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The objective of this site is to show examples of thinking in math, whether it is original solutions from students of problems, or ways to include an inquiry based approach in mathematics education. The idea for the project came from Chris Hunter as a comment on a blog post. I, David Wees, think it is such a terrific idea that I am working on implementing it. I welcome ideas and input from anyone who is interested and would like to help support student thinking in mathematics. Please send an email with your example of original mathematical thinking by a student, or an example of a project students can do to support inquiry in mathematics

LOG IN February 22, 2012 at 2pm Eastern US time: http://tinyurl.com/math20event During the event, John Mason will lead a conversation about multiplication as scaling, and answer questions about his books, projects and communities. All events in the Math Future weekly series: http://mathfuture.wikispaces.com/events The recording will be at: http://mathfuture.wikispaces.com/JohnMason Your time zone: http://bit.ly/wQYN1Y Event challenge! What good multiplication tasks about scaling do you know? Share links and thoughts! John writes about elastic multiplication: "It is often said that 'multiplication is repeated addition' when what is meant is that 'repeated addition is an instance of multiplication'. I have been developing some tasks which present 'scaling as multiplication' based around familiarity with elastic bands. Participants would benefit from having an elastic (rubber) band to hand which they have cut so as to make a strip; wider is better than thinner if you have a choice." About John Mason John Mason has been teaching mathematics ever since he was asked to tutor a fellow student when he was fifteen. In college he was at first unofficial tutor, then later an official tutor for mathematics students in the years behind him, while tutoring school students as well. After a BSc at Trinity College, Toronto in Mathematics, and an MSc at Massey College, Toronto, he went to Madison Wisconsin where he encountered Polya's film 'Let Us Teach Guessing', and completed a PhD in Combinatorial Geometry. The film released a style of teaching he had experienced at high school from his mathematics teacher Geoff Steel, and his teaching changed overnight. His first appointment was at the Open University, which involved among other things the design and implementation of the first mathematics summer school (5000 students over 11 weeks on three sites in parallel). He called upon his experience of being taught, to institute active-problem-solving sessions, w

Stimulating critical thinking using technology has the potential to create more in depth understanding of science and math content by students when engaged in learning activities which integrate in-class and on-line technology resources. Technology tools support stimulation of both inquiry-based and critical thinking skills by engaging students in exploring, thinking, reading, writing, researching, inventing, problem-solving, and experiencing the world outside their classroom. This is accomplished through learning content through the lens of video to multimedia to the internet (Using Technology to Improve Student Achievement, NCREL, 2005).

Think of a computer program that generates educational worksheets, and mathematics is the kind that immediately comes to mind. The ones you find here we think are some of the best around. Try them out and see if you think so too.

Abstract: "We encounter mathematical problems in various forms in our lives, thus making mathematical thinking an important human ability [6]. Of these problems, optimization problems are an important subset: Wall Street traders often have to take instantaneous, strategic decisions to buy and sell shares, with the goal of maximizing their profits at the end of a day's trade. Continuous research on game-based learning and its value [2] [3] led us to ask: can we develop and improve the ability of mathematical thinking in children by guising an optimization problem as a game? In this paper, we present Bublz!, a simple, click-driven game we developed as a first step towards answering our question."

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

Published November 2012. "The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. "

"In previous posts, I have summed up my position on Khan Academy as follows: Khan Academy teaches only one part of mathematics-procedures-and that isn't the most important part. Writing about mathematics, developing a disposition for mathematical thinking, demonstrating a conceptual understanding of mathematical topics are all more important than procedures. That said, procedures are still important, and Khan Academy provides one venue where students can learn them. In the end, I think every young person should have an account there. Even if only one in a thousand or ten thousand benefit, that would be a terrific outcome. "

Great math case study ideas. I think this would help teachers thinking about their own ideas for great math lessons.

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!

Encouraging students to use critical thinking is more than an extension activity in science and math lessons, it is the basis of true learning. Teaching students how to think critically helps them move beyond basic comprehension and rote memorization. They shift to a new level of increased awareness when calculating, analyzing, problem solving, and evaluating.

Inspired by the work of Magdeline Lampert, interactive problems offer educators a fun tool to help learners think about "mathematical principles" within the familiar context of coinage. We love her idea that playing with combinations and recombinations of denominations promotes engagement with multiplicative thinking, and have produced this as a result.

"The Middle School Stream aims to motivate and engage middle school students (grades 5 through 8) in STEM learning, 21st Century Literacy Skills and Systems Thinking by challenging them to design original video games. The High School Stream aims to motivate and engage high school students (grades 9 through 12) in STEM learning, 21st Century Literacy Skills and Systems Thinking by challenging them to design original video games. The Collegiate Stream challenges emerging game developers at the graduate and undergraduate levels to design video games for children (grades pre-K through 8) that teach key STEM concepts and foster an interest in STEM subject areas. The Educator Stream challenges educators to design video games for children (grades pre-K through 12) that teach key STEM concepts and foster an interest in STEM subject areas."

A maths and thinking skills site with hundreds of word puzzles to ponder over. Perfect for lesson warm ups and improving mental maths. http://ictmagic.wikispaces.com/Maths

A great site to use to have students extend their thinking about problems.

Companion pamphlet for Kevin Houston's book How to Think Like a Mathematician, outlining ten ways of questioning and reasoning

Math games to make you think

From the abstract: "this study investigated how the perspectives of the non-computer science educators changed after learning game-programming and how it could be fitted into the K-12 curriculum. Fourteen non-computer science educators and/or administrators in the K - 16 educational systems who made up a cohort at Sam Houston State University, Master of Education/Instructional Technology Program participated in this study. The participants were required to learn two free Web 2.0 game-programming applications and reflect on an article related to reviving interest in math and science as part of their program. Qualitative data consisted of online reflections, and peer-review processes through Facebook. A quantitative component was added to the analysis. The findings indicated that: (a) the perspectives of the participants changed from negative to positive as they reflected on their own game-programming learning experiences; (b) participants came to understand how game programming could build up students' logical concepts and critical thinking skills improving performances in math, science, and other subjects; and (c) due to the benefits of logical concepts and critical thinking skills game programming could have immense benefits if built into the K-12 curriculum."

LOGIN Wednesday February 15 at 3pm Eastern US time: http://tinyurl.com/math20event During the event, Dr. Keith Still of SaferCrowds.com will introduce his Crowd Sciences work and explain the relevance of mathematics in it: "If you don't do the maths, you could end up in court on a manslaughter charge!" All events in the Math Future weekly series: http://mathfuture.wikispaces.com/events The recording will be at http://mathfuture.wikispaces.com/CrowdSciences Pose questions and comments for Keith before the event Math Future wiki: http://mathfuture.wikispaces.com/message/list/CrowdSciences LinkedIn group: http://www.linkedin.com/groupItem?view=&gid=33207&type=member&item=94871153&qid=b29a6dbc-6474-425f-865a-b319bd33dcb9 Email group: http://groups.google.com/group/mathfuture/browse_thread/thread/931328aab6d87b03 How to join Follow this link at the time of the event: http://tinyurl.com/math20event Wednesday, February 15 2012 we will meet online at noon Pacific, 3 pm Eastern time. WorldClock for your time zone. Click "OK" and "Accept" several times as your browser installs the software. When you see Session Log-In, enter your name and click the "Login" button If this is your first time, come a few minutes earlier to check out the technology. Crowd Modelling + Crowd Monitoring + Crowd Management = Safer Crowds Crowd Modelling is the scientific approach to the development of safe, robust, crowd management plans. This can be achieved without the need for expensive, complex, time consuming computer simulations. In simple terms Crowd Modelling is understanding how, where, when and why crowds arrive, move around and leave an events/venues. The majority of this can be accomplished using tried, tested and simple to apply methodologies. "Keith Still is what I term an intuitive mathematician. He is one of the most creative and original thinkers that I know. He adds drive and determination, as well as considerable intellectual power to any group of which h

Interesting article from Britain regarding computational fluency. I don't disagree that being fluent with computation increases a students future capabilities, but there is not necessarily causal effect that 'traditional' approaches to teaching computation make stronger mathematics students. It's the rigorous approach that I think needs to be emphasized.