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NRCSL's research into the kind of learning demanded by modern life has been shaped by the understanding, based on earlier theoretical studies, that knowledge is actively constructed in the mind of the learner, not just accumulated and stored for use. The construction process requires the learner to link incoming information with existing knowledge and make sure the connections are sound. This means adjusting for contradictions and making appropriate, reasoned use of the understanding that develops. The process never ends. Each new situation in which understanding is applied generates further information and insights, and these in turn may call for subtle or radical reconfigurations of the learner's knowledge structures. Such knowledge structures are thus fluid and constantly changing.
In order to engage in such fluid knowledge "architecture," learners must eventually attain intellectual independence. Once they have become full-fledged workers, citizens, and consumers, most will have little access to direct instruction. So if instruction must eventually turn learning over to the learners, education research must investigate how it can do so.
But a fundamental concern of all NRCSL research is the relationship between knowledge and skill in effective learning. It is impossible either to reason without some piece of knowledge to reason about or to acquire that piece of knowledge without using some skill in reasoning. As NRCSL Director Lauren Resnick has said, students must learn to think and think to learn. They must learn to read but also learn to question, probe, and reason about the content of texts. They must learn to calculate but also understand which calculations to use when, and why. They must learn about scientific phenomena not only from texts and lectures but also by posing hypotheses, designing experimentation strategies, and analyzing the results of their experiments. In all cases, learners must become aware of what they do not know and be able to bridge the gaps in their knowledge.
In this sense, knowledge construction--the bridging of knowledge gaps--requires learners to reason with incomplete information. They must begin with what they already know, target what they want to learn, and think their way to truly "educated" guesses as to the skills and information that will connect the two. For example, a reader who opens a history text will already know something about the period it covers, if only the names of a few prominent figures or events from that time. But unless the text is truly well matched to the student's level of background knowledge--an infrequent case--the student will constantly have to monitor and adjust her comprehension. She must identify the points at which her understanding breaks down and figure out how to compensate for holes in both the text and her own knowledge.
Such inferential processes are central to deep learning, regardless of whether a student is questioning the validity of an author's message, broadening her intuitive, preschool knowledge of numbers and quantities to encompass early formal mathematics, or trying to explain an unfamiliar scientific phenomenon in terms of concepts she already grasps.
Sophisticated learning skills like these are important for all American students. The deep understanding that arises from a balanced interplay between thinking and learning, skill and knowledge, is valuable for its own sake but also empowers and motivates learners. Students who see beyond facts and procedures to the principles that bring them to life are likely to regard themselves as effective thinkers, people who can generate sound solutions to unexpected problems. Students who gain such confidence are the ones who indeed become the mindful architects that Robert Glaser describes. Reforms that can support such learning are needed everywhere, because most American classrooms still rely too heavily on rote or didactic methods that do little to promote true reasoning and problem solving.
Math Learning: Building on Children's Intuitive Understanding of Numbers and Quantities. A consistent characteristic of the knowledge children gain about numbers before they enter school is that their understanding requires no justification or explanation. Children do not need to ask whether, or why, drinking from a glass of juice leaves less juice in the glass. Experience tells them this is so, just as it tells them that cutting a pie into eight wedges does not change the total amount of pie in the pan. Children gain this kind of understanding from daily, real-life encounters with large and small objects and quantities and from observing and comparing them under many different circumstances.
A strand of analytic research at NRCSL examined children's pre-school grasp of fundamental math concepts and suggested that bringing preschoolers practical, hands-on experience with objects and quantities into the classroom could ease their transition to formal mathematics learning. It was thought that encouraging primary-grade students to invent and discuss their own solutions to mathematical puzzles could lead them to discover for themselves many concepts and procedures standardly taught in the early mathematics curriculum. This theory has been supported in a collaboration between the researchers who helped to generate it and an elementary mathematics teacher who joined with them in hopes of improving her young students arithmetic skills and comprehension. Over the past 4 years, this teacher, in consultation with the research team, has introduced, refined, and closely evaluated a variety of new teaching techniques, all designed to encourage children's discovery of arithmetic concepts and computations. Each year, standardized test scores have testified to steady improvements in these children's understanding of arithmetic and to their growing confidence in their ability to reason mathematically. The knowledge they have gained through experimentation, discussion, and group problem solving appears to be as clear and self-evident to them as children's pre-school understanding of quantities. The children in the reformed math classes are able to justify and explain their solutions to problems and to describe their pathways to those solutions.
This kind of learning, which shows an awareness of principles as well as methods, is deeper than that which is gained by learning facts and mechanical procedures alone. Nevertheless, one NRCSL study comparing the cognitive complexity of two different methods of subtraction suggests that, at least in some cases, it is easier for students to learn procedures than to grasp the underlying concepts and principles. Since learning with a deep understanding of concepts is richer and more useful over a lifetime than procedural learning alone, a challenge for research is to identify scientifically sound ways that instruction can make complex learning tasks more accessible.
Further evidence of the greater power of conceptual learning comes from another collaboration between research and practice. This project has introduced techniques that, like those described earlier, are based on guided student inquiry and discovery rather than on direct teaching. The reforms in this case were developed and broadly disseminated through teacher training materials written and produced by members of the American Federation of Teachers. The materials were based on these experienced teachers clinical expertise combined with their understanding of math education research at NRCSL and elsewhere. The union of the two forms of understanding gave rise to the new instructional materials, which have succeeded with both students and teachers. One teacher, for example, said that her goal was no longer just to teach basic skills but to use them to help her students become good thinkers and problem solvers. As she put new forms of instruction to use, she saw children who had never spoken in class begin to contribute, and she saw students devising a variety of valid solutions to problems. Their confidence and enthusiasm reached gratifying new levels.
The success of these two collaborations in mathematics education can be explained in part by other work at NRCSL that has continued to analyze children's acquisition of number sense and mathematical concepts. This work theorizes that children develop a rich cognitive understanding of quantities, numbers, and mathematical operations in a particular order; that all the levels of understanding they acquire can be useful at any time; but that the order in which they develop should not be ignored or violated by instruction. This notion of children's progression from intuitive understanding to an ability to grasp formal concepts is embodied in the new approaches to instruction that the two collaborative projects have developed.
Text Comprehension: Linking Background Knowledge to New Knowledge. NRCSL studies of text comprehension have identified a range of inferential processes, from relatively low-level abilities to highly sophisticated skills. In one study, for example, findings showed that basic reading skill, regardless of subject matter, requires the reader to infer numerous small pieces of information, such as the antecedent for a pronoun or the implicit object of an action. Such inferences are essential in all reading. They have more to do with text syntax and structure than with conceptual content, and they bridge very small knowledge gaps, sometimes without the reader's conscious effort.
When the knowledge gaps are larger--as when a history text mistakenly assumes young readers already understand a concept such as taxation without representation--a more focused and mindful use of inference can help to bridge those gaps. This possibility is illuminated in another text-comprehension project that closely analyzed both the content and intent of elementary school history texts in order to identify exactly where and why these texts presented problems for young readers. Researchers revised the problematic texts to compensate for the identified weaknesses and then gave groups of students either the original text or the revised text, alone or with supplementary background material. Students who read the revised version alone learned and understood the text's content better than students who read the original text with or without the background information. But students who read both the revised text and the background material performed the best of all, supporting the notion that coherent texts are most powerful when students have sufficient knowledge to reason well about their content.
Science Learning: Lessons from Effective Learners. The mathematics and text-comprehension research strongly implies that instruction can guide and discipline students' intuitive tendency to infer what they are not directly told by texts or teachers. The implication is further supported by research on science learning that compares the learning strategies of better and poorer learners in several settings.
The first of these science learning projects is connected to work on text comprehension because it examines the understanding that students gain from reading science texts. Students in this project were asked to read a problematic text on the human circulatory system and to assess their understanding of each sentence as it was read. Researchers supplied high-level prompts as the students read, asking them questions designed to stimulate a deeper probing of the content. A striking outcome was the finding that several of the more effective learners accurately inferred facts and concepts that the text covered poorly or not at all. Their means of doing so resembled the skills involved in the text revision processes described above, but these effective learners were not reading in order to improve the text or to generate explanations for classmates; they were compensating for text inadequacies even as they read, continually generating explanations that would fill gaps in the material presented.
Readers' responses to researchers' prompts suggested that significant textual inadequacies--large gaps that required a major piece of information to be added, such as the function of a circulatory system component--could sometimes be overcome by a gradual process in which numerous minute inferences were drawn from practical experience, common sense, background information on the subject, or earlier passages in the text. The cumulative effect of these seemingly insignificant inferences eventually supported the larger inference--the generation of the missing piece of information needed to bridge the comprehension gap.
This process of slowly amassing inferences often required learners to correct for errors along the way. An incorrect inference would come to light when the reader encountered contradictions in the text or when one inference failed to mesh satisfactorily with others. To address such cognitive conflicts, readers had to generate and test new inferences until the contradictions were resolved.
Self-explanation and cognitive conflict together make a powerful learning technique. The first, if viewed as an ability to be cultivated through careful instruction, provides the means of resolving the second. Although the good readers in the science text study were better able than poorer ones to take advantage of researchers' searching prompts, the work on self-explanation suggests that most students could be taught to ask themselves these kinds of questions. This could foster habits of thought through which readers would constantly evaluate written material for its completeness, clarity, consistency, and accuracy. These are the kinds of skills that motivate students, raise their confidence, and lead them eventually to intellectual independence from formal instruction.
Variations on the skills of self-explanation were investigated in another study of effective science learning, one that focused on scientific experimentation as a means of constructing new knowledge and linking it to existing knowledge. This research is especially informative about the inferential nature of deep learning because it not only compares good and poor strategies but also compares structures of learning in three science topics--microeconomics, electrical circuits, and the refraction of light. Students were asked to devise and carry out experiments in each topic as a means of discovering the topic's governing rules and principles. A computer microworld in each topic offered an environment for simulated, hands-on experimentation, and an intelligent on-line tutor helped students evaluate their experimentation strategies throughout.
Different strategies were effective in different topics, depending on such factors as the relationships among variables or the reliability of students' existing background knowledge. All students conducted experiments in all three microworlds, working in the refraction microworld last because successful discovery in that topic required a combination of the skills and techniques needed in the other two topics. Students' experimental and inferential skills improved steadily as they progressed through the three microworlds, suggesting that the skills they developed in the first two were helping them with their discovery processes in the third. In addition, the most successful students adapted their skills appropriately for different knowledge domains.
Researchers attributed this result to students' "learning how to learn." The students who learned the most about successful scientific discovery engaged in different kinds of experimenting activities than the students who learned less. For example, when effective learners searched for evidence of a microworld's governing principles, they typically arrived at tentative hypotheses after only one or two experiments and then attempted to confirm those hypotheses in a systematic way. Poorer learners did not distinguish between data that could suggest and data that could test hypotheses. Similarly, successful learners quickly recognized and responded appropriately to experimental outcomes that contradicted their hypotheses, whereas those who were less successful tended to misread or misinterpret such feedback and to persist in unproductive experiments.
These comparisons support the notion that focused, mindful inference-making processes tend to generate systematic, efficient learning activities that in turn foster a deep understanding of a topic. Like the research on mathematics learning and text comprehension, this work further implies that the knowledge gained from discovery activities and the deliberate use of inferential skills is authoritative, useful knowledge. Because it is imbued with both content and skill it is more likely to be useful in unfamiliar situations than knowledge comprised of facts and mechanical procedures alone.
Learning About Argumentation: The Value of Cognitive Conflict. At the heart of every discipline are strict standards for measuring the soundness of evidence concerning the discipline's principles, facts, and conclusions. In disciplines such as social science the defense of arguments and assertions often rests on informal reasoning as well as on empirical evidence. Because successful knowledge construction so often involves generating and testing arguments and claims, new learners need to grasp and observe the rules for doing so.
NRCSL research on argumentation demonstrates the value of deliberate instruction in the structure and evaluation of arguments. All students argue--just as all students draw inferences--but very few learn how to argue clearly and effectively. NRCSL research found that typical texts and classrooms do not offer many opportunities for students to practice or analyze argumentation skills--any more than they offer practice in text analysis, mathematical discovery and invention, or intensive experimentation. History texts that were examined, for example, did not analyze events and their causes but merely stated the facts of historical matters. It is not surprising, then, that student attempts to explore and defend their ideas are haphazard rather than carefully reasoned. By the end of middle school, this research indicated, few students are able to identify or evaluate the components of arguments--premises, examples, counterexamples, conclusions--and fewer still can construct an argument-based paragraph. Thus, they lack a form of reasoning that is essential to conceptual understanding in many subject matters, and they are unlikely to reach intellectual independence without this skill.
Although argumentation need not involve conflict, NRCSL research suggests that defending an opinion against opposing viewpoints in small-group discussion may promote learning. Instruction might capitalize on this possibility both by teaching the principles and standards of informal argument and by designing group interactions for practical experience in argument construction and justification.
Small-group research at NRCSL investigated different effects of cognitive conflict in minority- and majority-opinion holders and studied the degree to which the need to argue a minority or majority viewpoint stimulated study and research on the issue, the students' own position, and the opposing position. Findings indicated that just the anticipation of having to defend an opinion in front of others who may disagree strongly motivated students to learn and think about the topic being debated. The research also suggested that differences in the groups' minority/majority ratios and in the amount of confidence and background knowledge the arguers possessed could determine whether--and which--group members were likely to be swayed by the arguments of others.
Together, the strands of research on the learning that can arise from skill in argumentation and informal reasoning provide good evidence that practice in argument generation, analysis, and justification can make deliberate a process that everyone uses naturally but not always to greatest effect. Designing situations in which learners encounter and must respond to interpersonal cognitive conflict can provide settings for such practice.
For example, explanations at the heart of much instruction are inherently incomplete, just as texts and arguments are, and it falls to the teacher to provide sufficient detail and definition for her students' level of background knowledge. She may test for background knowledge at the beginning of instruction, but day to day she will have to monitor student comprehension, identify problem areas, and adjust her teaching to compensate. At the same time, her construction of explanations and her ability to guide classroom discourse require reasoning skills that she can model for her students even as she assesses and attempts to nurture their reasoning abilities.
These and countless other complex tasks are demanded by the need for higher educational performance in this country. But teachers cannot excel at such tasks unless they themselves are skilled at self-explaining, compensating for their own knowledge gaps, assessing their classroom performance, and perceiving and adjusting for weaknesses in their own and their students' arguments. Many teachers who wish to improve their instruction therefore find it necessary to pursue higher professional standards than they have been trained to achieve. It stands to reason that, if too many American schools are still bound to educational goals that stress the rote mastery of so-called basic skills, too few teachers have been encouraged and offered the opportunity to instill in their students the guided and fully intentional use of the inferential skills necessary for accurate knowledge construction and solid conceptual understanding. If teachers want their students to become mindful architects of their own knowledge, then the teachers themselves need to be mindful architects, too--not only of their own knowledge but of the fluid and complex teacher-student relationship called instruction. The teachers who participated in the mathematics collaborations at NRCSL, for example, all found the pursuit of higher professional standards integral to their goal of raising standards for their students.
Some of the groundwork for the NRCSL collaborations and for the recognition that teacher professionalism is crucial to successful education reform was laid by analytic research at NRCSL on the complex cognitive processes involved in expert instruction. This theoretical work helped to raise the research community's awareness of how intricate the processes of teaching are--how many considerations a teacher must juggle at one time, how subtly cues from students may signal comprehension difficulties, how expertise builds over years of practice. This research identified and described in detail many components of successful lessons and instructional techniques, often in the context of contrasting the methods of inexperienced teachers with the methods of experts.
However, researchers alone--even those who have conducted extensive classroom-based studies--do not continually experience the real-world difficulties and dilemmas of introducing reforms into an environment that may resist, obstruct, or merely fail to understand important departures from longstanding norms. Only teachers, once they have grasped research findings that support sound instructional innovations, can adapt those findings and innovations to the needs and realities of their classrooms, schools, students, and colleagues. Teachers who wish to promote the widespread, research-based reforms that American education urgently needs must not only achieve new levels of professionalism but must also train and mentor their colleagues.
The relationship between NRCSL research and classroom practice has been part of a research cycle in which theoretical investigations may eventually move into the development and refinement of new instructional methods, often through close collaboration with teachers. These efforts may well lead in turn to fully applied work in which the innovations are demonstrated in pilot classrooms and then disseminated to additional schools and school districts. Finally, these classroom applications may raise new questions for theoretical research. For example, a line of mathematics research at NRCSL that has been applied in classrooms for more than 3 years has now generated new work, a qualitative analysis of these classrooms that attempts to understand theoretically why the applications succeed.
In addition to the ongoing mathematics applications, research on science learning plans to study and develop instructional interventions in consultation with participating classroom teachers. The text processing project now works directly with students and with teachers, instructing them in text revision processes and studying the effects those processes have on learning and understanding. Finally, the work on informal reasoning and argumentation has moved beyond the basic investigations described above and now aims to develop and test instructional techniques for motivating and imparting the skills needed to construct and justify sound arguments. As these applications proceed, they too may confront new theoretical questions--questions that would never emerge at all if not for the intersection of research with classroom practice.
We know from theoretical work that active reasoning is crucial to a grasp of concepts and principles; and we know from many of the classroom interventions being developed, tested, and disseminated through NRCSL that instruction can indeed impart to students the critical, self-regulatory habits of mind that support conceptual understanding. But much remains to be accomplished, both at NRCSL and in the field as a whole. We need to learn more about why and how certain circumstances, tools, and techniques enhance the learning process. We need to understand more about each complex component of effective teaching, from explanations to the monitoring of students' comprehension. We need to see more clearly into the cognitive processes that support conceptual understanding so that we can continue to develop instructional methods that reflect and work with the mind's own activities. The success of every school child in the United States depends upon investigations such as these.
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[Introduction ]