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### Initial thoughts on "Focus in High School Mathematics: Reasoning and Sense Ma...- 8 views

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"Initial thoughts on "Focus in High School Mathematics: Reasoning and Sense Making" The book study begins!" Book study post on the new NCTM Series "Focus in High School Mathematics: Reasoning and Sense Making"

### Adventures in Mathematical Knitting- 1 views

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by dr. sarah-marie belcastro, "You might wonder why one would want to knit mathematical objects. One reason is that the finished objects make good teaching aids; a knitted object is flexible and can be physically manipulated, unlike beautiful and mathematically perfect computer graphics. And the process itself offers insights: In creating an object anew, not following someone else's pattern, there is deep understanding to be gained. To craft a physical instantiation of an abstraction, one must understand the abstraction's structure well enough to decide which properties to highlight. Such decisions are a crucial part of the design process, but for the specifics to make sense, we must first consider knitting geometrically."

### What does mathoverflow tell us about the production of mathematics?- 0 views

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From the abstract: "ew innovations by math- ematicians themselves are starting to harness the power of social computation to create new modes of mathematical production. We study the effectiveness of one such system, and make proposals for enhancement, drawing on AI and computer based mathematics. We analyse the content of a sample of questions and responses in the community ques- tion answering system for research mathematicians, math- overflow . We find that mathoverflow is very effective, with 90% of our sample of questions answered completely or in part. A typical response is an informal dialogue, allowing error and speculation, rather than rigorous mathematical argument: 37% of our sample discussions acknowledged er- ror. Responses typically present information known to the respondent, and readily checked by other users: thus the effectiveness of mathoverflow comes from information shar- ing. We conclude that extending and the power and reach of mathoverflow through a combination of people and machines raises new challenges for artificial intelligence and compu ta- tional mathematics, in particular how to handle error, anal - ogy and informal reasoning."

### Levi, M.: The Mathematical Mechanic: Using Physical Reasoning to Solve Problems.- 7 views

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Well received book on using physics to demonstrate mathematical concepts by Mark Levi, professor of mathematics at Pennsylvania State University

### Measurement: Exploring the Whimsical World of Mathematical Reality through Playful Patt...- 4 views

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A review of Paul Lockhart's new book with a focus on mathematical reasoning and geometry, with a video of the author.

### Interweaving Content and Pedagogy in Teaching and Learning to Teach: Knowing and Using ...- 0 views

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Darren challenged us to identify topics of interest last month and I responded that I would love to share some algebraic reasoning information.
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interweaving content and pedagogy in teaching and learning to teach knowing and using mathematics.pdf
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Interweaving Content and Pedagogy in Teaching and Learning to Teach: Knowing and Using Mathematics

### Resources optimization in (video) games: a novel approach to teach applied mathematics?- 2 views

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Abstract: "In spite of the efficacy of Operations Research (OR), its tools are still underused, due to the difficulties that people experience when describing a problem through a mathematical model. For this reason, teaching how to approach and model complex problems is still an open issue. A strong relation exists between (video) games and learning: for this reason we explore to which extent (real time) simulation video games could be envisaged to be an innovative, stimulating and compelling approach to teach OR techniques."

### Games that Encourage and Enhance Mathematical Reasoning and Sense-Making- 12 views

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Live recording of a webinar presented in August 2012 by Sarah DeLeeuw and Patrick Vennebush from the National Council of Teachers of Mathematics

### Street-Fighting Mathematics - The MIT Press- 14 views

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"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

### Math ∩ Programming- 2 views

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Subtitled "A Place for Elegant Solutions." From the author's description: "This blog is a presentation of the interesting solutions I come across, and an exploration of the deeper mathematical ideas therein. Most often this means exploring the mathematical structure of a problem to lubricate the cogs of algorithm design. In seldom cases, this involves using programs to reason about mathematical theory."

### Icons of Mathematics- 2 views

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

### blog on mathematical journals: More reasons to support the Elsevier boycott- 5 views

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Regarding researchers' boycotting Elsevier journals, a mathematician comments on the publisher's high priced mathematics titles as well as apparent lack of peer review.

### Mathematical Literacy for Everyone using Arithmetic Games- 4 views

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Abstract: "An innovative mathematics game shown to be effective for low-achieving mainstream students is tested in special education for learners with intellectual disabilities. The game relies on a graphical, intuitive representation for numbers and arithmetic operations to foster conceptual understanding and numbers sense, and provides a set of 2-player games to develop strategic thinking and reasoning skills. The game runs on computers and interactive white boards, and as an augmented reality application at a science centre. We compare its use in special education and mainstream education with respect to usage, performance levels and learning gain. The game has been used by teachers in special educations, with gains in mathematical understanding, strategic thinking and communication skills as effects."

### Link Theme for May 2009: Effective Pedagogy In Mathematics- 37 views

"I'd also like to ask that someone else suggest another "theme" for us for the month of June and each of the months that follow. " OK Darren, I'll take the challenge and suggest developing algebra...

### Handbook of Mathematical Induction: Theory and Applications (Hardback) - Taylor & Francis- 3 views

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"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."

### Exploring quadrilaterals in a small group computing environment- 2 views

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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."

### Pure Reasoning in 12-Month-Old Infants as Probabilistic Inference- 3 views

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From the abstract (full text requires subscription): "Many organisms can predict future events from the statistics of past experience, but humans also excel at making predictions by pure reasoning: integrating multiple sources of information, guided by abstract knowledge, to form rational expectations about novel situations, never directly experienced. Here, we show that this reasoning is surprisingly rich, powerful, and coherent even in preverbal infants. When 12-month-old infants view complex displays of multiple moving objects, they form time-varying expectations about future events that are a systematic and rational function of several stimulus variables. Infants' looking times are consistent with a Bayesian ideal observer embodying abstract principles of object motion. The model explains infants' statistical expectations and classic qualitative findings about object cognition in younger babies, not originally viewed as probabilistic inferences."

### Dim Sum Thinking- 2 views

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"Mathematics is not a series of Statement-Reason proofs punctuated by the occasional "QED". Mathematics, as Paul Lockhart writes in A Mathematician's Lament, is "wondering, playing, amusing yourself with your imagination.""

### Understanding Probability, 3rd edtition- 4 views

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"Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. ... The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus."

### Spatial training boosts math skills | MSUToday | Michigan State University- 1 views

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Research study at Michigan State University shows how developing spatial reasoning in young children (6-8) improves calculation
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