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first mathematics education seminar: Understanding Abstract Concepts in the Context of Abstract Algebra. Mathematics is a science of numbers, quantity, and space. All of the listed components are abstract ideas. How do we learn abstraction?"

Description: "The Innovation Fund is a challenge for educators, student teams, gamers, programmers, and anyone who has a great idea to create fun and engaging math educational media. WGBH Educational Foundation is seeking up to 100 educational media digital resources (videos, games, interactives, infographics, and manipulatives) that are directed towards middle school students and loosely aligned with the Common Core State Standards for Mathematics. The digital resources selected will be showcased on PBS LearningMedia as part of a middle school math resource collection. WGBH is looking for content that engages a wide range of students by reflecting a wide range of culturally responsive perspectives and learning styles. Digital resources should be engaging, rich in content and context, and go beyond strictly procedural teaching. In other words, no talking heads."

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"Measurement explains how math should be done. With plain English and pictures, [Lockhart] makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living."

Google Docs is an easy-to-use online word processor that enables you to create, store, share, and collaborate on documents with your science and math students. You can even import any existing document from Word and Simple Text. You can work from anywhere and with any computer platform to access your documents.

This list of "myths" written with a strong political bias. Take it in with a grain of salt. I like that they include references and links for why they believe what they do. This article would be good fodder for discussion.

I keep writing, in bits and pieces, about the middle way between the two approaches. For example, there should be enough discovery for every kid to firmly believe they could derive anything, if needed. This "just enough" will vary from student to student, too. In "The Glass Bead Game" Joseph took years to trace one short (highly abstract) game transcript to its very roots. He wanted to see for himself if the game was real. He did not do it for every game, though. The idea of "flow channels" between two opposite bad states comes to mind: http://www.secondlanguagewriting.com/explorations/elements/flow.jpg

Strategies are provided for classroom integration, creating survey, and science or math activities.

Mount Holyoke physics professor Mark Peterson argues that Galileo's applications of mathematics to Dante's Inferno laid the groundwork for his later discoveries (to be expanded on in a forthcoming book: ""Galileo's Muse: Renaissance Mathematics and the Arts" )

Applying mathematics to biology and complex life processes

"A McNugget number is a positive integer that can be obtained by adding together orders of McDonald's® Chicken McNuggets" While these numbers are interesting in themselves, I'm particularly taken by the idea of building an interesting problem based on consumer or popular culture. What other prompts might we find in a similar vien?

"A McNugget number is a positive integer that can be obtained by adding together orders of McDonald's® Chicken McNuggets" Find the largest number that IS NOT a McNugget number.

wiki where students will summarize their class notes, so that in a few semesters, this wiki should be an online textbook. This wiki is being produced to promote better understanding of certain ideas and concepts. It will also introduce you to a modern way of managing data.

if a student can't solve the problem and finds a resource that takes her through the proof step by step?

David Tall, emeritus professor from Warwick in the UK, published this book in 2013, and this links to his summary and a sample chapter. His papers and other math resources are on his website: http://homepages.warwick.ac.uk/staff/David.Tall/index.html