Linguistic Registers, Conceptual and Procedural Knowledge^©

 Tim Whiteford PhD  

 Overview

 1. Linguistic registers defined and identified.

 2. The nature of Conceptual and Procedural Knowledge.

3.  Two registers; two languages.

 Presentation at the VCTM Conference, Montpelier, VT

April 8, 2004

Linguistic Register 

A linguistic register is "a set of meanings that is appropriate to a particular function of language, together with the words and structures which express these meanings." Halliday (1975)

The NCTM Standards describe communication as "the ability to read and write mathematics and to interpret meanings and ideas."

Anachronistic Register 

Benjamin Greenleaf's "The Complete Arithmetic" (1881) makes extensive use of terms such as rod, chain, hectare, involution, evolution, surd, acre, troy, subtrahend and minuend. The following instructions are given by Mr. Greenleaf for anyone attempting to "reduce the integer to a denominate fraction." 

         "Change the given number of the smallest denomination to a fraction of the next larger.  Write the fraction as a part of the number of that larger denomination.  Change, in like manner, the number thus formed, and so proceed as far as required (p. 133).

Also:

           "Find the difference between 15lb.03oz.12pwt. and 9lb.1oz.17 pwt"

           "Multiply 11 bu. 3 pk. 2 qt by 7. "(p. 137)

  Cultural Register 

Mathematics differs from country to country in terms of the vocabulary, the meanings given to words and the conceptual structure derived from words and phrases.

 From the Daily Telegraph (UK).

           "Durham reached 124 for seven off 34 overs compared to Worcester's 128 for six, but the tail subsided... David Byas took his season's tally to 702, passing John Hampshire's 684 set in 1976, by hitting 54 as Yorkshire posted 214 for six.  Then Darrin Gough took a competition‑best five for 13 on his 24th birthday as Sussex were dismissed for 177.  Captain Alan Wells top‑scored with a battling 64 including five fours and a six off 70 balls.  Mike Watkinson, with four for 32, led Lancashire to a 47 run win over Leicestershire despite a broken thumb".

Some more: 

"nineteen and eleven". 

"sums".

 “6 and 9 from 10 bob is 3 and 3”. 

“I live in Elmwood Avenue”.

Personal Linguistic Register

Most people have several registers which are context dependent. Most people can move easily from one to another. 

Shared registers - similar understanding of concepts and ideas.

Conceptual Knowledge and Procedural Knowledge

James Hiebert identified two forms of knowledge involved in learning mathematics and communicating mathematically; procedural knowledge and conceptual knowledge.

Conceptual Knowledge is knowledge of ideas, concepts and relationships. Concepts are typically composed of many facets based on our experiences and how much we know about a particular idea. They can contain facts, ideas, feelings, relationships, senses, words, images, skills and so on. They usually occur in the form of schema and they are derived from the natural world.

Procedural knowledge is knowledge of the procedures, rules, formulae,  and symbols we use in mathematics. All procedural knowledge is ‘arbitrary’ knowledge.