Plank 2 Discussion

[James Infante]

Intellectual, artistic, mathematical and musical abilities are, like physical and mental health, partly the result of innate personal traits and partly the result of nurturing. We strongly believe that, irrespective of innate abilities, appropriate nurturing can lead to a high level of mathematical (as well as intellectual, artistic and musical) competencies irrespective of innate abilities, and promote the development of those with unusual abilities.

Mathematics competency, the end result of mathematics education, is determined by a very complex system of nurturing dependent on curriculum, teachers, schools, family and community; on the appropriateness and capabilities of the first three and on the expectations, encouragement and support that all these entities provide to the individual student. The system is inherently complex not only because of the many major contributors, but above all for the complexity of their interactions, and the diversity of effects on individual students. We think that this is analogous, in the arena of physical and mental health, to the nurturing provided by the very complex health system that sustains the physical well-being of individuals; it is a complex system composed of family, community, clinics, hospitals, doctors and nurses.

It is as a result of our understanding of the complexity of our educational enterprise, and of the diversity of the student population, that we do not believe that there exists a simple method, a magic curricular wand that one can wave (if only in just the right way) to produce universal mathematics competency. And this disbelief leads us to deep concern with a multitude of proponents of competing magic wands. Again, in analogy with the health system, we note that we do not rely for our health and well-being on magic potions or incantations, but on the science of modern medicine, which is based on research, guided by experimentation, and on rigorous evaluation of clinical trials. It is most instructive to understand, since the beginning of modern medicine in our country at the beginning of the last century, the level of investments in medical education and research, in clinical trials, and the substantive changes in the health system that have resulted in our significantly improved level of health and well- being. We believe that a similar approach in the broad area of education in general, and in mathematics education in particular, will yield equally significant improvements, with resulting similar major economic and societal benefits. But it will take time, investments, experimentation, careful evaluations and substantive changes, not magic wands.

We have acute concerns about the professional preparation and working conditions of our teachers. Again, in analogy with the health system, we cannot but note that the significant improvement in that nurturing health system was begun by the Flexnerian revolution of the 1920’s that brought about changes in the education and in the professional working condition of doctors and nurses. Our teachers need a similar revolution that will result in a significant improvement in their educational preparation, in their knowledge of the subjects that they teach and on teaching methods, and in the time available to them to continue to study and improve their knowledge, know-how, and lessons while engaged in their teaching functions. It is also the case that our teachers deserve a higher level of professional respect and regard from the society they serve. Indeed, we believe that they are as important to us, as a society, as medical doctors are. And they should be as competent.

We do not believe in magic wands. We do believe in, and must voice, expectations of the necessity of notable improvements in our educational system. As mathematicians and mathematics educators our particular expertise and concern is in mathematics education. We believe that, in our field, we have the knowledge and understanding that, with resources, patience, experimentation and trials followed by careful evaluation will lead to substantive changes that will yield notable improvements. We believe that mathematics education is ready and able to be the spearpoint of a new Flexerian revolution in K-12 education.

Jim Infante

[Joseph Malkevitch]

Dear Jim,

In a general way I agree with most of what you say. However, I do think a lot of "complexity" is hidden in the phrase "mathematical competency." What future employers are looking for in high school graduates or college graduates is often not specific mathematical skills but the ability to take situations their employee has not faced before and think about this situation in mathematical terms. The employer might also hope that students be aware that mathematical tools exist for certain kinds of problems even if the employee himself/herself can not solve such problems. For example, scheduling problems occur in many different employment situations but I see no reason why all high school graduates should not be made aware that such problems can often be solved in a better than ad hoc way using mathematics. Of course, those who will be engineers or operations researchers will be expected to have different skill sets from those who are bank managers or social workers. If one is to study to become a successful engineer, one needs to arrive in college with a different set of mathematical competencies from those that will be needed if one plans to become a sociologist; or, at the very least, to be prepared to deal with mathematics at college in a different way.

There are also topics involving mathematics that help students who will be participating in a democratic society to understand the issues that modern societies face and that they will have to face as citizens in such a society.

Though I agree that there is no magic curricular wand, I think that mathematics curriculum should change as mathematics provides new tools for obtaining insights into a broadening circle of applications.

Best wishes,

Joe