C-153. Introducing math

Our customary introductions to the 3R’s are elementary. Students are introduced to the elements of two technologies, language and math, already impressively advanced (albeit incompletely) – and thereby risking an imbalance of elementary over basic (XI; App. IV). Individuals and communities clearly need to adopt, support and practice skills in these two technologies for the problems and decisions they will encounter, alone or together. But all too often this introduction to math comes across as bitter and brief, especially, it seems, for girls. The lack of female vocational interest raises an important question. But the problem may be much deeper ... more basic. With increased technological power comes a remove. Applications to problems are furnished, after the fact, for using the skills learned … but what would be helpful before the skills are to be learned?

The elementary approach sees (technological) skills as desirable properties of behavioral entities (bE), with all the minding faults of the latter (0:S-P; C-39, 114). Both the entities and their parts, properties, qualities, attributes are treated as particulars ... as objects of attention; they are not formally introduced as particulars. (Which is unfortunate.*)

Attention to what? To collisions. In considering objects of attention in regard to collisions, it makes a difference how many entities one may have to deal with (i.e., counting) and it makes a difference how much of what even one entity or property – let alone more – may bring to a collision (i.e., measuring).

The student, as prospective R-entity (C-147), lacks an R-sense (C-128) of the needed functionality for which this and the rest of the technology is designed, having at best a limited sense of the usages (functions) for which applications have been found. (Few will attain a Grasp of the technology’s logical structure. Which suggests that such a Grasp can hardly serve as an effective introduction to math’s functionality: to what is called for [C-110], to what is being talked about and to what is being said.)

What would an R-sense introduction to math be like? The collision-relevant introduction above is a starting point. Then, however, it seems sensible to bring (and keep) Realization re needed functionality into the picture – i.e., what can be done about arranging useful collisions and what can be done about arranging to avoid dysfunctional collisions … and then to point out that the counting and measuring can be very helpful in developing the capacities and capabilities to better (and best) arrange needed and wanted collisions, to solve the problems that students (indeed, all humans) share.

Offer them a broad path forward, not a potential vocational niche. (See C-154, the potential interdependency and thereby the greater strength of the R-transform and the V-transform developed in concert. [The point OF the R-transform is that quality is not just something there is a quantity of. It is often needed functionality before there can be any quantity of it.])

It is important to acquaint students with distinguished historical figures who either brought science to bear on problem solving (e.g., Pasteur) or who as scientists found themselves later drawn to helping solve problems (e.g., Lewin). These scientists saw something of the interdependence. They didn’t mistake separateness (aka “ivory tower”) for the independence needed for developing interdependence.

* Especially unfortunate because that introduction may never be made. Even though dominant technologies of research (“variables”) and natural language (nouns, verbs, adjectives, etc.) are focus their emphasis on particulars (as part of the BPO bias: C-39; passim). “Particularitis” may be the most pervasive malady afflicting humans. (Seeing any and every condition as a “thing” [aka body, B, entity, object] is an accompanying symptom.) Given the R-entity’s need to focus attention in a world of body collisions makes the malady explicable – and to some extent sufferable. But it needs companion technology to alleviate it (i.e., C-135), using the R-transform to make the SGN correction, which brings the general, G, into the picture along with the particular … and the step, S, along with the body).

(c) 2016 R. F. Carter