Professions Based on the Ideal of Mathematics and Abstract Quantification
If there are professions free from human fallibility and vested interest, it is those based in mathematics, for presumably the study of abstract quantification favors no group over any other and, therefore, seems least likely to encourage or engender selfdeception in its practitioners. But even a cursory examination of the topic suggests a gap between ideal and reality even here.
Let us briefly review the promise of math instruction itself, a promise used to justify the large sums of money necessary to maintain math instruction at all levels of schooling. That promise can be stated in the following terms:
We live today in a world in which mathematics proficiency is increasingly important to success in life. Our world is complex and technological, and mathematics is crucial to both understanding its complexity and operating within its technological dimensions. Our investment in mathematics is sensible because, through it, we are providing society with the mathematicians, engineers, and technical experts necessary to meet worldwide competition. What is more, mathematics proficiency is important to everyone. Many problems and issues of daily personal and public life have an important quantitative dimension. Largescale math instruction provides the citizenry with the quantitative concepts, principles, and tools by means of which they are able to perform successfully in both their personal and public life. Through it, persons learn to transfer logical thinking to other domains of professional knowledge and thought.
To what extent is the ideal realized? How far are we from it? What are some of the hidden consequences deriving from largescale math instruction that the promise of the ideal does not take into account? What alternatives do we have to our present practice? To what extent are we getting what we are paying for? To what extent is our social investment in mathematics having the promised effect? To what extent are we realistic in our conception of the value and real consequences of largescale math instruction at every level of schooling?
In our view, there is a large gap between the promised social gain from math instruction and the actual result. The gap is twofold. The first problem is inherent in the negative consequences for persons unable to perform at some minimal level at school  those who fail at school math. The second problem is the failure of citizens who are certified by schools as competent in math who do not use mathematics successfully in dealing with public and social issues. We are alleging, then, that both the persons who fail officially and those who pass officially constitute evidence of a major problem in math instruction.
