The Development and Use of Representations in Teaching and Learning about Problem Solving: Exploring
Tim Boerst has explored instructional approaches that foster the development of representational skill and routine use of multiple representations in problem solving. In particular he has used the 'Rule of 3' (a structure employed in calculus reform materials that highlights the use of numerical, algebraic, and/or graphic representations in mathematical learning) to see whether an emphasis on multiple representations would deepen mathematical learning opportunities for a wide variety of students
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A primer in MathML
This course, as the name suggest, is intended to help authors who want to publish mathematical content on web. The emphasis here is to enable learners to quickly adapt to the extensive mathML markup language and begin writing codes even without a specialized editor, available commercially. The course is presented in the form of a tutorial, which essentially saves on unnecessary details. This tutorial is not intended currently (may be supplemented later with the help coming from others) to be a c
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Mathematics for Computer Science
A basic introduction to Calculus and Linear Algebra. The goal is to make students mathematically literate in preparation for studying a scientific/engineering discipline. The first week covers differential calculus: graphing functions, limits, derivatives, and applying differentiation to real-world problems, such as maximization and rates of change. The second week covers integral calculus: sums, integration, areas under curves and computing volumes. This is not meant to be a comprehensive calcu
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Patrons d'exercices pour Aplusix Une étape du développement de l'EIAH occasion d'un travail entre
Au cours du développement de l'EIAH APLUSIX, il y a eu de nombreuses occasions d'un travail partagé entre informaticiens et didacticiens. Quelques-unes sont décrites succinctement. Lors de la mise en place de patrons d'exercices et d'une carte de tests, une coopération plus approfondie a eu lieu, en respectant les disciplines de chacun. Cette mise en place de patrons d'exercices est décrite plus longuement.,Preprint
Author(s): Bouhineau Denis,Bronner Alain,Chaachoua Hamid,Nica

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Empirical Research Methods
Regression analysis is an enormously popular and powerful tool, used ubiquitously in the social and behavioral sciences. Most courses on the subject immediately dive into the mathematical aspects of the subject and illustrate the technique on problems that are already highly structured. As a result, most students come away with little idea of the wide range of problems to which regression analysis can be applied and how to represent those problems in a way that cleverly utilizes readily availabl
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Logic
Logic and Proofs is an introduction to modern symbolic logic. It provides a rigorous presentation of the syntax and semantics of sentential and predicate logic. However, the distinctive emphasis is on strategic argumentation. Students learn effective strategies for constructing natural deduction proofs. This learning is supported by the Carnegie Proof Lab: it provides a sophisticated interface, in which students can give arguments by strategically guided forward and backward steps.
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Private Universe Project in Mathematics: Workshop 3. Inventing Notations
We learn how to foster and appreciate students’ notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,Kenilworth Study: Pizzas In the fourth grade, the students encounter counting problems where the solutions cannot be built using standard manipulatives. As he invents his own notation systems, one student, Matt, builds on previous work to arrive at a solution
Author(s): Harvard-Smithsonian Center for Astrophysics

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Smithsonian Institution-Astrophysical Observatory "All Rights Reserved"

Private Universe Project in Mathematics: Workshop 2. Are You Convinced?
Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proof—proof by cases and proof by induction—naturally grow out of the need to justify and convince others.,25 min. Englewood, New Jersey—Teachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part
Author(s): Harvard-Smithsonian Center for Astrophysics

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Smithsonian Institution-Astrophysical Observatory "All Rights Reserved"

Private Universe Project in Mathematics: Workshop 2. Are You Convinced?
Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proof—proof by cases and proof by induction—naturally grow out of the need to justify and convince others.,Englewood, New Jersey—Teachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part to give
Author(s): Harvard-Smithsonian Center for Astrophysics

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Smithsonian Institution-Astrophysical Observatory "All Rights Reserved"

Private Universe Project in Mathematics: Workshop 4: Thinking Like a Mathematician
What does a mathematician do? What does it mean to think like a mathematician? This program parallels what a mathematician does in real life with the creative thinking of students.,How a Mathematician Approaches Problems - Fern Hunt, a mathematician at the National Institute for Standards and Technology, is seen as she collaborates with colleagues to solve difficult technical problems. Using the metaphor of the children’s game Towers of Hanoi, she explains her approach to solving problems. 15 m
Author(s): Harvard-Smithsonian Center for Astrophysics

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Smithsonian Institution-Astrophysical Observatory

Chemical Equilibrium in the Gas Phase
This website describes gas phase equilibrium chemistry and provides a tutorial on key concepts like LeChatelier's principal and includes on-line exercises in which the reader can check their understanding. Calculations of equilibrium constants expressed in terms of pressure and concentration are presented. This site will be most useful for high school and introductory university Chemistry courses in which students are developing an understanding of equilibrium chemistry.
Author(s): Gwen Sibert, Roanoke Valley Governor's School

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Copyright 2003 Virgina Tech

Middle School Portal: Math and Science Pathways (MSP2)
Six days a week, a new math problem is posted on this Web site to intrigue and challenge grade school students. Each Daily Brain has a different theme, considering some mathematical perspective of science, history, geography, and more. After solving the problem, or for a little help, students can look at a step-by-step solution that is also posted online. All old Daily Brains are kept in an archive, and as of May 2003, they numbered around 400. The problems are mostly intended for students betwe
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Middle School Portal: Math and Science Pathways (MSP2)
Located at the University of Wales, the Centre for the Popularisation of Mathematics brings a more artistic side to the often plainly presented subject. Several online exhibits and galleries illustrate sculptures and knots that have a basis in math. One of the most interesting and famous mathematical sculptures is the Mobius Band. The centre gives a description of the Mobius Band and its significance, as well as instructions on how to create one and interesting experiments to try. Many other scu
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Middle School Portal: Math and Science Pathways (MSP2)
M.C. Escher is a widely known and popular artist whose work depicts complex, and often impossible, geometrical patterns. This Web site examines the mathematics behind his drawings. Many examples of Escher's work are given, illustrating mathematical principles such as the shape and the logic of space. Tessellations and polyhedra are common building blocks of the drawings. It is quite interesting to see how basic designs are transformed into the intricacies depicted by Escher. The material is cert
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Approximating pi
This web page features mathematical information about Archimedes' successful approach to finding an approximation to pi and an interactive manipulative that replicates the approach. The user can approximate pi as a number between the lengths of the perimeters of two polygons, one inscribed inside a circle and one circumscribed around the circle. The number of sides for the polygons may be increased to 96 with the value for pi always being between the two approximations. Similarities and differen
Author(s): British Broadcasting Corporation (BBC)

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Copyright 1996-2003 WGBH Educational Foundation

Middle School Portal: Math and Science Pathways (MSP2)
In this online activity, students analyze predictions made by sportswriters about which basketball teams will win to determine which teams are playing each other. The Getting Started link describes how to set up a table to organize the given information. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The solution illustrates and explains three different ways to successfully organize information, includ
Author(s): National Council of Teachers of Mathematics (NCTM)

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Content copyright 1999-2002 National Council of Teachers of Mathematics.

Movie money : do movies make money?
The initial question for this online activity asks students to determine if showing movies makes money for theater owners. Given information about box office receipts, the percentage of receipts that theater owners pay to movie distributors, and overhead costs, students answer the question by making calculations and organizing information in a suggested table. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasi
Author(s): National Council of Teachers of Mathematics (NCTM)

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Content copyright 1999-2002 National Council of Teachers of Mathematics.

Middle School Portal: Math and Science Pathways (MSP2)
This online activity offers students a chance to analyze data stated as percentages to draw conclusions about the similarity of five archeological sites. Students analyze the data by making a table of the differences for each pair of sites by subtracting the smaller percentage from the larger for each of five types of evidence. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activity features a solu
Author(s): National Council of Teachers of Mathematics (NCTM)

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Content copyright 1999-2002 National Council of Teachers of Mathematics.

Middle School Portal: Math and Science Pathways (MSP2)
This online activity challenges students to determine which of four different size grape juice cans labeled with the grape juice concentration would have the strongest grape taste. The activity is one of 80 mathematical challenges featured on the Figure This! web site emphasizing real-world uses of mathematics. The Hint suggests forming ratios that are fractions to compare quantities. Two ways of answering the initial question are illustrated with tables. Related questions have students consider
Author(s): National Council of Teachers of Mathematics (NCTM)

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Content copyright 1999-2002 National Council of Teachers of Mathematics.

Mathematical Methods of Engineering Analysis
Mathematical Methods of Engineering Analysis
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