I'm not sure that I agree with all of the framing in this document, but the underlying ideas are well-founded. research indicates that students who are ESL &/or are "non-standard" dialect speakers may face instructional disadvantages in math, as well as literacy. https://twitter.com/ZaidJilani/status/1361076234378166278

I'm not sure what the document means in terms of "showing your work." I think this can be a good practice in terms of, say, an algebra problem, where teachers can see where you may have gone wrong. It's less good when teachers use it only as a tool to police cheating.

That said, the idea that current math instruction & evaluation is "white-oriented" in a way that can lead to further disadvantages for students of color is not incorrect. research has firmly established this in the literacy domain & is increasingly exploring it in mathematics.

Cause guess what? Math involves language. A lot. Even at the most basic level: numerical labels. The intersection btwn language & math is most obvious in word problems, but we've actually found correlations in more "pure math" domains, such as fractions.

research seems to indicate that the domain of language tapped might vary btwn math tasks, such that, for example, vocabulary, syntax, & verbal working memory are taxed in word problems (obvious), whereas Verbal working memory in particular is also taxed in pure numerical tasks.

Verbal working memory, in a basic sense, is how you store items in memory & then perform operations on them. So, when you hear a series of numbers & are then are asked to say them backwards or switch the order, etc., or, in the case of math, do a more complex ordering operation.

If you're wondering how language correlates w/ math even outside word problems, think about this: you are a native English speaker. You know how to count to 20 in Spanish. A teacher asks you to multiply 3/4 * 5/6 in Spanish & English. It will be easier for you to do in English.

That's b/c the English labels for numbers will have a stronger linguistic encoding for you than the Spanish analogs. Stronger encoding=better ability to hold items in memory. Better ability to hold items in memory=better ability to manipulate them (as in a verbal fraction task).

So, again, we need to do more educational advocacy for ESL & dialect speakers in the literacy domain. Luckily, we're gaining more awareness of how differences in language correlate w/ difference in mathematical performance. It's good if districts are trying to address this.

Again, I'm not sure if I agree w/ the framing in the document. I don't see "showing your work" as bad if it's used to help the student learn steps to solving a problem. At the same time, I think this shouldn't overly rely on language, certainly not at an evaluatory stage.

And I definitely don't think districts should be mocked for trying to see how whiteness, language, & the intersection of whiteness & language can inform all areas of instruction, learning, & evaluation.

Even small differences in language can correlate w/ diffs in working memory using the "standard language" which, in turn, can affect both overall performance as well as speed of performance, thus unjustly advantaging kids who speak the "standard" & disadvantaging those who do not

So, again, I think "showing your work," as I understand it, can be a good instructional tool, but is often misused. Like it's great if a kid does all the steps, gets one wrong, but then gets credit for the problem AND learns the missed step. That's not just how it's used though.

But that said, any district that is talking about addressing how the dominant culture (white) and language ("Standard" white English) can disadvantage students in not only literacy but other academic domains is actually on the right track, per empirical research.

And, to be clear, this isn't about *absolute* ability. No language/dialect is better than another. It's just that the education system is based on Standard (white) English, which is societally privileged due to racism.

If you're a speaker of a "Standard" dialect & your entire education was based in AAVE (a dialect that is just as equal in linguistic terms), you'd struggle. You'd struggle in literacy and you'd even struggle in math. It's not about your absolute "ability." It's about bias in ED.

A couple of people have rather pompously responded to this w/o actually reading or thinking about what I said. The responses are along the lines of "math is universal." I'm not talking about pure numeracy. I'm talking about *how* mathematics is taught & evaluated in school.

3/4 * 7/8 is a "universal" calculation. However it is not independent of language w/in instruction. How you teach it involves language. Word problems involve language. And, *verbal responses* using linguistic labels involve language (& memory!)

One other quick thing: strong determinism, such that language fully constrains perception, is not a thing (weaker forms are debated). But everyone who is saying "math" (as we know it) is universal is not technically correct. There are cultures w/ different numerical systems . . .

And although the answer to 3/4 * 7/8 is universal & would never vary, it is not true that this is a calculation where the symbol-numeric relationship is universal, nor are such computations universally used.