The Harmonious Mathematics of Music According to legend, the Ancient Greek Pythagoras was once walking on the streets of Samos, when the sounds of blacksmiths’ hammering suddenly gave him an epiphany. Pythagoras rushed into the shop and, as he analyzed mathematically the shapes of the blacksmiths’ hammers, he laid the foundations of music that today’s Rihanna, Shakira and others are building upon. Wait a minute… Are you talking about the guy from the Pythagorean theorem? I am. Math Manipulatives: About Virtual Manipulatives Math Manipulatives contains three pages of resources: About Virtual Manipulatives What is a virtual manipulative? In What are Virtual Manipulatives?, Patricia Moyer, Johnna Bolyard, and Mark Spikell (2002) defined a virtual manipulative as "an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge" (p. 373). Static and dynamic virtual models can be found on the Web, but static models are not true virtual manipulatives.
10 Unusual Ways to Explore Math I confess. I never really liked math. I played the school game well so I received pretty good grades, but after I passed the test (even after receiving an A in most cases), those rules, theorems and facts didn’t stick around for very long. The problem was everything was drilled into me, or as I like to think now, drilled out of me. from Wolfram MathWorld A special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial). Because of this ambiguity, two different notations are sometimes (but not always) used, with defined as the logarithmic derivative of the gamma function , and
Thinking Blocks - Model Your Math Problems Thinking Blocks is a nice site for elementary and middle school mathematics teachers. Thinking Blocks provides interactive templates in which students use brightly colored blocks to model and solve problems. As students work through the problems they are provided with feedback as to whether or not they are using the correct sequence to solve each problem. There are templates and problems for addition, multiplication, fractions, and ratios.
Fibonacci GCD's, please Fibonacci numbers exhibit striking patterns. Here's one that may not be so obvious, but is striking when you see it. Recall the Fibonacci numbers: n: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,... fn: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,... Know Students Better: 15 Tools for Formative Assessment When teachers know their students well, they can build strong connections that lead to better learning. Knowing students’ interests, strengths, and weaknesses help teachers tailor learning experiences for their students. Formative assessment involves the teacher collecting information about what students know, don’t know, and want to learn. A Random Math Fun Fact! From the Fun Fact files, here is a Random Fun Fact, at the Advanced level: The traditional proof that the square root of 2 is irrational (attributed to Pythagoras) depends on understanding facts about the divisibility of the integers. (It is often covered in calculus courses and begins by assuming Sqrt=x/y where x/y is in smallest terms, then concludes that both x and y are even, a contradiction. See the Hardy and Wright reference.)
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