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This is a compilation of Karl's Transparent Algebra posts. He does such an incredible job of making his thinking visible for all of us in how he is planning his course for the upcoming year. I share it because I think it's a valuable example of a reflective practitioner and worth sharing. If you have any teachers who might benefit from reading some of his reasoning, I encourage you to send them to his blog!

This gives students a real life example of how to use proportions

"Easily incorporate computational thinking into your curriculum with these classroom-ready lessons, examples, and programs"

"In this article we introduce the free educational mathematics software GeoGebra. This open source tool extends concepts of dynamic geometry to the fields of algebra and calculus. You can use GeoGebra both as a teaching tool and to create interactive web pages for students from middle school up to college level. Specifically designed for educational purposes, GeoGebra can help you to foster experimental, problem-oriented and discovery learning of mathematics. We will illustrate the basic ideas of the software and some of its versatile possibilities by discussing several interactive examples."

Complete mathematics Revision text - free pdf download. Numerous examples and solution

Online binder of activities created by Kelly Hines for her students. She uses this site (livebinders.com) to organize her online learning for her students. This is just a good example of what an online binder might look like. 

GASARCH discusses use of math concepts in the popular press with several examples. Are they used correctly?

"Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving" by Sanjoy Mahajan, published in 2010. "Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool-the general principle-from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest." Available as a free download (Creative Commons License), .pdf): http://mitpress.mit.edu/books/full_pdfs/Street-Fighting_Mathematics.pdf

Description of a University of Queensland study involving 36 infants, half 15 months and half 18 months. Tests with counting videos suggests that the 18 month old children have a grasp of counting rules before they can count (for example, understanding that objects can be counted only once." Further research using brain imaging is suggested.

Thanks - this will be useful for my "Math-rich baby" online class!

"This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics."

The game aims to help children associate fractions with percentages. A cartoon Santa Clause introduces a snow scene with a group of identical parcels that contain either a fraction or a percentage. It is operated using the mouse, and the goal is to pair up matches, for example 1/3 and 33%, which pop out of the boxes. There are no instructions, but the game would be quite intuitive to children, though perhaps not to less inquisitive adults.

I will be adding good examples of mathematics wiki's to this list....

Enjoy yourself while improving your maths!! Click on any title and solve the interactive exercises!!! You will find an example and exercises for each subject

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Interactive, animated maths dictionary for kids with over 600 common math terms explained in simple language. Math glossary with math definitions, examples, math practice interactives, mathematics activities and math calculators. © Jenny Eather 2007.

Lots of real life interactive examples in between....

"Technology has inevitably been inserted to nearly all aspects of our lives today. First and foremost, the use of computerised cash registers have been around for a few decades now. Trying to remember cash registers which operated without a digital display might be nearly impossible. The generation which might be able to do so has been replaced with a new generation who depend on technology to a large degree. The dependence on new technology is starting to 'show signs' of the effect of converting from our analogue counterparts. Below is an example that I recently experienced the effect of technology in a transaction at a doughnut shop."

"there are plenty of other infinite decimal (and infinitely useful) numbers to celebrate-Feb. 7 could have been e Day, for example, or Jan. 6, the Day of the Golden Ratio."

Published March 2013. "The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem."

"In Math on Trial, mathematicians Leila Schneps and Coralie Colmez tell the story of ten criminal trials in which mathematical arguments were used-and disastrously misused-as evidence. Using a wide range of examples, from the Dreyfus Affair to the Amanda Knox murder trial, they show how the improper application of mathematical concepts can mean the difference between walking free and life in prison. A colorful narrative of mathematical abuse featuring such characters as Charles Ponzi, Alfred Dreyfus, and Oliver Wendell Holmes, Math on Trial shows that legal expertise isn't always enough to prove a person innocent."