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

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.

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

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 proofproof by cases and proof by inductionnaturally grow out of the need to justify and convince others.,25 min. Englewood, New JerseyTeachers 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

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 proofproof by cases and proof by inductionnaturally grow out of the need to justify and convince others.,Englewood, New JerseyTeachers 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

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 childrens game Towers of Hanoi, she explains her approach to solving problems. 15 m

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.

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

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

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

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

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

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

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

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

Mathematical Methods of Engineering Analysis

Mathematical Methods of Engineering Analysis

Middle School Portal: Math and Science Pathways (MSP2)

This web site offers families, teachers, and tutors 80 mathematical challenges helpful for encouraging problem solving with students in grades 6 to 8. The math challenges focus on concepts and objects found in everyday life, such as how fast your heart beats, what shape container holds the most popcorn, and how much of me shows in a mirror. Each challenge contains an initial problem with a solution hint, a complete explanation of the answer, and additional problems related to the same challenge.

Middle School Portal: Math and Science Pathways (MSP2)

This challenge asks students to determine possible ways for combining stamps costing 15 and 33 cents to total 1 dollar 77 cents. It notes that this type of problem is similar to a process used for creating security codes. This online student activity is part of the Figure This! collection of 80 mathematical challenges. Students are encouraged to make a chart as they explore possible number combinations. The answer page describes and illustrates four different approaches to finding the solution,

From Algorithms to Z-Scores: Probabilistic and Statistical Modeling in Computer Science

The materials here form a textbook for a course in mathematical probability and statistics for computer science students. Computer science examples are used throughout, in areas such as: computer networks; data and text mining; computer security; remote sensing; computer performance evaluation; software engineering; data management; etc.

Mathematics Under the Microscope

This book inevitably asks the question "How does the mathematical brain work?" The author tries to reflect on the explosive development of mathematical cognition, an emerging branch of neurophysiology which purports to locate structures and processes in the human brain responsible for mathematical thinking. PDF file.