When New Math came to town in sixth grade they told me, to the extent that I could understand them, that you use arithmetic to find the answer and mathematics to demonstrate you know why.
Maybe you should ask them to show their work.
In general, I think there’s this popular semi-fallacy in the educational profession where people think that if students of color consistently do worse than white students at some type of assessment, it’s the assessment that is racist, rather than whatever educational disparities might be causing the performance gap. (I say “semi-fallacy” because it’s legitimately the case that the assessment can be the problem some of the time – for example, a test of reading skills where students with certain types of background knowledge will find most of the passages easier to comprehend than students without that knowledge.)
We have a natural bias toward changing the stuff we can change relatively easily, but often that’s not what actually needs to change. So, for example, you get colleges that go standardized-test-optional and pat themselves on the back for striking a blow for diversity, when addressing the actual problem – the factors that cause white and Asian students to score higher on such tests than students of other backgrounds – would be much harder and beyond the scope of any single institution.
So, this whole thing is FOX News “liberalz are dumb” outrage clickbait? I’ll pass.
The only other possible intelligent comment/instruction/question for the teacher to use here other than “Show your work” is “Did you cheat?”
This is unadulterated nonsense. It strikes me like the worship of Bloom’s taxonomy.
Hey, how are you supposed to know if you’re in the majority if you can’t do the math “correctly”?
That comment does make sense to me, as an area where there can be a bias built in.
If this treatise–too damn long to be called a pamphlet, IMHO–were to address stereotypes in the questions, I’d understand what they’re getting at and likely support it. What I’ve read thus far in that treatise and in this thread show me why those who wrote this treatise are wary of the written word.
Is there any evidence that this treatise is going to have any actual effect on Oregon’s math education. It’s an extremely silly manifesto, but can Demon Tree explain how this will actually effect Oregon math education? Show your work, Demon Tree.
Googling this doc I can find nothing but breathless screeds in The Daily Caller, The Epoch Times, The New York Post, etc. If I didn’t know better, I’d say this was a concern-trolling bad faith OP. But I know Demon Tree would never do that, so I await her detailed explanation of what she is worried about. (I assume she is an Oregon parent, for I can’t figure out why else she would care)
Ok, so I’ve read the document: I’m interested in teaching and have some background in teaching math.
Firstly, it says right up front:
This tool provides teachers an opportunity to examine their actions, beliefs, and values around teaching mathematics.
It’s not prescriptive, it’s not a curriculum or a methodology or even a ‘praxis’ 
It’s a tool for self examination.
Secondly, the meaning isn’t as bad as extracts from the text would suggest.
And thirdly, it is in itself an example of what it decries: a teaching tool that excludes people who don’t have the “correct” cultural and educational background and environment.
For reason number 3, I struggled to get through it … but I’m half forgiving, because it is such a good example of what they are talking about, and the exercise of parsing and mastering the document is such a good demonstration of the problem they are addressing.
Having struggled through the document, you are permitted to disagree with it (that’s part of the point), but actually there is nothing I could find to disagree with. The only danger I can see is that someone reading this, or reading about it, might completely miss the point – a danger that is possible because the point is somewhat hidden by the implied content and assumed cultural background.
For those of you who aren’t reading it and forming your own opinion, I think my summery is: you have to already know what they mean to make sense out of what they said.
To play devil’s advocate, because I’m not an expert by any means and am not positive I understand it, the logic of how “show your work” plays into a white-supremacist paradigm is as follows:
- The current power system is white supremacy (this is sort of the default starting point or you won’t get anywhere, so I’m not at all interested in debating this one).
- Systems of education rely heavily on the built-in inertia of the system of teaching itself, which was built and defined by that white-supremacist system.
- Specifically for math education these often rely on very regimented methods of demonstrating mathematical knowledge. These often go so far as to be an entirely separate language, which can be exceptionally difficult for students that don’t have strong English skills or a background that supports them learning this specialized language.
- When a student of color (or, really, any struggling student) fails to show their work using this particular language, they are judged as being “bad at math” (or, as mentioned above, as cheating). It’s entirely possible they actually do understand how to manipulate the numbers to get the correct answer (or at least close to it) but their lack of background in the language of expressing it cripples their learning.
Finally, since those students most likely to struggle are those without the background necessary to know the specialized language of mathematics, it perpetuates the cycle of “white/Asian kids are good at math, black kids aren’t”.
I don’t entirely buy it, but since the workshop is basically just asking teachers to examine themselves and their modes of teaching to attempt to identify areas where maybe they are not communicating to their entire class by locking themselves into particular methods I see absolutely no reason to get worked up about it. Unless, of course, you are into that sort of thing (or are interested in getting lots of click-though ad revenue, I suppose…).
I’m pretty sure the framing of “white supremacy” is unhelpful at this point, and wish advocacy groups would focus on alternative methods and inclusive teaching styles rather than relying on rhetoric that is guaranteed to inflame at least some of their potential audience.
Indeed. I appreciate and still think about a post that @Left_Hand_of_Dorkness made a few years ago:
Yup, this is a good point. A huge part of bad math teaching is the incorrect assumption that math is somehow independent of language, so if you’re not doing math successfully in the prescribed way, it must be because you’re bad at math.
So the students who struggle with understanding English, or who are insecure about their written English ability so they write down as little as they can, make mistakes in prescribed procedures and thus get labeled “bad at math”.
Yeah, I think there’s no question that a lot of the advice about rethinking the structure of math presentation and focusing on more thoughtful approaches would be helpful in producing more effective math education for students of all races. Emphasizing racial issues in math pedagogy reform undoubtedly reinforces the lazy stereotype that non-white students need “dumbed-down” math.
To be fair, though, in a historically and persistently racist society, whenever anything is presented in a thoughtlessly traditional way, it tends to perpetuate ideas of white people as the “default human beings”. How many non-white people were ever distinctly visible in 20th-century math textbooks, as authors, as mentioned historical figures, as characters in word problems, as anything? So while I see a lot of potential problems with this particular workbook approach, I also see where the authors are coming from.
All the teachers agreed the Lehrer kid was a real PIA.
Hah! Glad I made an impression.
Now that I’m specifically working with “gifted” kids, I can teach some more advanced mental math lessons, like how to solve 673-297 mentally (hint: 673-300+3). But after a student wrote on a test, under the “show your work” section, “I did it in my head like Mr. Dorkness taught me to,” I made a whole slide show about proving your work and the importance of doing so.
It’s fine to know mental math strategies, and indeed if you don’t eventually memorize your basic facts you’re gonna run into real troubles with later math. But you should always be able to prove your answer.
Having skimmed that document…meh. I’m pretty unconvinced.
Emphasis on getting the right answer can be kinda fucked up, of course, because (and this may be a shocker) I as the teacher already know the right answer, and I don’t need my students to tell me. My goal isn’t for them to get the right answer in my class, it’s for them to know how to find the answer to similar problems when they’re no longer in my class. What’s in their head–the concepts, the tricks, the reasoning–is the goal, not the scribbles on the page. But I’m not sure that’s what they mean, and I’m not sure calling it “white supremacy” really gets to the heart of the problem.
Same thing with “showing your work.” This shows up on standardized tests with problems like this:
“347 students attended the football game. 169 of these students later tested positive for COVID-19. Which of the following number lines could Principal Skinner use to determine how many of these students did not test positive for COVID-19?”
where you must demonstrate knowledge of specific methods for showing work, rather than showing the ability to reason conceptually toward an answer.
But the idea that a teacher asking students to show work is relying on a crutch? Not seeing it.
Now that I think about it, don’t students have to show their work in other classes as well? When I wrote a persuasive essay in English class I couldn’t just hand in a paper with two or three sentences for a conclusion I had to include paragraphs that supported it. Whenever we did an experiment in science, I had to show the teacher I had a working hypothesis, how I tested it, and how I analyzed the data to come up with the results. As an undergraduate and a graduate student in history, if I made a statement about something without backing it up the instructor would usually ask, “Why do you think that?” When I wrote a paper I had to demonstrate where I found this information I based my interpretation on.
Showing your work is important even once you leave the hallowed halls of our educational centers and suckle on the capitalist teat of corporate America. If I tell my VP one of the reasons the turnover among our programmers is so high because we don’t pay less than the prevailing wage he’s going to want to know where I got my data. If I tell him that management is ready to see a loosening of our dress code he’s going to want to see some concrete reasons behind my opinion before he agrees to change policy.
Fortunately, they’ve shown their work, and when you read the previous paragraph, and the next paragraph, you understand that their objection is to replacing education with ‘showing your work’, as if ‘showing your work’ was the purpose of math classes. And the statement about crutches does not say that ‘showing your work’ is always or even often a crutch: it just suggests that it can be used that way. Like an axe. Or a shopping trolley.
And, most important of all, the actual learning point is that there are alternative methods of showing your work, which invites the reflection that active observing / listening is part of being a good teacher.
Because this is a document focusing on the teacher.
I’m not sure what makes it “paternalism”. When I see things like this, I wonder whether social justice types just randomly open a page in the dictionary and blindly point to a word on the page to form their objections. It would make about as much sense.
Personally, I don’t object to teachers using crutches, and I don’t think any other teacher would either. For most of us, anything that helps the teaching is valid. But when doing self-reflection, a teacher should think about the place of the crutch in the classroom, and if it is helping or hindering.