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Conversion from meters to miles

The model for conversion of units in the typical textbook is shown below.

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It is well known that this does not work. ("My students just can't handle units!")

The reason this form of unit handling is used is that it uses minimum space on the printed page.

The reason it does not work is the overload of the short term memory that occurs in trying to apply this model. There is considerable need for knowledge of concepts as well as mastering the mechanics of entering the conversions into the expression. Only the more adept student can avoid confusion that arises when the short term memory is abused in this way.

A concept-based approach to unit conversion visibly uses the concepts and uses standard algebraic substitution methods to produce the resulting units. An example is shown below.

The absence of teaching and use of algebra in the K-12 curriculum places the student at a tragic disadvantage.

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In the presentation shown above the ideas, concepts that one wishes to embed, are explicitly displayed. Words are included to give continuity to the story. Standard algebraic methods are used in a logical sequence to effect the conversions. The development of the conversion shown above uses algebra. Since the teaching and use of algebra is not included in the K-12 curriculum students and teachers cannot understand the algebraic solution shown.

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Unit conversion in Coulomb's law

Unit conversions as might be needed in using Coulomb's law for the electric field, if the given quantities involve a mixture of units, are shown below using the unit handling model typically present in textbooks.

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In reading this expression you will be aware of the large amount of busy work involving the short term memory and probing of knowledge space needed to translate and verify the expression.

Students are expected to be able to write such expressions on the fly. Only the most adept students can succeed in doing this. There is substantial cognitive overload involved. 

A concept-based approach to carrying out the unit conversions is shown below.

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In the presentation shown above the ideas, the concepts that one wishes to embed, are explicitly displayed. Words are included to give continuity to the story. Standard algebraic methods are used in a logical sequence to effect the conversions.

Developing the needed unit conversions in steps, as done above, and including words to express verbally the idea used at each step are necessary to the process of reliable problem solving.

It is often expressed that students cannot verbalize the ideas involved and resort to mindless manipulation of symbols. A concept-based approach to problem solving responds positively to correcting this situation. Algebra is needed to do this. Introducing teaching and use of algebra in the K-12 curriculum is urgently needed.

The reason that students are weak in verbalization and in use of analytical methods is quite simply that they are rarely required to use these tools. Having little experience using these tools, they are, as one would expect, inept in making use of these tools.

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Conversion of liters to cubic meters

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Introducing algebra in the K-12 curriulum would make it possible for students to solve problems reliably.
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The problem solutions were developed by Howard C. McAllister using SureMath..