Hodges' model? Ah! You mean the naïve conceptual framework that ...
... thinks it's a theory! (i)
Yes, I suppose it is naïve, now you mention it. It's naïve in a number of ways:
- The assumed state of students - new learners; although of course, in healthcare and other professions for many years mature students - far from naïve - can make up a notable proportion;
- When a patient assessment begins, especially upon initial (and first) referral, the data gathering, our knowledge should then be assumed to be naïve.
- The quest for a theoretical underpinning of Hodges' model, may display naïve associations between concepts that are misplaced, misunderstood and wholly inappropriate.
Vinner, S. (1976). The Naive Concept of Definition in Mathematics. Educational Studies in Mathematics, 7(4), 413–429. http://www.jstor.org/stable/3481947
"As a matter of fact, all of us start to deal with definitions at a very young age when we start to leam our mother tongue. At this stage, various types of definition occur and the subject is too complicated to be dealt with here. After several years, especially at school, one type of definition becomes dominant; the lexical definition. In a lexical definition, the meaning of a certain word (or words) is explained by means of other words (we shall deal here only with the case in which the word and its definition are at the same language). This type of definition generally occurs in mono-lingual dictionaries." p.425.
"The sentence: 'A rectangle is a quadrangle that has four right angles' does not have in it any underlying assumptions about the role of definition in mathematics. It can be interpreted in any of the following three ways:Thus, not adding anything to definitions like the above we let the student choose his own interpretation out of the three mentioned (or even possibly more) interpretations. We claim that in most cases the student's choice will be the third one." pp.427-428.
- We (math teachers and math students) hereby agree that instead of saying, "a quadrangle that has four right angles" we will say: "a rectangle" (The formalistic approach).
- In the mathematical community the meaning of the word rectangle is a quadrangle that has four right angles (The lexical approach from the expert's point of view).
- The object denoted by the word 'rectangle' is a quadrangle that has four right angles (The lexical approach from the naive standpoint).
Does the diaeresis here point to forms of parity of esteem, oppositions, polarities, dichotomy?