Standards

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Standards for Course Material

How to Identify or Avoid Nonsense in Mathematics Texts

Ideally students will have clear and precise reading material, that is text and exercises, to follow or do, one at a time and one after another. Albeit, some school authorities may impose math textbooks of the scatter-brained type on teachers and students, a professional embarrassment for the teachers which puts students and parents. Not all is ideal. To help improve school textbooks, ask local mathematicians, domain experts with doctorates in mathematics to identify in public newspapers and in university mathematics department websites, the rational and irrational elements in local mathematics textbooks for local schools, primary to secondary. Do some muckraking. Math textbooks that are not self-contained with important terms high lighted or bold faces are like legal documents in which key terms and phrases are not explained. Confusion follows.

Remark: A monopoly on course design and text composition by professors of education more familiar with teaching style than substance - that is, the content and fine points (and limitations) of technical subjects and their exposition - can lead to nonsense. Hence there is a need to involve university professors outside of education in the development and monitoring of course design and delivery. What education requires are course designs and lesson plans easily understood and followed by instructors.

Since the 1990's, I have been looking at the plans of educational authorities and organizations in Quebec and the rest of North America with the intent of understanding them. But until recently, those plans or standards for mathematics education offer edu-babble, that is, general directions for instruction based on assumptions about the role of technology and based on assumptions about how students learn or should learn, without clear and full consideration of the underlying course content. With the details of what should be taught in mathematics inherited without much reflection, as is or weakened from earlier days. Content-related difficulties in the exposition or development of skills and concepts are persevered or compounded. An individual who done well in calculus should be able to read and understand the curricula or course design for primacy and secondary school mathematics before calculus. Anything less points to a lack of clarity and intelligence in North American course design and delivery. And in all this, mathematicians have no say in course design delivery due to their aversion to edubabble and the emphasis there-in of style over substance. The question where is the content and what should be taught needs to be well-understood before delivery styles are applied. Education is or should be an empirical matter in which hypotheses about how student learn and what to cover should be tried and tested on a small scale, before central planning, if any, begins.

People who advocate education reform should try and test those reforms in ideal to less than ideal situations, and then report how or where their ideas and material worked. Teachers parachuted into subject they have never taught before need materials, well-prepared and tested, to provide a lower bound for their instruction. Education reforms with directions, fresh and not tested, for instruction invite failure.