20160727 THROUGH PATTERNS TO ALGORITHMS:

Way to go.

Before I forgot, the word algorithm is obviously Arabic, but only recently I learned that it's the name of al-Khwarizmi. The post stamp on the right is Soviet. Al-Khwarizmi was born in Khwarezm, in Uzbekistan, which was a part of USSR.

I started thinking about teaching TLG algorithms thanks to Steven Leinwand. My first reaction was, come on, you guys can't even explain multiplication. Eventually, I decided it was worth trying, and tried.

The material for TLG's first algorithm was bare quantity. I believe, the study of quantity must come before numeracy, and, since numeracy tends to erode the prior knowledge, we must reteach the fundamentals as often as possible.

Quantity is a property of sets of objects. We can't see it (which is truly remarkable). We discover it mentally.

Quantity is something that the sets of countable objects have in common, no matter how different those objects are. I provided some explanation in SHNUMBERS. Now I suspect I will never have a chance to tell everything I want, so please allow me to write just a little bit more.

As counting tokens, calculi or pebbles are second to none. They are small, dirt cheap, low maintenance, rock solid, stone durable, they can be easily differentiated by colors and shapes and even painted. Sadly, people waste plastics buying counting bears, cubes, beads.

As soon as we understood that we can match pebbles to hurricanes one by one and find the number of the pebbles bigger, we are on the way to math. The first step, I believe, is to learn to compare quantities.

I gave TLG two quantities in the paper bags, added one more empty bag, and challenged her to compare without taking all the tokens out. She was upset at first, but quickly understood the she only needed to match two tokens at a time. After she found which quantity was bigger, I started drafting the flowchart. Instantly, TLG learned the language and finished the story.

There is a problem with flowcharts. Let me borrow a piece from CODEPEGS to tell what it is.

Long time ago, when computer programming was in its infancy, we had statements allowing to leap back or forth and continue execution from any point. In 1968 a prominent Mufti named Edsger Wybe Dijkstra published a fatwa, in which he claimed that such statements are evil, and "should be abolished". So abolished they were.

Flowcharts allow to direct the flow of control to any point, so abolished they must be. I did not question the wisdom behind this decision and/or the outcome of it. I simply admit that recently I taught my 6 years 10 months old offspring use three kinds of blocks and lines with arrows to describe algorithms. Moreover, I am going to use flowcharts reteaching her every algorithm she has learned this far (and she is quickly approaching long division).

Three years ago, TLG underwent a course of procedural thinking. Back then, I did not understand what I was teaching her, and how this teaching was linked to my homegrown course of arithmetic. Only recently, I borrowed the unifying concept of spatiotemporal patterns.

Edsger Dijkstra wrote: "My second remark is that our intellectual powers are rather geared to master static relations and that our powers to visualize processes evolving in time are relatively poorly developed."

The "processes evolving in time" are spatiotermporal patterns, and they emerge from the procedures as we play them out. This was what TLG learned by the age of four.

Here is a very basic "checkerboard" pattern, which I temporalized in 6 different ways. I did it using FIREPEGS, which mimics much younger child. A year later the same child would build the same patterns procedurally.

What's next? I already have CODEPEGS. Soon (if not already) TLG may become able to build the patterns through JavaScript.