Mathematicians’ role in the education of

teachers

H. Wu

School mathematics education needs the involvement of research mathematicians.

• Mathematical flaws are common in state mathematics standards, in textbooks, and in assessment items.

• Pre-service and in-service teachers are not taught the mathematics they need in the classroom.

• Remedy of the situation requires a strong mathematical input.

• Most of these problems can be traced to the separation between educators and mathematicians in the past decades.

• When school mathematics is cut off from mainstream mathematics, it must evolve into something different. (Simple Darwinism.)

• Research mathematicians take for granted that techniques cannot be separated from ideas.

• However, most textbooks teach only techniques but not ideas, and most new textbooks almost ignore techniques in order to teach “understanding”.

• Research mathematicians take for granted that every argument is backed by a proof.

• However, most textbooks have little or no proof, and most new textbooks either confuses a heuristic argument with a proof, or cannot offer a proof because no technique is available.

• Research mathematicians not only prove theorems, but they also know why they want to prove those theorems.

• However, most textbooks present only a litany of procedures with no motivation, while many new textbooks equate motivation with a proof.

• Research mathematicians take the need of trials-and-errors for granted; open-ended problems are their staple.

• However, most textbooks present only iron-clad decrees, while most new textbooks often present ill-posed open-ended problems and do not bring closure to chaotic trials-and-errors.

• One consequence of this polarization, in the context of the education of mathematics teachers, is that most of our math teachers have never been exposed to any genuine mathematics.

• THIS IS UNFAIR.

• Do research mathematicians really want to keep it hidden that, in mathematics, there is a seamless integration between skills and conceptual understanding, that precise definitions and logical reasoning are sine qua non in any discussion, and grappling with open-ended problems is a fact of mathematical life?

• Do research mathematicians really want to keep it hidden that the depth of content knowledge needed for a meaningful discussion of K-12 mathematics is far from trivial?

• Teachers need to know these facts in order to teach mathematics better, but these facts have remained largely a well-kept secret in the world of mathematics education.

• It may be time for mathematicians to re-assimilate themselves into the world of mathematics education in order to make these facts known again.

• The significance of the involvement of MSRI, a research organization, in mathematics education lies in providing a forum for, as well as giving credibility to this re-assimilation.