Beyond Reason: Eight Great Problems That Reveal the Limits of Science


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For example, the concept of the equivalence of mass and energy emerged from the mathematical analysis conducted by Einstein, based on the premises of special relativity. Modern theoretical physics is so heavily imbued with mathematics that it would make no sense to try to divide it into mathematical and nonmathematical parts. In much of modern science, predictions and inferences have a probabilistic nature, so understanding the mathematics of probability and of statistically derived inferences is an important part of understanding science.

Computational tools enhance the power of mathematics by enabling calculations that cannot be carried out analytically. For example, they allow the development of simulations, which combine mathematical representations of. Computational methods are also potent tools for visually representing data, and they can show the results of calculations or simulations in ways that allow the exploration of patterns.

Engineering, too, involves mathematical and computational skills. For example, structural engineers create mathematical models of bridge and building designs, based on physical laws, to test their performance, probe their structural limits, and assess whether they can be completed within acceptable budgets. Virtually any engineering design raises issues that require computation for their resolution.

Although there are differences in how mathematics and computational thinking are applied in science and in engineering, mathematics often brings these two fields together by enabling engineers to apply the mathematical form of scientific theories and by enabling scientists to use powerful information technologies designed by engineers. Both kinds of professionals can thereby accomplish investigations and analyses and build complex models, which might otherwise be out of the question. Mathematics including statistics and computational tools are essential for data analysis, especially for large data sets.

The abilities to view data from different perspectives and with different graphical representations, to test relationships between variables, and to explore the interplay of diverse external conditions all require mathematical skills that are enhanced and extended with computational skills. As soon as students learn to count, they can begin using numbers to find or describe patterns in nature. At appropriate grade levels, they should learn to use such instruments as rulers, protractors, and thermometers for the measurement of variables that are best represented by a continuous numerical scale, to apply mathematics to interpolate values, and to identify features—such as maximum, minimum, range, average, and median—of simple data sets.

Students should have opportunities to explore how such symbolic representations can be used to represent data, to predict outcomes, and eventually to derive further relationships using mathematics. Students should gain experience in using computers to record measurements taken with computer-connected probes or instruments, thereby recognizing how this process allows multiple measurements to be made rapidly and recurrently. Likewise, students should gain experience in using computer programs to transform their data between various tabular and graphical forms, thereby aiding in the identification of patterns.

Students should thus be encouraged to explore the use of computers for data analysis, using simple data sets, at an early age. For example, they could use spreadsheets to record data and then perform simple and recurring calculations from those data, such as the calculation of average speed from measurements of positions at multiple times. Later work should introduce them to the use of mathematical relationships to build simple computer models, using appropriate supporting programs or information and computer technology tools. As students progress in their understanding of mathematics and computation, at.

Because science seeks to enhance human understanding of the world, scientific theories are developed to provide explanations aimed at illuminating the nature of particular phenomena, predicting future events, or making inferences about past events. Theories are not mere guesses, and they are especially valued because they provide explanations for multiple instances. A scientific hypothesis is neither a scientific theory nor a guess; it is a plausible explanation for an observed phenomenon that can predict what will happen in a given situation.

A hypothesis is made based on existing theoretical understanding relevant to the situation and often also on a specific model for the system in question. Scientific explanations are accounts that link scientific theory with specific observations or phenomena—for example, they explain observed relationships between variables and describe the mechanisms that support cause and effect inferences about them.

Very often the theory is first represented by a specific model for the situation in question, and then a model-based explanation is developed. For example, if one understands the theory of how oxygen is obtained, transported, and utilized in the body, then a model of the circulatory system can be developed and used to explain why heart rate and breathing rate increase with exercise. Scientific theories are developed to provide explanations aimed at illuminating the nature of particular phenomena, predicting future events, or making inferences about past events.

Engaging students with standard scientific explanations of the world—helping them to gain an understanding of the major ideas that science has developed—is a central aspect of science education. Asking students to demonstrate their own understanding of the implications of a scientific idea by developing their own explanations of phenomena, whether based on observations they have made or models they have developed, engages them in an essential part of the process by which conceptual change can occur. Explanations in science are a natural for such pedagogical uses, given their inherent appeals to simplicity, analogy, and empirical data which may even be in the form of a thought experiment [ 26 , 27 ].

And explanations are especially valuable for the classroom because of, rather than in spite of, the fact that there often are competing explanations offered for the same phenomenon—for example, the recent gradual rise in the mean surface temperature on Earth. Deciding on the best explanation is a matter of argument that is resolved by how well any given explanation fits with all available data, how much it simplifies what would seem to be complex, and whether it produces a sense of understanding. Because scientists achieve their own understanding by building theories and theory-based explanations with the aid of models and representations and by drawing on data and evidence, students should also develop some facility in constructing model- or evidence-based explanations.

This is an essential step in building their own understanding of phenomena, in gaining greater appreciation of the explanatory power of the scientific theories that they are learning about in class, and in acquiring greater insight into how scientists operate. In engineering, the goal is a design rather than an explanation. The process of developing a design is iterative and systematic, as is the process of developing an explanation or a theory in science.

These elements include specifying constraints and criteria for desired qualities of the solution, developing a design plan, producing and testing models or prototypes, selecting among alternative design features to optimize the achievement of design criteria, and refining design ideas based on the performance of a prototype or simulation. Early in their science education, students need opportunities to engage in constructing and critiquing explanations.

Using their measurements of how one factor does or does not affect. For example, in investigating the conditions under which plants grow fastest, they may notice that the plants die when kept in the dark and seek to develop an explanation for this finding. They should be encouraged to revisit their initial ideas and produce more complete explanations that account for more of their observations. By the middle grades, students recognize that many of the explanations of science rely on models or representations of entities that are too small to see or too large to visualize.

In the later stages of their education, students should also progress to using mathematics or simulations to construct an explanation for a phenomenon. In some ways, children are natural engineers. They spontaneously build sand castles, dollhouses, and hamster enclosures, and they use a variety of tools and materials for their own playful purposes.

Thus a common elementary school activity is to challenge children to use tools and materials provided in class to solve a specific challenge, such as constructing a bridge from paper and tape and testing it until failure occurs. Furthermore, design activities should not be limited just to structural engineering but should also include projects that reflect other areas of engineering, such as the need to design a traffic pattern for the school parking lot or a layout for planting a school garden box.

In middle school, it is especially beneficial to engage students in engineering design projects in which they are expected to apply what they have recently learned in science—for example, using their now-familiar concepts of ecology to solve problems related to a school garden. Middle school students should also. At the high school level, students can undertake more complex engineering design projects related to major local, national or global issues.

Whether they concern new theories, proposed explanations of phenomena, novel solutions to technological problems, or fresh interpretations of old data, scientists and engineers use reasoning and argumentation to make their case. In science, the production of knowledge is dependent on a process of reasoning that requires a scientist to make a justified claim about the world. Their arguments can be based on deductions from premises, on inductive generalizations of existing patterns, or on inferences about the best possible explanation.

Argumentation is also needed to resolve questions involving, for example, the best experimental design, the most appropriate techniques of data analysis, or the best interpretation of a given data set. In short, science is replete with arguments that take place both informally, in lab meetings and symposia, and formally, in peer review. Over time, ideas that survive critical examination even in the light of new data attain consensual acceptance in the community, and by this process of discourse and argument science maintains its objectivity and progress [ 28 ].

Becoming a critical consumer of science is fostered by opportunities to use critique and evaluation to judge the merits of any scientifically based argument. In engineering, reasoning and argument are essential to finding the best possible solution to a problem. At an early design stage, competing ideas must be compared and possibly combined to achieve an initial design, and the choices are made through argumentation about the merits of the various ideas pertinent to the design goals.

At a later stage in the design process, engineers test their potential solution, collect data, and modify their design in an iterative manner. The results of such efforts are often presented as evidence to argue about the strengths and weaknesses of a particular design. Although the forms of argumentation are similar, the criteria employed in engineering are often quite different from those of science.

For example, engineers might use cost-benefit analysis, an analysis of risk, an appeal to aesthetics, or predictions about market reception to justify why one design is better than another—or why an entirely different course of action should be followed. The study of science and engineering should produce a sense of the process of argument necessary for advancing and defending a new idea or an explanation of a phenomenon and the norms for conducting such arguments.

In that spirit, students should argue for the explanations they construct, defend their interpretations of the associated data, and advocate for the designs they propose. Meanwhile, they should learn how to evaluate critically the scientific arguments of others and present counterarguments. Constructing and critiquing arguments are both a core process of science and one that supports science education, as research suggests that interaction with others is the most cognitively effective way of learning [ ].

Computing, mathematics, and science

Young students can begin by constructing an argument for their own interpretation of the phenomena they observe and of any data they collect. They need instructional support to go beyond simply making claims—that is, to include reasons or references to evidence and to begin to distinguish evidence from opinion. As they grow in their ability to construct scientific arguments, students can draw on a wider range of reasons or evidence, so that their arguments become more sophisticated. In addition, they should be expected to discern what aspects of the evidence are potentially significant for supporting or refuting a particular argument.

Students should begin learning to critique by asking questions about their own findings and those of others. Later, they should be expected to identify possible weaknesses in either data or an argument and explain why their criticism is justified.


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As they become more adept at arguing and critiquing, they should be introduced to the language needed to talk about argument, such as claim, reason, data, etc. Exploration of historical episodes in science can provide opportunities for students to identify the ideas, evidence, and arguments of professional scientists. In so doing, they should be encouraged to recognize the criteria used to judge claims for new knowledge and the formal means by which scientific ideas are evaluated today.

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In particular, they should see how the practice of peer review and independent verification of claimed experimental results help to maintain objectivity and trust in science. Being literate in science and engineering requires the ability to read and understand their literatures [ 34 ]. Science and engineering are ways of knowing that are represented and communicated by words, diagrams, charts, graphs, images, symbols, and mathematics [ 35 ].

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Even when students have developed grade-level-appropriate reading skills, reading in science is often challenging to students for three reasons. First, the jargon of science texts is essentially unfamiliar; together with their often extensive use of, for example, the passive voice and complex sentence structure, many find these texts inaccessible [ 37 ].

Second, science texts must be read so as to extract information accurately. Because the precise meaning of each word or clause may be important, such texts require a mode of reading that is quite different from reading a novel or even a newspaper. Third, science texts are multimodal [ 38 ], using a mix of words, diagrams, charts, symbols, and mathematics to communicate. Thus understanding science texts requires much more than simply knowing the meanings of technical terms.

Communicating in written or spoken form is another fundamental practice of science; it requires scientists to describe observations precisely, clarify their thinking, and justify their arguments. Science simply cannot advance if scientists are unable to communicate their findings clearly and persuasively. Communication occurs in a variety of formal venues, including peer-reviewed journals, books, conference presentations, and carefully constructed websites; it occurs as well through informal means, such as discussions, email messages, phone calls, and blogs. New technologies have extended communicative practices, enabling multidisciplinary collaborations across the globe that place even more emphasis on reading and writing.

Increasingly, too, scientists are required to engage in dialogues with lay audiences about their work, which requires especially good communication skills. Being a critical consumer of science and the products of engineering, whether as a lay citizen or a practicing scientist or an engineer, also requires the ability to read or view reports about science in the press or on the Internet and to recognize the salient science, identify sources of error and methodological flaws, and distinguish observations from inferences, arguments from explanations, and claims from evidence.

All of these are constructs learned from engaging in a critical discourse around texts. Engineering proceeds in a similar manner because engineers need to communicate ideas and find and exchange information—for example, about new techniques or new uses of existing tools and materials. As in science, engineering communication involves not just written and spoken language; many engineering ideas are best communicated through sketches, diagrams, graphs, models, and products.

Also in wide use are handbooks, specific to particular engineering fields, that provide detailed information, often in tabular form, on how best to formulate design solutions to commonly encountered engineering tasks. As such, every science or engineering lesson is in part a language lesson, particularly reading and producing the genres of texts that are intrinsic to science and engineering.

Students need sustained practice and support to develop the ability to extract the meaning of scientific text from books, media reports, and other forms of scientific communication because the form of this text is initially unfamiliar—expository rather than narrative, often linguistically dense, and reliant on precise logical flows. Students should be able to interpret meaning from text, to produce text in which written language and diagrams are used to express scientific ideas, and to engage in extended discussion about those ideas. From the very start of their science education, students should be asked to engage in the communication of science, especially regarding the investigations they are conducting and the observations they are making.

Careful description of observations and clear statement of ideas, with the ability to both refine a statement in response to questions and to ask questions of others to achieve clarification of what is being said begin at the earliest grades. Beginning in upper elementary and middle school, the ability to interpret written materials becomes more important.

Early work on reading science texts should also include explicit instruction and practice in interpreting tables, diagrams, and charts and coordinating information conveyed by them with information in written text. Throughout their science education, students are continually introduced to new terms, and the meanings of those terms can be learned only through opportunities to use and apply them in their specific contexts.

It follows that to master the reading of scientific material, students need opportunities to engage with such text and to identify its major features; they cannot be expected simply to apply reading skills learned elsewhere to master this unfamiliar genre effectively. Students should write accounts of their work, using journals to record observations, thoughts, ideas, and models. They should be encouraged to create diagrams and to represent data and observations with plots and tables, as well as with written text, in these journals. They should also begin to produce reports or posters that present their work to others.

As students begin to read and write more texts, the particular genres of scientific text—a report of an investigation, an explanation with supporting argumentation, an experimental procedure—will need to be introduced and their purpose explored. Furthermore, students should have opportunities to engage in discussion about observations and explanations and to make oral presentations of their results and conclusions as well as to engage in appropriate discourse with other students by asking questions and discussing issues raised in such presentations.

In high school, these practices should be further developed by providing students with more complex texts and a wider range of text materials, such as technical reports or scientific literature on the Internet. Moreover, students need opportunities to read and discuss general media reports with a critical eye and to read appropriate samples of adapted primary literature [ 40 ] to begin seeing how science is communicated by science practitioners. In engineering, students likewise need opportunities to communicate ideas using appropriate combinations of sketches, models, and language.

They should also create drawings to test concepts and communicate detailed plans; explain and critique models of various sorts, including scale models and prototypes; and present the results of simulations, not only regarding the planning and development stages but also to make compelling presentations of their ultimate solutions. Understanding how science has achieved this success and the techniques that it uses is an essential part of any science education. Although there is no universal agreement about teaching the nature of science, there is a strong consensus about characteristics of the scientific enterprise that should be understood by an educated citizen [ ].

For example, the notion that there is a single scientific method of observation, hypothesis, deduction, and conclusion—a myth perpetuated to this day by many textbooks—is fundamentally wrong [ 44 ]. Scientists do use deductive reasoning, but they also search for patterns, classify different objects, make generalizations from repeated observations, and engage in a process of making inferences as to what might be the best explanation.

Thus the picture of scientific reasoning is richer, more complex, and more diverse than the image of a linear and unitary scientific method would suggest [ 45 ]. What engages all scientists, however, is a process of critique and argumentation. The ideas that survive this process of review and criticism are the ones that become well established in the scientific community.

Our view is that the opportunity for students to learn the basic set of practices outlined in this chapter is also an opportunity to have them stand back and reflect on how these practices contribute to the accumulation of scientific knowledge. For example, students need to see that the construction of models is a major means of acquiring new understanding; that these models identify key features and are akin to a map, rather than a literal representation of reality [ 13 ]; and that the great achievement of science is a core set of explanatory theories that have wide application [ 46 ].

Understanding how science functions requires a synthesis of content knowledge, procedural knowledge, and epistemic knowledge. Procedural knowledge refers to the methods that scientists use to ensure that their findings are valid and reliable. It includes an understanding of the importance and appropriate use of controls, double-blind trials, and other procedures such as methods to reduce error used by science. As such, much of it is specific to the domain.

Epistemic knowledge is knowledge of the constructs and values that are intrinsic to science. Students need to understand what is meant, for example, by an observation, a hypothesis, an inference, a model, a theory, or a claim and be able to readily distinguish between them. An education in science should show that new scientific ideas are acts of imagination, commonly created these days through collaborative efforts of groups of scientists whose critiques and arguments are fundamental to establishing which ideas are worthy of pursuing further. Ideas often survive because they are coherent with what is already known, and they either explain the unexplained, explain more observations, or explain in a simpler and more elegant manner.

Thus any new idea is initially tentative, but over time, as it survives repeated testing, it can acquire the status of a fact—a piece of knowledge that is unquestioned and uncontested, such as the existence of atoms. Scientists use the resulting theories and the models that represent them to explain and predict causal relationships. When the theory is well tested, its predictions are reliable, permitting the application of science to technologies and a wide variety of policy decisions. In other words, science is not a miscellany of facts but a coherent body of knowledge that has been hard won and that serves as a powerful tool.

Engagement in modeling and in critical and evidence-based argumentation invites and encourages students to reflect on the status of their own knowledge and their understanding of how science works. And as they involve themselves in the practices of science and come to appreciate its basic nature, their level of sophistication in understanding how any given practice contributes to the scientific enterprise can continue to develop across all grade levels.

Layton, D. DeBoer, G. New York: Teachers College Press. Driver, R. Buckingham, England: Open University Press. Schwab, J. The Teaching of Science as Enquiry. Florman, S. The Existential Pleasures of Engineering. New York: St. Petroski, H. Collins, H. Cambridge, England: Cambridge University Press. Pickering, A. Chicago: University of Chicago Press. Latour, B. Longino, H.

The Fate of Knowledge. Bazerman, C. Shaping Written Knowledge. Madison: University of Wisconsin Press. Nercessian, N. Model-based reasoning in scientific practice. Duschl and R. Grandy Eds. Rotterdam, the Netherlands: Sense. Visualization and cognition: Drawing things together. Lynch and S. Woolgar Eds. Lehrer, R.

Cultivating model-based reasoning in science education. Sawyer Ed. Giere, R. Understanding Scientific Reasoning. Belmont, CA: Thomson Wadsworth. Millar, R. Beyond processes. Studies in Science Education, 14 , Abd-El-Khalick, F. Inquiry in science education: International perspectives. Science Education, 88 3 , Ford, M.

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Disciplinary authority and accountability in scientific practice and learning. Science Education, 92 3 , Berland, L. Making sense of argumentation and explanation. Science Education, 93 1 , Klahr, D. Dual space search during scientific reasoning. Cognitive Science, 12 1 , Kind, P. A Model for Scientific Reasoning. Stanford University. Schwarz, C. Developing a learning progression for scientific modeling: Making scientific modeling accessible and meaningful for learners.

Journal of Research in Science Teaching, 46 6 , Committee on K Engineering Education. Katehi, G. Pearson, and M. Feder Eds. National Academy of Engineering. Standards for K Engineering Education? Committee on Standards for K Engineering Education. Ogborn, J. Explaining Science in the Classroom. Duit, R. On the role of analogies and metaphors in learning science.

Science Education, 75 6 , Science as Social Knowledge. Goldacre, B. Bad Science. London, England: HarperCollins. Zimmerman, C. Public Understanding of Science, 10 1 , Alexander, R.

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York, England: Dialogos. Chi, M. Active-constructive-interactive: A conceptual framework for differentiating learning activities. Topics in Cognitive Science, 1 , Resnick, L. How well-structured talk builds the mind. Sternberg and D. Preiss Eds. New York: Springer. Norris, S. How literacy in its fundamental sense is central to scientific literacy. Science Education, 87 , Lemke, J. Multiplying meaning. Martin and R. Veel Eds. London, England: Routledge.

Tenopir, C. Communication Patterns of Engineers. Hoboken, NJ: Wiley. Martin, J. Reading Science. Kress, G. London, England: Hodder Arnold. Yarden, A. Reading scientific texts: Adapting primary literature for promoting scientific literacy. Research in Science Education, 39 3 , Osborne, J. Journal of Research in Science Teaching, 40 7 , Mccomas, W. The nature of science in international science education standards documents. McComas Ed. Dordrecht, the Netherlands: Kluwer.

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Gott, R. Durham, England: Durham University. Science, engineering, and technology permeate nearly every facet of modern life and hold the key to solving many of humanity's most pressing current and future challenges. The United States' position in the global economy is declining, in part because U. To address the critical issues of U. A Framework for K Science Education outlines a broad set of expectations for students in science and engineering in grades K These expectations will inform the development of new standards for K science education and, subsequently, revisions to curriculum, instruction, assessment, and professional development for educators.

This book identifies three dimensions that convey the core ideas and practices around which science and engineering education in these grades should be built. These three dimensions are: crosscutting concepts that unify the study of science through their common application across science and engineering; scientific and engineering practices; and disciplinary core ideas in the physical sciences, life sciences, and earth and space sciences and for engineering, technology, and the applications of science.

The overarching goal is for all high school graduates to have sufficient knowledge of science and engineering to engage in public discussions on science-related issues, be careful consumers of scientific and technical information, and enter the careers of their choice.

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A Framework for K Science Education is the first step in a process that can inform state-level decisions and achieve a research-grounded basis for improving science instruction and learning across the country. The book will guide standards developers, teachers, curriculum designers, assessment developers, state and district science administrators, and educators who teach science in informal environments. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website. Jump up to the previous page or down to the next one.

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Do you enjoy reading reports from the Academies online for free? Sign up for email notifications and we'll let you know about new publications in your areas of interest when they're released. Get This Book. Visit NAP. Looking for other ways to read this? No thanks. Page 42 Share Cite. Page 43 Share Cite. Understanding How Scientists Work The idea of science as a set of practices has emerged from the work of historians, philosophers, psychologists, and sociologists over the past 60 years.

Page 44 Share Cite. How the Practices Are Integrated into Both Inquiry and Design One helpful way of understanding the practices of scientists and engineers is to frame them as work that is done in three spheres of activity, as shown in Figure Page 45 Share Cite. Page 46 Share Cite. How Engineering and Science Differ Engineering and science are similar in that both involve creative processes, and neither uses just one method. Page 47 Share Cite. Page 48 Share Cite. Please review the types of cookies we use below.

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Beyond Reason: Eight Great Problems That Reveal the Limits of Science Beyond Reason: Eight Great Problems That Reveal the Limits of Science
Beyond Reason: Eight Great Problems That Reveal the Limits of Science Beyond Reason: Eight Great Problems That Reveal the Limits of Science
Beyond Reason: Eight Great Problems That Reveal the Limits of Science Beyond Reason: Eight Great Problems That Reveal the Limits of Science
Beyond Reason: Eight Great Problems That Reveal the Limits of Science Beyond Reason: Eight Great Problems That Reveal the Limits of Science
Beyond Reason: Eight Great Problems That Reveal the Limits of Science Beyond Reason: Eight Great Problems That Reveal the Limits of Science

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