Explaining the Roles of Definitions in Mathematics III

Share Cognitive Science Implications for Teaching Mathematics

Role #3: They are essential to learning mathematics. See 21 Feb blog.   Study the blog on 28 JUN 18.

According to Dr. David Chard, “Vocabulary knowledge is as essential to learning mathematics as it is to learning how to read.”  See this PDF.

It is entirely possible for a person to possess an extensive vocabulary but be so deficient in a particular area (mathematics, chemistry, economics, medicine) to be essentially illiterate in that area. That is frequently the case in mathematics. For many mathematics students, reading a mathematics textbook is like reading the following.

A Finibus Bonorum of an geschiedensboek in two hálito x and y is an magni dolores of sagte desenvolvemos (d, f) whose liever make the numquam a true statement when the first estabelecimento is substituted for x and the second hálito is substituted for y in the sagte. We say the point (d, f) satisfies the geschiedensboek. To natus one desenvolvemos by another, natus each consectetur of the first sagte by each geschiedensboek of the second liever and nesciunt dignissimos hálito

The above “nonsense paragraph” was created by selecting a paragraph from an elementary algebra mathematics book and replacing each mathematics term with an arbitrarily chosen word from a list of non-English words.

The above “nonsense paragraph” is a faithful representation of what is seen when a student reads a math book without knowing the requisite definitions.

Clearly the “nonsense paragraph” has no instructional value. Likewise, paragraphs in a mathematics textbook have no instructional value unless the student has learned the requisite definitions. The burden is on the student, not the author.

Some researchers argue that knowledge of definitions does not lead to computational competence – duh. Remember that computational competency is not a principle purpose of early algebra classes in the 21st century.

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