding, shifted the attention of educational psychologists from product to process. Finally, cognitive psychologists fostered understanding of two basic processes of reading: phonemic awareness and automaticity. Phonemic awareness is the ability to think and manipulate sounds and plays a central role in the study of reading development. Automaticity regards the ability to process perceptual information necessary to the decoding of print with a minimum cognitive load, thus freeing attention for meaning making purposes; within this process, accuracy and speed emerged as good predictors of comprehension (Stanovich, 1990). These findings suggest the soundness of a balanced reading program, in which mastering basic processes and meaningful engagement with text reinforce each other. The social constructivist perspective highlighted the social dimension of learning. Thus, the definition of text was extended beyond the printed words to include conversation, media, and more generally, social discourse. This perspective also implied a crucial epistemological shift, since it defined knowledge as the consensus reached by the community of knowledgeable peers for the time being. Thus, according to this view, the external world may exist, but knowledge is not defined anymore by a correspondence to it (Bruffee, 1986). Such a view also suggested that thinking is an internalized version of conversation; thus learning happens first on the social plane and then it is internalized by the individual (Vygotsky, 1934/1986). Pedagogically, this perspective advocated practices such as reciprocal teaching and whole language approach. This framework also drew attention on the influence of the context on the meaning making process.
Writing
The importance of writing for communication, learning, and knowledge transmission can hardly be overstated. However, the scientific study of the process of writing is relatively recent (Graham, 2006). In the previous section, we considered the influence of different theoretical approaches on the study of literacy in general and described their pedagogical suggestions in terms of reading. In this section, we focus on that body of research that specifically addressed the writing process and on its pedagogical implications. Relying mainly on analyses of think-aloud protocols collected from individuals of different ages and levels of expertise while composing texts, researchers in this domain emphasized that writing is a self-directed process. Often proceeding in a non-linear fashion, this process requires individuals to attend simultaneously to several cognitive demands, and thus entails a high level of effort. Although most of the research focused on cognitive processes, motivational and contextual factors were also found to influence writing (e.g., competence beliefs, and environmental support). Most theorists view writing as the interplay of three main components (Hayes & Flower, 1980). The first comprises factors external to the writer, such as topic, audience, and text produced so far. The second component regards the cognitive processes involved in writing and includes planning (e.g., setting goals, generating ideas, and organizing ideas into a plan), text production (e.g., translating plans into a written text), and reviewing (critically reading the text, determining how to address emerged problems, and editing). The final component is the writer’s long-term memory, which includes knowledge of the topic, of the intended audience, and of rhetorical devices, as well as general plans to perform the writing task. This body of research suggests that teaching writing should address all its components (Hillocks, 1984). In particular, direct teaching of strategies for planning and revising has proven particularly effective (Graham, 2005). At the same time, mastering of basic skills such as handwriting and spelling is also crucial to allow individuals to attend to the multiplicity of writing demands. The learning environment can sustain students’ development of writing strategies by offering appropriate scaffolding and peer-interactions. Finally, increased awareness of the processes of reading and writing, of their differences as well as of their similarities, can foster the development of programs that facilitate development in both domains (Shanahan, 2005).
History
Although there is general agreement in identifying the domain of history with the past, psychological research has associated strikingly different processes to learning in history. In the first decades of the twentieth century, for example, learning history was viewed as the acquisition of temporal perspective and moral ideals (Hall, 1911), the maturation of chronological and causal thinking (Judd, 1915), and the development of historic sense (Bell, 1917). Educational researchers overall agreed that learning history could not be reduced to answering factual questions; however, they also realized that this component of learning was the easiest to test. Behaviorism further restricted the study of domain specific topics; in the case of history, research was limited to study how to apportion facts in order to facilitate memorization. It was only with the cognitive revolution that the attention of researchers focused on the psychological processes involved in learning history (Wineburg, 1996). Aided by the use of qualitative methodologies, educational psychologists explored learners’ background knowledge, trying to uncover beliefs and conceptions that may foster or hinder thinking in history (e.g., ideas about time and chronology, sparse information about historical people and events, and beliefs about the nature of history). They also studied how historians and novices generated historical understanding while reading primary and secondary sources about specific events (Wineburg, 2001). This body of research suggested that learning history entails developing familiarity with concepts and ideas that allow a description of the past (i.e., substantive knowledge) and also becoming acquainted with the strategies employed by historical inquirers to research and interpret the past (i.e., procedural knowledge). In particular, the development of substantive knowledge includes being able to answer who, what, when, where, and how questions about the past (i.e., first-order knowledge), but also developing an understanding of concepts such as causation, change, historical significance, empathy, evidence, and account that allow historical investigators to interpret the past (i.e., second-order knowledge; Lee, 2005). By comparison, procedural knowledge regards being able to use strategies such as assessing the status of sources, corroborating sources, contextualizing events, constructing evidence-based arguments, and writing accounts (VanSledright & Limón, 2006). The difference of these processes with the experience of memorization of information commonly associated to learning history is striking. Although research in the past twenty years has increased understanding of the process of learning history and highlighted its specificity, the intense debate about the role of history in the school curriculum makes it difficult to translate these findings into pedagogical practice. In schools, the goal of developing historical thinking is often countered by the will to use history to build a collective, national identity. While the first purpose is well served by pedagogical approaches that foster a view of history as a critical inquiry into the past, the second is better pursued by the transmission of a specific narrative viewed as coinciding with the past. In addition, more research is needed to understand how to prepare teachers able to foster historical thinking in their students.
Mathematics
Historically, the characterization of mathematics evolved from a science of numbers and space to a science of patterns. More recently, the view of mathematics as a human activity defined within historical, cultural, and social contexts also emerged. In psychological research, specific aspects of mathematics learning were often used for studying general theories and pedagogical approaches. However, the specificity of thinking within this domain was usually ignored (De Corte, Greer, & Verschaffel, 1996). As surfaced in other domains considered herein, different psychological theories of cognitive development espoused distinctive views of mathematics, used a various array of research methodologies, focused on particular aspects of mathematics learning, and thus reached different pedagogical conclusions. Behaviorism and connectionism, for example, favored drill and practice of well-defined information, skills, and associations. The view of mathematics learning changed remarkably with the cognitive revolution, shifting the focus on the processes involved in thinking mathematically. In characterizing the domain, researchers highlighted the dual nature of mathematics. Rooted in the perception and description of the order of objects and events, once mathematics succeeds in modeling these structures through a process of symbolical representation, these representations become amenable to study in an abstract fashion, independent from their real world roots. The pedagogical consequence of acknowledging this feature of the domain is a shift of focus from computation to modeling (i.e., the thinking of the mathematician; Davis, 1992). A second characteristic of the domain regards the fact that, historically, mathematical concepts evolved hierarchically, through a series of restructuring of previously developed concepts, definitions, and functions. The parallel with Piagetian characterization of cognitive growth through a series of restructuring engendered by a situation of disequilibrium perhaps explains why mathematics was so often used by cognitive psychologists to study general cognitive development. Pedagogically, this feature of the domain supports practices that help the child relive the developmental process of the discipline (Freudenthal, 1991). This indication does not suggest that children need to reinvent the product of this development (e.g., the definition of rational numbers), rather that they have to trod the same cognitive path of people facing mathematical problems (e.g., abstracting and formalizing). Finally, development in mathematics requires that individuals are comfortable with multiple modes of representation (e.g., verbal/syntactic, visual/spatial, and formal/symbolic) and fluent in translating from one system to the other. In particular, researchers theorized that mathematical thinking implies the interplay of external representations (e.g., language, symbols on a page, and objects), and internal mental processes, which include internal representations, affective processes, and executive functions (e.g., planning, and monitoring; Goldin, 1992). Pedagogically, this theory suggests that learning mathematics means fostering the development of internal representations well connected and consistent with conventional external representations; fluid movement across different systems of representation needs also to be promoted. In schools, mathematics is often associated to “doing” mathematics rather than thinking mathematically. Thus, problem solving takes a central place in the curriculum and a large body of research in mathematics focused on investigating this process. From these studies, it emerged that problem solving involves the interplay of four factors: domain-specific knowledge; heuristic methods; metacognitive knowledge; and affection (beliefs and emotion). Domain-specific knowledge refers to definitions, formulas, symbols, algorithms, and concepts typical of the domain. Although this knowledge in experts is well organized and thus flexibly accessible, misconceptions and defective skills often hinder problem solving in novices. In addition, experts tend to categorize problems according to their mathematical structure, whereas novices focus on problem surface characteristics (Chi, Glaser, & Farr, 1988; Confrey, 1990). Heuristics are general guidelines that facilitate a systematic approach to the task and thus favor arriving at a solution (e.g., identifying the data of the problem, looking for related problems, and checking the results). However, knowledge of isolated heuristics is usually not very helpful. Research suggests that a more successful approach requires teaching heuristics concurrently with metacognitive skills and while exposing students to a variety of situations, so that learners may understand when and how to use a certain heuristic (Schoenfeld, 1992). Metacognitive knowledge regards knowledge of one’s own cognitive functioning and self-monitoring of these cognitive activities. Skilled problem solvers demonstrate high control of their actions, including planning, monitoring, and if necessary make the required corrections to a previously implemented strategy. Finally, affective components of problem solving include beliefs about the self and about mathematics, and emotions such as interest in the task (McLeod, 1990). Research on problem solving has shown that it is possible to teach students to plan and monitor more effectively (Schoenfeld, 1985). In addition, when the learning environment is structured in such a way as to favor reflective practice and talk among students about their thinking, mathematical learning is usually improved (Lampert, 1990).
Science
Reflecting a trend evidenced in other domains, the definition of what it means to learn science and of what psychological processes are central to its development have been influenced by theories of cognitive development. The meaning of learning science has increasingly broadened to include an understanding of substantive concepts and of the nature of science, logical reasoning, procedures used to develop scientific explanations, and metacognitive awareness (Linn, Songer, & Eylon, 1996). Comparisons between expert and novice thinking demonstrated that novices’ knowledge is organized around concrete factors (e.g., formulas), while experts’ knowledge tends to be hierarchically organized around abstract elements (Chi, Feltovich, & Smith, 1981). Beginning in the late seventies, researchers increasingly distinguished between development of logical skills and development of scientific concepts (Pfundt & Duit, 1991). In addition, research extended beyond the acquisition of science information to investigate learners’ ideas about the nature of science (Hestenes, 1992). The acknowledgment of the role of metacognition in learning paralleled this shift in focus, suggesting that monitoring one’s own cognition is an important component in learning science, once one abandons the idea that science consists of universal truth contained in textbooks (White, 1988). The interpretation of students’ misconceptions also changed; previously conceptualized as instances signaling faulty reasoning on the students’ part, these ideas began to be interpreted as alternative intuitions or framework to model the world. Researchers noted that students’ misconceptions may originate from inaccurate implications drawn from accurate observations, on a focus on inessential characteristics of phenomena, or on the adoption of standards of evidence and views of science markedly different from those espoused by the scientific community (Kuhn, Amsel, & O’Loughlin, 1988). From these insights, two lines of research developed; the first one focused on conceptual change, the second on the restructuring of knowledge. Consistent to Piagetian theory, conceptual change tended to be promoted by using cognitive conflict as a mechanism to foster scientific understanding. More recently, researchers studied what can motivate students to change their current understandings and found that, in addition to facing disconcerting evidence about their current concepts, students also need to confront clear alternatives (Strike & Posner, 1985). This new approach prompted teachers to focus on fostering and guiding the reasoning process of students while they investigate phenomena rather then contradicting the conclusions they reach. The investigation of experts’ organization of scientific knowledge showed that scientists often use qualitative models (e.g., free-body diagrams) as aid in problem-solving. They also tend to chunk knowledge in patterns that can be used in a variety of situations, developing production rules that link a condition (e.g., “the object in contact have different temperature”) to a consequent action (e.g., “the objects will tend toward equilibrium”). In addition, experts tend to entertain several models of scientific phenomena and to choose on which one to rely according to the specific problem they face (Reif & Larkin, 1991). Studies of novices found that students often entertain conflicting interpretations of scientific phenomena. Some researchers hypothesized that students’ scientific knowledge tends to be fragile and fragmented (diSessa et al., 2002); other studies showed that students tend to contextualize their views, applying one set of ideas to interpret phenomena within the classroom context and another set to deal with the same instance out of class (Gilber & Boulter, 2000). In addition, novices’ ability to generalize a model across a range of experiences is usually limited. These findings supported a change in the goals set for science education, with the focus shifting from acquiring science information and concepts to developing the ability to reason scientifically about phenomena (Linn & Eylon, 2006). Pedagogically, this view suggests that students are exposed to a variety of explanatory models and provided with criteria for selecting among them according to the problem considered. Far from engaging students in inquiry or discovery activities for their own sake, this approach highlights the development of background knowledge, modeling and discussion of key processes and strategies, instructional guidance, feedback, use of evidence to test one’s own ideas, and monitoring of one’s progress (Alexander, 2006).
Concluding Thoughts The roots of current disciplines and domains of study reach well back in history. These areas of knowledge and practice have not only reflected societies and cultures of their time, but have also influenced them, especially through formal educational systems. The differences in domains continue to shape the landscape of academic practice due to their inherent and socially-constructed nature. Here we have explored several of those features that define contemporary domains and their instantiation in educational practice.
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