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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.

Fabulous site for math problem-solving! Requires a fair amount of reading but kids love these.

Free math tutorials and problems to help you explore and gain deep understanding of math, calculus, trigonometry and geometry topics.

Highlights "Real World Math," lessons based on Google Earth focusing on students in grades 5-10

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The most AMAZING compilation of math problems EVER!

Avoid Hard Work gives a playful view on ten powerful problem-solving techniques. These techniques were first published by the Mathematical Association of America to help high school students with advanced math courses. We adapted the ten techniques and the sample problems for much younger children. The book is for parents, teachers, math circle leaders, and others who work with children ages three to ten. It will come out in the Fall of 2016.

Equations and word problems

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

"we are asked to solve problems instead of also creating them"

Prize for solving the Beal Conjecture hypothesis, proposed in 1997, has risen to $1 million

from the abstract: "Mathematics is now at a remarkable in exion point, with new technology radically extending the power and limits of individuals. Crowd- sourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. The Study of Mathematical Practice is an emerging interdisciplinary eld which draws on philoso- phy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question-answering system mathover ow contains around 40,000 mathe- matical conversations, and polymath collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of \soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a \social machine", a new paradigm, identi- ed by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathe- matics, and to transform the reach, pace, and impact of mathematics research."

From the abstract: "is research develops around a technological intervention intended to transform a peer produced reference resource into a peer produced learning environment. An early Web 2.0 community for mathematics, PlanetMath.org, will henceforth become a mathematical practicum, and a laboratory for learning science."

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."

The role of mathematics in complex economic problems such as the consumer price index

Each day of the school year I present my students with an estimation challenge. I love helping my students improve both their number sense and problem solving skills. I'd like to share the estimation challenges with you and your students. Here's a handout for your students. Happy Estimating!

I'm rubbish at Maths' are words that regularly come out of mouth during my adult life. This fixed mindset is deep rooted. When faced with a Maths challenge I have immediate flashbacks to those bottom set Maths lessons where everyone else were given more complicated problems with bigger numbers to solve. I may have a fixed mindset in terms of my own capabilities, but I believe every child has the capacity to be a fantastic Mathematician, if they are given the opportunity and are encouraged to have the belief in the 'power of yet'.

A Kickstarter project for a children's math and science-oriented detective story: "This is the made up story about two very real girls - Ada, the world's first computer programmer, and Mary, the world's first science fiction author - caught up in a steampunk world of hot-air balloons and steam engines, jewel thieves and mechanical contraptions. For readers 8-12. "This is a pro-math, pro-science, pro-history and pro-literature adventure novel for and about girls, who use their education to solve problems and catch a jewel thief. Ada and Mary encounter real historical characters, such as Percy Shelley, Charles Babbage, Michael Faraday, and Charles Dickens - people whom the girls actually knew. If Jane Austen wrote about zeppelins and brass goggles, this would be the book."

"Chances are you've seen this symbol before, because it's one of the most well-known Egyptian symbols. It's called the Eye of Horus. It's been in the background of plenty of mummy movies, and been turned into a lot of necklace charms. Some people think it's writing. Actually, it's math."