Education in the 21st Century Mathematics

In the nineteenth century prodigious skills of arithmetic computation was a prerequisite for top employment. During the course of the twentieth century the need for this skill diminished as technology was able to automate arithmetic. In the 21st Century we still insist that the calculation skill is somehow the basis of the rest of mathematics. If a child cannot learn arithmetic, an obsolete skill, he will have a major problem in school. Suddenly poor computational skills becomes a "math disability".

I do not advocate that schools abolish teaching computation. Let there be arithmetic courses, but also let there be mathematical courses where arithmetic is invisible. How you make arithmetic invisible is a matter of taste, but let me share mine.

Use a spreadsheet to present problems in arithmetic facts like an worksheet but with instant feedback and automatic storage of the results. Use a spreadsheet to teach and sharpen the estimation skills of the student.

At the same time you show the commands and formulas one can write in a spreadsheet to automatically get the answers in that same worksheet. That child has learned the arithmetic facts and the spreadsheet becomes an electronic manipulative.

During the rest of Mathematics, arithmetic is invisible and the student is given work problems and uses the spreadsheet to solve them.

For example,

Teach them to use Goal Seek to solve one variable algebra and solver for multivariate equations. If they have learned enough Algebra to write those equations in a spreadsheet then let the spreadsheet take care of the arithmetic.

Another example,

A spreadsheet can produce 2 and 3 dimensional objects that could be used in the more graphic mathematics as Geometry and Trigonometry. The cosine and sine functions are arithmetic free but you have to know when to use them.

This is, of course, is merely a preliminary outline, but the thrust will not change. Teach arithmetic as a desirable skill but teach other parts of mathematics where the student can take the arithmetic for granted. Just like in the workplace of the 21st Century.

Education in the 21st Century Reading

In the 19th Century Reading was as important a skill as it is today and phonetic decoding was the basic tool use to teach reading. The 20th century did relatively little to the reading process. Probably more than half the population prefer reading from paper than from a screen or a Kindle. One thing, however, has remained as strong across 3 Centuries: Phonics!!!

The main point of phonics is that if you sound out the word and can hear it you will know what it means. For the most part it is an effective strategy and those for whom it does not work, we simply call reading disabled.

Let us take a step back. The purpose of reading is to get meaning from the printed word. A phonetic approach requires you to look at the word and auditorize it (at least mentally) and when you hear the word, you will know what it means. This assumes that English is inherently phonetic and the reader knows the word to begin with. Neither are necessarily true, but let us accept the phonetic premise.

I learned to read in a phonics environment and fortunately it worked for me. But it does not work for everyone, so let us not mandate it for everyone. What alternative are there? One solution is a whole word approach, but the phonics proponents are wont to point out how the Chinese have to memorize 10,000 symbols rather than 26 letters. My first reaction is that the Chinese are a country with the largest population in the world, the fastest growing economy, and an impressive Olympic showing. They are not perfect...but they are patient.

The Phonecians, on the other hand, have been all but absorbed in Lebonon. In Japan, children start out with phonetic Kana, but when they are ready to advance, they move to the pictographic Kanji.

That being said, let me assume there is validity in making a connection between the printed word and it sound. A phonics approach says let the sound be created by the student decoding print. One alternative approach would be to pair the word with its auditory counterpart so the connection between the sound and the letters of the word are given to the student rather than requiring the student to produce the sound of the word. The basic premise of phonetic approach are retained, but it may be an easier approach for some students.

Some students will learn to connect the printed word with its meaning better by speaking and phonetic decoding but others will learn better by hearing which still teaches the connection between the printed word and its sound, but it does so by turning the standard phonetic approach upside down.

These two approaches will work best for students who learn best by speaking or hearing, but what about visual learners or those who learn by writing. There are as many ways to teach reading as there are people who read. Phonics has its place as one of the ways to teach reading, but it should not be the only way. We cannot adopt a one size fits all mentality in Education, especially if that one is bogged down in the 19th Century.

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