- Values and Attitudes
- Computation and Estimation
- Manipulation and Observation
- Communication Skills
- Critical-Response Skills

Throughout history, people have concerned themselves with the transmission of shared values, attitudes, and skills from one generation to the next. All three were taught long before formal schooling was invented. Even today, it is evident that family, religion, peers, books, news and entertainment media, and general life experiences are the chief influences in shaping people's views of knowledge, learning, and other aspects of life. Science, mathematics, and technology—in the context of schooling—can also play a key role in the process, for they are built upon a distinctive set of values, they reflect and respond to the values of society generally, and they are increasingly influential in shaping shared cultural values. Thus, to the degree that schooling concerns itself with values and attitudes—a matter of great sensitivity in a society that prizes cultural diversity and individuality and is wary of ideology—it must take scientific values and attitudes into account when preparing young people for life beyond school.

Similarly, there are certain thinking skills associated with science, mathematics, and technology that young people need to develop during their school years. These are mostly, but not exclusively, mathematical and logical skills that are essential tools for both formal and informal learning and for a lifetime of participation in society as a whole.

Taken together, these values, attitudes, and skills can be thought of as habits of mind because they all relate directly to a person's outlook on knowledge and learning and ways of thinking and acting.

Science for All Americans

In Science for All Americans, Project 2061 expresses the view that education has multiple purposes and that those purposes should serve as criteria for specifying what students need to know and be able to do. The criteria are philosophical and utilitarian, individual and social. While they speak to the intrinsic value of knowing for its own sake, they emphasize also the need for education to prepare students to make their way in the real world, a world in which problems abound—in the home, in the workplace, in the community, on the planet.

Hence, preparing students to become effective problem solvers, alone and in concert with others, is a major purpose of schooling. Science, mathematics, and technology can contribute significantly to that end because in their different ways they are enterprises in the business of searching for solutions to problems ranging from the highly theoretical to the entirely concrete. Moreover, in their interactions with society, science and technology create the context for many personal and community issues.

There is a large and growing literature on problem solving. Aside from exhortation, a staple of most educational writing (including this document, to be sure), the problem-solving literature deals mostly with what skills need to be learned, why skills should be expressed behaviorally, and how to teach the desired skills. After a study of that literature, wide consultation with experts, and intense discussion, Project 2061 has reached conclusions that are reflected in the content and language of this chapter. Chief among them are the following:

Students' ability and inclination to solve problems effectively depend on their having certain knowledge, skills, and attitudes.

Quantitative, communication, manual, and critical-response skills are essential for problem solving, but they are also part of what constitutes science literacy more generally. That is why they are brought together here as scientific habits of mind rather than more narrowly as problem-solving skills or more generally as thinking skills.

Learning to solve problems in a variety of subject-matter contexts, if supplemented on occasion by explicit reflection on that experience, may result in the development of a generalized problem-solving ability that can be applied in new contexts; such transfer is unlikely to happen if either varied problem-solving experiences or reflection on problem solving is missing.

The problem of rote learning is primarily a pedagogical one that applies to skills as well as knowledge, and it is not solved simply by stating learning goals in one way instead of another.

In the light of those conclusions, it is useful to explain why the skill goals in this chapter are separated from the knowledge goals in Chapters 1 through 11. One reason is that the knowledge called for in the previous 11 chapters responds to all of the science literacy criteria mentioned earlier, not solely those having to do with problem solving. Another reason is that the skills advocated in this chapter need to be learned in the context of all of the knowledge chapters and thus would have to be repeated chapter after chapter if we tried to present knowledge and skill goals in tandem. Finally, the skills are significant in their own right as part of what it means to be science-literate, and presenting them together should make it easier to consider them as such.

It is widely argued that listing intended learning goals in specific detail is unwise because teachers will simply have their students memorize the individual entries as isolated facts. The same danger applies to stating skills in detail—procedures also can be memorized without comprehension, as veterans of "the scientific method" and mathematics algorithms can attest. Project 2061's response is the same in both cases, namely that there are better ways to deal with the problem of rote learning than by remaining vague on what knowledge and skills we want students to acquire.

The phrase "Students should know that …" used in benchmarks in the preceding chapters means that students should be able to connect one idea to other ideas and use it in thinking about new situations and in problem solving. But we surely want students to be likely to make such connections, not merely be able to do so. Similarly, with respect to this chapter, we want students not only to acquire certain skills but also to be inclined to use them in new situations, outside as well as inside school. Thus when the benchmarks specify that "Students should be able to" do something, we take that to mean they will in fact do so when appropriate circumstances present themselves.

One manifestation of such inclination is what someone thinks about when reading news articles. For example, on reading that trees were being logged for an important new drug found in their bark, the science-literate person might wonder about the yield from a single tree, the amount of drug needed, and how long a new tree would take to grow; or about the possibility of synthesizing the drug instead; or about what species in the forest might suffer from the loss of those particular trees; or about how complex ecological interactions are and the need for computer software to track the implications; or about possible bias in whoever was responsible for considering those various possibilities.

## A. Values and Attitudes |

Honesty is a desirable habit of mind not unique to people who practice science, mathematics, and technology. It is highly prized in the scientific community and essential to the scientific way of thinking and doing. The importance of honesty is urged on children from every quarter, and most children are able to say what the general principle is. What honesty means in practice, however, probably comes from their seeing firsthand how it is applied in many different situations. In school science, mathematics, and technology, there are numerous opportunities to show what honesty means and how it is valued. Science: Always report and record what you observe, not what you think it ought to be or what you think the teacher wants it to be, and do not erase your notes. Math: Do not change an answer from a calculation because it is different from what others get. Technology: If your design has limitations, say so.

Children are curious about things from birth. Curiosity does not have to be taught. The problem is the reverse: how to avoid squelching curiosity while helping students focus it productively. By fostering student curiosity about scientific, mathematical, and technological phenomena, teachers can reinforce the trait of curiosity generally and show that there are ways to go about finding answers to questions about how the world works. Students will gradually come to see that some ways of satisfying one's curiosity are better than others and that finding good answers and solutions is as much fun as raising good questions.

Balancing open-mindedness with skepticism may be difficult for students. These two virtues pull in opposite directions. Even in science itself, there is tension between an openness to new theories and an unwillingness to discard current ones. As students come up with explanations for what they observe or wonder about, teachers should insist that other students pay serious attention to them. Students hearing an explanation of how something works proposed by another student or by teachers and other authorities should learn that one can admire a proposal but remain skeptical until good evidence is offered for it.

## Kindergarten through Grade 2 |

Highest priority should be given to encouraging the curiosity about the world that children bring to school. Natural phenomena easily capture the attention of these youngsters, but they should be encouraged to wonder about mathematical and technological phenomena as well. Questions about numbers, shapes, and artifacts, for example, should be treated with the same interest as those about rocks and birds. Typically, children raise questions that are hard to answer. But some of their questions are possible to deal with, and some of the impossible questions can be transformed.

As students learn to write, they should start keeping a class list of things they wonder about, without regard to how easy it might be to answer their own questions. Teachers should then help them learn to pick from the list the questions they can find answers to by doing something such as collecting, sorting, counting, drawing, taking something apart, or making something. At this level, questions that can be answered descriptively are to be preferred over those requiring abstract explanations. Students are more likely to come up with reasonable answers as to "how" and "what" than as to "why."

Still, students should not be expected to confine themselves to empirical questions only. Some questions requiring an explanation for an answer can be taken up to foster scientific habits of thought. Thus, to the question, "Why don't plants grow in the dark?" students should learn that scientists would respond by asking, "Is it true that plants don't grow in the dark?" and "How do you know?" or "How can we find out if it is true?" If the facts are correct, then reasons can be offered. Presumably children, like scientists, will propose different explanations, and some children may have a need to establish whose ideas are good or best. Comparisons will come in time, when students are able to imagine ways to make judgments. Everyone's ideas should be valued, and differing opinions should be regarded as interesting and food for thought.

By the end of the 2nd grade, students should

## Grades 3 through 5 |

Sustaining curiosity and giving it a scientific cast is still a high priority. Students should advance in their ability to frame their questions about the world in ways that lead to their finding answers by conducting investigations, building and testing things, and consulting reference works. In doing so, whether working alone or in teams, students should be required to keep written records in bound notebooks of what they did, what data they collected, and what they think the data mean. Emphasis should be placed on honesty in record-keeping rather than on reaching correct conclusions. To the extent that a judgment is made by one group of students about another's conclusions, it should be on the basis of its correspondence to the evidence presented, not on what a book says is true.

The thrust of the science experience is still to learn how to answer interesting questions about the world that can be answered empirically. But now students should also sometimes think up and propose explanations for their findings. In this introduction to the world of theory, the main point to stress is that for any given collection of evidence, it is usually possible to invent different explanations, and it is not always easy to tell which will prove to be best. That is one reason that scientists pay attention to ideas that may differ from what they personally believe.

## Grades 6 through 8 |

The scientific values and attitudes that are the focus of this section have all been introduced in the previous grades. Now they can be reinforced and developed further. Care should be taken, in an effort to cover content, not to stop fostering curiosity. Time needs to be found to enable students to pursue scientific questions that truly interest them. Inquiry projects, individual and group, provide that opportunity. Such projects also establish realistic contexts in which to emphasize the importance of scientific honesty in describing procedures, recording data, drawing conclusions, and reporting conclusions.

Consideration of the nature and uses of hypotheses and theory in science can give operational substance to the scientific habits of openness and skepticism. Hypotheses and explanations serve somewhat different purposes, but they both are judged, ultimately, by reference to evidence. Students can come to see that a hypothesis does not have to be correct—one can believe it or not—but that to be taken seriously, it should indicate what evidence would be needed to decide whether or not it is true, thus incorporating the notions of both openness and skepticism.

In this same vein, a start can be made toward legitimizing the notion that there are often several different ways of making sense out of a body of existing information. Having teams invent two or more explanations for a set of observations, or having different teams independently come up with explanations for the same set of observations, can lead to discussions of the nature of scientific explanation that are grounded in reality. Developmental psychologists doubt that alternative explanations are seriously examined by most students at this level, but at least the possibility of alternatives can be planted, not as an abstract notion but as something stemming from students' own experience.

By the end of the 8th grade, students should know that

By the end of the 8th grade, students should

- Know why it is important in science to keep honest, clear, and accurate records. 12A/M1

In the current version of Benchmarks Online, this benchmark has been deleted because the ideas in it are addressed in benchmark 1C/M7. - Know that hypotheses are valuable, even if they turn out not to be true, if they lead to fruitful investigations. 12A/M2
- Know that often different explanations can be given for the same evidence, and it is not always possible to tell which one is correct. 12A/M3

## Grades 9 through 12 |

Skepticism is not just a matter of willingness to challenge authority, though that is an aspect of it. It is a determination to suspend judgment in the absence of credible evidence and logical arguments. Students can learn its value in science, and that is important. Given that most of them will not be scientists as adults, the educational challenge is to help students internalize the scientific critical attitude so they can apply it in everyday life, particularly in relation to the health, political, commercial, and technological claims they encounter.

Openness to new and unusual ideas about how the world works can now be developed in the study of historical cases as well as in the context of continuing inquiry projects. The Copernican Revolution, for example, illustrates the eventual success of ideas that were initially considered outrageous by nearly everyone. This and other cases also illustrate that ideas in science are not easily or quickly accepted. Some such mixture of openness and conservatism will serve most people and societies well.

By the end of the 12th grade, students should

- Exhibit traits such as curiosity, honesty, openness, and skepticism when making investigations, and value those traits in others. 12A/H1*
- View science and technology thoughtfully, being neither categorically antagonistic nor uncritically positive. 12A/H2

and students should know that

- In science, a new theory rarely gains widespread acceptance until its advocates can show that it is borne out by the evidence, is logically consistent with other principles that are not in question, explains more than its rival theories, and has the potential to lead to new knowledge. 12A/H3** (SFAA)
- Scientists value evidence that can be verified, hypotheses that can be tested, and theories that can be used to make predictions. 12A/H4** (SFAA)
- Curiosity motivates scientists to ask questions about the world around them and seek answers to those questions. Being open to new ideas motivates scientists to consider ideas that they had not previously considered. Skepticism motivates scientists to question and test their own ideas and those that others propose. 12A/H5*

By the end of the 12th grade, students should

- Know why curiosity, honesty, openness, and skepticism are so highly regarded in science and how they are incorporated into the way science is carried out; exhibit those traits in their own lives and value them in others. 12A/H1
- View science and technology thoughtfully, being neither categorically antagonistic nor uncritically positive. 12A/H2

## B. Computation and Estimation |

The scientific way of thinking is neither mysterious nor exclusive. The skills involved can be learned by everyone, and once acquired they can serve a lifetime regardless of one's occupation and personal circumstances. That is certainly true of the ability to think quantitatively, simply because so many matters in everyday life, as in science and many other fields, involve quantities and numerical relationships.

Computation is the process of determining something by mathematical means. Its value is acknowledged by the prominence accorded mathematics in school systems everywhere. Unfortunately, that preferred status has not been matched by results. It turns out that being able to get correct answers to the problems at the end of the chapter or on a work sheet or test is no guarantee of problem-solving ability in real situations. That ought not to be surprising, given that in traditional mathematics teaching, problems lack interesting real-world contexts; that memorization of algorithms by drill is not matched by learning when to use them; that numbers are used without units or attention to significance; and that students receive little, if any, help in learning how to judge how good their answers are.

In the real world, there is no need for people to make a calculation if the answer to their question is already known and easily available; they just need to know how to look it up—which is, of course, something that scientists and engineers do frequently. But in most situations, answers are not known and so making judgments about answers is as much a part of computation as the calculation itself. That is why the benchmarks in this section emphasize the need for students to develop estimation skills and the habit of checking answers against reality.

Estimation skills can be learned, but only if teachers make sure that students have lots of practice estimating (which happens if estimation is routinely treated as a standard part of problem solving). But there is no fixed set of all-purpose steps for students to memorize. If students are frequently called upon to explain how they intend to calculate an answer before carrying it out, they find that making step-by-step estimations is not hard and contributes to thinking through the problem at hand. They also gain confidence in their ability to figure out ahead of time approximately what the answer will be—bigger than this and smaller than that—if they do the calculation properly.

But a computationally "correct" answer is not necessarily a sensible one. If a computation leads to the result that an adult elephant weighs 1.2 pounds, most people know that something is wrong, because elephants are enormous animals and a pound isn't much weight. Reality tells them to check their computation. Did they use appropriate mathematics? Were the numerical inputs correct? Is the decimal point in the right place? What about the unit the answer is expressed in?

Developing good quantitative thinking skills and learning about the world go together. It is not sufficient for students to learn how to perform mathematical operations in the abstract if they are to become effective problem solvers and to be able to express their arguments quantitatively whenever appropriate. Hence, at every level, the teaching of science, technology, social studies, health, physical education, and perhaps other subjects should include problem solving that requires students to make calculations and check their answers against their estimates and their knowledge of whatever the problem pertains to. As much as possible, the problems should emerge from student activities—surveys, laboratory investigations, building projects, physical-education performance data, etc.—and the content being studied rather than from prepackaged word problems. Computational skills can be learned in contexts outside of mathematics courses.

Where do calculators and computers come into the picture? The answer is, nearly everywhere. Computers imbedded in cash registers, self-help gasoline pumps, automatic teller machines, and the like do much of the arithmetic that adults formerly had to do by paper and pencil. The inexpensive, hand-held calculator makes it possible for people to apply their knowledge of basic mathematics to the quantitative matters they encounter throughout the day instantly and on the spot. And computers, with their easy-to-use spreadsheet, graphing, and database capabilities, have become tools that everyone can use, at home and at work, to carry out extensive quantitative tasks.

Undoubtedly calculators and computers can vastly extend the mathematical capabilities of everyone, for they offer a precision and speed that few people can match. But their power can be of no avail, or even detrimental, unless they are used skillfully and with understanding. These instruments do not compensate for human reasoning errors or for poor mathematics, often deliver answers with misleading precision, and are prone to operator error.

Science literacy includes being able to use electronic tools thoughtfully and with confidence. This skill calls for students to be able to select appropriate algorithms, carry out basic mathematical operations on paper, judge the reasonableness of the results of a calculation, and round off insignificant numbers. Students should start using calculators and computers early and use them in as many different contexts as possible. That will increase the likelihood that students will learn to use them effectively, including learning when it is sufficient to make a mental estimate, when to use paper and pencil, and when to draw on the help of a calculator or computer. This early, continuing, and broadly based experience has another advantage: Properly used over time, calculators and computers can actually help students learn mathematics and acquire quantitative thinking skills.

In this section and those that follow, there are no grade-level commentaries. According to reviewers, skill benchmarks are less likely to be misunderstood than knowledge or attitude benchmarks, and hence, section essays are sufficient to cover all grades.

## Kindergarten through Grade 2 |

By the end of the 2nd grade, students should be able to

- Use whole numbers in ordering, counting, identifying, measuring, and describing objects and events. 12B/P1*
- Give the sums and differences of single-digit numbers. 12B/P2*
- Explain to other students how they go about solving numerical problems. 12B/P4
- Make quantitative estimates of time intervals and the lengths and weights of familiar objects. 12B/P5*

By the end of the 2nd grade, students should be able to

- Use whole numbers and simple, everyday fractions in ordering, counting, identifying, measuring, and describing things and experiences. 12B/P1
- Readily give the sums and differences of single-digit numbers in familiar contexts where the operation makes sense to them and they can judge the reasonableness of the answer. 12B/P2
- Give rough estimates of numerical answers to problems before doing them formally. 12B/P3

In the current version of Benchmarks Online, this benchmark has been moved to grades 9–12 and recoded as 12B/E11**. - Explain to other students how they go about solving numerical problems. 12B/P4
- Make quantitative estimates of familiar lengths, weights, and time intervals and check them by measurements. 12B/P5

## Grades 3 through 5 |

By the end of the 5th grade, students should be able to

- Make calculations when necessary to solve real-world problems and decide whether to make the calculation mentally, on paper, or with the help of a calculator or computer. 12B/E1*
- Use fractions and decimals, translating when necessary between commonly encountered fractions (halves, fourths, fifths, tenths, and hundredths) and their decimal equivalents. 12B/E2*
- Judge whether measurements and computations of quantities such as length, weight, or time are reasonable by comparing them to familiar values. 12B/E3*
- State the purpose of each step in a calculation. 12B/E4
- Read and follow step-by-step instructions in a calculator or computer manual when learning new procedures. 12B/E5
- Add or subtract any two whole numbers between 1 and 100. 12B/E6** (SFAA)
- Multiply any two whole numbers between 1 and 10 and multiply or divide any number by 2, 10, or 100. 12B/E7** (SFAA)
- Use a calculator to add, subtract, multiply, and divide any two whole or decimal numbers. 12B/E8** (SFAA)
- Use appropriate units when describing quantities. 12B/E9**
- Add and subtract fractions with common denominators. 12B/E10**
- Make rough estimates of numerical calculations and use them to judge whether the results of a calculation done on a calculator are reasonable. 12B/E11** (BSL)

By the end of the 5th grade, students should be able to

- Add, subtract, multiply, and divide whole numbers mentally, on paper, and with a calculator. 12B/E1
- Use fractions and decimals, translating when necessary between decimals and commonly encountered fractions—halves, thirds, fourths, fifths, tenths, and hundredths (but not sixths, sevenths, etc.). 12B/E2
- Judge whether measurements and computations of quantities such as length, area, volume, weight, or time are reasonable in a familiar context by comparing them to typical values. 12B/E3
- State the purpose of each step in a calculation. 12B/E4
- Read and follow step-by-step instructions in a calculator or computer manual when learning new procedures. 12B/E5

## Grades 6 through 8 |

By the end of the 8th grade, students should be able to

- Find what part one number is of another and express it as a fraction or a percentage. 12B/M1a*
- Find what number is a given percentage of another number. 12B/M1b*
- Use, interpret, and compare numbers in several equivalent forms such as integers, fractions, decimals, and percents. 12B/M2
- Calculate the circumferences and areas of rectangles, triangles, and circles, and the volumes of rectangular solids. 12B/M3
- Find the mean, median, and mode of a set of data. 12B/M4*
- Estimate distances and travel times from maps and the actual size of objects from scale drawings. 12B/M5
- Insert instructions into computer spreadsheet cells to program arithmetic calculations. 12B/M6
- Use the units of the inputs to a calculation to determine what units (such as seconds, square inches, or dollars per tankful) should be used in expressing an answer. 12B/M7a*
- Convert quantities expressed in one unit of measurement into another unit of measurement when necessary to solve a real-world problem. 12B/M7b*
- Decide what degree of precision is adequate and round off the result of calculator operations to enough significant figures to reasonably reflect those of the inputs. 12B/M8
- Express numbers like 100, 1,000, and 1,000,000 as powers of ten. 12B/M9
- Estimate probabilities of outcomes in familiar situations on the basis of history or the number of possible outcomes. 12B/M10

By the end of the 8th grade, students should be able to

- Find what percentage one number is of another and figure any percentage of any number. 12B/M1
- Use, interpret, and compare numbers in several equivalent forms such as integers, fractions, decimals, and percents. 12B/M2
- Calculate the circumferences and areas of rectangles, triangles, and circles, and the volumes of rectangular solids. 12B/M3
- Find the mean and median of a set of data. 12B/M4
- Estimate distances and travel times from maps and the actual size of objects from scale drawings. 12B/M5
- Insert instructions into computer spreadsheet cells to program arithmetic calculations. 12B/M6
- Determine what unit (such as seconds, square inches, or dollars per tankful) an answer should be expressed in from the units of the inputs to the calculation, and be able to convert compound units (such as yen per dollar into dollar per yen, or miles per hour into feet per second). 12B/M7
- Decide what degree of precision is adequate and round off the result of calculator operations to enough significant figures to reasonably reflect those of the inputs. 12B/M8
- Express numbers like 100, 1,000, and 1,000,000 as powers of 10. 12B/M9
- Estimate probabilities of outcomes in familiar situations, on the basis of history or the number of possible outcomes. 12B/M10

## Grades 9 through 12 |

By the end of the 12th grade, students should be able to

- Use appropriate ratios and proportions, including constant rates, when needed to make calculations for solving real-world problems. 12B/H1*
- Find answers to real-world problems by substituting numerical values in simple algebraic formulas and check the answer by reviewing the steps of the calculation and by judging whether the answer is reasonable. 12B/H2*
- Make up and write out simple algorithms for solving real-world problems that take several steps. 12B/H3*
- Use computer spreadsheet, graphing, and database programs to assist in quantitative analysis of real-world objects and events. 12B/H4*
- Compare data for two groups by representing their averages and spreads graphically. 12B/H5
- When describing and comparing very small and very large quantities, express them using powers-of-ten notation. 12B/H6*
- Trace the source of any large disparity between an estimate and the calculated answer. 12B/H7
- Consider the possible effects of measurement errors on calculations. 12B/H9

By the end of the 12th grade, students should be able to

- Use ratios and proportions, including constant rates, in appropriate problems. 12B/H1
- Find answers to problems by substituting numerical values in simple algebraic formulas and judge whether the answer is reasonable by reviewing the process and checking against typical values. 12B/H2
- Make up and write out simple algorithms for solving problems that take several steps. 12B/H3
- Use computer spreadsheet, graphing, and database programs to assist in quantitative analysis. 12B/H4
- Compare data for two groups by representing their averages and spreads graphically. 12B/H5
- Express and compare very small and very large numbers using powers-of-ten notation. 12B/H6
- Trace the source of any large disparity between an estimate and the calculated answer. 12B/H7
- Recall immediately the relations among 10, 100, 1000, 1 million, and 1 billion (knowing, for example, that 1 million is a thousand thousands). 12B/H8

In the current version of Benchmarks Online, this benchmark has been deleted because the ideas in it are addressed in benchmark 12B/M9. - Consider the possible effects of measurement errors on calculations. 12B/H9

## C. Manipulation and Observation |

Construing habits of mind to include manipulation and observation skills raises no eyebrows in science. Scientists know that finding answers to questions about nature means using one's hands and senses as well as one's head. The same is true in medicine, engineering, business, and many other fields, and so it should be in everyday life.

Tools, from hammers and drawing boards to cameras and computers, extend human capabilities. They make it possible for people to move things beyond their strength, move faster and farther than their legs can carry them, detect sounds too faint to be heard and objects too small or too far away to be seen, project their voices around the world, store and analyze more information than their brains can cope with, and so forth. In daily living, people have little need to use telescopes, microscopes, and the sophisticated instruments used by scientists and engineers in their work. But the array of mechanical, electrical, electronic, and optical tools that people can use is no less than awesome.

What people use tools for and how thoughtfully they use them is another matter, however. Tools can of course be used for banal or noble, even ignoble, purposes, and used with or without much regard for consequences. Education for science literacy implies that students be helped to develop the habit of using tools, along with scientific and mathematical ideas and computation skills, to solve practical problems and to increase their understanding, throughout life, of how the world works. A very common problem people encounter is that things don't work right. In many instances, the problem can be diagnosed and the malfunctioning device fixed using ordinary troubleshooting techniques and tools.

## Kindergarten through Grade 2 |

By the end of the 2nd grade, students should be able to

- Use hammers, screwdrivers, clamps, and scissors to shape materials and fasten them together. 12C/P1*
- Assemble, take apart, and reassemble constructions using interlocking blocks or other interconnecting pieces. 12C/P2*
- Make something out of paper, cardboard, cloth, wood, plastic, metal, or existing objects that can actually be used to perform a task. 12C/P3*
- Measure the length in whole units of objects using rulers and tape measures. 12C/P4*
- Weigh objects using a scale. 12C/P5**

By the end of the 2nd grade, students should be able to

- Use hammers, screwdrivers, clamps, rulers, scissors, and hand lenses, and operate ordinary audio equipment. 12C/P1
- Assemble, describe, take apart and reassemble constructions using interlocking blocks, erector sets, and the like. 12C/P2
- Make something out of paper, cardboard, wood, plastic, metal, or existing objects that can actually be used to perform a task. 12C/P3
- Measure the length in whole units of objects having straight edges. 12C/P4

## Grades 3 through 5 |

By the end of the 5th grade, students should be able to

- Choose appropriate common materials for making simple mechanical constructions and repairing things. 12C/E1
- Measure out a prescribed amount of a liquid or dry powder using a measuring cup, measuring spoon, or scale. 12C/E2*
- Keep written or electronic records of information so that the records are understandable weeks or months later. 12C/E3*
- Use audio and video recording devices for capturing information. 12C/E6** (BSL)

By the end of the 5th grade, students should be able to

- Choose appropriate common materials for making simple mechanical constructions and repairing things. 12C/E1
- Measure and mix dry and liquid materials (in the kitchen, garage, or laboratory) in prescribed amounts, exercising reasonable safety. 12C/E2
- Keep a notebook that describes observations made, carefully distinguishes actual observations from ideas and speculations about what was observed, and is understandable weeks or months later. 12C/E3
- Use calculators to determine area and volume from linear dimensions, aggregate amounts of area, volume, weight, time, and cost, and find the difference between two quantities of anything. 12C/E4

In the current version of Benchmarks Online, this benchmark has been deleted because the ideas in it are addressed in benchmark 12B/E8**. - Make safe electrical connections with various plugs, sockets, and terminals. 12C/E5

In the current version of Benchmarks Online, this benchmark has been moved to grades 6-8 and recoded as 12C/M6**.

## Grades 6 through 8 |

By the end of the 8th grade, students should be able to

- Use calculators to compare amounts proportionally. 12C/M1
- Use computer databases to store and retrieve information. 12C/M2*
- Make accurate measurements of length, volume, weight, elapsed time, rates, and temperature by using appropriate devices. 12C/M3*
- Analyze simple mechanical devices and describe what the various parts are for; estimate what the effect of making a change in one part of a device would have on the device as a whole. 12C/M5*
- Make safe electrical connections with various plugs, sockets, and terminals. 12C/M6** (BSL)
- Select the proper tool for completing a particular task. 12C/M7**
- Maintain tools and simple devices so they are in good working order. 12C/M8**

By the end of the 8th grade, students should be able to

- Use calculators to compare amounts proportionally. 12C/M1
- Use computers to store and retrieve information in topical, alphabetical, numerical, and key-word files, and create simple files of their own devising. 12C/M2
- Read analog and digital meters on instruments used to make direct measurements of length, volume, weight, elapsed time, rates, and temperature, and choose appropriate units for reporting various magnitudes. 12C/M3
- Use cameras and tape recorders for capturing information. 12C/M4

In the current version of Benchmarks Online, this benchmark has been moved to grades 3-5 and recoded as 12C/E6**. - Inspect, disassemble, and reassemble simple mechanical devices and describe what the various parts are for; estimate what the effect that making a change in one part of a system is likely to have on the system as a whole. 12C/M5

## Grades 9 through 12 |

By the end of the 12th grade, students should be able to

- Follow instructions in manuals or seek help from an experienced user to learn how to operate new mechanical or electrical devices. 12C/H1*
- Troubleshoot common mechanical and electrical systems, check for possible causes of malfunction, and decide on that basis whether to fix it themselves or get help from an expert. 12C/H3*
- Develop simple computer databases to store and retrieve information. 12C/H5**

By the end of the 12th grade, students should be able to

- Learn quickly the proper use of new instruments by following instructions in manuals or by taking instructions from an experienced user. 12C/H1
- Use computers for producing tables and graphs and for making spreadsheet calculations. 12C/H2

In the current version of Benchmarks Online, this benchmark has been deleted because the ideas in it are addressed in benchmark section 12B grades 6-8 benchmark 12B/M6 and section 12D grades 6-8 benchmark 12D/M1. - Troubleshoot common mechanical and electrical systems, checking for possible causes of malfunction, and decide on that basis whether to make a change or get advice from an expert before proceeding. 12C/H3
- Use power tools safely to shape, smooth, and join wood, plastic, and soft metal. 12C/H4

In the current version of Benchmarks Online, this benchmark has been deleted because the ideas in it are addressed in benchmark 12C/M7** and 12C/H1*.

## D. Communication Skills |

Good communication is a two-way street. It is as important to receive information as to disseminate it, to understand other's ideas as to have one's own understood. In the scientific professions, tradition places a high priority on accurate communication, and there are mechanisms, such as refereed journals and scientific meetings, to facilitate the sharing of new information and ideas within various disciplines and subdisciplines. Science-literate adults share this respect for clear, accurate communication, and they possess many of the communication skills characteristic of the scientific enterprise.

Accurate communication within a science discipline results in part from the use of technical language. An unintentional side effect of reliance on specialized terms, however effective it may be within a discipline, is that it impedes communication between specialists and between the specialists and the general public. For the general public, science writers for newspapers, magazines, and television undertake to translate the highly technical language of each discipline into language accessible to the educated adult. In doing that, they assume that an educated reader is familiar with some of the central ideas of science and is able to read material that uses the basic language and logic of mathematics. Science for All Americans describes the knowledge base for such educated readers, and Benchmarks points the way to the development of such adults. The communication skills below are intended to complement that knowledge base.

There is an aspect of quantitative thinking that may be as much a matter of inclination as skill. It is the habit of framing arguments in quantitative terms whenever possible. Instead of saying that something is big or fast or happens a lot, a better approach is often to use numbers and units to say how big, fast, or often, and instead of claiming that one thing is larger or faster or colder than another, it is better to use either absolute or relative terms to say how much so. Communication becomes more focused when "big" is replaced with "3 feet" or "250 pounds" (very different notions of what constitutes bigness) and "happens a lot" with "17 times this year compared to 2 or 3 times in each of the previous 10 years" or "90 to 95% of the time." And just as students should develop this way of thinking, they should demand it of others and not be satisfied with vague claims when quantitative ones are possible and relevant.

## Kindergarten through Grade 2 |

By the end of the 2nd grade, students should be able to

- Describe and compare real-world objects in terms of number, shape, texture, size, weight, color, and motion. 12D/P1*
- Draw pictures that portray some features of the thing being described. 12D/P2*
- Interpret pictures, drawings, and videos of real-world objects and events. 12D/P3**
- Interpret oral descriptions of real-world objects and events. 12D/P4**

## Grades 3 through 5 |

By the end of the 5th grade, students should be able to

- Give written and oral instructions that others can follow to carry out a procedure. 12D/E1*
- Make sketches or diagrams to aid in explaining procedures or ideas. 12D/E2*
- Use numerical data in describing and comparing objects and events. 12D/E3
- Read simple tables and graphs produced by others and describe what the tables and graphs show. 12D/E4** (BSL)
- Find locations on maps and globes, interpret information displayed on maps, and use maps to navigate. 12D/E5** (BSL)
- Interpret written descriptions of real-world objects and events. 12D/E6**
- Write a clear and accurate description of a real-world object or event. 12D/E7**
- Locate information in print and electronic resources. 12D/E8** (BSL)

By the end of the 5th grade, students should be able to

## Grades 6 through 8 |

By the end of the 8th grade, students should be able to

- Organize information in simple tables and graphs and identify relationships they reveal. 12D/M1
- Read simple tables and graphs produced by others and describe in words what they show. 12D/M2
- Locate information in reference books, back issues of newspapers and magazines, compact disks, and computer databases. 12D/M3
- Understand oral, written, or visual presentations that incorporate circle charts, bar and line graphs, two-way data tables, diagrams, and symbols. 12D/M4*
- Find and describe locations on maps with rectangular and polar coordinates. 12D/M5
- Present a brief scientific explanation orally or in writing that includes a claim and the evidence and reasoning that supports the claim. 12D/M6**
- Seek to gain a better understanding of a scientific idea by asking for an explanation, restating an explanation in a different way, and asking questions when some aspect of an explanation is not clear. 12D/M7**
- Explain a scientific idea to someone else, checking understanding and responding to questions. 12D/M8**
- Prepare a visual presentation to aid in explaining procedures or ideas. 12D/M9**
- Describe spatial relationships in geometric terms such as perpendicular, parallel, tangent, similar, congruent, and symmetrical. 12D/M10** (BSL)
- Interpret simple symbolic equations. 12D/M11**

By the end of the 8th grade, students should be able to

- Organize information in simple tables and graphs and identify relationships they reveal. 12D/M1
- Read simple tables and graphs produced by others and describe in words what they show. 12D/M2
- Locate information in reference books, back issues of newspapers and magazines, compact disks, and computer databases. 12D/M3
- Understand writing that incorporates circle charts, bar and line graphs, two-way data tables, diagrams, and symbols. 12D/M4
- Find and describe locations on maps with rectangular and polar coordinates. 12D/M5

## Grades 9 through 12 |

By the end of the 12th grade, students should be able to

- Make and interpret scale drawings. 12D/H1
- Choose appropriate summary statistics to describe group differences, always indicating the spread of the data as well as the data's central tendencies. 12D/H3
- Use and correctly interpret relational terms such as
*if… then…*,*and*,*or*,*sufficient*,*necessary*,*some*,*every*,*not*,*correlates with*, and*causes*. 12D/H5 - Participate in group discussions on scientific topics by restating or summarizing accurately what others have said, asking for clarification or elaboration, and expressing alternative positions. 12D/H6
- Use tables, charts, and graphs in making arguments and claims in oral, written, and visual presentations. 12D/H7*
- Use symbolic equations to represent relationships between objects and events. 12D/H8**

By the end of the 12th grade, students should be able to

- Make and interpret scale drawings. 12D/H1
- Write clear, step-by-step instructions for conducting investigations, operating something, or following a procedure. 12D/H2

In the current version of Benchmarks Online, this benchmark has been deleted because the ideas in it are addressed in benchmark 12D/E1*. - Choose appropriate summary statistics to describe group differences, always indicating the spread of the data as well as the data's central tendencies. 12D/H3
- Describe spatial relationships in geometric terms such as perpendicular, parallel, tangent, similar, congruent, and symmetrical. 12D/H4

In the current version of Benchmarks Online, this benchmark has been moved to grades 6-8 and recoded as 12D/M10**. - Use and correctly interpret relational terms such as
*if . . . then . . . , and, or, sufficient, necessary, some, every, not, correlates with*, and*causes*. 12D/H5 - Participate in group discussions on scientific topics by restating or summarizing accurately what others have said, asking for clarification or elaboration, and expressing alternative positions. 12D/H6
- Use tables, charts, and graphs in making arguments and claims in oral and written presentations. 12D/H7

## E. Critical-Response Skills |

In everyday life, people are bombarded with claims—claims about products, about how nature or social systems or devices work, about their health and welfare, about what happened in the past and what will occur in the future. These claims are put forth by experts (including scientists) and nonexperts (including scientists), by honest people and charlatans. In responding to this barrage, trying to separate sense from nonsense, knowledge helps.

But apart from what they know about the substance of an assertion, individuals who are science literate can make some judgments based on its character. The use or misuse of supporting evidence, the language used, and the logic of the argument presented are important considerations in judging how seriously to take some claim or proposition. These critical response skills can be learned and with practice can become a lifelong habit of mind.

## Kindergarten through Grade 2 |

By the end of the 2nd grade, students should

## Grades 3 through 5 |

By the end of the 5th grade, students should

- Buttress their statements with facts found in books, articles, and databases, and identify the sources used and expect others to do the same. 12E/E1
- Recognize when comparisons might not be fair because some conditions are not kept the same. 12E/E2
- Seek reasons for believing something rather than just claiming "Everybody knows that…" or "I just know" and discount such claims when made by others. 12E/E3*

By the end of the 5th grade, students should

- Buttress their statements with facts found in books, articles, and databases, and identify the sources used and expect others to do the same. 12E/E1
- Recognize when comparisons might not be fair because some conditions are not kept the same. 12E/E2
- Seek better reasons for believing something than "Everybody knows that . . ." or "I just know" and discount such reasons when given by others. 12E/E3

## Grades 6 through 8 |

By the end of the 8th grade, students should

- Question claims based on vague attributions (such as "Leading doctors say…") or on statements made by celebrities or others outside the area of their particular expertise. 12E/M1
- Compare consumer products and consider reasonable personal trade-offs among them on the basis of features, performance, durability, and cost. 12E/M2
- Be skeptical of claims based on very small samples or biased samples. 12E/M3*
- Notice and criticize the reasoning in arguments in which fact and opinion are intermingled. 12E/M5a
- Notice and criticize the reasoning in arguments in which the claims are not consistent with the evidence given. 12E/M5b*
- Be skeptical of claims based only on analogies. 12E/M5c*
- Notice and criticize the reasoning in arguments in which no mention is made of whether control groups are used or whether the control groups are very much like the experimental group. 12E/M5d*
- Be skeptical of arguments in which all members of a group (such as teenagers or chemists) are implied to have nearly identical characteristics that differ from those of other groups. 12E/M5e

By the end of the 8th grade, students should

- Question claims based on vague attributions (such as "Leading doctors say...") or on statements made by celebrities or others outside the area of their particular expertise. 12E/M1
- Compare consumer products and consider reasonable personal trade-offs among them on the basis of features, performance, durability, and cost. 12E/M2
- Be skeptical of arguments based on very small samples of data, biased samples, or samples for which there was no control sample. 12E/M3
- Be aware that there may be more than one good way to interpret a given set of findings. 12E/M4

In the current version of Benchmarks Online, this benchmark has been deleted. - Notice and criticize the reasoning in arguments in which (1) fact and opinion are intermingled or the conclusions do not follow logically from the evidence given, (2) an analogy is not apt, (3) no mention is made of whether the control groups are very much like the experimental group, or (4) all members of a group (such as teenagers or chemists) are implied to have nearly identical characteristics that differ from those of other groups. 12E/M5

## Grades 9 through 12 |

By the end of the 12th grade, students should

- Notice and criticize claims based on the faulty, incomplete, or misleading use of numbers, such as in instances when (1) average results are reported but not the amount of variation around the average, (2) a percentage or fraction is given but not the total sample size, (3) absolute and proportional quantities are mixed, or (4) results are reported with overstated precision. 12E/H1*
- Check graphs to see that they do not misrepresent results by using inappropriate scales or by failing to specify the axes clearly. 12E/H2
- Consider whether some event of interest might have occurred just by chance. 12E/H3*
- Insist that the key assumptions and reasoning in any argument—whether one's own or that of others—be made explicit; analyze the arguments for flawed assumptions, flawed reasoning, or both; and be critical of the claims if any flaws in the argument are found. 12E/H4*
- Notice and criticize claims that people make when they select only the data that support the claim and ignore any that would contradict it. 12E/H5*
- Notice and criticize arguments in which data, reasoning, or claims are represented as the only ones worth considering, with no mention of other possibilities. 12E/H6a*
- Suggest alternative trade-offs in decisions and designs and criticize those in which major trade-offs are not acknowledged. 12E/H6b

By the end of the 12th grade, students should

- Notice and criticize arguments based on the faulty, incomplete, or misleading use of numbers, such as in instances when (1) average results are reported, but not the amount of variation around the average, (2) a percentage or fraction is given, but not the total sample size (as in "9 out of 10 dentists recommend..."), (3) absolute and proportional quantities are mixed (as in "3,400 more robberies in our city last year, whereas other cities had an increase of less than 1%), or (4) results are reported with overstated precision (as in representing 13 out of 19 students as 68.42%). 12E/H1
- Check graphs to see that they do not misrepresent results by using inappropriate scales or by failing to specify the axes clearly. 12E/H2
- Wonder how likely it is that some event of interest might have occurred just by chance. 12E/H3
- Insist that the critical assumptions behind any line of reasoning be made explicit so that the validity of the position being taken—whether one's own or that of others—can be judged. 12E/H4
- Be aware, when considering claims, that when people try to prove a point, they may select only the data that support it and ignore any that would contradict it. 12E/H5
- Suggest alternative ways of explaining data and criticize arguments in which data, explanations, or conclusions are represented as the only ones worth consideration, with no mention of other possibilities. Similarly, suggest alternative trade-offs in decisions and designs and criticize those in which major trade-offs are not acknowledged. 12E/H6

VERSION EXPLANATION

During the development of Atlas of Science Literacy, Volume 2, Project 2061 revised the wording of some benchmarks in order to update the science, improve the logical progression of ideas, and reflect the current research on student learning. New benchmarks were also created as necessary to accommodate related ideas in other learning goals documents such as Science for All Americans (SFAA), the National Science Education Standards (NSES), and the essays or other elements in Benchmarks for Science Literacy (BSL). We are providing access to both the current and the 1993 versions of the benchmarks as a service to our end-users.

The text of each learning goal is followed by its code, consisting of the chapter, section, grade range, and the number of the goal. Lowercase letters at the end of the code indicate which part of the 1993 version it comes from (e.g., “a” indicates the first sentence in the 1993 version, “b” indicates the second sentence, and so on). A single asterisk at the end of the code means that the learning goal has been edited from the original, whereas two asterisks mean that the idea is a new learning goal.

Copyright © 1993,2009 by American Association for the Advancement of Science