I previously made the distinction between inaccuracies that come from oversimplifying a concept (particularly by using less precise, nontechnical language) and those that come from not understanding that concept. The first type is regrettable but occasionally unavoidable (at least in lower level classes); there is no real excuse for the second.

When writers make mistakes while explaining technical concepts with non-technical language, it can be often be difficult to decide which kind of mistake they're making (think Malcolm Gladwell). If, on the other hand, the writers drag the readers through impenetrable technical explanations and still get things wrong...

We've already established that there are lots of mistakes in the Eureka Math materials (with more examples to come), but it's important to note that the mistakes we are talking about do not come from oversimplifying the concepts or making them accessible to younger learners. Instead the lessons are often filled with formal and painfully dense mathematical explanations.

Here's an example from the parent section of Eureka Math ("a suite of tools that will help you to help your child learn more"). Keep in mind, the target audience is parents who are having trouble with the homework their eighth graders are bringing home.

Check this one out.

Here's a more readable version (at least in terms of font size):

Dilation: A transformation of the plane with center O and scale factor r(r > 0). IfThis wouldn't be A-level work in a graduate math class (I had to read through this a couple of times before I realized that O was supposed to be the center of dilation. Dangling modifiers are a bad idea in a formal definition), but the language would be appropriate. For the target audience, though, you might as well be speaking Sanskrit.

D(O) = O and if P ≠ O, then the point D(P), to be denoted by Q, is the point on the ray OP so that |OQ| = r|OP|. If the scale factor r ≠ 1, then a dilation in the coordinate plane is a transformation that shrinks or magnifies a figure by multiplying each coordinate of the figure by the scale factor.

Congruence: A finite composition of basic rigid motions—reflections, rotations,

translations—of the plane. Two figures in a plane are congruent if there is a congruence that maps one figure onto the other figure.

Similar: Two figures in the plane are similar if a similarity transformation exists, taking one figure to the other.

Similarity Transformation: A similarity transformation, or similarity, is a composition of a finite number of basic rigid motions or dilations. The scale factor of a similarity transformation is the product of the scale factors of the dilations in the composition; if there are no dilations in the composition, the scale factor is defined to be 1.

Similarity: A similarity is an example of a transformation.

If you're reading this, it's likely you're a math person, and there's a good chance you've taken classes like abstract algebra and real analysis. If so, I'd like you to try a bit of sympathetic imagination and put yourself in the place of someone who struggles to understand the eighth grade math homework his or her children bring home. Now go back and read this section.

I can't imagine anyone who actually needs help getting anything out of this, while the people who can follow these definitions could probably do a better job writing them on their own.

[Later in the same PDF, the authors make an appalling mistake explaining corresponding sides, but that's a topic for another post.]

They should get Ed Wegman to punch up the prose a bit!

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