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From the abstract (full text requires subscription or purchase): "Though cooperative learning has been a topic of considerable interest in educational research, there has been little study specific to learning in the mathematics content area of geometry. This paper seeks to address that gap through a design experiment featuring a novel small-group computing environment for supporting student learning about quadrilaterals. In this design, each student controls a unique point in a shared geometric space, and those points are linked such that a group of four students collectively forms a quadrilateral. We first present results from pre- and post-measures to show how the students learned from the activities and developed in terms of geometric reasoning. We then present three episodes, elaborated with the notion of appropriation, to explain how students took up ways of using the technological tools and of talking about geometric concepts from one another in the interactive environment. Our study found that students achieved learning gains in this novel environment, that the environment provided rich opportunities for peer interaction around geometric objects, and that student learning opportunities and interactions were characterized by processes of appropriating ways of talking about and using software features."

Forthcoming June 2012: "From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure."

"Mathematical Expeditions is a collection of over 500 culturally and historically diverse mathematical problems carefully chosen to enrich mathematics teaching from middle school through the college level." Forthcoming June 2012.

"This book explores 20 geometric diagrams that play crucial roles in visualizing mathematical proofs."

Abstract: "A Learning Assistant program that recruits strong STEM undergraduates to become mathematics teachers was explored through a qualitative study. Three program participants were purposely selected and interviewed. The program reaffirmed one participant's choice to become a teacher and clarified for one that it might be a career for him."

"Braingenie builds deep mastery and sharpens problem-solving skills. Learn, practice, and quiz yourself on 5,000+ skills. Compete in real-time multiplayer matches. Win badges and go for a top spot on the leaderboard. Sign up now (it's free!) Explore Learning Zone"

Prometheus Books The Glorious Golden Ratio [978-1-61614-423-4] - "For centuries, mathematicians, scientists, artists, and architects have been fascinated by a ratio that is ubiquitous in nature and is commonly found across many cultures. It has been called the "Golden Ratio" because of its prevalence as a design element and its seemingly universal esthetic appeal. From the ratio of certain proportions of the human body and the heliacal structure of DNA to the design of ancient Greek statues and temples as well as modern masterpieces, the Golden Ratio is a key pattern that has wide-ranging and perhaps endless applications and manifestations. What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. With their talent for elucidating mathematical mysteries, veteran educators and prolific mathematics writers Alfred S. Posamentier and Ingmar Lehmann begin by tracing the appearance of the Golden Ratio throughout history. They demonstrate a variety of ingenious techniques used to construct it and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. They also point out the intriguing relationship between the Golden Ratio and other famous numbers (such as the Fibonacci numbers, Pythagorean triples, and others). They then explore its prevalence in nature as well as in architecture, art, literature, and technology. "

Abstract "This article reports on a case study of the web-based educational maths application, Mathletics. The findings are drawn from an ethnographic study of children's technology use in Melbourne, Australia. We explore the experience, governance and commerce of children's Mathletics use, and offer insights into the developing possibilities and challenges emerging through the adoption of Web 2.0 applications for learning and education." (Full text requires subscription or purchase)

Published 2012 "Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--"Don't disturb my circles"--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction."

Compiled by Drexel University "The Internet Math Library is our best resource for teachers, students and parents looking for web sites across the Internet on math topics. Sites are gathered from our own explorations and submissions from users like yourself."

Good collection of math related links

LOG IN January 24th 9pm ET: http://tinyurl.com/MathFutureEvent Music and mathematics have been linked together for thousands of years, but rarely have students had the opportunity to explore the many connections that exist between them. To try to fill this gap, Mike Thayer of Hyperbolic Guitars is developing a course. At the event, we will discuss the course outline, as well as math and music links in general. All events in the Math Future weekly series: http://mathfuture.wikispaces.com/events The recording will be at http://mathfuture.wikispaces.com/HyperbolicGuitarsCourse Event challenge! Help Mike find a resource - a web page, a video, a music piece - to go with one of the topics in the course outline. Full syllabus and details of the outline: http://hyperbolicguitars.wikispaces.com/Math+%26+Music+Course Major topics: What is sound, anyway? The physics of waves The mathematics of waves Resonance Elasticity The generation of sound by "simple" systems The vibrating string The vibrating rod The vibrating plate (e.g., drumhead or cymbal) Open and closed pipes The Helmholtz resonator (--> the vocal chords) White noise, pink noise The concept of "timbre" The perception of sound Human listeners Other "listeners": Digital recording The interaction between the generator and the listener: the science of acoustics What makes sound become music? What does a listener "listen for" in music? Basics of music and musical notation: Musical descriptions Basics of music: Psycho-physical (auditory) descriptions What makes sound "musical" (

"intrinsic approach to designing educational games" studied in experiments with Zombie Division to teach math to 7 and 11 year olds

"In In Pursuit of the Unknown, celebrated mathematician Ian Stewart uses a handful of mathematical equations to explore the vitally important connections between math and human progress."

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

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

Collection of Math pictures

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The Middle School Portal 2: Math and Science Pathways project (MSP2) is a component of the National Science Digital Library (NSDL) that supports middle school educators and youth by offering contextualized, high-quality resources and promotes interactivity, collaboration, and knowledge-sharing among its users. Educators can access MSP2 to increase content knowledge in the areas of science, mathematics, and technology, and to build knowledge on developmentally appropriate pedagogy for youth aged 10 to 15. MSP2 also connects middle school youth to fun and engaging information on math, science, and technology, as well as health, safety, and career exploration. Web tools such as blogs, wikis, podcasts, RSS feeds, and social networking services are being used in the continued development of MSP2 to transform passive, text-based information into a dynamic, collaborative experience that promotes the creation, modification, and sharing of resources, and facilitates professional development. MSP2 is a project of The Ohio State University, National Middle School Association, and Education Development Center, Inc., and is funded by the National Science Foundation.

Pattern blocks are great tools for developing conceptual understanding. I hope to continue to see them used in classrooms, but the virtual kind can allow students to share their thinking with other students virtually. I like using screen capture, cut/paste, upload to a wiki, comment on characteristics/size/description of '1'/and sharing with students so that their thikning can be revisited from multiple venues (home, classroom, internet-broader audience).