Math Equity

[Jimmy Higgins]

So the right-wing Internet lost it's mind over Math Equity. Of course, the right-wing is fast to lose their shit over anything that dares to question inertia. One thing that popped up with 'showing work'. I figured this was taken out of context, and I think in part it is... but in part, it seems kind of crazy, though there can be a context I suppose I'm not thinking of.

Math teachers ask students to show work so that teachers know what students are thinking, but that centers theteacher’s need to understand rather than student learning. It becomes a crutch for teachers seeking to understandwhat students are thinking and less of a tool for students in learning how to process. Thus, requiring students toshow their work reinforces worship of the written word as well as paternalism.

link

Okay, this does confuse. In the next page, there is a 'reflection' section about how students can otherwise show mastery. To me, that indicates trying to think outside the box as a teacher (though of course, the poor teachers have enough trouble trying to teach kids). It is a nice philosophical question. But the above "worship of the written word" and "paternalism"? What now? Maybe I'm not getting the phrase right, but to me, "showing the work" is to indicate the process that the student is undergoing to get to the answer. It helps prevent cheating and if an error in calcs is made, credit can still be applied to the work, if an appropriate method. Showing the work, provides a student an opportunity to solve in an alternate way (if reproducible for other types of problems).

I'm not one to say rethinking methods is a bad idea (except fuck you LRFD), but what they present above, does seem misguided, convoluted, and wildly off-target.

Then I go down more on "real world math"... and we get this:

Often the emphasis is placed on learning math in the “real world,” as if our classrooms are not a part of the realworld. This reinforces notions of either/or thinking because math is only seen as useful when it is in a particularcontext. However, this can result in using mathematics to uphold capitalist and imperialist ways of being and understandings of the world.

Again, starts off on a potential philosophical, lets think about how we think about this... and then seems to derail into insanity.

Is the rest of Math Equity this problematic?

 

[Shadowy Man]

Is showing work a new thing? I was a TA for freshman physics over twenty five years ago and the students were required to show their work. Showing work is showing understanding. Whoever criticizes this probably isn’t very good at math.

ETA: oh, wait. Is it the showing of work that is supposed to be the bad thing? The thing that discriminates against people?

 

[skepticalbip]

Is showing work a new thing? I was a TA for freshman physics over twenty five years ago and the students were required to show their work. Showing work is showing understanding. Whoever criticizes this probably isn’t very good at math.

ETA: oh, wait. Is it the showing of work that is supposed to be the bad thing? The thing that discriminates against people?

"Showing work" is definitely not a new thing. I was in school back in the dark ages and it was 'a thing' then. The purpose, as I understand it, is to insure that the student understands the process rather than just guessing (or copying some other student's answer). Without the work being shown, the teacher can not determine if the student needs more instruction in order for them to understand.

I even had one physics prof. that was only concerned with 'the work' showing an understanding of the physics. He explained that it wasn't a math class so he wouldn't grade on the right final answer but on an understanding of the physics. This worked out to be helpful in completing exams because I would go through the problems and set up the equations for each problem then go back and complete the math as time allowed. Other physics profs I had gave partial credit if the physics was understood but but some math error was made in the final solution.

 

[Shadowy Man]

Is showing work a new thing? I was a TA for freshman physics over twenty five years ago and the students were required to show their work. Showing work is showing understanding. Whoever criticizes this probably isn’t very good at math.

ETA: oh, wait. Is it the showing of work that is supposed to be the bad thing? The thing that discriminates against people?

"Showing work" is definitely not a new thing. I was in school back in the dark ages and it was 'a thing' then. The purpose, as I understand it, is to insure that the student understands the process rather than just guessing (or copying some other student's answer). Without the work being shown, the teacher can not determine if the student needs more instruction in order for them to understand.

I even had one physics prof. that was only concerned with 'the work' showing an understanding of the physics. He explained that it wasn't a math class so he wouldn't grade on the right final answer but on an understanding of the physics. This worked out to be helpful in completing exams because I would go through the problems and set up the equations for each problem then go back and complete the math as time allowed. Other physics profs I had gave partial credit if the physics was understood but but some math error was made in the final solution.

Yes. That is exactly how we approached physics. The numerical result was a very small fraction of the credit for a problem.

Since most of my students were not actually physics majors I was astounded how little they seemed to understand the actual physics though.

 

[Keith&Co.]

I have taught math. Back in the later dark ages.

It is definitely possible to write a story problem which allows an uncorrect method to be used to coincidentally find the right answer. Which really frustrates teacher and student if you cannot figure out why they can do one book problem, but not the other two.

Always show work so you can say things like, "this step? That's not how you simplify." or, "tell me again how you divided by zero?"

Also, i remember doing polar-rectangular conversions in A school to become a missile tech. I memorized the formula and did it each time.
Classmates i had bragged about programming their calculators to do it, so they didn't have to remember. Arrogant bastards.
But the final test was story problems, with different parts of the conversion supplied. I could deconstruct the formula, but they didn't have the tools to do so. So, "show all work" on previous assignments might at least have driven the formula into their skulls and saved them a week of extra study time.

 

[skepticalbip]

... snip ...

So, "show all work" on previous assignments might at least have driven the formula into their skulls and saved them a week of extra study time.

More importantly, it is good to actually learn how to solve a problem rather than relying only on computer memory just in case a solution is desperately and urgently needed and the laptop that has the algorithm needed has a dead battery. It is sorta the difference in knowing how to operate a computer and understanding how to solve real world problems.

 

[bigfield]

Is the rest of Math Equity this problematic?

I skimmed the materials and most of it just seems like reasonable - if somewhat vague - guidance for teachers.

It seems like the nutty stuff is in "Stride 1".

For example:



All this seems to accomplish is to make the teachers' job harder and makes lessons more complicated for students.

And for what? It seems to me that some ideologue is trying to push "there are no objective truths" critical theory onto teachers. That philosophy might work in literary studies, where things often come down to interpretation, but maths regularly involves problems where the problem solver has complete information and can arrive at the one and only correct answer.

 

[Angra Mainyu]

Is showing work a new thing? I was a TA for freshman physics over twenty five years ago and the students were required to show their work. Showing work is showing understanding. Whoever criticizes this probably isn’t very good at math.

ETA: oh, wait. Is it the showing of work that is supposed to be the bad thing? The thing that discriminates against people?

"Showing work" is definitely not a new thing. I was in school back in the dark ages and it was 'a thing' then. The purpose, as I understand it, is to insure that the student understands the process rather than just guessing (or copying some other student's answer). Without the work being shown, the teacher can not determine if the student needs more instruction in order for them to understand.

I even had one physics prof. that was only concerned with 'the work' showing an understanding of the physics. He explained that it wasn't a math class so he wouldn't grade on the right final answer but on an understanding of the physics. This worked out to be helpful in completing exams because I would go through the problems and set up the equations for each problem then go back and complete the math as time allowed. Other physics profs I had gave partial credit if the physics was understood but but some math error was made in the final solution.

That's even how we approach math. If the result is correct but they do not show the process, for all we know they might have cheated; that exercise will give them very little points. If the process is correct except there is a mistake in some computation, or they got a sign wrong, etc., they'll get most of the points of the exercise.

 

[laughing dog]

Perhaps what math equity is getting at is that there is usually more than one valid route to the right answer. I have experienced math teachers who have insisted there was one and only one right way to get an answer even when there more ways. And by "right way", I don't mean the best way or the specified methods but that any alternative method that would get the right answer was invalid.

 

[Keith&Co.]

Perhaps. I mean, sure, there are multiple methods for any question. But in a given class on a given day, we teach a given method, not as THE answer-getting method, but one tool the student may use, and needs to understand, before going on to others.

Maybe math equity would be better expressed as a general teacher attitude, where we and the students recognize we're supplying tools, not holy writ.

 

[Jimmy Higgins]

Perhaps what math equity is getting at is that there is usually more than one valid route to the right answer. I have experienced math teachers who have insisted there was one and only one right way to get an answer even when there more ways. And by "right way", I don't mean the best way or the specified methods but that any alternative method that would get the right answer was invalid.

Yes, but more than one way to answer a question would still require 'showing your work' to show how the alternate method worked. However, I didn't get that vibe, as the the 'reflection' sections asks teachers to provide mechanisms other than showing work to have students indicate they understand the content. Which is weird.

I've seen visa versa, where a teacher adapts a concept, like using a moving pie eating robot to model Doppler Effect, and it was up to the student to understand the parallel.

 

[J842P]

It's not taken out of context, it is just stupid.

 

[thebeave]

It's not taken out of context, it is just stupid.

Worse, its some of the worst racist garbage I've seen, despite the intent being that its "anti-racist". The phrase:

White supremacy culture shows up in math classrooms when the focus is on getting the "right" answer.

As if non-whites don't value truth and accuracy in mathematics and/or are too fucking dumb to get the "right" answer.

 

[ronburgundy]

Both quotes have some educational validity up until their last sentences where they try to turn it into some leftists political stance.

The reasons to "show your work" are obvious and already articulated by others. But a less obvious concern with requiring students to "show their work" is that having to make one's thought processes explicit to someone else in a particular format so they can easily evaluate it requires additional and different types of processing that are not themselves not always important for being able to do math. That added and different kind of processing could actually impede some students math progress. IOW, they could get the right answer in a reliable way across problems, but the added demand of "show your work" impedes their ability to get the right answer. It's possible this would be more of a concern with some types of problems than others. I don't know of research about math in particular, but I know that in educational research more generally, such as with reading comprehension, there is an evidence-supported concern that forcing learners to make their thought processes explicit (which is useful for research trying to identify causal mechanisms) can impede the learning process itself. Whether such forced exposition about one's thinking helps or impedes learning is likely to be context and task specific as well as depend upon the what skill level the learner is currently at.

As for the second quote, there is some evidence that making problems too concrete and situated in "real world" contexts makes the problems easier to solve, but impedes students from abstracting the underlying principles needed for them to realize what approach they should apply when given a problem in a novel context not part of the teaching.

But notice that none of this has to do with racial equity or the ramblings in those last sentences about "paternalism" or "capitalism"

 

[Shadowy Man]

Perhaps. I mean, sure, there are multiple methods for any question. But in a given class on a given day, we teach a given method, not as THE answer-getting method, but one tool the student may use, and needs to understand, before going on to others.

Maybe math equity would be better expressed as a general teacher attitude, where we and the students recognize we're supplying tools, not holy writ.

But, apparently, if the method is the one taught historically to white students then the method is supporting the idea that the white race is superior to people of color, who need to be subjugated to their will, and is therefore inherently a racist method.

Sorry, am I misinterpreting the math equity toolkit materials?

 

[J842P]

It seems to me that some ideologue is trying to push "there are no objective truths" critical theory onto teachers.

Some ideologue is trying? It's called the academic discipline of Education, which is entirely captured by ideologues, promoting a particular brand of activism. This is not some mystery. If you've gotten a degree in Education in the last couple of decades you've been indoctrinated into being an activist.

 

[Bomb#20]

Whether such forced exposition about one's thinking helps or impedes learning is likely to be context and task specific as well as depend upon the what skill level the learner is currently at.

Reminds me of the old joke about the centipede who went on Oprah, and she asked him how he decided which foot to move next. He never walked again.

 

[Loren Pechtel]

While I can see merit to showing work in my experience it was only done by lazy teachers wanting to ensure you didn't just copy the answer.

The worst I had was a physics teacher who insisted the class couldn't be properly taught in the summer session and spent the whole first class period telling us why we should drop it. The material wasn't a problem, his "show work" requirement was. I kept getting dinged on the homework for not showing enough work--the hardest part was figuring out how to show enough "work" to make him happy. To me, show "work" means writing out what work I actually did. To him it meant spelling out basic algebra that was so simple I didn't think about it--this was a class that had second semester calculus as a prerequisite, at that point simple algebra is not something you think about when the numbers are small. (I have a sneaking suspicion that his graders were looking at volume rather than contents.)

 

[Shadowy Man]

While I can see merit to showing work in my experience it was only done by lazy teachers wanting to ensure you didn't just copy the answer.

The worst I had was a physics teacher who insisted the class couldn't be properly taught in the summer session and spent the whole first class period telling us why we should drop it. The material wasn't a problem, his "show work" requirement was. I kept getting dinged on the homework for not showing enough work--the hardest part was figuring out how to show enough "work" to make him happy. To me, show "work" means writing out what work I actually did. To him it meant spelling out basic algebra that was so simple I didn't think about it--this was a class that had second semester calculus as a prerequisite, at that point simple algebra is not something you think about when the numbers are small. (I have a sneaking suspicion that his graders were looking at volume rather than contents.)

If you were a good physics student you may not have appreciated just how bad some of the bad students could be.

 

[skepticalbip]

Perhaps what math equity is getting at is that there is usually more than one valid route to the right answer. I have experienced math teachers who have insisted there was one and only one right way to get an answer even when there more ways. And by "right way", I don't mean the best way or the specified methods but that any alternative method that would get the right answer was invalid.

That doesn't sound like a system problem but a teacher problem. That particular teacher needs the dean to give them an attitude adjustment.