Teaching Math Students to show their work and seek right answers = White Supremacy?!!

[Condessa]

The Oregon Department of Education is promoting this course for math teachers:

https://equitablemath.org/?utm_medium=email&utm_source=govdelivery

https://content.govdelivery.com/accounts/ORED/bulletins/2bfbb9b

 

Quote from 'Dismantling Racism in Mathematics Instruction' download for the course:  "White supremacy culture shows up in math classrooms when... the focus is on getting the “right” answer. The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so. Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict." p.65

 

[Not_a_Number]

31 minutes ago, Condessa said:

The Oregon Department of Education is promoting this course for math teachers:

https://equitablemath.org/?utm_medium=email&utm_source=govdelivery

https://content.govdelivery.com/accounts/ORED/bulletins/2bfbb9b

 

Quote from 'Dismantling Racism in Mathematics Instruction' download for the course:  "White supremacy culture shows up in math classrooms when... the focus is on getting the “right” answer. The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so. Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict." p.65

 

Oh gosh. This kind of nonsense. Like math teachers aren’t already bad enough in math on average.

I’m not even going to click on that, since it’ll raise my blood pressure.

[ieta_cassiopeia]

Mathematics is supposed to be objective, that's much of the point.

Teaching that there are multiple solutions to some types of mathematical questions (primarily in mathematical investigations) is important. As is teaching the underlying assumptions behind subjective statements about maths which are presented as objective (practical statistics in everyday life is full of this). However, the foundation of symbolic maths is that the proposition 1 + 1 = 2 is equally true regardless of who's looking at it (Alfred North Whitehead and Bertrand Russell spent 2 books of the Prinicipia Mathematica proving it).

Given that one of the authors quoted about the other that, "After some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica was an Indo-European one", perhaps I can be a little more sympathetic with the Oregon Department of Education apparently not being aware of this. Only a little...

Edited February 14, 2021 by ieta_cassiopeia
Inconsistent italicisation

[Hillcottagemom]

I'm not sure that the course would really be all that alarming. Reading between the lines, they're suggesting that the focus of math instruction should be on the process rather than the result. I doubt anyone is suggesting that the results don't matter. Math isn't purely objective. There isn't always a right or wrong answer. It also looks like they're focusing on promoting deeper understanding and, in my limited experience, that usually does mean focusing on the hows and whys more than on getting that answer down. Overall, I'm encouraged to see that districts are thinking about these issues to address math disparities between white and minority students. 

[Not_a_Number]

5 minutes ago, Hillcottagemom said:

I'm not sure that the course would really be all that alarming. Reading between the lines, they're suggesting that the focus of math instruction should be on the process rather than the result. I doubt anyone is suggesting that the results don't matter. Math isn't purely objective. There isn't always a right or wrong answer. It also looks like they're focusing on promoting deeper understanding and, in my limited experience, that usually does mean focusing on the hows and whys more than on getting that answer down. Overall, I'm encouraged to see that districts are thinking about these issues to address math disparities between white and minority students. 

Yeah... I dunno. This seems bizarre: 

 

White supremacy culture shows up in math classrooms when... Students are required to “show their work.” Instead... Math teachers ask students to show work so that teachers know what students are thinking, but that centers the teacher’s need to understand rather than student learning. It becomes a crutch for teachers seeking to understand what students are thinking and less of a tool for students in learning how to process. Thus, requiring students to show their work reinforces worship of the written word as well as paternalism.

 

You know what's REALLY paternalistic? Deciding that kids don't need basic skills like "how to show their work." I agree that whenever possible, you should make sure to give kids lots of avenues to explain their ideas. However, the ability to WRITE DOWN your ideas is incredibly useful in one's studies. One should certainly teach it. 

Edited February 14, 2021 by Not_a_Number

[Condessa]

1 hour ago, Hillcottagemom said:

I'm not sure that the course would really be all that alarming. Reading between the lines, they're suggesting that the focus of math instruction should be on the process rather than the result. I doubt anyone is suggesting that the results don't matter. Math isn't purely objective. There isn't always a right or wrong answer. . .

The author has certain key words/phrases that he refers to over and over again as fundamental to white supremacy culture.  One is 'objectivity'--not the suggestion that math is always purely objective, but the idea of objectivity itself.  You can see it in the quote in my first post.  "Upholding the idea that there are always right and wrong answers perpetuate objectivity".  Some other examples of these key words are 'defensiveness', 'perfectionism', 'fear of open conflict', 'individualism', 'paternalism', 'right to comfort', and 'worship of the written word'.

Edited February 15, 2021 by Condessa

[Lucy the Valiant]

1 hour ago, Not_a_Number said:

Yeah... I dunno. This seems bizarre: 

 

White supremacy culture shows up in math classrooms when... Students are required to “show their work.” Instead... Math teachers ask students to show work so that teachers know what students are thinking, but that centers the teacher’s need to understand rather than student learning. It becomes a crutch for teachers seeking to understand what students are thinking and less of a tool for students in learning how to process. Thus, requiring students to show their work reinforces worship of the written word as well as paternalism.

 

You know what's REALLY paternalistic? Deciding that kids don't need basic skills like "how to show their work." I agree that whenever possible, you should make sure to give kids lots of avenues to explain their ideas. However, the ability to WRITE DOWN your ideas is incredibly useful in one's studies. One should certainly teach it. 

Spoken (written) by someone who obviously hasn't spent much time with real live actual middle-level / teen-age kids who "suddenly" and miraculously "get it" when required to logically demonstrate step-by-step mathematical thinking. 

No, dear Oregon DOE, that is not white supremacy. 

[Condessa]

1 hour ago, Hillcottagemom said:

Overall, I'm encouraged to see that districts are thinking about these issues to address math disparities between white and minority students. 

I did think it sounded like it could be a positive thing, until I actually read what's in it.  I don't see anything encouraging in math educators being taught that they are perpetuating white supremacy by correcting their students' work, focusing on having them able to do the work independently and answer correctly, and having students show their work.

[Condessa]

Another quote: "Teachers often treat mistakes as problems by equating them with wrongness, rather than treating them opportunities for learning—which reinforces the ideas of perfectionism (that students shouldn’t make mistakes) and paternalism (teachers or other experts can and should correct mistakes)."  (emphasis added)

[Not_a_Number]

16 minutes ago, Condessa said:

I did think it sounded like it could be a positive thing, until I actually read what's in it.  I don't see anything encouraging in math educators being taught that they are perpetuating white supremacy by correcting their students' work, focusing on having them able to do the work independently and answer correctly, and having students show their work.

And again, this attitude is incredibly condescending. For some kids, education IS their way out of poverty. By not teaching kids important subjects and not teaching them how to learn, you remove that option from them 😕 . 

I'm all for being tolerant and inclusive in the classroom. And for making sure to include examples and names from a variety of cultures. And for making sure to include both genders. And for letting kids demonstrate knowledge verbally when they are having writing difficulties. 

But in my opinion, this document is written by someone who doesn't know any math. 

Edited February 15, 2021 by Not_a_Number

[daijobu]

Ah, if only I knew to call this racism back in the 1980s.  These are my actual corrected test papers from high school.  It still stings, lol, but it got me in to Stanford.    

List of my favorite feedback:

"Arithmetic!"

"NO!!"

"What???"

"Yuk!"

"Think about it!"

"Look at the picture!!!!"

And the always helpful:

" !!! "  

Little did I know this feedback in high school would pale in comparison to college when I encountered such gems as "And the rest is trivial!"  

ETA:  Or maybe I should call this paternalism?  After all, my math teacher was male.

Edited February 15, 2021 by daijobu

[Clemsondana]

One of the more disorienting things that happened when I was volunteering is when checked a student's homework, found a systemic mistake that caused them to miss several problems (some sort of regrouping error), sat to explain the mistake, and had a student say that he was correct and I was doing 'white people math'.  We found one of the paid workers, most of whom were black college students and all of whom could do arithmetic, and he told the student that all of the adults could do math and all of us would get the same answer.  The student not knowing how to do the problems was OK - they were making a predictable, age-appropriate mistake - but I don't know what they were thinking.  It could have just been a way of saying 'I don't want to redo my math' but I wondered if they really did think that the black, white, and hispanic students in the class were all getting different answers.  

[mom2scouts]

18 hours ago, Condessa said:

Another quote: "Teachers often treat mistakes as problems by equating them with wrongness, rather than treating them opportunities for learning—which reinforces the ideas of perfectionism (that students shouldn’t make mistakes) and paternalism (teachers or other experts can and should correct mistakes)."  (emphasis added)

In some professions, math mistakes really are problems and are not only wrong, but they can cause people to DIE and professionals to lose their license forever. I don't want to drive over a bridge or go into a high rise building designed by an architect or engineer who doesn't think mistakes are a problem. Yes, students learn by making mistakes and working to correct them, but at some point they need to learn how to get the correct answer and it's not uncommon for those who are experts to have other experts check their work. I'll take the perfectionist engineer any day!

[EKS]

For people interested in the origins of this sort of thing, I highly recommend reading the book Cynical Theories.  

[Roadrunner]

I am afraid to speak up now. Nobody wants to debate, just call you racist and privileged. 
Do you know what I call racist? Believing brown people need different gloves for math. 

[Not_a_Number]

4 hours ago, EKS said:

For people interested in the origins of this sort of thing, I highly recommend reading the book Cynical Theories.  

Oooh, poking around, I see the author was involved in the next iteration of this: 

https://en.wikipedia.org/wiki/Sokal_affair

I've always approved of this hoax, lol. 

[EKS]

7 minutes ago, Not_a_Number said:

Oooh, poking around, I see the author was involved in the next iteration of this: 

https://en.wikipedia.org/wiki/Sokal_affair

I've always approved of this hoax, lol. 

Those are the folks!  

[EKS]

21 minutes ago, Roadrunner said:

I am afraid to speak up now. Nobody wants to debate, just call you racist and privileged. 
Do you know what I call racist? Believing brown people need different gloves for math. 

Here's an article that speaks to this issue.

[Roadrunner]

5 minutes ago, EKS said:

Here's an article that speaks to this issue.

Thanks. I will read it. 

[Not_a_Number]

22 minutes ago, EKS said:

Here's an article that speaks to this issue.

These are hard conversations, because they inevitably get coopted by actual racists. 

I really have no right to speak on this subject, although I occasionally speak on subjects I do have a right to speak about, such as the complicated issue of the number of women in the hard sciences, and whether that's related to nature or nurture. My answer is that it's both. But as soon as someone who is NOT a woman in the hard sciences says that, someone will inevitably latch on to it as a reason that we don't need to do anything to make the hard sciences more welcoming to women, which isn't at all what one wants. 

Edited February 16, 2021 by Not_a_Number

[EKS]

28 minutes ago, Not_a_Number said:

These are hard conversations, because they inevitably get coopted by actual racists. 

Just to be clear, the article wasn't written by an actual racist.

29 minutes ago, Not_a_Number said:

I really have no right to speak on this subject, although I occasionally speak on subjects I do have a right to speak about, such as the complicated issue of the number of women in the hard sciences, and whether that's related to nature or nurture. My answer is that it's both. But as soon as someone who is NOT a woman in the hard sciences says that, someone will inevitably latch on to it as a reason that we don't need to do anything to make the hard sciences more welcoming to women, which isn't at all what one wants.

I have some very non-PC opinions about the reasons there are fewer women in STEM. 

[Noreen Claire]

Speaking as someone who has taught math at a highschool that was 85% children of color (predominantly Hispanic) and who is now teaching at a (noncompetitive, small) University that is significantly more diverse than the state as a whole... I think that workbook is fabulous. Thanks for linking to it - I have forwarded it to my department chair and plan on working through it as best I can. 

[Not_a_Number]

17 minutes ago, EKS said:

Just to be clear, the article wasn't written by an actual racist.

Oh, I know. But they always do get coopted. 

 

17 minutes ago, EKS said:

I have some very non-PC opinions about the reasons there are fewer women in STEM. 

You can PM them to me if you like 🙂 . Having watched how mathy girls get treated from the perspective of a mother of such a girl, my opinions have swung further towards nurture than they had been when I was younger. 

[Not_a_Number]

13 minutes ago, Noreen Claire said:

Speaking as someone who has taught math at a highschool that was 85% children of color (predominantly Hispanic) and who is now teaching at a (noncompetitive, small) University that is significantly more diverse than the state as a whole... I think that workbook is fabulous. Thanks for linking to it - I have forwarded it to my department chair and plan on working through it as best I can. 

So... I'm curious. What appeals about it? 

[Roadrunner]

The best advice I got when my kids were starting K is not to put down on application that any language other than English was spoken around children. 
If anybody were to offer my kids a different math workbook due to their status (skin or immigrant), I would probably lose it right on the spot. 

 

Conversations are worth having. Silence resolves very little. 

[Not_a_Number]

Just now, Roadrunner said:

Conversations are worth having. Silence resolves very little. 

Yeah, but I think the conversations need to involve the affected communities. I don't feel super comfortable with a bunch of people for whom this is academic spouting off. In the same way that I kind of don't want to hear a group of non-Jews talk about all the "cultural issues" that Jewish people have. They may even be right, and I may even agree with them, but I kind of don't care -- it would bother me. 

[Roadrunner]

1 minute ago, Not_a_Number said:

Yeah, but I think the conversations need to involve the affected communities. I don't feel super comfortable with a bunch of people for whom this is academic spouting off. In the same way that I kind of don't want to hear a group of non-Jews talk about all the "cultural issues" that Jewish people have. They may even be right, and I may even agree with them, but I kind of don't care -- it would bother me. 

We are talking about math on educational forum. 

[Not_a_Number]

Just now, Roadrunner said:

We are talking about math on educational forum. 

Oh, sure, that I'm fine talking about. I'm also happy to talk about women in STEM, lol. That's not what I mean. 

[daijobu]

There was a related article just published in the NYT last week.  

https://www.nytimes.com/2021/02/09/world/europe/france-threat-american-universities.html

Will American Ideas Tear France Apart? Some of Its Leaders Think So
Politicians and prominent intellectuals say social theories from the United States on race, gender and post-colonialism are a threat to French identity and the French republic.

[Noreen Claire]

28 minutes ago, Not_a_Number said:

So... I'm curious. What appeals about it? 

First - from the quick read through that I did, I think that the ways to reflect and engage with the way we (I) currently teach math, and the example ways to re-center, re-focus, and improve my instruction would benefit every student in my classroom.

Second - It was written by a group entirely made up of BIPOC math educators, and I respect and value their experience as math students and math teachers and their unique insights that can help me improve my own teaching (as a white woman who went to private, nearly-white-only schools k-12).

I teach at a school that does not value mathematics at all - they just eliminated the math major! - and the students who I have in my (remedial) college math classes do not enjoy math. They see it as a set of rules, disconnected from their life, that you have to follow to get an answer. They have no interest in learning math for math's sake, or for wanting to explore concepts for understanding. They want me to tell them how to do the thing to get the answer. Saints forbid I provide a problem with multiple paths or no ready solution! I once put a quadratic equation on the board and proceeded to solve it four different ways (graphing, factoring, completing the square, and quadratic formula). When I was done, the only questions was "which was the right way?" The recommendations that I saw in that workbook were about relating math to students' lives, centering the learner rather than the teacher,  and teaching students to think of math as the journey, rather than the map. It all looked good to me.

[Not_a_Number]

On 2/15/2021 at 10:37 PM, Noreen Claire said:

The recommendations that I saw in that workbook were about relating math to students' lives, centering the learner rather than the teacher,  and teaching students to think of math as the journey, rather than the map. It all looked good to me.

I think it's both, though. I don't think it's reasonable to say it's only the journey. 

 

On 2/15/2021 at 10:37 PM, Noreen Claire said:

I teach at a school that does not value mathematics at all - they just eliminated the math major! - and the students who I have in my (remedial) college math classes do not enjoy math. They see it as a set of rules, disconnected from their life, that you have to follow to get an answer. They have no interest in learning math for math's sake, or for wanting to explore concepts for understanding. They want me to tell them how to do the thing to get the answer. Saints forbid I provide a problem with multiple paths or no ready solution!

Having taught a wide range of kids... this is a pretty pervasive problem even in schools that aren't largely full of minority kids. And I do think it's related to how we teach math. We don't teach math as if it relates to life, and so people don't think it does. And we don't teach math so that it's knowable, and then it seems like it's not. 

I already teach math in a discovery fashion that tries really hard to make it accessible to kids. However, sometimes I do need to have kids show their work. And sometimes, I need to be able to tell them that they got the wrong answer. This course seems to be throwing out the baby with the bathwater to me. 

Edited February 19, 2021 by Not_a_Number

[Noreen Claire]

9 hours ago, Not_a_Number said:

However, sometimes I do need to have kids show their work. And sometimes, I need to be able to tell them that they got the wrong answer. This course seems to be throwing up the baby with the bathwater to me. 

The document doesn't say that you cannot require students to show work or cannot tell students that their answers are wrong. It says that you should not center your class on ONLY written work, and you should not focus on ONLY what they got wrong. It asks the teacher to think about other ways that students can express their knowledge or methods of solving problems (I do this with my own DS11, who refuses to write out solutions). It asks teachers to think about ways we can engage what is correct with student work, rather than what is wrong with it. I think that these are good ideas, and it is likely that you are already doing them to some extent (I am definitely trying and struggling in my time-limited asynchronous/synchronous virtual courses).

...I say this gently to anyone who would read thought the document and react with "This is how I learned/do/teach math. They are calling me a white supremacist and a racist!" that this is most definitely NOT what the authors are doing. They are merely suggesting ways that the 'sage on a stage" and other traditional methods of teaching mathematics have become very teacher-centered, and do a disservice to our students, and a significant disservice to our populations of minority students. It merely asks for a re-framing of math to be about the learner and not the teacher. If the same recommendations were presented, without the references to 'paternalism', 'white supremacy', etc, would we be more likely to see them as the basis of good teaching?

With that, I'm out.

 

[Not_a_Number]

1 minute ago, Noreen Claire said:

If the same recommendations were presented, without the references to 'paternalism', 'white supremacy', etc, would we be more likely to see them as the basis of good teaching?

If the same recommendations were presented without references to white supremacy, it would be a much less loaded document. Also, it's one thing to say "you shouldn't use written work as the only way of evaluating your students" and another to say "when you ask kids to show their work, you're exhibiting white supremacy." I'm not trying to make a pun here, but the latter is much black and white. It doesn't only suggest that written work shouldn't be the only means of evaluating kids. It suggests that using written work is bad. 

 

4 minutes ago, Noreen Claire said:

t says that you should not center your class on ONLY written work, and you should not focus on ONLY what they got wrong.

Does it, in fact, say that? Because that's not what I'm reading. 

 

I'm not mostly reacting to the "racism" phrasing here, for the record. This also reminds me of the Jo Boaler thing in the Bay Area, where they've decided that math isn't about the right answers, tests are bad, and teamwork is the best possible way to learn mathematics. They've then implemented this in lots of Bay Area public schools without first testing it much... and of course, given the ethos of the movement, you really CAN'T test it, given that tests are supposed to be an invalid way to figure out how much students know. And reviews have been decidedly mixed. For instance, as anyone who's gone to school may have told you, sometimes teamwork doesn't result in beautiful cooperative learning. Often, it results in the most advanced kids in the group doing the work and feeling resentful, while others goof off. 

But anyway, I'm not at all convinced that this is what we need to fix inequitable math instruction. I do 100% believe that math needs to be learner-centered, but I don't think making "right answers" and "proficiency" less important is what makes math actually feel meaningful to kids. What makes math feeling meaningful to kids, in my experience, is feeling like they can understand it and feeling like it relates to their lives. And often, the right way to make math comprehensible is to allow an expert to communicate ways of thinking about it. 

I'd love to see better schools in minority communities. And better teachers. And better mental health supports, so that there was a way to deal with disruptive kids. I love math and think that access needs to be more equitable. I just don't think this would fix anything. 

[Dmmetler]

11 hours ago, Noreen Claire said:

First - from the quick read through that I did, I think that the ways to reflect and engage with the way we (I) currently teach math, and the example ways to re-center, re-focus, and improve my instruction would benefit every student in my classroom.

Second - It was written by a group entirely made up of BIPOC math educators, and I respect and value their experience as math students and math teachers and their unique insights that can help me improve my own teaching (as a white woman who went to private, nearly-white-only schools k-12).

I teach at a school that does not value mathematics at all - they just eliminated the math major! - and the students who I have in my (remedial) college math classes do not enjoy math. They see it as a set of rules, disconnected from their life, that you have to follow to get an answer. They have no interest in learning math for math's sake, or for wanting to explore concepts for understanding. They want me to tell them how to do the thing to get the answer. Saints forbid I provide a problem with multiple paths or no ready solution! I once put a quadratic equation on the board and proceeded to solve it four different ways (graphing, factoring, completing the square, and quadratic formula). When I was done, the only questions was "which was the right way?" The recommendations that I saw in that workbook were about relating math to students' lives, centering the learner rather than the teacher,  and teaching students to think of math as the journey, rather than the map. It all looked good to me.

FWIW, this was what the math course L did that focused on teaching math went through, and a big part of common core as well. It wasn’t focused on “minority students need to learn in different ways”, but on there are different approaches to learn how math works. 
 

I chose to send S, who really struggles with math, to the same class, not because S has any chance of teaching math, but because they needed to learn it, and of the options that would fulfill the math requirement, it seemed the most likely to actually lead to understanding as opposed to learning what buttons to push to get the right answer. 

[Drama Llama]

On 2/14/2021 at 6:23 PM, Not_a_Number said:

Yeah... I dunno. This seems bizarre: 

 

White supremacy culture shows up in math classrooms when... Students are required to “show their work.” Instead... Math teachers ask students to show work so that teachers know what students are thinking, but that centers the teacher’s need to understand rather than student learning. It becomes a crutch for teachers seeking to understand what students are thinking and less of a tool for students in learning how to process. Thus, requiring students to show their work reinforces worship of the written word as well as paternalism.

 

You know what's REALLY paternalistic? Deciding that kids don't need basic skills like "how to show their work." I agree that whenever possible, you should make sure to give kids lots of avenues to explain their ideas. However, the ability to WRITE DOWN your ideas is incredibly useful in one's studies. One should certainly teach it. 

Did you read the whole document?

I haven't finished reading it, so I'm hesitant to comment, but I'll say that for me, as a math teacher working in a high poverty school with majority BIPOC students, there's been a lot so far that's resonated.  I'll come back when I've read the whole thing.  

 

[Not_a_Number]

Just now, BaseballandHockey said:

Did you read the whole document?

I haven't finished reading it, so I'm hesitant to comment, but I'll say that for me, as a math teacher working in a high poverty school with majority BIPOC students, there's been a lot so far that's resonated.  I'll come back when I've read the whole thing.  

I haven't read the whole document, no, but I didn't scan it for outrageous quotes, either. I just skimmed it and took down something that seemed representative. 

For the record, I've seen this approach before. I think its heart is in the right place, in some sense, but like many proposed things that are supposed to fix inequality, I don't think it's the answer. 

[Not_a_Number]

I'm reading through more of it, and if you strip out the anti-racist terminology, it sounds a lot like Jo Boaler's stuff, complete with being against "tracking." 

I don't want to know what they'd think about my Zoom classes, where each kids does their own work depending on what they are working on 😉 . Of course, given that one of my kids can't multiply yet and one of my kids is working on high school algebra, and the other kids are at various stages in between, I'm not really sure what else I'm supposed to do. Maybe have them all do teamwork, I don't know. (And in fact, we do all play the same games together, and we incorporate working together. But yes, I track.) 

Edited February 16, 2021 by Not_a_Number

[Drama Llama]

2 minutes ago, Not_a_Number said:

I haven't read the whole document, no, but I didn't scan it for outrageous quotes, either. I just skimmed it and took down something that seemed representative. 

For the record, I've seen this approach before. I think its heart is in the right place, in some sense, but like many proposed things that are supposed to fix inequality, I don't think it's the answer. 

So, right after the text you linked, it gave the example of a better task, which would be to ask a kid the following:

"If you were working with a fellow mathematician who was absent this day, what might you tell them to help them learn it?"

Do you think that's a worse question to ask?  To me it's better.  

The comment about asking kids to "show their work" resonated with me.  It's a concern that I've had for a while, and I thought they laid out the problem well.  As a math teacher, both at school and at home, I'm pretty passionate about getting kids talking and writing about math.  But I can also tell you that my students, at home and at school, always do better when things are presented in a context that is meaningful to them, and that this is particularly true of my high school students who have experienced marginalization at school.

Showing your work, so that you get a good grade, isn't a context that makes sense to a lot of my students. 

Writing while you're working, so that your thinking is more organized and you get the answer you need.

Writing about your work, so you can help someone else learn to do the same thing.

Documenting your work, so that you can defend it if someone challenges it.

Those are contexts that make a lot more sense. 

I could go on, but I'm at work.  I can justify reading the document as "work", because it's directly related to what I do, but it's hard to justify posting here. 

[EKS]

1 minute ago, BaseballandHockey said:

"If you were working with a fellow mathematician who was absent this day, what might you tell them to help them learn it?"

As an aside, I can't stand the trend toward calling students "mathematicians" or "scientists" or "historians" or whatever.

Mathematicians, scientists, and historians are experts.  Students are novices.  The way experts think is fundamentally different from the way novices think.  It denigrates expertise to insinuate that a novice is in any way similar to an expert.  I believe that this trend in education is one of several that has contributed to things like the widespread science denial we're seeing in our society.

[Clemsondana]

Is 'Show your work to get a good grade' a thing that is commonly said?  I tell my kids 'Show your work so that if there's a mistake it's easy to find' and 'Show your work so that I can see what you DO know even if you don't know how to do it all'.  

The show your work thing is fascinating because I had a college prof who wouldn't help unless you had something written down.  It could be a drawing, a list, an equation, anything to show that you had started on the question/problem.  I thought he was nuts until I realized how often just getting something down on paper led me most of the way towards an answer, and if I went off the rails somewhere then it was easy enough for him to see what the problem was.  I'm not exaggerating when I say that it changed how I do any difficult academics - reading papers, how I planned experiments and made models back when I was in the lab, how I approach math that I've forgotten when I need to help my kids - so I'm intrigued at the idea of helping kids by giving the exact opposite advice.  

[Not_a_Number]

38 minutes ago, BaseballandHockey said:

So, right after the text you linked, it gave the example of a better task, which would be to ask a kid the following:

"If you were working with a fellow mathematician who was absent this day, what might you tell them to help them learn it?"

Do you think that's a worse question to ask?  To me it's better.  

Is that a worse question to ask asking them to show their work? It really depends on the task. If it's on a test, I would be requesting them to show their work so I can evaluate what they know. If they are working out things themselves, I tend to only ask them to write down whatever they need to to keep track of what they are doing, but then I've so far worked with young kids who find writing things down arduous. I do find that asking kids to write down MORE than they personally need to follow the logic is not very effective. 

At least with the age groups I've worked with in person, asking kids to imagine how to teach a non-existent person is a very difficult and time-consuming task, so I personally don't go with that angle. I do like to have kids explain things to each other occasionally, especially in situations in which that's possible without making some kids feel bad, slow, or left out. 

Again, I already teach mathematics as a living subject that's supposed to be related to their life. I have no qualms at all about that aspect. 

[Not_a_Number]

31 minutes ago, Clemsondana said:

The show your work thing is fascinating because I had a college prof who wouldn't help unless you had something written down.  It could be a drawing, a list, an equation, anything to show that you had started on the question/problem.  I thought he was nuts until I realized how often just getting something down on paper led me most of the way towards an answer, and if I went off the rails somewhere then it was easy enough for him to see what the problem was. 

I do think that being taught to write something down can ward away the "tyranny of the blank page." So I think it's useful advice. 

The most common advice I give to kids whose problem-solving I am troubleshooting is to try some examples. (This is usually for kids who are past the elementary curriculum.) About 90% of the time, if the kids are willing to follow the trail of the examples, they'll find a more general answer. I think that's a related piece of advice: even if you don't know where to start, if you try some stuff, you get some ideas and get less intimidated 🙂 . 

Edited February 16, 2021 by Not_a_Number

[Not_a_Number]

I'm going to copy and paste a whole page, to demonstrate how I'm feeling about the whole thing. 

 

Quote

White supremacy culture shows up in math classrooms when...

Teachers enculturated in the USA teach mathematics the way they learned it.

Instead... This reinforces the idea that there is only one right way to do math. The history of mathematics, its colonization, and what is deemed as “acceptable” knowledge is rich and complex, therefore, the way that mathematics is taught in the United States needs to be interrogated because it currently centers Western, Eurocentric ways of processing and knowing information. When students are required to learn in this way, they either have to unlearn their learned native traditions to meet teacher expectations, or they are deprived of learning math in their ancestral history. For teachers, teaching the way they learned also reinforces the right to comfort for teachers because to conform is easier than to challenge themselves to teach math differently. Incorporate the history of mathematics into lessons.

This is a weird mishmash. It's basically impossible to learn math that doesn't tell you that 2+2 = 4 or that 16 + 18 = 34. There might be different methods for calculations, but ultimately, you're supposed to get the same answer however you do it. You could argue there are lots of artifacts of our civilization in our mathematics (the operations; how we write numbers; the equals sign; etc), but I would argue that NOT teaching those conventions is not going to serve the students well. 

 

Quote

• Verbal Example: Why do you think we call it Pythagorean’s theorem, when it was used before he was even born? What should we call it instead?

Well, "Pythagorean's theorem" is ungrammatical, so don't call it that. It's either "the Pythagorean theorem" or "Pythagoras' theorem." 

As for what we should call it, we should call it one of the names above, or no one will know what you're talking about. However, I think talking about the history of the theorem is fascinating and talking about how mathematical truths keep being rediscovered in different cultures is a great venue for inclusivity and cultural exploration. 

 

Quote

• Classroom Activity: Learn about different bases and numerical ideas: Base 2, binary and connections to computer programming, how the Yoruba of Nigeria used base 20, and how the Mayans conceptualized the number 0 before the first recording of it.

Excellent idea. Binary is a wonderful enrichment topic (although why it's listed separately from base 2, as if it's a different topic, I don't know.) Yes, do this, and tie this to other cultures. 

 

Quote

• Professional Development: Learn the history of mathematics. Take a course, go to a conference, read historically and culturally accurate books, and use the resources in this workbook. Focus on different approaches to learning concepts.

Sure. That sounds absolutely great. People should do that! 

 

So, for me, this is a bizarre mix of ideas that sound ridiculous and ideas that sound great. But I certainly can't recommend these suggestions without reservation. 

Edited February 16, 2021 by Not_a_Number

[Roadrunner]

13 minutes ago, Not_a_Number said:

 

White supremacy culture shows up in math classrooms when...

Teachers enculturated in the USA teach mathematics the way they learned it.

Instead... This reinforces the idea that there is only one right way to do math. The history of mathematics, its colonization, and what is deemed as “acceptable” knowledge is rich and complex, therefore, the way that mathematics is taught in the United States needs to be interrogated because it currently centers Western, Eurocentric ways of processing and knowing information. When students are required to learn in this way, they either have to unlearn their learned native traditions to meet teacher expectations, or they are deprived of learning math in their ancestral history. For teachers, teaching the way they learned also reinforces the right to comfort for teachers because to conform is easier than to challenge themselves to teach math differently. Incorporate the history of mathematics into lessons.

(Not directed at you. Just using this quote). So what happens when somebody walks inside a classroom with this ideology? Do they scan a classroom for color and ethnicity and start to make assumptions that some children need to be taught math differently? 
 

I think debating how best to teach mathematics is a worthwhile endeavor. I think debating how best to teach when certain learning issues are present is another worthwhile endeavor. But assuming my brown kid needs to be taught differently because of his ethnicity is unacceptable. 

[daijobu]

I skimmed over the paper, and my thought was that if a teacher is going to entertain students who arrive at alternative methods or algorithms or even different answers in a way that respects the student, then that teacher needs to be fully 100% confident in their mathematics.  

Too often, teachers see the work written by a student, and it isn't the way the teacher taught it, so the student is counted wrong.  Only with a strong understanding of mathematics can the teacher read and understand where the student was waylaid can they point out what the student got right or find something positive to say about the approach.  

I think in order to implement these principles, teachers need to be better trained in mathematics.  How many teachers can explain other bases, like 12 or binary, let alone base 10?  I think the number of teachers who understand base 10 is very small.    

[daijobu]

This document reminded my DH about his experience in high school chemistry.  The teacher presented some weird way to balance chemical equations that the students weren't understanding.  DH came up with his own algorithm which was easier to understand and implement.  The other students basically told the teacher "I'm going to use DH's way!"  The teacher responded that if they got the wrong answer, he would not award partial because he didn't understand DH's method.  

If the teacher had a strong enough background in chemistry, he could have at least attempted to understand the other method.  

We have poor STEM teachers who are incapable of this flexibility, especially in mathematics.  But telling teachers to be more like this is different from actually training to be capable of this behavior.  

[daijobu]

3 hours ago, Clemsondana said:

The show your work thing is fascinating because I had a college prof who wouldn't help unless you had something written down.  It could be a drawing, a list, an equation, anything to show that you had started on the question/problem.  I thought he was nuts until I realized how often just getting something down on paper led me most of the way towards an answer, and if I went off the rails somewhere then it was easy enough for him to see what the problem was.  I'm not exaggerating when I say that it changed how I do any difficult academics - reading papers, how I planned experiments and made models back when I was in the lab, how I approach math that I've forgotten when I need to help my kids - so I'm intrigued at the idea of helping kids by giving the exact opposite advice.  

Like like like.  

I recall in high school trying to solve a problem and deciding I could not do it.  I went to class the next day to review our homework.  Our math teacher solved the problem at the board and it dawned on me that I was considering his approach to solving the problem, but I hadn't tried it because I wasn't sure if it would work.  

Of course, with difficult problems, you don't know if it will work unless and until you try it!  I resolved I would never make that mistake again.  

Always try something.   

[Condessa]

18 hours ago, Noreen Claire said:

First - from the quick read through that I did, I think that the ways to reflect and engage with the way we (I) currently teach math, and the example ways to re-center, re-focus, and improve my instruction would benefit every student in my classroom.

Second - It was written by a group entirely made up of BIPOC math educators, and I respect and value their experience as math students and math teachers and their unique insights that can help me improve my own teaching (as a white woman who went to private, nearly-white-only schools k-12).

I teach at a school that does not value mathematics at all - they just eliminated the math major! - and the students who I have in my (remedial) college math classes do not enjoy math. They see it as a set of rules, disconnected from their life, that you have to follow to get an answer. They have no interest in learning math for math's sake, or for wanting to explore concepts for understanding. They want me to tell them how to do the thing to get the answer. Saints forbid I provide a problem with multiple paths or no ready solution! I once put a quadratic equation on the board and proceeded to solve it four different ways (graphing, factoring, completing the square, and quadratic formula). When I was done, the only questions was "which was the right way?" The recommendations that I saw in that workbook were about relating math to students' lives, centering the learner rather than the teacher,  and teaching students to think of math as the journey, rather than the map. It all looked good to me.

I really appreciate you coming and giving a well thought-out differing viewpoint.  We all benefit hearing and considering different ideas, whether we wind up agreeing or not.

[Clemsondana]

2 hours ago, daijobu said:

I skimmed over the paper, and my thought was that if a teacher is going to entertain students who arrive at alternative methods or algorithms or even different answers in a way that respects the student, then that teacher needs to be fully 100% confident in their mathematics.  

Too often, teachers see the work written by a student, and it isn't the way the teacher taught it, so the student is counted wrong.  Only with a strong understanding of mathematics can the teacher read and understand where the student was waylaid can they point out what the student got right or find something positive to say about the approach.  

I think in order to implement these principles, teachers need to be better trained in mathematics.  How many teachers can explain other bases, like 12 or binary, let alone base 10?  I think the number of teachers who understand base 10 is very small.    

This has been a huge problem when I volunteer.  I have at times had to keep showing methods until I hit on the one that the kids recognize as the 'right' one and then only help using that method.  Kids across multiple schools have told me that if they do it a different way then it will be marked wrong.  It is insanely frustrating.  There are a couple of biology topics that are like this, and I always tell my students that I'll keep trying explanations until I come across one that makes sense to them.  It is hard to look at a kid who can't figure out equivalent fractions, know that there are several methods that they could use, and not be able to show one because it's not the right method.  

I would love for there to be more history and application in math.  I think it will help some studentts. But, I also wouldn't be surprised if its impact is limited.  I mean, I teach biology.  Almost every topic is something that I relate to something that students might care about - I mention poisons as inhibitors of metabolic pathways, cancer and how tumors develop, various genetic diseases, GMOs, etc as they come up in class.  Some students love it, and some students still don't care.  And, in a way, that seems fair...I mean, many people on this board who are experts in something will comment on how they really don't like some other subject or don't know much about it.  I think that one of the main reasons that students don't like subjects is  because they don't feel capable of doing them, and fixing that would go a long way.  One of the things that I noticed is that the kids who most easily did their math work were the kids who knew their math facts quickly.  Most said that they had been required to learn them by a parent, sibling, or other relatve, not the school, which is an issue in its own right.  But, there are still plenty of people who are adept at something but don't particularly like it.  

[Condessa]

9 hours ago, Noreen Claire said:

The document doesn't say that you cannot require students to show work . . .  It says that you should not center your class on ONLY written work . . .  It asks the teacher to think about other ways that students can express their knowledge or methods of solving problems.

 

Is this in a section I haven't read yet?  I am not finding this.  Where does it say requiring students to show written work is not bad?  The section I read on requiring students to show their work is quoted below.  Is there something I'm missing?

 

"White supremacy culture shows up in math classrooms when... Students are required to “show their work.” Math teachers ask students to show work so that teachers know what students are thinking, but that centers the teacher’s need to understand rather than student learning. It becomes a crutch for teachers seeking to understand what students are thinking and less of a tool for students in learning how to process. Thus, requiring students to show their work reinforces worship of the written word as well as paternalism. 

Instead...

Ask other questions that will demonstrate learning when it is not clear to you how students know the answer.

• Verbal Example: If you were working with a fellow mathematician who was absent this day, what might you tell them to help them learn it?

• Classroom Activity: Number talks, where students have to engage with mental mathematics not limited to computations.

• Professional Development: As a department, solve complex problems without writing and share with each other about that process.

Offer a variety of ways to demonstrate thinking and knowledge.

• Verbal Example: Show your thinking with words, pictures, symbols.

• Classroom Activity: Have students create TikTok videos, silent films, or cartoons about mathematical concepts or procedures.

• Professional Development: Practice with math colleagues how to answer mathematical problems without using words or numbers."