It is apropos to begin this website with a short article on Textbook School Mathematics (or TSM), which math education engineers are dedicated to eradicating from U.S. Schools Systems. Coined by Hung-Hsi Wu, Professor of Mathematics, UC Berkeley, it roughly means “something resembling mathematics as defined by standard K-12 mathematics textbooks.” Hung-Hsi Wu talks about it in more detail in his Fall 2011 American Educator article, Phoenix Rising,
Before the CCSMS came along, America long resisted the idea of commonality of standards and curriculum—but it did not resist such commonality in actual classrooms. Despite some politicians’ rhetoric extolling the virtues of local control, there has been a de facto national mathematics curriculum for decades: the curriculum defined by the school mathematics textbooks. There are several widely used textbooks, but mathematically they are very much alike. Let’s call this de facto mathematics curriculum Textbook School Mathematics (TSM). In TSM, precise definitions usually are not given and logical reasoning is hardly ever provided (except in high school geometry texts) because the publishers mistakenly believe that intuitive arguments and analogies suffice. Thus, fractions are simultaneously (and incomprehensibly) parts of a whole, a division, and a ratio; decimals are taught independently from fractions by appealing to the analogy with whole numbers; negative numbers are taught by using patterns and metaphors; the central idea of beginning algebra is the introduction of the concept of a variable (which implies, wrongly, that something is going to vary), when it ought to be becoming fluent in using symbols so as to do generalized arithmetic; solving equations is explained by the use of a balance to weigh variables on the weighing platforms; etc.
TSM to a student is like eating a cold can of Spam for dinner. Sure, it is a meat product that was once made out of real ham, it functionally fills the stomach, it is vaguely nutritious, but somehow it is worse than going to bed hungry. TSM currently is the curriculum for both traditional and reform styles of teaching in the U.S. Both traditions get the actual mathematics incorrect (see Wu’s article for examples).
Professional teachers have for a long time sensed that there was something wrong with the mathematics they taught—why didn’t it make sense? They often rebelled against TSM, but having grown-up with TSM themselves, they did not have the mathematical background to be able to express why TSM was wrong or how to address its failure.
The goal is to help teachers make math make sense again to their students, to engineer a new mathematics curriculum that is mathematically correct and ready for consumption by school students. The Eureka curriculum writers thought of themselves as engineering school mathematics in the sense that we are customizing abstract, university-level mathematics in a way that can be easily digested by school students. Let’s end with another quote from Hung-Hsi Wu article, which states,
Let us put [school mathematics engineering] into context. Engineering is the discipline of customizing abstract scientific principles into processes and products that safely realize a human objective or function. So, chemical engineering begins with chemistry and results in Plexiglas tanks in aquariums, the gas you pump into your car, shampoo, Lysol, etc. Electrical engineering transforms the abstract theory of electromagnetism into computers, iPods, lights in your hall, hybrid motors, etc. And in the same vein, mathematical engineering takes abstract, university-level mathematics and customizes it into school mathematics (distinct from TSM) that can be correctly taught, and learned, in K-12 classrooms.
We only add that “correctly taught and learned” in the quote above is the work of curriculum writers and dedicated teachers, who through years of experience, know how to engineer lessons that bring real mathematics to life in ways that TSM doesn’t.
CHANNEL: Engineering School Mathematics
© 2015 Scott Baldridge