In recent days I've been brushing up on my math, a subject I haven't touched since high school - decades ago. I was very careful in my couple incomplete years at the university to not touch math all. As I think about it, the distaste I had with math was how algebra was pushed upon us kids in high school... without enough focus on the visual eye candy you have when you get into functions and such things. I was definitely an A student in math as far as I pursued it. However, it's interesting to see how little what I learned has done for me in my adult life. I think that you have to go into a career like engineering which uses mathematics in order to benefit from the courses that all young people are required to take.

As I see it, these different forms of math are the old computers that people used before folks had invented silicon chips. It was very important even back in the ancient Greek empire and ancient China and India to have the tools to be able to build things and to calculate taxes and all that stuff.

I think it's still valuable to teach young people the concepts of mathematics. However, it's important that they see these different "maths" as invented tools, rather than as natural phenomena. It's also important that they learn the history of when which parts of mathematics were invented, and why it occurred. What were the tasks that needed to be tackled?

There have been some great films I've seen in recent years which were aired on the BBC. There's one called "The story of one," and there is a series by Marcus du Sautoy called "The story of maths." These have really piqued my interest and filled in a lot of gaps for me, that were left by primary and secondary school teachers who neglected to talk about historical context when they drilled us on math technique.

Just a few days ago, I discovered the Khan Academy which is a free set of internet tools and videos that people can use to brush up on their math. Some schools even use the website to help their kids in the classroom.

Here's a video presentation by Salman Khan, who started this website:

At any rate, one thing I've remembered as I work through the Khan Academy exercises is that calculation technique with pencil and paper is very important. I don't believe I'm up to snuff. I've been inventing new ways to more quickly calculate problems.

I've been enthused to learn about the lattice method of multiplication which was not taught to me and my peers when we were kids.

One thing that I think is important is working from left to right - rather than right to left - when adding, subtracting, or multiplying. Where you have a sequence of calculations where the former ones affects the latter ones, there's a danger of losing precision in the latter calculations. In real life situations, it's best that the error affects the precision of the number, rather than the bulk of it.

I've also always been curious about savants like Daniel Tammet - and how they can sometmes do big mathematical tasks in their minds quickly. I figure that multiplication and division problems are the hardest because we have to roll up or unpack these decimal numbers in order to calculate them.

I decided to make myself a little computer program to help me start looking at the patterns that different sequences of numbers make across tables of decimal numbers. It's always kind of nagged me that there are these sequences that I haven't ever bothered to learn about - which might really help me when I am down in the trenches calculating a problem.

This is the program if you want to try it out for yourself. I've named it simply: "Tenschart."

• An executable for Windows XP, Vista, 7

• An executable for Linux

This guy clearly enunciates what I have long thought about math education. It shouldn't be about learning hand calculations; it should be about learning the larger concepts.

It's interesting to look at a culture as an outsider.

I've been watching several different documentary television shows in the past couple days which involve a glimpse into the life of British children.

I feel a very strong kinship with the UK. Watching the BBC helps me learn a lot about my own culture... and myself. I love the ethic of reasoning which the British have when they talk about things. I can talk to a Brit for hours about deep ideas. However, as an outsider, there are things one sees that the society is doing wrong. And typically in that case, the mindset of people is that the solution to their problems lies in the opposite direction of where it really does.

There's a reality tv series called "The world's strictest parents" which takes British teenagers who have fallen out with their parents and who are just biding their time until they can leave home, and places them for a week with families in other countries. The latest one had a couple of teens from different families staying together with a very Christian family near Orlando Florida.

It's interesting how these British television producers think that we in the USA are especially "strict" with our kids. That's the word which they would use to describe the authoritative approach that parents use in the USA.

I was in Germany as exchange student for my senior year of high school years ago... and I remember this same cultural thing we see in Britain, where many if not most kids get alienated from their parents in their teen years, and become very rebellious. My appraisal of this, would be that early in their children's lives, British parents and teachers are authoritarian in their approach to children. When parents are hard on kids when they're young, using corporal punishment and an authoritarian approach, that emotional bond with the child never can take root. They burn the social bridge with the child. The kids resolve bitterly in their hearts that they will find their own way in life, and their parents are not going to tell them what to do.

Ironically, it appears British parents and caregivers and teachers believe that the answer for raising better kids is to be stricter... when that's not true. There's a very good American series of books about parenting called the "Love and Logic". They teach the same kind of things to parents that I learned when I was working on my Early Childhood Education certification in Oregon, years ago. I wish British parents and teachers would learn about this ethic - this way of raising children. The two parenting styles that research says are not effective are

1. The Authoritarian style, where you tell kids "Do what I say, because I said so." These kind of parents might use corporal punishment.

2. The Laissez-faire style - where kids are given no structure, or guidance, and allowed to completely make all the mistakes they will make

3. The child guidance style which is preferred, is called by many names... but my teachers at the university called it "Authoritative." This is a very hands on approach to raising children. When a child is a toddler, he basically gets an adult hovering over him all the time. The parent is there to facilitate the child's activities... to help him explore the world, and to be there to teach and to nurture. The child is waited on hand and foot when he's very young. The adult sets limits and removes a young child from situations where he is not handling himself well. The adult clearly explains why it's ok to act in manner x but not in manner y. This is now the most common parenting style in the USA. In return for all this attention and help and love, the child offers her or his obedience and affection and admiration. In this way the adult remains the respected authority figure and role model well into the child's teen years.

It's fascinating how the producers of this television show seemed to believe that this firm but gentle parenting style had to do with the Florida family's Christian religion. It doesn't. It's an American style of child rearing. And the children buy into it, because of the love and nurture they receive from the parents. This kind of child guidance technique facilitates quite a meaningful emotional bond between the parent and the child.

British society would become so much more cordial, friendly, and happy overall... if they would switch over to this other parenting style.

The problem I think that's there, is that there are certain scientific models about children's minds and the way children learn in the USA that undergird this model of parenting when the child is very young which are unpalatable to Brits. The idea of the "developing mind" is the model that young US parents believe and it necessitates them spending so much time and energy with their kids when they're very young. It also is the root of the idea that young kids are not entirely responsible for their actions... and so there's warmth and forgiveness even when the small child does something bad.

I believe that British people see their own kids as being a lot smarter than the level of intelligence American parents would assign to their progeny. So there would have to be another parallel body of research which leads to slightly adjusted premises that would encourage UK parents and caregivers to change their child guidance style.

One can also look at this the other way around, however. I believe that having what I would consider to be a "tough childhood" might be one of major things that makes British people so very intelligent. Necessity is the mother of invention, and if you need to be resourceful, and if you are given a lot independence from an early age and allowed to make a lot of mistakes and learn from them... hmmm... it's quite possible that this wonderful sensible British character is forged in that crucible. No other anglophone country seems to have this character trait with people who so universally believe in reasoning together about things when they talk.

I think that the sheltered American childhood where kids are thought to be very dumb... kind of creates a self-fulfilling prophecy (my apologies to any American readers for my broad generalization), where teens grow up into adulthood not really not knowing how to reason with others well, or how to plan and execute projects as efficiently as folks would, in a place like the UK.

So, it's important that in thinking about strategies for raising children, we look around and take the best of what each society has to offer in their traditions and techniques.

I met a man today.

He was sitting next to me in the computer lab at my university. He saw me using Finale - a brand of music editing software - in order to map out a choral piece that my men's choir was doing. Immediately, he wanted to share his own music with me - he passed me his Iphone - which had an mp3 on it which he had composed. He had me watch a film he had made at a university where he transferred from. He remarked on a beautiful pencil drawing that someone had left on the scanner glass next to my machine - he said that's what he used to do in high school - when he was ignoring the teachers' lectures. He was very interested in Japanese culture. The more I think about him, this evening several hours later, the more steamed I get at this joke of an "education system" that has failed him. He's reminds me of myself. He has skills and talent and promise which he will probably never use in any professional sense - because no one has taken the time to mentor him. Instead, he was sold the same bill of goods that everyone else was, during his 13 or 14 years of education so far.

The education system in the USA at the secondary and tertiary level is all a farce, in my opinion. It's made up of people who pretend to teach their students. They aren't there to fulfill the needs of their students - they see their job as being wholly encompassed by meeting the responsibilities deigned by the department head, or the state standards. Test scores are the method by which these "teachers" pull off their charade. Standard test procedures are by no means an effective method of measuring what a student has actually learned. Students routinely put the information that is required for the test out of their mind as soon as the term is over. Besides that, information does not an education make. A true education is about inquiry, and curiousity, and passion, and application.

This evening I watched the third in a series of excellent BBC films about the history of mathematics. God, I love the BBC! I swear, I can learn more in a week of watching their programming than in a year or two of formal education at the university. In this program, they talked about the developments in mathematics by famous Europeans in the 1600s through the 1800s: Descartes, Fermat, Newton, Leibniz, the Bernoullis, Euler, Von Humboldt, and more. These are the sorts of people we should be trying to create in our universities. These folks were not specialists in one field. They were generalists. They were dilettantes - and they had the privilege of having the time to explore all their various interests, because they were valued by the royal class.

An honorable education system would have classrooms where teachers had their eyes peeled for their students' unique aptitudes and interests. Then, those students would be sent into coursework where those things were focused on more heavily.

The first step in designing this sort of curriculum would be change the question those who create the state standards ask themselves. When it comes to math, for example - the question should not be: "What will kids need to know when they step into a university classroom?" but rather: "When will these students need to use math, and why?" The same question should be asked about art, technology, history, and other subject areas.

Last night I was watching this historic debate between the leaders of the three main political parties in Britain. One very poignant question was from a high school student - Joel Weiner - who complained about the very rigorous assessment regime they have for students in the UK. He said that students were "over-examined and under taught." Gordon Brown and David Cameron really pooh-poohed his concern - obviously enraptured with the idea that high test scores are synonymous with successful schools. The phrase which they used was "maintaining the level of standards" - and of course, this word "standards" is a synonym which means various things including rigorous testing practices and personal sense of ethical conduct. It's difficult to talk sense into folks who use this kind of politically-expedient language.

This last term in my university classes, I noticed that a lot of the academic research from the USA tended to use test scores to try to prove a b or c. Test scores represent a wonderfully easy data set to look at. Scientists love this kind of data - crunching numbers always makes their studies appear more rigorous. Unfortunately, one problem with science is that the data that is most presently available isn't always the kind of data which is relevant to the thing being studied. I am adamant that test scores are not a great metric of student achievement. And many educators would agree with this standpoint to some extent.

One thing I researched during the term was the school system in Australia. I was very impressed with how wholistic the education system there is. The main goal in Australia is to prepare children with what they themselves need as human beings when they go out into the world as adults at the age of 18; they call this "Outcomes Based Education." In contrast to this, states in the USA focus on academics; they go around asking professionals in various fields what they believe children should be taught about their particular academic area.

Even as a student at a small state university here in the Rocky Mountains I felt put-off by the essentialist style of my professors. It dawned on me yesterday a way to reform at least tertiary education in the States - so that students enjoy their time more, and learn more quickly and efficiently. I think we ought to separate education from assessment. I believe that teachers ought to introduce students to all the skills and concepts which are relevant to the subject area they are studying - but in a forum where there is no assessment to see how much the students are learning. If the students have to hold down a job, or if they are taking a 25 credit courseload because of special circumstances, they wouldn't be penalized for not getting work in, over the course of the term. Then, when students feel that they have gained the relevant skills and knowledge, they can opt into a two week or a month-long assessment regime - where they demonstrate what they have learned.

The way the typical university education is set up now - it's almost absurd. At the beginning of the term - you're walking into a classroom with three to eight unknown professors - each of which will demand a certain slice of your life for the next 9 to 16 weeks. And there's nothing preventing them from asking so much of your time that you really don't have the time to get the work done properly. And this wouldn't be because you aren't able to demonstrate the skills or knowledge - it's just because of the capricious schedule which is laid upon you by all the various syllabuses of your professors.

I don't know why no one seems to have recognized this, before. It's as obvious as the light of day to me that children and young people learn a lot more easily and quickly when they are not being micromanaged. Micromanagement tends to teach children how to parrot what the teacher wants from them... and on a strict syllabus schedule, you don't have time to devote to absorbing the material in a way that you would get the most out of it. Kids who are more talented either rebel against such a regime, or they just give up on all of the other things that are important in their life - like peers and social development.

Also, yesterday, I watched a PBS Frontline program on the rise of alternative for-profit tertiary institutions in the USA. I really hope one of these businesses would see the possibility in profiting off of a new model of education like the one I propose. They could really set some progressive trends.

I believe that in the West we should really separate the concepts of "teaching" as compared to "credentialing."

What educators call an "essentialist" style of instruction is very common in the USA as you go into high school, and as you go on to upper crust universities. This is a system where someone lectures, and then tests you to see if you've gained a certain requisite amount of knowledge and skills. It used to even be a common method in elementary schools. In fact, the phrase "toeing the line" was coined when children would stand up in front of the room with their toes in a neat line, and recite what they had learned.

This essentialist technique, in my opinion, is not teaching. It doesn't qualify as such.

According to my sensibilities - a teacher, by definition, cannot pass or fail or grade his students in any way shape or form. This practice runs counter to the aims of teaching. A teacher does not let the student who doesn't understand the material, or who is not gaining the skills, slip through the cracks. A teacher can assess how well he himself is teaching the children - by seeing how much they're learning. But that's a grade the teacher gives himself - not a grade he gives the students.

Now, a person offering a credential, must test the knowledge and skills of those seeking that credential. Indeed, some people will pass that test, and some will not. Certainly, passing fifth grade, and graduating from high school are both credentials - so you need to have someone there who will test the children... and assess whether they have met the requirements of the credential. But that ought not to be the teacher's job.

The fact that we conflate these two ideas - teaching, and credentialing - really hurts our society, in my estimation. All over the net you see people offering tutorials in technical trade knowledge who have no idea what teaching is. They have run through the gamut of the credential system at a demanding university, and they thought that they were being taught. In reality, they were teaching themselves well enough to get their credential.

I watched a few MIT lectures the other day on introductory computer programming. This "professor" was not a teacher, in my book. He was throwing out concept a b c and d, and expecting his students to pick up the pieces. It's shocking to me that we regale this kind of practice as if it were the best kind of teaching in the USA.

It's also disturbing to me that university students don't know how to demand a better educational product from their schools. People in tertiary education are typically fresh out of their parents' homes. They've been children their entire life. And they're used to being told what to do, and complying. They meekly accept whatever odd curveballs their department or their professors throw at them; if they can't get an assignment done because they simply didn't have enough time or resources, they are cowed and hang their head in shame, and believe it's their fault. Somehow, these young people rate their college choices based on a rating institution's assessment of the university. Youth believe that they need to work hard in order to get into a "selective university." Instead, they ought to realize that they are the customers with money in hand, who are going to give this money to a business called "a university." They, as customers, are the ones who need to call the shots - demanding the kind of educational product which they want. Uni students need to demand better pedagogy from their schools.

Recently, I've been very impressed with what I've learned about the Australian educational system. I don't know much about uni over there - but their high schools and elementary schools seem to have a really cool pedagogy. Their high schools are very much focused on vocational skills - and on what that person will need for his life when he leaves home at 18 years of age. They call this "Outcomes Based Education." In contrast, we in the USA have "Standards Based Education;" educators in North America think that the most important thing is that kids get a foundation of knowledge in science, and social studies, and literature, and so forth.

You young people at the university aren't kids anymore. Wake up and demand better professors... and yes, be willing to work hard for credentials. However, please don't confuse teaching with credentialing. They are two very separate things.

Personally, I've clearly seen the very bad effects of corporal punishment on children. It saddens me that there isn't currently a budding body of research about this, amongst educators and child psychologists.

I've worked with small groups of kids in many different settings. And what I've seen is that regular spanking of small children can cause a couple different outcomes. The child can become hyperactive - in other words, the child becomes squirrely, because this behavior is a way to get the parent in a better mood, and avoid the slap for awhile.

I've also seen elementary school kids who become bullies of their peers in school, and the neighbor kids - because that's what they're learning from their unwitting parent. The kids are learning that you ought to impose morality on others using physical agression.

Sweden outlawed spanking or smacking of kids in 1979. The law is very well written, in that it doesn't provide for any punishment of perpetrators. However, if what the parent did to the child can be defined as assault, there are laws which come into effect there.

Here's a great explanation about the Swedish policy by Adrienne Haeuser

One problem which seems to be prevalent in Australian schools - violence. According to a Queensland schools website - 16,000 kids in the state were suspended at one point or another last year because of physical aggression.

Here's a news report from Adelaide - a city in South Australia:

I have been enrolled in a teacher education program at my local university this last few months, and for one of the projects, I was asked to research and present on another country. I decided to check out the education system of a country which has caught my interest recently - Australia.

I was really impressed with what I learned - that Australia has a constructivist pedagogy - students learn things in a hands-on way. And they take this all the way up through high school - so that vocational skills are really focused on a lot in their upper grades.

Australian teachers also seem to have a profound respect for children's intellect. They believe that children are reasonable people, and that they can achieve great things right now. It's very refreshing, and certainly parallels my view on children which I had thought was very unusual, until I saw that all of Australia seems to see things the same way.

More specifically, the pedagogy folks have in Australia is what they call "Outcomes Based Education." Australians would contrast that with what we have in the USA - they call our system "Standards based education." Tests are not as important to Australian educators as they are to usa educators. The main goal in the Australian education system is to prepare the kids for real life - whereas the main goal in the usa system is to make certain kids have a basic competency in academic areas like science, and math and social studies, and so forth.

Here are some films which I found particularly inspirational - of Australian schools and Australian kids. You can see the spark of intelligence in the kids which you usually don't see in American kids. I attribute that to the better pedagogy (teaching style) of Australian educators.