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Abstract Orderism Fractal 67 – Art by G. Stolyarov II

Abstract Orderism Fractal 67 – Art by G. Stolyarov II

Abstract Orderism Fractal 67 - by G. Stolyarov II

Abstract Orderism Fractal 67 – by G. Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

This is a frosty fractal of spirals upon spirals.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.

Abstract Orderism Fractal 66 – Floral Fractal – Art by G. Stolyarov II

Abstract Orderism Fractal 66 – Floral Fractal – Art by G. Stolyarov II

Abstract Orderism Fractal 66 - by G. Stolyarov II

Abstract Orderism Fractal 66 – by G. Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

This vibrant floral fractal displays layer upon layer of exquisite patterns.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.

Abstract Orderism Fractal 65 – Art by G. Stolyarov II

Abstract Orderism Fractal 65 – Art by G. Stolyarov II

Abstract Orderism Fractal 65 - by G. Stolyarov II

Abstract Orderism Fractal 65 – by G. Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

This fractal consists of intersecting luminous strands.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.

Abstract Orderism Fractal 64 – Art by G. Stolyarov II

Abstract Orderism Fractal 64 – Art by G. Stolyarov II

Abstract Orderism Fractal 64 - by G. Stolyarov II

Abstract Orderism Fractal 64 – by G. Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

This ornate rotational fractal conveys intricacy and nobility.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.

Abstract Orderism Fractal 63 – Art by G. Stolyarov II

Abstract Orderism Fractal 63 – Art by G. Stolyarov II

Abstract Orderism Fractal 60 - by G. Stolyarov II

Abstract Orderism Fractal 63 – by G. Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

This fractal conveys an impression of sharp, determined, multi-layered rotation.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.

Math Education Should Be Set Free – Article by Bradley Doucet

Math Education Should Be Set Free – Article by Bradley Doucet

The New Renaissance Hat
Bradley Doucet
February 12, 2015
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At different times in my life, I have earned my living tutoring high school math, helping struggling students struggle a little less with quadratic equations and trigonometric functions. I always excelled at math when I was in high school, and my temperament is well-suited to being patient with kids who are not understanding, and to figuring out why they’re not understanding. The experience of assisting a couple of hundred different students over the years has convinced me that just about anyone can learn to understand high school math. Some people simply need more time than others to become proficient with numbers and graphs and such.
 ***
Given my background, I read with interest The Globe and Mail’s write-up in January 2014 on what they are calling the Math Wars, “a battle that’s been brewing for years but heated up last month when this country dropped out of the top 10 in international math education standings.” Specifically, since the year 2000, Canada has fallen from 6th to 13th in the OECD’s Programme for International Student Assessment (PISA). Robert Craigen, a University of Manitoba mathematics professor, points out that this slippage coincides with the move away from teaching basic math skills and the adoption of discovery learning. In much of Canada today, this latest fad has children learning (or failing to learn) math by “investigating ideas through problem-solving, pattern discovery and open-ended exploration.”
 ***

Interestingly, when the Canadian provinces are included in the PISA rankings, Quebec is first among them, places 8th overall, and has lost practically no ground over the last dozen years. Why is Quebec suddenly ahead of the pack? Another Globe and Mail article from last month says that little work has been done on this question, but that “researchers have started focusing on Quebec’s intensive teacher training and curriculum, which balances traditional math drills with problem-solving approaches.” Basic math skills and problem solving sounds like a winning combination to me—and I bet the extra teacher training doesn’t hurt either.

Personally, I have long thought that math students should be allowed to progress at different rates. Currently, the brightest students shine out by scoring 90s and 100s while weaker students flounder with 60s and 70s and are forced to move on to more complex topics without having mastered more basic ones, almost ensuring their continued difficulties. With student-paced learning, the brightest students could still shine out by progressing more quickly, but weaker students would be given the time they need to master each topic before tackling harder problems. Everyone would get 90s and 100s; some would just get them sooner. Teaching would have to change, of course, in such a system. Maybe students would end up watching pre-recorded lessons, a la Khan Academy, and teachers could become more like flexible aides in the classroom, in addition to monitoring individual students to make sure they aren’t slacking off.

The Globe and Mail ended its editorial on Canada’s math woes last Thursday with a call to action: “If our students’ success in math really matters—and it does—it’s time to a have national policy discussion on how to move forward. Everything should be on the table, including curriculum reform. Let’s think big.” I can’t think of a worse idea. Even if you put me in charge of developing this national policy, it would still be a bad idea. After all, who’s to say if I’m correct in supposing that learning at your own pace is the way to go, that it would help everyone succeed and take away some of the anxiety many feel about math? Maybe it would be good for some, and less good for others. Maybe some people need the thrill of competing for top marks, while others would thrive in a less overtly competitive environment. Maybe people are different.

It’s bad enough that governments fix policies for entire provinces; the last thing we need is for everyone in the entire country to be doing the same thing. To the extent that there is a better way (or that there are better ways) to teach math, ways that we may not have even tried yet, the best means of discovering them is to allow different schools to teach math differently, to vary curriculum and teaching style and class size and whatever else they think might help. Let them compete for students, and let the best approaches win, and the worst approaches fall by the wayside, instead of having everyone follow the latest fad and doing irreparable damage to an entire cohort of kids.

It’s very hard to imagine this happening, though, in a system that is financed through taxation. Even though it’s ultimately the same people paying, whether directly as consumers or indirectly as taxpayers, people get into the mental habit of thinking that the government is paying, as if the government had a source of income other than the incomes of its people. And if the government is paying, then the government has to make sure it’s getting its money’s worth, and it’s only natural then that the government (i.e., politicians and bureaucrats) should set the curriculum and educational approach and make sure everyone is progressing at the same pace, in flagrant disregard of human diversity. It seems that we have a choice between “free” education and setting education free. Politicians and bureaucrats won’t give up control without a fight, though, which is a shame in the short term. But it may not matter in the longer term, as private initiatives like the Khan Academy make government schooling increasingly irrelevant.

I love math, and I furthermore believe that it is important for people to learn math. Mastery of math does indeed matter, which is precisely why we should think small and avoid the siren song of a “national policy discussion on how to move forward” on the educational front. Instead, we should let a thousand flowers bloom, and work with, not against, the natural diversity of humankind.

Bradley Doucet is Le Québécois Libre‘s English Editor and the author of the blog Spark This: Musings on Reason, Liberty, and Joy. A writer living in Montreal, he has studied philosophy and economics, and is currently completing a novel on the pursuit of happiness.
Abstract Orderism Fractal 62 – Art by G. Stolyarov II

Abstract Orderism Fractal 62 – Art by G. Stolyarov II

Abstract Orderism Fractal 60 - by G. Stolyarov II

Abstract Orderism Fractal 62 – by G. Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

This colorful, intricate fractal resembles the ornaments on a peacock’s tail.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.

Abstract Orderism Fractal 61 – Art by G. Stolyarov II

Abstract Orderism Fractal 61 – Art by G. Stolyarov II

Abstract Orderism Fractal 60 - by G. Stolyarov II

Abstract Orderism Fractal 61 – by G. Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

This fractal consists of spiral upon radiant spiral, spreading forth in glorious illumination.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.

Abstract Orderism Fractal 60 – Art by G. Stolyarov II

Abstract Orderism Fractal 60 – Art by G. Stolyarov II

Abstract Orderism Fractal 60 - by G. Stolyarov II

Abstract Orderism Fractal 60 – by G. Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

This is a fractal of exquisitely intertwined spiral patterns, incorporating both rounded and angular elements.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.

Abstract Orderism Fractal 59 – Art by G. Stolyarov II

Abstract Orderism Fractal 59 – Art by G. Stolyarov II

Abstract Orderism Fractal 59 - by G. Stolyarov II

Abstract Orderism Fractal 59 – by G. Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

This fractal resembles a feather emerging out of a spiral.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.