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Topic: Proportionality (mathematics)

	Mathematics - MSN Encarta
		The Greeks adopted elements of mathematics from the Babylonians and the Egyptians.
		The new element in Greek mathematics was the invention of an abstract mathematics founded on a logical structure of definitions, axioms (propositions accepted as self-evident), and proofs.
		The mathematics that had existed before their time was a collection of conclusions based on observation.
	encarta.msn.com /encyclopedia_761578291_5/Mathematics.html (1222 words)

	Proportionality (mathematics) Summary
		In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.
		The circumference of a circle is proportional to its diameter, with the constant of proportionality equal to π.
		The amount of force acting on a certain object from the gravity of the Earth at sea level is proportional to the object's mass, with the gravitational constant being the constant of proportionality.
	www.bookrags.com /Proportionality_(mathematics) (1793 words)

	Archived: Improving Mathematics in Middle School: Lessons from TIMSS and Related Research
		Moreover, students' mathematics achievement is regularly monitored, and mathematical competence is often used to determine access to educational and employment opportunities at the postsecondary level.
		The view that most people have limited ability to learn mathematics may be tied to the widely held belief that students must master all the "basics"--typically defined to be sets of arithmetic facts and procedures--before attempting to solve challenging mathematical problems or studying other areas of mathematics (e.g., algebra or geometry).
		A belief that high-level mathematical performance expectations are not appropriate for all students also appears to undergird forms of instruction that have generally been found in research studies of schools serving students from low-income communities, many of whom are assigned to "lower track" instruction.
	www.ed.gov /inits/Math/silver.html (3608 words)

	Proportionality (mathematics) - Wikipedia, the free encyclopedia
		is called the proportionality constant or constant of proportionality of the proportionality relation.
		The circumference of a circle is proportional to its diameter, with the constant of proportionality equal to π.
		The amount of force acting on a certain object from the gravity of the Earth at sea level is proportional to the object's mass, with the gravitational constant being the constant of proportionality.
	en.wikipedia.org /wiki/Proportionality_(mathematics) (627 words)

	Mathematics - Secondary Course Description - Mathematics - Pre-Algebra (Site not responding. Last check: 2007-08-20)
		Mathematics is incorrectly viewed as a collection of rigid rules and mysterious procedures that seem to be unrelated to each other and require total mastery with little or no understanding.
		Mathematics is perceived by many to be difficult and demanding and is considered to be a subject in which it is socially acceptable to do poorly.
		Mathematics learned in school is considered to be irrelevant, unnecessary, and unrelated to the mathematics students will encounter in their professional and personal lives.
	www.uen.org /core/core.do?courseNum=5200 (2347 words)

	MAKING CONNECTONS: A CASE FOR PROPORTIONALITY
		In the mathematics classroom, proportionality surfaces when properties of similar triangles are examined, when scaling problems are investigated, and when trigonometric functions are defined.
		One critical mathematical characteristic of proportional situations is the multiplicative relationship that exists among the quantities that represent the situation.
		Understanding proportionality by using several representations enables students to evaluate problem situations critically and to determine whether the context is proportional or nonproportional.
	education.umn.edu /rationalnumberproject/93_3.html (2566 words)

	[No title]
		Mathematics is a science created to understand the nature and the use of natural phenomena to improve human life.
		The mathematics program at the University of Great Falls is designed to provide students with an opportunity to develop their reasoning powers and problem solving skills.
		The content of elementary and middle school mathematics is applied and extended with respect to the topics of geometry, mathematical modeling, and measurement.
	www.ugf.edu /academics/Mathematics/Index.aspx (1062 words)

	[No title]
		The American Mathematical Association of Two-Year College (AMATYC) recommends that students in their first two years of college should engage in substantial problem solving, expand their mathematical reasoning, and learn to communicate mathematical ideas, in addition to knowing and understanding mathematics content.
		Because the objectives of the course are different from most other mathematics classes, alternate assessments such as written work (both short response and more developed essays/explanations), presentations, portfolios, group activities, etc., will be used in addition to exams.
		The student will define terms related to proportionality (ratio, rate, proportion, percent, etc.) and use them appropriately; performance will be satisfactory if the definitions are consistent with those given in the text and usage is appropriate.
	www.tamu-commerce.edu /teacher/AAT/AATsyllabi/MATH1350TarrantCounty.doc (1372 words)

	Chapter 6: Standards for Grades 6 - 8
		In the middle-grades mathematics classroom, young adolescents should regularly engage in thoughtful activity tied to their emerging capabilities of finding and imposing structure, conjecturing and verifying, thinking hypothetically, comprehending cause and effect, and abstracting and generalizing.
		The understanding of proportionality should also emerge through problem solving and reasoning, and it is important in connecting mathematical topics and in connecting mathematics and other domains such as science and art.
		Principles and Standards for School Mathematics proposes an ambitious and rich experience for middle-grades students that both prepares them to use mathematics effectively to deal with quantitative situations in their lives outside school and lays a solid foundation for their study of mathematics in high school.
	www.usi.edu /science/math/sallyk/Standards/document/chapter6/index.htm (1254 words)

	Crossroads in Mathematics
		Mathematics faculty will actively involve students in meaningful mathematics problems that build upon their experiences, focus on broad mathematical themes, and build connections within branches of mathematics and between mathematics and other disciplines so that student swill view mathematics as a connected whole relevant to their lives.
		Mathematics faculty will provide learning activities, including projects and apprenticeships, that promote independent thinking and require sustained effort and time s o that students will have the confidence to access and use needed mathematics and other technical information independently, to form conjectures from an array of specific examples, and to draw conclusions form general principles.
		The idea that mathematics competence is acquired through a curriculum that is carefully structured to include the necessary content at the appropriate time and the use of diverse instructional strategies is an underlying principle of this document.
	www.imacc.org /standards/standards.html (4745 words)

	Lesson Plans, Sec III
		Mathematics course design needs to provide lessons and lesson plans that are easily understood and repeated, and also effective in the classroom.
		Parts A and D of Secondary III mathematics may consolidate and extend the arithmetic, algebraic and geometric skills and sense met in secondary I and II.
		Secondary IV and V mathematics school and college mathematics may introduce and expand upon the role of logic and assumptions (assumed patterns) in codifying mathematics and provide logic-based foundation and structure for pure and some applied mathematics.
	www.whyslopes.com /Secondary_Three_Mathematics.html (3497 words)

	NCTM: News & Media: Online Chat with Cathy Seeley (Site not responding. Last check: 2007-08-20)
		Cautions against accelerating: make sure the student is motivated to continue mathematics study every year in high school; make sure there are good course offerings for students in 11th and 12th grade; ensure that students have the benefit of the rich mathematics (especially proportionality) that should be part of the middle school program.
		I taught mathematics for 15 years in California, and the schools in which I taught had this form of "traditional mathematics." However, I tutored students who were attending schools that had adopted "integrated mathematics." Their understanding of mathematics was shallow and they felt scattered.
		These are as essential to the teaching of mathematics as maps and globes to the teaching of social studies or science equipment to the teaching of science.
	www.nctm.org /news/pastpresident/chat_092404.htm (12104 words)

	Mathematical Competency Areas and the Sciences
		Since all scientific work is based upon experimentation, mathematics is often applied to the analysis of experimental data in the sciences.
		In the INSS, as a result, the mathematical tools associated with the competencies are used primarily to uncover the behaviors of physical phenomena.
		We see, therefore, that if a proportionality is plotted, it will produce a straight line with a slope equal to the constant in equation (2).
	campus.udayton.edu /~physics/jee/INSSModule/competencyareas.htm (1680 words)

	Achievement Gaps: The Key to Black Achievement is Criteria, not Comparison
		Racial proportionality means having the same proportion of fls in all social institutions as there are in the general population.
		So, for instance, if 12% of the US population is fl, racial proportionality would mean that 12% of US congressmen and senators would be fl, 12% of students at elite colleges would be fl, 12% of school janitors would be fl, 12% of CEOs of Fortune 500 companies would be fl, and so on.
		A person's cognitive skill level is an estimate of his or her general ability to handle increasingly complex cognitive tasks—from something as simple as balancing a checkbook to something as complex as forecasting the financial projections of an organization or industry.
	www.learningpt.org /gaplibrary/text/thekey.php (1872 words)

	Mathematics Framework for the 2005 National Assessment of Educational Progress (Site not responding. Last check: 2007-08-20)
		The distribution of items among the various mathematical content areas is a critical feature of the assessment design, as it reflects the relative importance and value given to each of the curricular content areas within mathematics.
		Proportionality (such as “a is to b as c is to d”) is foundational for understanding many algebraic concepts, such as rate of change, variation, linear relationships, slope, and functions, as well as concepts in other advanced mathematics courses and in other disciplines.
		Because the main NAEP assessment is designed to assess all five content areas of mathematics at grade 8, it is not possible to obtain indepth data about students’ understanding of fundamental topics in algebra or proportionality.
	www.nagb.org /pubs/m_framework_05/chap2.html (1869 words)

	NCTM: Curriculum Focal Points: Grade 7 (Site not responding. Last check: 2007-08-20)
		Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multistep problems in numerous contexts.
		Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed.
		They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.
	www.nctm.org /focalpoints/bygrade_7.asp (845 words)

	[No title]
		There was considerable variability across countries on the mathematics test, with scores ranging from a low of 24 percent in South Africa to a high of 79 percent in Singapore.
		Seventy-five percent of mathematics teachers and 68 percent of science teachers in Canada reported that Grade 8 students have access to calculators although reported usage rates were somewhat lower.
		Achievement in mathematics in fraction and number sense, algebra, data analysis, and proportionality is higher among Newfoundland students than the international scores.
	www.cdli.ca /Community/Prospects/v3n4/timss.html (892 words)

	Marietta College: Mathematics
		125, 224, 301, and any combination of Mathematics courses numbered 200 or higher leading to a total of 18 hours or more, where at least one of the additional courses is not required for the student's major.
		The power of these mathematical systems to explain and predict such real world phenomena as population growth and biological mutations is critically evaluated.
		Mathematical methods for application in management applications, techniques of linear programming including simplex method, sensitivity analysis, and introduction to game theory.
	www.marietta.edu /~math/courses.html (834 words)

	[No title]
		Although this course is conceptually based, some mathematics is required since the language of mathematics is used by those involved i the technical sciences.
		Notice that the proportionality does not imply that the constant of proportionality cannot be changed.
		The ideal gas law is a proportionality of the form PV T, where P is the pressure, V is the volume, and T is the temperature of the gas.
	www.udayton.edu /~physics/jee/mathintr.htm (1024 words)

	Fractions, Ratios, Proportions For Teachers, Tutors and (?) Teenagers
		They also provide the algebraic ways to represent rates and proportionality constants as quantities and to extend algebra beyond the realm of real numbers to the realm of calculation with units or quantities.
		Past mathematics curriculums called for an efficient mastery and comprehension of on paper methods for arithmetic with whole numbers and fractions to serve as a basis for algebra.
		In equivalent two-term ratios, the the first term is proportional to the second term with proportionality constant equal to common value of the associated equivalent fractions.
	whyslopes.com /etc/fractions (1748 words)

	Second Year High School Math - Lesson Plans with an algebra focus
		Pure modern mathematics with its context free development and codification of numbers and coordinate systems apart from the connection of the latter to the physical space we habit is I suspect, a codification of the empirically and thus inductively established skills and concepts.
		In other words, the modern mathematics curricula were inconsistent with the pure mathematics they supposed echoed and also inconsistent with the continuation and extension of the common knowledge of decimal arithmetic and geometry.
		The introduction of mathematics from counting to calculus may aim to provide the algebraic-deductive maturity and the context needed for the optional study of the or an axiomatic codification of mathematics while supporting and extending, not constraining, the common knowledge of decimals and geometry with and without coordinates.
	www.whyslopes.com /Secondary_Two_Mathematics.html (5784 words)

	PROPORTIONAL REASONING: THE EFFECT OF TWO CONTEXT VARIABLES, RATE TYPE, AND PROBLEM SETTING
		It is debatable whether mathematics courses, at least as they are now constituted, would ever be able to prepare students well enough in proportional thinking for them to transfer it to unfamiliar science contexts.
		As long as mathematics teachers see their job as teaching an abstract concept of proportions that only subsequently is used in "applications," there may be no ground for modifying their approach.
		The other direction is for science teachers to abandon their reliance on proportional reasoning being previously taught in mathematics classes and undertake to teach it as emerging from the very contexts in which they would wish to apply it.
	education.umn.edu /rationalnumberproject/89_6.html (4382 words)

	All Elementary Mathematics - Study Guide - Arithmetics - Ratio and proportion. Proportionality... (Site not responding. Last check: 2007-08-20)
		Two mutually dependent values are called proportional ones, if a ratio of their values is saved as invariable.
		This invariable ratio of proportional values is called a factor of a proportionality.
		Thus, a factor of a proportionality in this example is density.
	www.bymath.com /studyguide/ari/ari16.html (168 words)

	Read This: Using History to Teach Mathematics: An International Perspective
		She also emphasizes the importance of context when viewing mathematical artifacts, and emphasizes how mathematics is the product of the society from which it arises.
		If we are to keep mathematics out of the museum, somewhere between the mastodon bones and the mummy, then we should keep it connected to its roots.
		Ed Sandifer (sandifer@wcsu.ctstateu.edu) is a professor of mathematics at Western Connecticut State University and an enthusiastic fan of Leonhard Euler.
	www.maa.org /reviews/usinghist.html (1003 words)

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