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Mathematics — Study and Teaching
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61.

When I Was in School [electronic resource]: Implementing Assessment Reform

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Explains the importance of communication in encouraging support for new assessment strategies. Focuses on the importance of collaboration among teachers, administrators, and especially parents, when implementing assessment reform in a school or district.
Online
1997
62.

Calculating Change [electronic resource]

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On-location reports from five innovative programs across America, show how parents and communities can work together to promote better, more creative math and science education. A youth services director in Lorain, Ohio, works with gang members and uses a pool table to teach them basic math while helping them develop self-confidence. A mother in Reston, Virginia, invents a colorful shapes-and-patterns game to teach geometry and other advanced math concepts in an after-school program. Bob Moses and David Dennis, former 60s voting rights activists, today focus on teaching African American students math skills and confidence through the Algebra Project. A New York City class learns fractions, ratio, proportion, and geometric principles while designing and building models of a housing p [...]
Online
1994
63.

Two Dance Collaborations [electronic resource]

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In a first-time collaboration, a dance teacher and a science teacher explore the laws of motion with a seventh- and eighth-grade dance class. At another school, a dance teacher and a math teacher work with sixth graders on imaginative interpretations of the idea of circles.
Online
2005
64.

Logarithmic Functions [electronic resource]

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Addresses the logarithmic relationship, the use of logarithmic properties, and the handling of a scientific calculator and explains how radiocarbon dating and the Richter scale depend on the properties of logarithms. Many rules and tests from previous programs are also incorporated into the lesson.
Online
1991
65.

The Language of the Universe [electronic resource]: Mathematics in Ancient Times

In this program, Professor Marcus du Sautoy explores mathematical milestones of ancient Egypt, Mesopotamia, and Greece. Topics include Egypt's unusual method of multiplication and division, as well as Egyptians' understanding of binary numbers, fractions, and solids such as the pyramid; Babylon's base-60 number system - the foundation of minutes and hours - and Babylonians' use of quadratic equations to measure land; and the contributions of four of Greece's mathematical giants: Plato, Euclid, Archimedes, and Pythagoras.
Online
2008
66.

Scientists in Schools [electronic resource]: A New Approach for School Science

Statistics show school students' interest in science and mathematics is declining, So how do we reverse this trend? In this video segment, learn about an innovative Australian program in which classrooms adopt their very own working scientist to interact with students.
Online
2010
67.

Surprises in Mind [electronic resource]

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Demonstrates that mathematical creativity as expressed in art, architecture, music and industry is built into the brain and can flourish under the right conditions. Reviews the remarkable 12-year study, led by Professor Carolyn Maher of Rutgers University, that followed students from first grade through high school to demonstrate the brain's surprising natural abilities for learning math.
Online
2001
68.

Management Science Overview [electronic resource]

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Program 1 introduces Management science or the study of scheduling (people, workflow) in order to maximize efficiency and effectiveness. Algorithms are used to generate accurate and optimal solutions to problems involving street networks (garbage collection, postal deliveries), scheduling (airlines), and routing problems (salespeople, telephone relays). Overview conveys the scope and applicability of management science concepts.
Online
1986
69.

Street Smarts [electronic resource]

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Program 2 illustrates that routing problems that involve traversing streets in a city can be solved by graphing. It also shows how to find efficient travel routes using graphs and Euler circuits. Curb inspections and other street-related jobs provide concrete illustrations of the central concepts.
Online
1986
70.

Trains, Planes and Critical Paths [electronic resource]

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Program 3 highlights nearest-neighbor and greedy algorithms to show how they aid in solving complex routing problems. Critical path analysis is also featured, as are order requirement directed graphs (digraphs). Demonstrates how to find approximate solutions to the traveling salesman problem (TSP) and how to distinguish between Euler circuits and the TSP.
Online
1986
71.

Juggling Machines [electronic resource]

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Program 4 demonstrates how the scheduling requirements of airliners and police patrol cars illustrate how crucial algorithms are to everyday life. List processing algorithms are used in simplified scheduling problems, constructed to provide insight into the behavior of scheduling processors. Bin packing problems and heuristic algorithms are also featured.
Online
1986
72.

Juicy Problems [electronic resource]

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Program 5 demonstrates that economies depend on the optimal use of resources to produce goods and services at maximum profit. It introduces linear programming as a powerful tool for determining the best combination of manpower and resource use. The corner principle, simplex method, and potentially faster linear programming methods are also discussed.
Online
1986
73.

Statistics Overview [electronic resource]

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Program 6 moves from baseball scores and roulette odds to national unemployment figures and quality control testing, to show that statistics help us to understand information and make better decisions. This overview introduces the subject, featuring professionals in labor statistics and medicine who use statistical methods to determine probable outcomes in their fields.
Online
1986
74.

Behind the Headlines [electronic resource]

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Program 7 illustrates how data are collected for specific purposes by sampling or experimentation. Random sampling is employed to eliminate bias, and experiments are controlled to discover cause-and-effect relationships. Randomized comparative experiments are explained, as is the use of Latin square designs for statistical data gathering.
Online
1986
75.

Picture This [electronic resource]

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Program 8 demonstrates that exploratory data analysis is the art of looking for unanticipated patterns in data. Uses of histograms, box plots, and scatterplots are explained, as are the meanings of mean, median, quartiles, and outliers in statistical parlance. Illustrations are drawn from examples relating to seismic analysis, Napoleon's march, and baseball.
Online
1986
76.

Place Your Bets [electronic resource]

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Program 9 demonstrates that random events have unpredictable outcomes that over time follow a predictable pattern. Visits a casino to capture first-hand footage of this phenomenon in action. Includes sampling distribution, normal curves, standard deviation, expected value, and the central limit theorem.
Online
1986
77.

Confident Conclusions [electronic resource]

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Program 10 compares formal statistical inference, as opposed to exploratory data analysis, based on calculations of probability. Defines confidence intervals and demonstrates how to find a 95% confidence interval for a population proportion p. Application examples are drawn from a health study, manufacturing, and Gallup poll interviews.
Online
1986
78.

Social Choice Overview [electronic resource]

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Program 11 highlights how individual choices and taking chances are analyzed using game theory, one of the important developments of twentieth-century mathematics. Collective choice is analyzed using election theory, weighted voting, and apportionment. Real-life examples show the utility of the concepts.
Online
1986
79.

The Impossible Dream [electronic resource]

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Program 12 discusses five voting methods: plurality, plurality with runoff, Condorcet, Borda, and sequential runoff voting. Dramatic reenactments of a political convention and a news broadcast are presented to clarify concepts. An example of Nobelist Kenneth Arrow's theorem on voting theory is also featured.
Online
1986
80.

Zero Sum Games [electronic resource]

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Program 14 shows how Game theory deals with strategies employed by parties with conflicting needs. Optimal strategies (pure and mixed) are described mathematically, and game matrices are explained. Expected value equations, a graphical interpretation, a restaurant illustrating the minimax technique, and an illegal parking example are presented.
Online
1986