Designing Your Own Free Education Online

When designing a course of independent study, some of the most useful tools available can be found online. When you design your own education, you can tailor the content to your needs -- rather than the needs of an institution, a government accreditation agency, or a "society."

Online, you can select from individual tutorials, or you can take an entire course online -- for credit or not for credit. You can even combine different courses to obtain an online certification in a field of study.

Many organisations provide free access to educational materials from K-12 through university graduate study level. Here are a few examples:

540 Free Online Courses from Top Universities

Alison.com -- over free 400 courses in over 10 different categories

Open Courseware Consortium

Coursera.org -- Free online courses from 33 top universities

EdX.org -- Free courses from MIT, Harvard, Berkeley, and the U. Texas system

All of those sites and more offer free online access to a wide selection of courses from fine institutions. But not everyone is ready to take maximum advantage of these valuable courses -- many of which can be very difficult if one is not prepared ahead of time.

Take college mathematics, for example. Higher mathematics is the cornerstone of the modern technical professions and sciences. An inability to understand the basics of higher mathematics can make the difference between a successful career in science, engineering, computer science, or a technical profession -- and perhaps having to settle for less than one may have wanted.

Khan Academy can be helpful in working through difficult mathematical concepts, and filling in missing holes in one's technical background. But another -- and often more fundamentally useful -- website for helping a person to wrap his mind around difficult maths concepts is Better Explained.

Preparing ahead of time is generally the best approach. But sometimes one must be satisfied with "better late than never." Higher mathematics should be learned intuitively, rather than by rote learning of application of formulas. A rote learner is limited in how far he can go, whereas one who takes an intuitive approach can often advance his field of study, or one that is related.

One interesting website approach to teaching intuitive maths to younger students is "Visual Math Learning." The site uses visual animations to assist a student in learning foundational ideas in basic maths, so that he can go on to more difficult things.

Merlot.org provides a number of unique learning aids in maths and a large number of other subject areas. It is a site well worth browsing -- time and again.

You will have to start with what you can find, and adapt it to your needs, and the needs of your children. Cultivate the special skills and knowledge of family members, acquaintances, and other persons in your community. You never know who will be in possession of a skill, trick, shortcut, or secret that will make all the difference in learning a particular subject.

Remember, there is no safer place to be than in close proximity to a Dangerous Child. It is never too late to have a dangerous childhood.

Foundations for Maths Must be Built Long Before School

The educational-industrial complex of the US is successful at one thing: Creating generations of psychological neotenates. The entire approach to education as taken by government schools is self-serving and self-perpetuating -- more concerned over the system itself, than for the welfare and progress of learning children.

It is wrong for parents to surrender the education of their children to corrupt bureaucratic institutions. But it is also wrong for the educational-industrial complex to pretend that it is safe for parents to abdicate this responsibility.

Let's take maths in particular. Educational researchers have decided that students must be switched onto maths, to reverse the disastrous trends in maths failure that have become so commonplace. Other educational researchers have decided that maths teachers must be better trained, in order to reverse the disastrous failures in maths education.

But the truth is that if the mental foundations for maths are not constructed long before school curricula finally get around to needing them, it is probably too late for most students. This means that parents must expose their children to the patterns and mechanisms of real world forces and events, rather than leaving the education of the child up to television, video games, teachers, peers, and popular culture.

Mathematics is not about numbers, primarily. Mathematics is about patterns -- both static and dynamic, and sometimes chaotic. Number sense should be developed early, utilising game forms. But number sense is just a preliminary foundation for pattern sense, and relational sense. Learning these more complex forms of maths foundational skills requires exposure, which is not likely to occur accidentally.

The most optimal ways of learning these foundational conceptual skills have not been devised yet. Educational researchers are decades away from even understanding the need for them. Researchers into neurodevelopment and developmental psychology are likewise too often barking up the wrong tree, following the leads of the organisations which supply research grants.

It looks as if the rest of us have a lot of work to do to compensate for the incompetence and distractedness of "the experts."

Human Babies Born with Intuitive Sense of Numbers

Humans have an intuitive sense of number that allows them, for example, to readily identify which of two containers has more objects without counting. This ability is present at birth, and gradually improves throughout childhood

_ScienceDaily

Johns Hopkins scientists have tested the Approximate Number Sense (ANS) in human pre-schoolers, then compared their ANS scores with later standard tests of math ability administered in school at age 6. They discovered a high correlation between the ANS score in preschool and the later math ability scores at age 6.

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.

...Further longitudinal studies are needed to evaluate whether and how mediators of the relationship between ANS skills and symbolic mathematics vary as a function of other child characteristics, and how ANS skills might predict not only math performance at a given time but also trajectories of growth in formal mathematics skills over development. _PLoS (Full paper)

The authors were unable to determine whether ANS skills could be improved through early childhood intervention. But their findings add to a growing body of knowledge demonstrating a wide range of cognitive abilities between individuals, starting from a very early age. One should note that ANS precision correlates only to later math skills, and not to language skills.

It is important for scientists and educators to determine how much of individual cognitive capacity can be improved, and how much is relatively fixed. This should be done on an individual-to-individual basis to avoid prejudgement, and to better customise and optimise the education experience for each child.

This Johns Hopkins study offers some suggestive hints as to the nature of pre-verbal and non-verbal metaphor development in young children, prior to any formal math training.

La Griffe to Feminists: Men Are Better at Math. Get Used to It!

Two recent publications on the math gender gap have claimed that there is actually no math gender gap. These findings were celebrated by feminist academics and journalists, but were always suspect in that they contradicted a huge body of scientific evidence. Now perennial fact-checker and ne-er do well, La Griffe du Lion, takes a look at the two studies and declares them wanting in logic, reason, and hard facts.

In brief, we have seen tonight that the gender gap in mathematics has been stable for at least half a century; that sex differences in ability-distribution means and variance ratio are independent of race, culture and geography; that female math performance is closest to that of males in high-IQ countries; that culture plays a role in math performance, albeit small; and that the theory of Everyone accounts for all of the above. If these results are unsettling, take comfort knowing that no presentation of fact, regardless how compelling, will keep the gap buster from her noble calling. _LaGriffeduLion via Dennis Mangan

To follow the reasoning that leads to LGdL's conclusions, you will need to read his article at the link above. It is accompanied by a large array of graphs which aid an intuitive grasp of the statistics involved.

The gender gap is ubiquitous geographically and culturally, and is persistent over time. The gap is somewhat narrower in societies with higher average IQs, such as Europe, North America, East Asia, and Oceania, but still quite undeniably present and persistent.

The continuing effort of feminists in academia and journalism to deny what is obvious to anyone who looks at the issue scientifically, undermines the credibility of feminists on a wide range of issues which straddle both the scientific and political spheres.

Mathematical Ability in Men and Women

La Griffe du Lion has a new essay on intelligence guaranteed to burn the thong off any self-respecting professor of Women's Studies. Liz Spelke and Nancy Hopkins may have trouble with occasional dizzy spells if they are unwise enough to read it. Donna Shalala should likewise maintain her distance.

The world of data can be cruel to one's ideological conceits.

Thanks to iSteve.

Update: This article in the Independent goes even further in claiming that there are twice as many men with IQ > 120 than women with IQ > 120.

Dr Paul Irwing is a senior lecturer in organisational psychology at Manchester University. He claims that men are more intelligent than women.

All the research I've done points to a gender difference in general cognitive ability. There is a mean difference of about five IQ points. The further you go up the distribution the more and more skewed it becomes. There are twice as many men with an IQ of 120-plus as there are women, there are 30 times the number of men with an IQ of 170-plus as there are women.

I don't know why this is, all I can say is that we have a huge amount of data.

In my 2005 paper in the British Journal of Psychology we looked at 22 surveys sampling 20,000 university students. In 21 out of the 22 studies males always had an advantage.

Hat tip Fatknowledge Blog.

The above research appears to fit with work by J. Phillippe Rushton, Richard Lynn, and Helmuth Nyborg. In addition, such research should exonerate Larry Summers, if not for the perverse bias caused by radical political correctness in academic circles.