Posts Tagged ‘education’

Here is how to fix the education system

November 4, 2018

Every school, at every level, has these two mantras:

  • Learning is a lifelong process
  • Look longer and see more

The teachers repeat these mantras to their students, often. And at every level (1st grade, 2nd grade, …, 12th grade).

Every teacher exhibits, daily, a pure joy and love for learning.

No more summer vacations. School is year-round. 10 days off each year – a day off for Christmas, a day off for New Years, etc.

No more rushing to get through a curriculum. Slow down. The teacher introduces a concept and then lots of time is given for the students to explore the concept from all sides, see how it fits in with other things they’ve learned … let the concept become part of the student.

No more tests. Instead, students write, write, and write. “I don’t know what I think until I write it down”

Do these things and it will revolutionize our world.

The education system is broken and needs to change

October 13, 2018

Learning is a lifelong thing. We should stop treating it as something you do just in your youth. Teachers should stop flying through a curriculum for the sake of pronouncing “We covered all the material”.

I was a good student in school. I did well in all the tests. But as I reflect on my schooling, I realize that my learning was superficial. I didn’t deeply understand the material. I didn’t internalize the material. Internalizing a new idea comes about only by spending lots of time with it, looking at the idea from various angles, and relating the idea to other things. It’s only now, after many years away from school, that I am deeply understanding things. How? By slowing down and spending lots of time thinking about each idea.

Look longer and see more.

Learn within a meaningful context

May 29, 2014

I am reading a book on a certain technology. The author of the book explains why it is useful to learn the technology: the technology contains many topics that are generally useful. The author lists the topics. Then the author says this, which I found to be profound:

Although each of these [topics] can be studied in isolation, it is educationally more valuable and satisfying to do so in a meaningful context.

Interesting and surprising statements about education

April 24, 2014

I think this is a great statement:

Education is an engine
for upward mobility.

This statement about colleges and universities surprised me:

It is cheaper to attend
private schools than it
is to attend public schools.
The reason is that private
schools provide lots of
grants, whereas public
schools do not.

Ways To Specify Things Precisely And Clearly

February 23, 2014

I am interested in hearing your thoughts on this:

Need Precision And Clearness

In work and in daily life it is important to be precise and clear. Mathematics is one way to achieve precision and clearness, if the problem is numerical in nature. However, there are many problems that require precision and clearness and are not numerical in nature. I think our educational system devotes too much time to mathematics as a way to express precision and clearness, and not enough time to the other means to express precision and clearness.

Allow me to explain please…

My Kitchen Has 10 Pieces Of Fruit

In my kitchen I always keep 10 pieces of fruit on hand. Of the 10 pieces of fruit I always have two varieties: bananas and oranges, pears and kiwis, etc. If I wanted to rigorously specify this, I could create a mathematical equation:

x + y = 10

where x represents one kind of fruit and y the other.

Equations are great for precisely and clearly specifying things that are numerical, such as the count of pieces of fruit in my kitchen.

Being able to specify things precisely and clearly is important. Mathematical equations are great for this: they are succinct, they are abstract (free of irrelevant details such as the fruit’s color, shape, and texture), and they avoid the clumsiness of the English language (“I have 10 pieces of fruit and of them I have two varieties” is clumsy compared to “x + y = 10“).

Non-Numerical Problems Need Precision And Clearness

Not everything that we want to specify precisely and clearly is numerical. For instance, it would be useful to precisely and clearly specify the format of a Web page (i.e., HTML): an HTML document must have html at the beginning (the root element) and it must contain a head element followed by a body element; the head must contain zero or more meta elements and a title element, and so forth. Some very smart people have developed a succinct, precise way of specifying the HTML format, using something called a “BNF grammar.”  A BNF grammar contains “rules” and each rule specifies the content of each element, e.g.,

<html> ::= <head> <body>
<head> ::= <meta>* <title>
<body> ::= …

That notation might look strange. That illustrates my point. Here we have something that is non-numerical and needs a precise and clear specification. The BNF grammar notation is something that our educational system should expose to students early in their education.

Students need to see that (1) things need to be specified precisely and clearly, (2) not everything is numerical, and (3) non-numerical things can be expressed as precisely and clearly as numerical things.

There are many other non-numerical things that would benefit from a precise and clear specification. For example, think about the shipping requirements of Fedex and UPS. In order to ship a package from point A to point B it may have to go through point C. But if point C is unavailable (heavy snow storm there) then the package needs to be re-routed to point D and then E. You get the idea. A precise and clear specification of the routing problem is needed. It is not a numerical problem and so mathematical equations are of limited use. Some very smart people have developed a succinct and precise formalism for this type of thing, called graphs. I won’t go into an explanation of them. The point to be made here is that this is another example of a non-numerical problem for which we need precision and clearness, and students should learn at an early age these formalisms.


Mathematical equations are great for expressing numerical problems precisely and clearly. Our educational system exposes students early to this way of specifying problems. But there are other problems that are not numerical, require precision and clearness, and for which ways have been created for  specifying them. I think that our educational system should expose students early to these other ways. I think that by the time a student is 10 years old he/she should have been exposed to BNF grammars, graph theory, Turing machines, finite automata, and probably several other things.