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
"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
Forthcoming July 2011, available for pre-order. a biography of the 13th century Italian mathematician Leonardo of Pisa, better known as Fibonacci, who introduced the Hindu-Arabic system of numbers to the west. "Fibonacci's book Liber Abbaci (The Book of Calculation) was the first to recognize the power of the 10 numerals, and to aim them at the world of commerce."
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Report from the National Academies. Summary: "The mathematical sciences are part of nearly all aspects of everyday life-the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. The Mathematical Sciences in 2025 examines the current state of the mathematical sciences and explores the changes needed for the discipline to be in a strong position and able to maximize its contribution to the nation in 2025. It finds the vitality of the discipline excellent and that it contributes in expanding ways to most areas of science and engineering, as well as to the nation as a whole, and recommends that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, the report emphasizes that universities and the government need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term."
Abstract: "Students' attitudes toward mathematics and its learning have been subject to numerous
studies in the past six decades. These studies treat such attitudes as both desirable learning
outcomes and correlates of mathematics achievement. Many Likert-type attitude scales have
been devised to measure significant constructs underlying mathematics-related attitudes,
such as confidence, anxiety, and utility of mathematics. The psychometric properties of these
attitude scales may be culture and age dependent. As part of a research project called
Singapore Mathematics Assessment and Pedagogy Project (SMAPP), an effort was made to
devise and validate an attitude toward learning mathematics scale that can be used with
lower secondary school students in Singapore. This paper explains the use of exploratory and
confirmatory factor analyses to reduce an initial 57-item questionnaire to one with 24 items
that cover these six dimensions: Checking solutions, Confidence, Enjoyment, Use of IT in
mathematics learning, Multiple solutions, and Usefulness of mathematics. The data comprise
responses from about 890 Secondary 1 (Grade 7) students in 2010, who took the 57-item
questionnaire, and another 850 students who took the 24-item questionnaire in 2011. The
nature of the final questionnaire is discussed. This effort contributes to the continual effort to
devise validated attitude scales that are suitable for different cultures and student groups."
"a century ago this week. Mathematician Andrey A. Markov delivered a lecture that day to the Imperial Academy of Sciences in St. Petersburg on a computational technique now called the Markov chain.
Little noticed in its day, his idea for modeling probability is fundamental to all of present-day science, statistics, and scientific computing. Any attempt to simulate probable events based on vast amounts of data - the weather, a Google search, the behavior of liquids - relies on Markov's idea."
"Most of these books are beginner level books, simply introducing the concept and terminology. However, there are a few at the end that are really great, and begin to introduce equivalent fractions and even discuss the numerator and denominator."
University of Delaware researchers find: "Even [when their children are] as young as 22 months, American parents draw boys' attention to numerical concepts far more often than girls'. Indeed, parents speak to boys about number concepts twice as often as they do girls. For cardinal-numbers speech, in which a number is attached to an obvious noun reference - "Here are five raisins" or "Look at those two beds" - the difference was even larger. Mothers were three times more likely to use such formulations while talking to boys."