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These pages demonstrate visual phenomena, and »optical« or »visual illusions«. The latter is more appropriate, because most effects have their basis in the visual pathway, not in the optics of the eye. When I find the time I will expand the explanations, to the degree that these phenomena are really understood; any nice and thoughtful comment welcome.

if a student can't solve the problem and finds a resource that takes her through the proof step by step?

"overview of the landscape of K-12 STEM education by considering different school models, highlighting research on effective STEM education practices, and identifying some conditions that promote and limit school- and student-level success in STEM. It can serve as a guide for those involved in K-12 education at all levels: policy makers; decision makers at the school and district levels; local, state, and federal government agencies; curriculum developers; educators; and parent and education advocacy groups." Findings, according to a Science magazine news story indicate that STEM teaching matters more than specialized STEM schools. Report does indicate steps to improve STEM education, involving investments in resources and teacher training, see :http://bit.ly/kRPyH3

A great resource rich site that's been put together by a teacher. Find superb reasources for English, Maths, science, ICT and more. http://ictmagic.wikispaces.com/Cross+Curricular

A superb site to find a vast collection of maths worksheets for the whole of the curriculum. Answer keys are supplied for easy marking. http://ictmagic.wikispaces.com/Maths

A superb place to find games and questions for the whole of the maths curriculum. Join for free to track progress or just play the games. http://ictmagic.wikispaces.com/Maths

GeoGebra: Do the Math is a series of screencast tutorials for teachers and/or students. The tutorials were initiated as a project to support Maine math teachers in the integration of technology in the classroom. What is GeoGebra provides an overview of the program and its capabilities. Several tutorials present the program's menu options and tools in step-by-step format. Another group of tutorials provides examples of GeoGebra learning activities in major math content areas. These tutorials are intended as a visual supplement to printed guides and documentation. GeoGebra users can find a wealth of guidance and examples at www.geogebra.org. A web search such as "GeoGebra Pythagorean Theorem" will yield hundreds of additional articles, examples, and applets.

created a fully functional, browser-based  graphing calculator. The calculator performs all of the functions you would expect to see in a graphing calculator with a couple of extras that you don't find in typical graphing calculators. Desmos allows you to share your equations and graphs through a Bit.ly link. Desmos graphs your equations as you type them and redraws them as you alter your equations.

"How does STEM education differ between these countries? Who is doing it 'best'? We've done our research and these are the findings"

"For the first time, scientists have identified the brain pathway that links a positive attitude toward maths to achievement in the subject. In a study of elementary school students, researchers at the Stanford University School of Medicine found that having a positive attitude about maths was connected to the better function of the hippocampus, an important memory centre in the brain, during the performance of arithmetic problems. The findings will be published online Jan. 24 in Psychological Science."

"I love patterns, diagrams and pictures. Ask me to record information and it gets plastered over a page in bubbles, a mind map or random boxes. I'm not particularly artistic but I find I like to store information in this way. Even with telephone numbers - I remember the pattern the digits make, not the number itself."

"In September we introduced the new curriculum across all subjects and all of our school. This was scaffolding using the Chris Quigley's Essentials materials, during the previous year we had used a numeracy curriculum created by teachers within the Deal Learning Alliance, which a great source and piece of collaborative work in its own right, held too many links back to APP statement and old national curriculum levels. As as school we were finding that the DLA maths document did not provide the scaffold for the raised expectations in mathematics primary curriculum, furthermore, the deeper into the curriculum we delved, the harder it seemed to make the teaching, learning and assessment work efficiently."

In the portal you'll find a dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more built by Wolfram education experts. Absolutely a great resource. Builds in representations, applets, explanations of variable use etc. Great tool.  Since it is in Beta, I am wondering how long it will be free and what their plans are for the future. 

"This paper describes a research project on Year 3 primary school students in Malaysia in their use of computer-based video game to enhance learning of multiplication facts (tables) in the Mathematics subject. This study attempts to investigate whether video games could actually contribute to positive effect on children's learning or otherwise. In conducting this study, the researchers assume a neutral stand in the investigation as an unbiased outcome of the study would render reliable response to the impact of video games in education which would contribute to the literature of technology-based education as well as impact to the pedagogical aspect of formal education. In order to conduct the study, a subject (Mathematics) with a specific topic area in the subject (multiplication facts) is chosen. The study adopts a causal-comparative research to investigate the impact of the inclusion of a computer-based video game designed to teach multiplication facts to primary level students. Sample size is 100 students divided into two i.e., A: conventional group and B conventional group aided by video games. The conventional group (A) would be taught multiplication facts (timetables) and skills conventionally. The other group (B) underwent the same lessons but with supplementary activity: a computer-based video game on multiplication which is called Timez-Attack. Analysis of marks accrued from pre-test will be compared to post- test using comparisons of means, t tests, and ANOVA tests to investigate the impact of computer games as an added learning activity. The findings revealed that video games as a supplementary activity to classroom learning brings significant and positive effect on students' retention and mastery of multiplication tables as compared to students who rely only upon formal classroom instructions."

Published March 2013. "The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem."

Abstract: "This study examined the benefits and challenges associated with implementing RtI [Response to Intervention] in the area of math ematics in an elementary and a middle school in a rural district in the northeastern United States. We sought to document the ways in which two schools approached implementation of RtI and to explore the issues they encountered with respect to instruction , intervention, and assessment. Five themes were identified that described implementation of the RtI framework: Shifting roles and changing structures, increasing opportunities for collaboration and communication, inc reasing instruction al an d assessment su pport for students who struggle in math, increasing knowledge of support strategies for learners who struggle with math, and "spreading the word" and enhancing the use of the model. The results of this study suggest that the RtI model has potential to impr ove how math instruction is approached in elementary and middle schools. "

Visit uStudyhall .com for 7th grade math problems page to practice math problems in an easy and fun way. uStudyhall provide online learning education for student by which they improve their school performance with the help of uStudyhall online practice tools!

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."

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."