<?xml version="1.0" encoding="UTF-8"?>
<xsd:schema xmlns:xsd="http://www.w3.org/2001/XMLSchema" elementFormDefault="qualified" attributeFormDefault="unqualified" version="0.6.50">
	<xsd:annotation>
		<xsd:documentation>
		**********************************************************************  Overview  **************************************************************
			Definition: 			Controlled vocabulary schema for DLESE metadata frameworks
			Framework use: 	ADN-I (item)
			Source org:			American Association for the Advancement of Science (AAAS); http://www.aaas.org/
			Vocab values:		http://www.project2061.org/tools/benchol/bolframe.htm
			Vocab last update:	
			DPC last update:		2003-02-10
			Notes: 				This is nature of mathematics and the mathematical world.	
		</xsd:documentation>
	</xsd:annotation>
	<xsd:annotation>
		<xsd:documentation>*** LICENSE INFORMATION *****
		Copyright 2002, 2003 DLESE Program Center
		University Corporation for Atmospheric Research (UCAR)
		P.O. Box 3000, Boulder, CO 80307, United States of America
		email: support@dlese.org. 
These schemas are free software; you can redistribute them and/or modify them under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.  These schemas are distributed in the hope that they will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this project; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA  
		</xsd:documentation>
	</xsd:annotation>
	<xsd:annotation>
		<xsd:documentation>****************************** History of Change *************************
2003-02-10:Added comments below to indicate where changes exist between AAAS website and DPC XML schema encoding.
2003-02-10:Learned there more new benchmarks that are not on the AAAS website. Not dealing with those yet.
		</xsd:documentation>
	</xsd:annotation>
	<xsd:annotation>
		<xsd:documentation>***********************  Simple Types (alpha order) *************************************</xsd:documentation>
	</xsd:annotation>
	<xsd:simpleType name="AAAScontentMathType">
		<xsd:annotation>
			<xsd:documentation>
				***************************************  AAAScontentMathType  ***************************************
				Lists the values that will appear in the metadata record
			</xsd:documentation>
		</xsd:annotation>
		<xsd:restriction base="xsd:string">
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:K-2:Circles, squares, triangles, and other shapes can be found in things in nature and in things that people build."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:K-2:Patterns can be made by putting different shapes together or taking them apart."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:K-2:Things move, or can be made to move, along straight, curved, circular, back-and-forth, and jagged paths."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:K-2:Numbers can be used to count any collection of things."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:3-5:Mathematics is the study of many kinds of patterns, including numbers and shapes and operations on them. Sometimes patterns are studied because they help to explain how the world works or how to solve practical problems, sometimes because they are interesting in themselves."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:3-5:Mathematical ideas can be represented concretely, graphically, and symbolically."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:6-8:Usually there is no one right way to solve a mathematical problem; different methods have different advantages and disadvantages."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:6-8:Logical connections can be found between different parts of mathematics."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:9-12:Mathematics is the study of any patterns or relationships, whereas natural science is concerned only with those patterns that are relevant to the observable world. Although mathematics began long ago in practical problems, it soon focused on abstractions from the material world, and then on even more abstract relationships among those abstractions."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:9-12:As in other sciences, simplicity is one of the highest values in mathematics. Some mathematicians try to identify the smallest set of rules from which many other propositions can be logically derived."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:9-12:Theories and applications in mathematical work influence each other. Sometimes a practical problem leads to the development of new mathematical theories; often mathematics developed for its own sake turns out to have practical applications."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Patterns and relationships:9-12:New mathematics continues to be invented, and connections between different parts of mathematics continue to be found."/>
<!--			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:K-2:No benchmarks for this level."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:3-5:No benchmarks for this level."/> -->
			<!--In the next benchmark, the phrase 'endeavor, from' originally had an m-dash between the words endeavor and from. The m-dash was changed to a comma because then an entity reference does not need to be used in the XML and a comma is grammatically fine.-->
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:6-8:Mathematics is helpful in almost every kind of human endeavor, from laying bricks to prescribing medicine or drawing a face. In particular, mathematics has contributed to progress in science and technology for thousands of years and still continues to do so."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:9-12:Mathematical modeling aids in technological design by simulating how a proposed system would theoretically behave."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:9-12:Mathematics and science as enterprises share many values and features: belief in order, ideals of honesty and openness, the importance of criticism by colleagues, and the essential role played by imagination."/>
			<!--In the next benchmark, the phrase 'technology to' originally had an m-dash between the words technology and to. The m-dash was changed to a space because then an entity reference does not need to be used in the XML and a space is grammatically fine.-->
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:9-12:Mathematics provides a precise language for science and technology to describe objects and events, to characterize relationships between variables, and to argue logically."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:9-12:Developments in science or technology often stimulate innovations in mathematics by presenting new kinds of problems to be solved. In particular, the development of computer technology (which itself relies on mathematics) has generated new kinds of problems and methods of work in mathematics."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:9-12:Developments in mathematics often stimulate innovations in science and technology."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematical inquiry:K-2:Numbers and shapes can be used to tell about things."/>
			<!--In the next benchmark, the phrases 'shapes, and' and 'them, help' originally had an m-dash between the words shapes and and and them and help. The m-dash was changed to a comma because then an entity reference does not need to be used in the XML and a comma is grammatically fine.-->
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematical inquiry:3-5:Numbers and shapes, and operations on them, help to describe and predict things about the world around us."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematical inquiry:3-5:In using mathematics, choices have to be made about what operations will give the best results. Results should always be judged by whether they make sense and are useful."/>
			<!--In the next benchmark, the phrases 'things' and 'all equal-sided triangle' and 'all odd numbers' originally had double quotes surrounding them. The double quotes were replaced with single quotes because a double quote is a reserved character in XML schema.-->
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematical inquiry:6-8:Mathematicians often represent things with abstract ideas, such as numbers or perfectly straight lines, and then work with those ideas alone. The 'things' from which they abstract can be ideas themselves (for example, a proposition about 'all equal-sided triangles' or 'all odd numbers')."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematical inquiry:6-8:When mathematicians use logical rules to work with representations of things, the results may or may not be valid for the things themselves. Using mathematics to solve a problem requires choosing what mathematics to use; probably making some simplifying assumptions, estimates, or approximations; doing computations; and then checking to see whether the answer makes sense. If an answer does not seem to make enough sense for its intended purpose, then any of these steps might have been inappropriate."/>
			<!--In the next benchmark, the phrase 'game, mathematicians' originally had an m-dash between the words game and mathematicians. The m-dash was changed to a comma because then an entity reference does not need to be used in the XML and a comma is grammatically fine.-->
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematical inquiry:9-12:Some work in mathematics is much like a game, mathematicians choose an interesting set of rules and then play according to those rules to see what can happen. The more interesting the results, the better. The only limit on the set of rules is that they should not contradict one another."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematical inquiry:9-12:Much of the work of mathematicians involves a modeling cycle, which consists of three steps: (1) using abstractions to represent things or ideas, (2) manipulating the abstractions according to some logical rules, and (3) checking how well the results match the original things or ideas. If the match is not considered good enough, a new round of abstraction and manipulation may begin. The actual thinking need not go through these processes in logical order but may shift from one to another in any order."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:K-2:Numbers can be used to count things, place them in order, or name them."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:K-2:Sometimes in sharing or measuring there is a need to use numbers between whole numbers."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:K-2:It is possible (and often useful) to estimate quantities without knowing them exactly."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:K-2:Simple graphs can help to tell about observations."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:3-5:The meaning of numerals in many-digit numbers depends on their positions."/>
			<!--In the next benchmark, the word '0' originally had double quotes surrounding it. The double quotes were replaced with single quotes because a double quote is a reserved character in XML schema.-->
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:3-5:In some situations, '0' means none of something, but in others it may be just the label of some point on a scale."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:3-5:When people care about what is being counted or measured, it is important for them to say what the units are (three degrees Fahrenheit is different from three centimeters, three miles from three miles per hour)."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:3-5:Measurements are always likely to give slightly different numbers, even if what is being measured stays the same."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:6-8:There have been systems for writing numbers other than the Arabic system of place values based on tens. The very old Roman numerals are now used only for dates, clock faces, or ordering chapters in a book. Numbers based on 60 are still used for describing time and angles."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:6-8:A number line can be extended on the other side of zero to represent negative numbers. Negative numbers allow subtraction of a bigger number from a smaller number to make sense, and are often used when something can be measured on either side of some reference point (time, ground level, temperature, budget)."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:6-8:Numbers can be written in different forms, depending on how they are being used. How fractions or decimals based on measured quantities should be written depends on how precise the measurements are and how precise an answer is needed."/>
			<!--In the next benchmark, the phrase 'other, one' originally had an m-dash between the words other and one. The m-dash was changed to a comma because then an entity reference does not need to be used in the XML and a comma is grammatically fine.-->
			<!--In the bechmark below the mathetical symbols for add, subtract, muliply and divide had to changed to words other corruption of the shcema file occurs. So the words of  'of addition', 'subtraction', 'with mulitplication' and 'division' were previouslu symbols.-->
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:6-8:The operations of addition and subtraction are inverses of each other, one undoes what the other does; likewise with multiplication and division."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:6-8:The expression a/b can mean different things: a parts of size 1/b each, a divided by b, or a compared to b."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:6-8:Numbers can be represented by using sequences of only two symbols (such as 1 and 0, on and off); computers work this way."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:6-8:Computations (as on calculators) can give more digits than make sense or are useful."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:9-12:Comparison of numbers of very different size can be made approximately by expressing them as nearest powers of 10."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:9-12:Numbers can be written with bases different from ten (which people probably use because of their 10 fingers). The simplest base, 2, uses just two symbols (1 and 0, or on and off)."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:9-12:When calculations are made with measurements, a small error in the measurements may lead to a large error in the results."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Numbers:9-12:The effects of uncertainties in measurements on a computed result can be estimated."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:K-2:Similar patterns may show up in many places in nature and in the things people make."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:K-2:Sometimes changing one thing causes changes in something else. In some situations, changing the same thing in the same way usually has the same result."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:3-5:Mathematical statements using symbols may be true only when the symbols are replaced by certain numbers."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:3-5:Tables and graphs can show how values of one quantity are related to values of another."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:6-8:An equation containing a variable may be true for just one value of the variable."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:6-8:Mathematical statements can be used to describe how one quantity changes when another changes. Rates of change can be computed from differences in magnitudes and vice versa."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:6-8:Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease indefinitely, increase or decrease in steps, or do something different from any of these."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:9-12:In some cases, the more of something there is, the more rapidly it may change (as the number of births is proportional to the size of the population). In other cases, the rate of change of something depends on how much there is of something else (as the rate of change of speed is proportional to the amount of force acting)."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:9-12:Symbolic statements can be manipulated by rules of mathematical logic to produce other statements of the same relationship, which may show some interesting aspect more clearly. Symbolic statements can be combined to look for values of variables that will satisfy all of them at the same time."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:9-12:Any mathematical model, graphic or algebraic, is limited in how well it can represent how the world works. The usefulness of a mathematical model for predicting may be limited by uncertainties in measurements, by neglect of some important influences, or by requiring too much computation."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:9-12:Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:9-12:When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes more than one, and sometimes maybe not at all."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Symbolic relationships:9-12:The reasonableness of the result of a computation can be estimated from what the inputs and operations are."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:K-2:Shapes such as circles, squares, and triangles can be used to describe many things that can be seen."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:3-5:Length can be thought of as unit lengths joined together, area as a collection of unit squares, and volume as a set of unit cubes."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:3-5:If 0 and 1 are located on a line, any other number can be depicted as a position on the line."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:3-5:Graphical display of numbers may make it possible to spot patterns that are not otherwise obvious, such as comparative size and trends."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:3-5:Many objects can be described in terms of simple plane figures and solids. Shapes can be compared in terms of concepts such as parallel and perpendicular, congruence and similarity, and symmetry. Symmetry can be found by reflection, turns, or slides."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:3-5:Areas of irregular shapes can be found by dividing them into squares and triangles."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:3-5:Scale drawings show shapes and compare locations of things very different in size."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:6-8:Some shapes have special properties: triangular shapes tend to make structures rigid, and round shapes give the least possible boundary for a given amount of interior area. Shapes can match exactly or have the same shape in different sizes."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:6-8:Lines can be parallel, perpendicular, or oblique."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:6-8:Shapes on a sphere like the earth cannot be depicted on a flat surface without some distortion."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:6-8:The graphic display of numbers may help to show patterns such as trends, varying rates of change, gaps, or clusters. Such patterns sometimes can be used to make predictions about the phenomena being graphed."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:6-8:It takes two numbers to locate a point on a map or any other flat surface. The numbers may be two perpendicular distances from a point, or an angle and a distance from a point."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:6-8:The scale chosen for a graph or drawing makes a big difference in how useful it is."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:9-12:Distances and angles that are inconvenient to measure directly can be found from measurable distances and angles using scale drawings or formulas."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:9-12:There are formulas for calculating the surface areas and volumes of regular shapes. When the linear size of a shape changes by some factor, its area and volume change disproportionately: area in proportion to the square of the factor, and volume in proportion to its cube. Properties of an object that depend on its area or volume also change disproportionately."/>
			<!--In the next benchmark, the phrase 'numbers and' originally had an m-dash between the words numbers and and. The m-dash was changed to a space because then an entity reference does not need to be used in the XML and a space is grammatically fine.-->
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:9-12:Geometric shapes and relationships can be described in terms of symbols and numbers and vice versa. For example, the position of any point on a surface can be specified by two numbers; a graph represents all the values that satisfy an equation; and if two equations have to be satisfied at the same time, the values that satisfy them both will be found where their graphs intersect."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Shapes:9-12:Different ways to map a curved surface (like the earth's) onto a flat surface have different advantages."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:K-2:Some things are more likely to happen that others. Some events can be predicted well and some cannot. Sometimes people aren't sure what will happen because they don't know everything that might be having an effect."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:K-2:Often a person can find out about a group of things by studying just a few of them."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:3-5:Some predictions can be based on what is known about the past, assuming that conditions are pretty much the same now."/>
			<!--In the next benchmark, the phrase 'experience it and' originally had an m-dash between the words it and and. The m-dash was changed to a space because then an entity reference does not need to be used in the XML and a space is grammatically fine.-->
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:3-5:Statistical predictions (as for rainy days, accidents) are typically better for how many of a group will experience something than for which members of the group will experience it and better for how often something will happen than for exactly when."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:3-5:Summary predictions are usually more accurate for large collections of events than for just a few.  Even very unlikely events may occur fairly often in very large populations."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:3-5:Spreading data out on a number line helps to see what the extremes are, where they pile up, and where the gaps are.  A summary of data includes where the middle is and how much spread is around it."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:3-5:A small part of something may be special in some way and not give an accurate picture of the whole.  How much a portion of something can help to estimate what the whole is like depends on how the portion is chosen. There is a danger of choosing only the data that show what is expected by the person doing the choosing."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:3-5:Events can be described in terms of being more or less likely, impossible, or certain."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:6-8:How probability is estimated depends on what is known about the situation. Estimates can be based on data from similar conditions in the past or on the assumption that all the possibilities are known."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:6-8:Probabilities are ratios and can be expressed as fractions, percentages, or odds."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:6-8:The mean, median, and mode tell different things about the middle of a data set."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:6-8:Comparison of data from two groups should involve comparing both their middles and the spreads around them."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:6-8:The larger a well-chosen sample is, the more accurately it is likely to represent the whole. But there are many ways of choosing a sample that can make it unrepresentative of the whole."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:9-12:Even when there are plentiful data, it may not be obvious what mathematical model to use to make predictions from them or there may be insufficient computing power to use some models."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:9-12:When people estimate a statistic, they may also be able to say how far off the estimate might be."/>
			<!--In the next benchmark, the phrase 'misleading when' originally had an m-dash between the words misleading and when. The m-dash was changed to a space because then an entity reference does not need to be used in the XML and a space is grammatically fine.-->
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:9-12:The middle of a data distribution may be misleading when the data are not distributed symmetrically, or when there are extreme high or low values, or when the distribution is not reasonably smooth."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:9-12:The way data are displayed can make a big difference in how they are interpreted."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:9-12:Both percentages and actual numbers have to be taken into account in comparing different groups; using either category by itself could be misleading."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:9-12:Considering whether two variables are correlated requires inspecting their distributions, such as in two-way tables or scatter plots. A believable correlation between two variables doesn't mean that either one causes the other; perhaps some other variable causes them both or the correlation might be attributable to chance alone. A true correlation means that differences in one variable imply differences in the other when all other things are equal."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:9-12:The larger a well-chosen sample of a population is, the better it estimates population summary statistics. For a well-chosen sample, the size of the sample is much more important than the size of the population. To avoid intentional or unintentional bias, samples are usually selected by some random system."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Uncertainty:9-12:A physical or mathematical model can be used to estimate the probability of real-world events."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:K-2:People are more likely to believe your ideas if you can give good reasons for them."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:3-5:One way to make sense of something is to think how it is like something more familiar."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:3-5:Reasoning can be distorted by strong feelings."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:6-8:Some aspects of reasoning have fairly rigid rules for what makes sense; other aspects don't. If people have rules that always hold, and good information about a particular situation, then logic can help them to figure out what is true about it. This kind of reasoning requires care in the use of key words such as if, and, not, or, all, and some. Reasoning by similarities can suggest ideas but can't prove them one way or the other."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:6-8:Practical reasoning, such as diagnosing or troubleshooting almost anything, may require many-step, branching logic. Because computers can keep track of complicated logic, as well as a lot of information, they are useful in a lot of problem-solving situations."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:6-8:Sometimes people invent a general rule to explain how something works by summarizing observations. But people tend to over generalize, imagining general rules on the basis of only a few observations."/>
			<!--In the next benchmark, the phrase 'If A ... either' originally had double quotes surrounding it. The double quotes were replaced with single quotes because a double quote is a reserved character in XML schema.-->
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:6-8:People are using incorrect logic when they make a statement such as 'If A is true, then B is true; but A isn't true, therefore B isn't true either.'"/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:6-8:A single example can never prove that something is always true, but sometimes a single example can prove that something is not always true."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:6-8:An analogy has some likenesses to but also some differences from the real thing."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:9-12:To be convincing, an argument needs to have both true statements and valid connections among them. Formal logic is mostly about connections among statements, not about whether they are true. People sometimes use poor logic even if they begin with true statements, and sometimes they use logic that begins with untrue statements."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:9-12:Logic requires a clear distinction among reasons: A reason may be sufficient to get a result, but perhaps is not the only way to get there; or, a reason may be necessary to get the result, but it may not be enough by itself; some reasons may be both sufficient and necessary."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:9-12:Wherever a general rule comes from, logic can be used in testing how well it works. Proving a generalization to be false (just one exception will do) is easier than proving it to be true (for all possible cases). Logic may be of limited help in finding solutions to problems if one isn't sure that general rules always hold or that particular information is correct; most often, one has to deal with probabilities rather than certainties."/>
			<!--In the next benchmark, the word 'supposed' originally had double quotes surrounding it. The double quotes were replaced with single quotes because a double quote is a reserved character in XML schema.-->
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:9-12:Once a person believes in a general rule, he or she may be more likely to notice cases that agree with it and to ignore cases that don't. To avoid biased observations, scientific studies sometimes use observers who don't know what the results are 'supposed' to be."/>
			<xsd:enumeration value="AAASbenchmarks:The mathematical world:Reasoning:9-12:Very complex logical arguments can be made from a lot of small logical steps. Computers are particularly good at working with complex logic but not all logical problems can be solved by computers. High-speed computers can examine the validity of some logical propositions for a very large number of cases, although that may not be a perfect proof."/>
		</xsd:restriction>
	</xsd:simpleType>
	<xsd:simpleType name="AAAScontentMathLeafType">
		<xsd:annotation>
			<xsd:documentation>
				***************************************  AAAScontentMathLeafType  ***************************************
				Lists leaf values
			</xsd:documentation>
		</xsd:annotation>
		<xsd:restriction base="xsd:string">
			<xsd:enumeration value="Circles, squares, triangles, and other shapes can be found in things in nature and in things that people build."/>
			<xsd:enumeration value="Patterns can be made by putting different shapes together or taking them apart."/>
			<xsd:enumeration value="Things move, or can be made to move, along straight, curved, circular, back-and-forth, and jagged paths."/>
			<xsd:enumeration value="Numbers can be used to count any collection of things."/>
			<xsd:enumeration value="Mathematics is the study of many kinds of patterns, including numbers and shapes and operations on them. Sometimes patterns are studied because they help to explain how the world works or how to solve practical problems, sometimes because they are interesting in themselves."/>
			<xsd:enumeration value="Mathematical ideas can be represented concretely, graphically, and symbolically."/>
			<xsd:enumeration value="Usually there is no one right way to solve a mathematical problem; different methods have different advantages and disadvantages."/>
			<xsd:enumeration value="Logical connections can be found between different parts of mathematics."/>
			<xsd:enumeration value="Mathematics is the study of any patterns or relationships, whereas natural science is concerned only with those patterns that are relevant to the observable world. Although mathematics began long ago in practical problems, it soon focused on abstractions from the material world, and then on even more abstract relationships among those abstractions."/>
			<xsd:enumeration value="As in other sciences, simplicity is one of the highest values in mathematics. Some mathematicians try to identify the smallest set of rules from which many other propositions can be logically derived."/>
			<xsd:enumeration value="Theories and applications in mathematical work influence each other. Sometimes a practical problem leads to the development of new mathematical theories; often mathematics developed for its own sake turns out to have practical applications."/>
			<xsd:enumeration value="New mathematics continues to be invented, and connections between different parts of mathematics continue to be found."/>
<!--			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:K-2:No benchmarks for this level."/>
			<xsd:enumeration value="AAASbenchmarks:Nature of mathematics:Mathematics, science, and technology:3-5:No benchmarks for this level."/> -->
<!--				In the next benchmark, the phrase 'endeavor, from' originally had an m-dash between the words endeavor and from. The m-dash was changed to a comma because then an entity reference does not need to be used in the XML and a comma is grammatically fine.-->
			<xsd:enumeration value="Mathematics is helpful in almost every kind of human endeavor, from laying bricks to prescribing medicine or drawing a face. In particular, mathematics has contributed to progress in science and technology for thousands of years and still continues to do so."/>
			<xsd:enumeration value="Mathematical modeling aids in technological design by simulating how a proposed system would theoretically behave."/>
			<xsd:enumeration value="Mathematics and science as enterprises share many values and features: belief in order, ideals of honesty and openness, the importance of criticism by colleagues, and the essential role played by imagination."/>
			<!--In the next benchmark, the phrase 'technology to' originally had an m-dash between the words technology and to. The m-dash was changed to a space because then an entity reference does not need to be used in the XML and a space is grammatically fine.-->
			<xsd:enumeration value="Mathematics provides a precise language for science and technology to describe objects and events, to characterize relationships between variables, and to argue logically."/>
			<xsd:enumeration value="Developments in science or technology often stimulate innovations in mathematics by presenting new kinds of problems to be solved. In particular, the development of computer technology (which itself relies on mathematics) has generated new kinds of problems and methods of work in mathematics."/>
			<xsd:enumeration value="Developments in mathematics often stimulate innovations in science and technology."/>
			<xsd:enumeration value="Numbers and shapes can be used to tell about things."/>
			<!--In the next benchmark, the phrases 'shapes, and' and 'them, help' originally had an m-dash between the words shapes and and and them and help. The m-dash was changed to a comma because then an entity reference does not need to be used in the XML and a comma is grammatically fine.-->
			<xsd:enumeration value="Numbers and shapes, and operations on them, help to describe and predict things about the world around us."/>
			<xsd:enumeration value="In using mathematics, choices have to be made about what operations will give the best results. Results should always be judged by whether they make sense and are useful."/>
			<!--In the next benchmark, the phrases 'things' and 'all equal-sided triangle' and 'all odd numbers' originally had double quotes surrounding them. The double quotes were replaced with single quotes because a double quote is a reserved character in XML schema.-->
			<xsd:enumeration value="Mathematicians often represent things with abstract ideas, such as numbers or perfectly straight lines, and then work with those ideas alone. The 'things' from which they abstract can be ideas themselves (for example, a proposition about 'all equal-sided triangles' or 'all odd numbers')."/>
			<xsd:enumeration value="When mathematicians use logical rules to work with representations of things, the results may or may not be valid for the things themselves. Using mathematics to solve a problem requires choosing what mathematics to use; probably making some simplifying assumptions, estimates, or approximations; doing computations; and then checking to see whether the answer makes sense. If an answer does not seem to make enough sense for its intended purpose, then any of these steps might have been inappropriate."/>
			<!--In the next benchmark, the phrase 'game, mathematicians' originally had an m-dash between the words game and mathematicians. The m-dash was changed to a comma because then an entity reference does not need to be used in the XML and a comma is grammatically fine.-->
			<xsd:enumeration value="Some work in mathematics is much like a game, mathematicians choose an interesting set of rules and then play according to those rules to see what can happen. The more interesting the results, the better. The only limit on the set of rules is that they should not contradict one another."/>
			<xsd:enumeration value="Much of the work of mathematicians involves a modeling cycle, which consists of three steps: (1) using abstractions to represent things or ideas, (2) manipulating the abstractions according to some logical rules, and (3) checking how well the results match the original things or ideas. If the match is not considered good enough, a new round of abstraction and manipulation may begin. The actual thinking need not go through these processes in logical order but may shift from one to another in any order."/>
			<xsd:enumeration value="Numbers can be used to count things, place them in order, or name them."/>
			<xsd:enumeration value="Sometimes in sharing or measuring there is a need to use numbers between whole numbers."/>
			<xsd:enumeration value="It is possible (and often useful) to estimate quantities without knowing them exactly."/>
			<xsd:enumeration value="Simple graphs can help to tell about observations."/>
			<xsd:enumeration value="The meaning of numerals in many-digit numbers depends on their positions."/>
			<!--In the next benchmark, the word '0' originally had double quotes surrounding it. The double quotes were replaced with single quotes because a double quote is a reserved character in XML schema.-->
			<xsd:enumeration value="In some situations, '0' means none of something, but in others it may be just the label of some point on a scale."/>
			<xsd:enumeration value="When people care about what is being counted or measured, it is important for them to say what the units are (three degrees Fahrenheit is different from three centimeters, three miles from three miles per hour)."/>
			<xsd:enumeration value="Measurements are always likely to give slightly different numbers, even if what is being measured stays the same."/>
			<xsd:enumeration value="There have been systems for writing numbers other than the Arabic system of place values based on tens. The very old Roman numerals are now used only for dates, clock faces, or ordering chapters in a book. Numbers based on 60 are still used for describing time and angles."/>
			<xsd:enumeration value="A number line can be extended on the other side of zero to represent negative numbers. Negative numbers allow subtraction of a bigger number from a smaller number to make sense, and are often used when something can be measured on either side of some reference point (time, ground level, temperature, budget)."/>
			<xsd:enumeration value="Numbers can be written in different forms, depending on how they are being used. How fractions or decimals based on measured quantities should be written depends on how precise the measurements are and how precise an answer is needed."/>
			<!--In the next benchmark, the phrase 'other, one' originally had an m-dash between the words other and one. The m-dash was changed to a comma because then an entity reference does not need to be used in the XML and a comma is grammatically fine.-->
			<!--In the bechmark below the mathetical symbols for add, subtract, muliply and divide had to changed to words other corruption of the shcema file occurs. So the words of  'of addition', 'subtraction', 'with mulitplication' and 'division' were previouslu symbols.-->
			<xsd:enumeration value="The operations of addition and subtraction are inverses of each other, one undoes what the other does; likewise with multiplication and division."/>
			<xsd:enumeration value="The expression a/b can mean different things: a parts of size 1/b each, a divided by b, or a compared to b."/>
			<xsd:enumeration value="Numbers can be represented by using sequences of only two symbols (such as 1 and 0, on and off); computers work this way."/>
			<xsd:enumeration value="Computations (as on calculators) can give more digits than make sense or are useful."/>
			<xsd:enumeration value="Comparison of numbers of very different size can be made approximately by expressing them as nearest powers of 10."/>
			<xsd:enumeration value="Numbers can be written with bases different from ten (which people probably use because of their 10 fingers). The simplest base, 2, uses just two symbols (1 and 0, or on and off)."/>
			<xsd:enumeration value="When calculations are made with measurements, a small error in the measurements may lead to a large error in the results."/>
			<xsd:enumeration value="The effects of uncertainties in measurements on a computed result can be estimated."/>
			<xsd:enumeration value="Similar patterns may show up in many places in nature and in the things people make."/>
			<xsd:enumeration value="Sometimes changing one thing causes changes in something else. In some situations, changing the same thing in the same way usually has the same result."/>
			<xsd:enumeration value="Mathematical statements using symbols may be true only when the symbols are replaced by certain numbers."/>
			<xsd:enumeration value="Tables and graphs can show how values of one quantity are related to values of another."/>
			<xsd:enumeration value="An equation containing a variable may be true for just one value of the variable."/>
			<xsd:enumeration value="Mathematical statements can be used to describe how one quantity changes when another changes. Rates of change can be computed from differences in magnitudes and vice versa."/>
			<xsd:enumeration value="Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease indefinitely, increase or decrease in steps, or do something different from any of these."/>
			<xsd:enumeration value="In some cases, the more of something there is, the more rapidly it may change (as the number of births is proportional to the size of the population). In other cases, the rate of change of something depends on how much there is of something else (as the rate of change of speed is proportional to the amount of force acting)."/>
			<xsd:enumeration value="Symbolic statements can be manipulated by rules of mathematical logic to produce other statements of the same relationship, which may show some interesting aspect more clearly. Symbolic statements can be combined to look for values of variables that will satisfy all of them at the same time."/>
			<xsd:enumeration value="Any mathematical model, graphic or algebraic, is limited in how well it can represent how the world works. The usefulness of a mathematical model for predicting may be limited by uncertainties in measurements, by neglect of some important influences, or by requiring too much computation."/>
			<xsd:enumeration value="Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another."/>
			<xsd:enumeration value="When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes more than one, and sometimes maybe not at all."/>
			<xsd:enumeration value="The reasonableness of the result of a computation can be estimated from what the inputs and operations are."/>
			<xsd:enumeration value="Shapes such as circles, squares, and triangles can be used to describe many things that can be seen."/>
			<xsd:enumeration value="Length can be thought of as unit lengths joined together, area as a collection of unit squares, and volume as a set of unit cubes."/>
			<xsd:enumeration value="If 0 and 1 are located on a line, any other number can be depicted as a position on the line."/>
			<xsd:enumeration value="Graphical display of numbers may make it possible to spot patterns that are not otherwise obvious, such as comparative size and trends."/>
			<xsd:enumeration value="Many objects can be described in terms of simple plane figures and solids. Shapes can be compared in terms of concepts such as parallel and perpendicular, congruence and similarity, and symmetry. Symmetry can be found by reflection, turns, or slides."/>
			<xsd:enumeration value="Areas of irregular shapes can be found by dividing them into squares and triangles."/>
			<xsd:enumeration value="Scale drawings show shapes and compare locations of things very different in size."/>
			<xsd:enumeration value="Some shapes have special properties: triangular shapes tend to make structures rigid, and round shapes give the least possible boundary for a given amount of interior area. Shapes can match exactly or have the same shape in different sizes."/>
			<xsd:enumeration value="Lines can be parallel, perpendicular, or oblique."/>
			<xsd:enumeration value="Shapes on a sphere like the earth cannot be depicted on a flat surface without some distortion."/>
			<xsd:enumeration value="The graphic display of numbers may help to show patterns such as trends, varying rates of change, gaps, or clusters. Such patterns sometimes can be used to make predictions about the phenomena being graphed."/>
			<xsd:enumeration value="It takes two numbers to locate a point on a map or any other flat surface. The numbers may be two perpendicular distances from a point, or an angle and a distance from a point."/>
			<xsd:enumeration value="The scale chosen for a graph or drawing makes a big difference in how useful it is."/>
			<xsd:enumeration value="Distances and angles that are inconvenient to measure directly can be found from measurable distances and angles using scale drawings or formulas."/>
			<xsd:enumeration value="There are formulas for calculating the surface areas and volumes of regular shapes. When the linear size of a shape changes by some factor, its area and volume change disproportionately: area in proportion to the square of the factor, and volume in proportion to its cube. Properties of an object that depend on its area or volume also change disproportionately."/>
			<!--In the next benchmark, the phrase 'numbers and' originally had an m-dash between the words numbers and and. The m-dash was changed to a space because then an entity reference does not need to be used in the XML and a space is grammatically fine.-->
			<xsd:enumeration value="Geometric shapes and relationships can be described in terms of symbols and numbers and vice versa. For example, the position of any point on a surface can be specified by two numbers; a graph represents all the values that satisfy an equation; and if two equations have to be satisfied at the same time, the values that satisfy them both will be found where their graphs intersect."/>
			<xsd:enumeration value="Different ways to map a curved surface (like the earth's) onto a flat surface have different advantages."/>
			<xsd:enumeration value="Some things are more likely to happen that others. Some events can be predicted well and some cannot. Sometimes people aren't sure what will happen because they don't know everything that might be having an effect."/>
			<xsd:enumeration value="Often a person can find out about a group of things by studying just a few of them."/>
			<xsd:enumeration value="Some predictions can be based on what is known about the past, assuming that conditions are pretty much the same now."/>
			<!--In the next benchmark, the phrase 'experience it and' originally had an m-dash between the words it and and. The m-dash was changed to a space because then an entity reference does not need to be used in the XML and a space is grammatically fine.-->
			<xsd:enumeration value="Statistical predictions (as for rainy days, accidents) are typically better for how many of a group will experience something than for which members of the group will experience it and better for how often something will happen than for exactly when."/>
			<xsd:enumeration value="Summary predictions are usually more accurate for large collections of events than for just a few.  Even very unlikely events may occur fairly often in very large populations."/>
			<xsd:enumeration value="Spreading data out on a number line helps to see what the extremes are, where they pile up, and where the gaps are.  A summary of data includes where the middle is and how much spread is around it."/>
			<xsd:enumeration value="A small part of something may be special in some way and not give an accurate picture of the whole.  How much a portion of something can help to estimate what the whole is like depends on how the portion is chosen. There is a danger of choosing only the data that show what is expected by the person doing the choosing."/>
			<xsd:enumeration value="Events can be described in terms of being more or less likely, impossible, or certain."/>
			<xsd:enumeration value="How probability is estimated depends on what is known about the situation. Estimates can be based on data from similar conditions in the past or on the assumption that all the possibilities are known."/>
			<xsd:enumeration value="Probabilities are ratios and can be expressed as fractions, percentages, or odds."/>
			<xsd:enumeration value="The mean, median, and mode tell different things about the middle of a data set."/>
			<xsd:enumeration value="Comparison of data from two groups should involve comparing both their middles and the spreads around them."/>
			<xsd:enumeration value="The larger a well-chosen sample is, the more accurately it is likely to represent the whole. But there are many ways of choosing a sample that can make it unrepresentative of the whole."/>
			<xsd:enumeration value="Even when there are plentiful data, it may not be obvious what mathematical model to use to make predictions from them or there may be insufficient computing power to use some models."/>
			<xsd:enumeration value="When people estimate a statistic, they may also be able to say how far off the estimate might be."/>
			<!--In the next benchmark, the phrase 'misleading when' originally had an m-dash between the words misleading and when. The m-dash was changed to a space because then an entity reference does not need to be used in the XML and a space is grammatically fine.-->
			<xsd:enumeration value="The middle of a data distribution may be misleading when the data are not distributed symmetrically, or when there are extreme high or low values, or when the distribution is not reasonably smooth."/>
			<xsd:enumeration value="The way data are displayed can make a big difference in how they are interpreted."/>
			<xsd:enumeration value="Both percentages and actual numbers have to be taken into account in comparing different groups; using either category by itself could be misleading."/>
			<xsd:enumeration value="Considering whether two variables are correlated requires inspecting their distributions, such as in two-way tables or scatter plots. A believable correlation between two variables doesn't mean that either one causes the other; perhaps some other variable causes them both or the correlation might be attributable to chance alone. A true correlation means that differences in one variable imply differences in the other when all other things are equal."/>
			<xsd:enumeration value="The larger a well-chosen sample of a population is, the better it estimates population summary statistics. For a well-chosen sample, the size of the sample is much more important than the size of the population. To avoid intentional or unintentional bias, samples are usually selected by some random system."/>
			<xsd:enumeration value="A physical or mathematical model can be used to estimate the probability of real-world events."/>
			<xsd:enumeration value="People are more likely to believe your ideas if you can give good reasons for them."/>
			<xsd:enumeration value="One way to make sense of something is to think how it is like something more familiar."/>
			<xsd:enumeration value="Reasoning can be distorted by strong feelings."/>
			<xsd:enumeration value="Some aspects of reasoning have fairly rigid rules for what makes sense; other aspects don't. If people have rules that always hold, and good information about a particular situation, then logic can help them to figure out what is true about it. This kind of reasoning requires care in the use of key words such as if, and, not, or, all, and some. Reasoning by similarities can suggest ideas but can't prove them one way or the other."/>
			<xsd:enumeration value="Practical reasoning, such as diagnosing or troubleshooting almost anything, may require many-step, branching logic. Because computers can keep track of complicated logic, as well as a lot of information, they are useful in a lot of problem-solving situations."/>
			<xsd:enumeration value="Sometimes people invent a general rule to explain how something works by summarizing observations. But people tend to over generalize, imagining general rules on the basis of only a few observations."/>
			<!--In the next benchmark, the phrase 'If A ... either' originally had double quotes surrounding it. The double quotes were replaced with single quotes because a double quote is a reserved character in XML schema.-->
			<xsd:enumeration value="People are using incorrect logic when they make a statement such as 'If A is true, then B is true; but A isn't true, therefore B isn't true either.'"/>
			<xsd:enumeration value="A single example can never prove that something is always true, but sometimes a single example can prove that something is not always true."/>
			<xsd:enumeration value="An analogy has some likenesses to but also some differences from the real thing."/>
			<xsd:enumeration value="To be convincing, an argument needs to have both true statements and valid connections among them. Formal logic is mostly about connections among statements, not about whether they are true. People sometimes use poor logic even if they begin with true statements, and sometimes they use logic that begins with untrue statements."/>
			<xsd:enumeration value="Logic requires a clear distinction among reasons: A reason may be sufficient to get a result, but perhaps is not the only way to get there; or, a reason may be necessary to get the result, but it may not be enough by itself; some reasons may be both sufficient and necessary."/>
			<xsd:enumeration value="Wherever a general rule comes from, logic can be used in testing how well it works. Proving a generalization to be false (just one exception will do) is easier than proving it to be true (for all possible cases). Logic may be of limited help in finding solutions to problems if one isn't sure that general rules always hold or that particular information is correct; most often, one has to deal with probabilities rather than certainties."/>
			<!--In the next benchmark, the word 'supposed' originally had double quotes surrounding it. The double quotes were replaced with single quotes because a double quote is a reserved character in XML schema.-->
			<xsd:enumeration value="Once a person believes in a general rule, he or she may be more likely to notice cases that agree with it and to ignore cases that don't. To avoid biased observations, scientific studies sometimes use observers who don't know what the results are 'supposed' to be."/>
			<xsd:enumeration value="Very complex logical arguments can be made from a lot of small logical steps. Computers are particularly good at working with complex logic but not all logical problems can be solved by computers. High-speed computers can examine the validity of some logical propositions for a very large number of cases, although that may not be a perfect proof."/>
		</xsd:restriction>
	</xsd:simpleType>
</xsd:schema>

