MATH ANXIETY FAQ
What is MA?
Math anxiety is a pathology produced in many individuals during their school years, due to weakness in the math program followed by their school. It is widespread in the USA especially, due to the conformity of most schools to a seriously flawed curriculum.
What are its effects?
Math anxiety is a cognitive disability, in which a natural human capacity for mathing is rather completely lost. Even some people who succeed in technical and mathematical professions may be functionning at a frction of their full potential due of the debiliating effects of this acquired disease. Its primary symptom of course is a flush of anxiety (math anxiety) or the urge to flee (math avidance syndrome) when when math comes up.
What are its causes?
This is my theory. The school curriculum has a bug, such that a math topic is presented sooner or later (frequently around grade 7 or 8) which cannot be acquired, as prerequiste concepts or cognitive skills are unavailable. The student cannot engulf the new topic, does not master it, and gets the erroneous impression that he or she is at fault. More specifically, these are the usual problems:
- multiple representations are required, but one (usually the visual representation) is missing
- geometric constructions, which build visual inteligence (cf Howard Gardner) have been omitted from the program (they belong in the curriculum from th earliesst grades onward)
- the concept of an unknown number (basic to algebra) is introudced to early or too abruptly
- the historical order of math (basic to euclid, and to the history-based curriculum) has been recently replaced by the logical order, violating the Sheldrake Principle.
Who is Sheldrake?
Rupert Sheldrake is a contemporary biologist, author of the theory of formative causation, according to which, knowledge evolves in a knowledge field, from which we learn by a process of resonance.
What is the Sheldrake Principle?
The Sheldrake Principle, in the area of education, says that concepts are most easily learned in historical order
Who is Thompson?
William Irwn Thompson is a contemporary cultural historian, who has organised world cultural history in a sequence of major stages, like the ancient Egyptians, Vico, and others. But the Thompson scheme is characterized by mathematical styles, and is the basis of a new curriculum developed by Thompson and Abraham (T&A) for the Ross School.
What is the Thompson Scheme?
The Thompson Scheme has four stages:
- riverine, arithemetic, R (4000bc - 500bc)
- classical, geometric, G (500bc - 1689ad)
- modern, dynamic, D (1700 - 1970)
- biospheric, chaotic, X (from 1970 on)
What is the T&A curriculum?
The T&A curriculum is a mapping of world cultural history onto the grades:
This mapping attemps to coordinate the major bifurcations of world cultural history (according to the Thompson Scheme) with the stages of child development according to Piaget and others.
- epipaleolithic (late stone age) to K, 1
- mesolithic and early neolithic (agriculture) to 2, 3
- riverine (first city states) to 4, 5 (ancient indus, sumer, egypt)
- classical (greek, roman, etc) incl med to 6, 7, 8
- modern to 9,
- biospheric to 11, 12
What are the cognitive styles, intelligences?
It has long been known that math requires the coordinated modes of verbal, visual, and symbolic representation, as in the dynapic technique. More recently, this traditional view has received support in the work of hHward Gardner on multiple intelligences (originally there were seven). We believe that the coordination ov the various cognitive modes and their balanced development in childhood are encouraged by correct math training.
What is the dynapic technique?
The dynapic technique is the method mathematcians use to communicate among thmselves: verbal description is multiplexed with symbolic statements, in synch with a drawing made line by line.
What are the standard tests, and what role do they play in MA?
Standard tests dominate the programs in schools, public or private, and cripple the evolutionary tendency of teachers, pupils, and parents to adapt the curriculum to the individual skills and needs. This worldwide tendency is antievolutinary in that the standard tests are very expensive and therefore slow to change. Perhaps more in math than in other subjects, the cognitive modes used in the tests are poorly adapted to the subject, and training for the test deviates from a balanced and coordinated development of modes. In particular, the visual mode is under utilized, or uncoordinated with verbal and symbolic modes: no dynapics on the printed page.
How could we avoid MA?
To avoid MA, the math curriculum should follow historical order, and make use of the dynapic technique. Multimedia suuplemental materials maybe used to augment the traditional textbook-based program, beginning in middle schools at least. It would be neccesary to bypass the standard tests, or to resist training for multiple choice questions at least, to make space in the program for the dynapic presentation of historical material, for example, the constructions of euclid