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Current reforms in mathematics education emphasise the need for pedagogy because it offers learners opportunities to develop their proficiency with complex high-level cognitive processes. One has always associated the ability to make mathematical connections, together with the teacher's role in teaching them, with deep mathematical understanding. This article examines the nature and quality of the mathematical connections that the teachers' representations of those connections enabled or constrained. The researchers made video recordings of four Grade 11 teachers as they taught a series of five lessons on algebra-related topics. The results showed that the teachers' representations of mathematical connections were either faulty or superficial in most cases. It compromised the learners' opportunities for making meaningful mathematical connections. The researchers concluded by suggesting that helping teachers to build their representation repertoires could increase the effectiveness of their instructional practices.

In brief, it contrasts the modern understanding of causality (and the mathematics this presupposes) with the more recent, perhaps in a sense "postmodern" understanding of causality (again with a concomitant mathematical model) and on the basis of this distinction, draws some interesting parallels between economics and natural events.

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."

The popular educational portal www.kidsworldfun.com is organizing a unique Little Champs Video Contest for preschoolers (3-6 years old) around the world. The contest intends to discover the very young bright stars around the world who are exceptional in a variety of activities such as reading, writing, singing, dancing, doing chores around home, playing with friends, gardening, and so on. Parents, who are interested, should make a video portfolio of their child, of about 3-5 minutes duration, stringing together the various activities he/she engages in at different times, in natural situations. The winners will be selected based on how well and happily the child engages in the task, how independently he/she is able to perform, how much effort is put in, and how skilled he/she is, in each activity engaged in. The terms and conditions of the contest are given at http://www.kidsworldfun.com/video-contest/ The Little Champs Video Contest is the second international contest that the KidsWorldFun is organizing, the first being the prestigious International Short Story Contest for School Children that debuted in 2016.

"An interesting group participation project for the Manchester Science Fair: growing sunflowers" Includes video on Fibonacci sequences in nature with the example of sunflowers

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. "

"Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers - a 'Diophantine' problem. The abc conjecture, proposed independently by David Masser and Joseph Oesterle in 1985, might not be as familiar to the wider world as Fermat's Last Theorem, but in some ways it is more significant. "The abc conjecture, if proved true, at one stroke solves many famous Diophantine problems, including Fermat's Last Theorem," says Dorian Goldfeld, a mathematician at Columbia University in New York. "If Mochizuki's proof is correct, it will be one of the most astounding achievements of mathematics of the twenty-first century." See additional commentary at: http://bit-player.org/2012/the-abc-game?utm_src=HN2

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

A group in New York City. "The School of Mathematics was founded to cultivate a natural and stress-free environment where anyone can study, discuss, explore, and experience mathematics. No prior knowledge is assumed. Whether you are an avid student of mathematics or have always shied away saying "math is not for me", you are welcome. " Features a Meetup page listing events and articles describing mathematical principles. See "The Power of Mathematics" http://pulse.me/s/3iW2A and A Mathematician's Lament http://thewe.net/math/lockhart.pdf

Interactive whiteboards (IWB) allow science and math teachers to teach multi-sensory lessons, seamlessly jumping from one type of media to another. Interactive science or math lessons can easily integrate text, sound, video, and graphics based on the tactile nature of the IWB.

Does your child need qualified help with math homework? Academically speaking, some subjects are naturally easier for some students than others. When the material is understandable, learning can be enjoyable and the assignments are no big deal. But, if the concepts are difficult to comprehend, like mathematics, help with math homework is so important.

Most of today's students either own or use iPods, iPod Touches, MP3 Players, and computers everyday. These digital tools provide a natural strategy to support student learning - Podcasts!

"Don't know much about the French I took..." but this looks like some interesting analysis of shapes in the physics world. Worth looking at if you 

A case study of a teacher using twitter to collect probability statements in natural language

The OpenScience project is dedicated to writing and releasing free and Open Source scientific software. We are a group of scientists, mathematicians and engineers who want to encourage a collaborative environment in which science can be pursued by anyone who is inspired to discover something new about the natural world.

When the great mathematician Isaac Newton explained the colours of the rainbow with refraction the poet John Keats was horrified. Keats complained (through poetry of course) that a mathematical explanation robbed these marvels of nature of their magic, conquering "all mysteries by rule and line". But as we will see, the mathematical explanation, requiring just the basic geometry of lines and circles, is just as elegant as the rainbows themselves.

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."

"Schoolhouse Rock may be the standard for music-based educational videos, but YouTube is leading the renaissance of educational songs and dances. Using music as a lure for educational content isn't new, but it's being widely adopted, thanks to the accessible and sharable nature of YouTube."

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