Another Math Miracle, Dept.

This promo piece is about Nashua NH public schools adopting Eureka Math. In keeping with the tradition and style of such articles that pass as objective reporting, it contains the usual disparagement of algorithms, memorization, and of course tests that are not “formative”.

To wit and for example:

“It builds student confidence, year by year, by helping students achieve true understanding of math, not just algorithms,” said Fitzpatrick, adding students are focusing on applying math as opposed to memorizing math formulas. By implementing Eureka Math for kindergarten up to eighth grade, she said it will provide a continuous standard progression and help build conceptual understanding and abstract skills. It also encourages consistent math terminology and common assessments that are formative and summative, explained Fitzpatrick.

It is more than a little discouraging to see the premises of Kamii and Dominick (famous for their seminal piece that supposedly provides evidence that teaching standard algorithms is harmful) being taken so seriously.  The obsession with conceptual understanding continues, with little regard that the end product is usually students parroting back what the teachers want to hear — what I refer to as “rote understanding”.

Programs such as Eureka math consist of a steady diet of drilling confusing and ineffective strategies that supposedly ingrain the conceptual underpinning of the standard algorithms.  (For more on this, see this article.) In fact, the strategies being used to teach the conceptual understanding are not new at all, and were used in previous eras after mastery of the standard algorithms.  The standard algorithms were the main course, and the strategies, presented later were the side dishes, meant to then provide more perspective of the conceptual underpinning.  

Missing in all these discussions about the holy grail of “understanding” is that there are various levels of understanding, which are built upon in subsequent math courses over the years.  In freshman calculus classes, for example, the concepts of limits and continuity are presented in an intuitive approach, allowing students to progress to the powerful applications of derivatives and integrals. Later in upper level math courses, more formal and rigorous definitions of limits and continuity are provided–which would result in a lot of confusion for many first-time calculus students.

But the myth persists that the reason American students do poorly in math is because they lack “understanding”. A glance at how Singapore and other Asian countries provide math instruction would show that the approach used in teaching the standard algorithms is very similar to how math used to be taught in the US many years ago.

With the myth comes the programs, and with the programs come more help at home, tutors, and learning centers for those who can afford it.  And also with the myth comes a willing ignorance as indicated in this telling paragraph about a teacher’s comment on Eureka Math:

She acknowledged that with Eureka, fluency with math facts is not a daily practice, however teachers are finding other ways to introduce math facts into the middle school curriculum. There is also a 45-minute time crunch for Eureka Math, meaning there may not be as much time for remediation if concepts are not fully understood, said Porpiglia. There is currently a list of highly rated support resources that are being vetted to encourage visual models and a greater algebraic understanding for middle schoolers, she added.

So what the reformers mean by “understanding” are visual models–i.e., drawing pictures and going back to first principles each and every time you solve a problem. This supposedly provides the “greater algebraic understanding”– even if it takes remediation. And math facts?  Well, relax. Never mind that no one is bothering to express surprise that math facts need to be introduced as late as middle school.  It’s all for the greater good until the next bright shiny new thing is introduced.