My lunch partner and I were discussing the general question of wokeness and "critical race theory" in schools today, and I promised to look into the whole thing a little more deeply than I have so far (which is roughly zero). I'm not sure I'll follow up on that promise, but when I got home I found that at least a few corners of the internet were frothing over an alleged attempt by the state of California to destroy math education. This turned out to be prompted by an article in Reason, written by Robby Soave, about California's latest draft framework for K-12 math.
The bill of particulars is basically that (1) the framework wants to eliminate advanced math courses, especially calculus, and (2) it spends lots of time on connecting math to social justice concepts like bias and racism.
Does it? You guys don't pay me enough to read the whole framework, but I did demonstrate my dedication to the cause by reading chapters 1 and 2. I will say up front that the framework is practically bursting with edu-jargon and references to allegedly scholarly papers. This is not my cup of tea, but I won't hold it against anyone. So what does the framework say?
First off, it does indeed spend a lot of time connecting math to social justice concepts, but it's worth noting that this is done in a fairly conventional way. Everyone has agreed for decades that math needs to be made "relevant" by posing problems connected to the real world, and the new framework carries on this tradition. The big difference is that some of their examples involve social justice issues. For example:
Ms. Ross selects three word problems to connect with the class’s current read-aloud of George, a novel by Alex Gino that shares the story of a 10-year-old transgender fourth grader and her struggles with acceptance among friends and family.
There are other examples like this, and they're mostly just updated versions of the story problems that we all dreaded back when we were in math classes. I don't see much harm here, though I suppose your mileage will vary.
Second, the framework takes on the issue of tracking, which has been the source of math pedagogy wars since before I was born. The new framework comes down firmly on the anti-tracking side up through middle school, based on the idea that recent neurological research shows that (a) anyone can learn math up to high levels,¹ and (b) advanced kids who take the standard Common Core classes do better than those who are tracked into honors classes:
The overall achievement of the students after the de-tracking significantly increased. The cohort of students who were in eighth-grade mathematics in 2015 were 15 months ahead of the previous cohort of students who were mainly in advanced classes (MAC & CAASPP 2015).
As for calculus, the authors are unhappy about a "rush to calculus" that's mostly motivated by an insane competition for entrance to elite universities and "does not lead to depth of understanding or appreciation of the content." However, they also explicitly say this:
All students can take Common Core-aligned mathematics 6, 7, and 8 in middle school and still take calculus, data science, statistics, or other high-level courses in high school.
These are not the words of people who hate high school calculus.
In the end, the framework is guilty of the following sins:
- Offering examples that incorporate issues of racism, sexism, etc.
- Urging teachers to develop lesson plans that take into account the needs of English language learners.
- Insisting that tracking is bad in lower grades because it encourages teachers to give up on "slow" students—very often children of color—who could learn more if they were given the chance.
- Promoting an approach that leads to deeper learning by rejecting the current approach of memorizing a laundry list of concepts that students can't connect to any real-world problems. (It's maybe worth noting that every math framework ever written promises this.)
- Offering calculus for those who want it, but not encouraging it as much as we do now.
- Using an ungodly mix of pedagogy jargon and social justice buzzwords.
I won't pretend that I agree with all of this, but neither do I think it spells the end of decent math education here in the Golden State. The bottom line is that if you hate the idea of schools incorporating social justice into their classrooms then you'll hate it here too. If not, then you won't. But either way, I doubt that it will have much effect one way or the other on the ability of students to learn math.
¹Without diving too deeply into this, I'll note that this belief is driven in large part by mindset theory, which says that children learn better if they are taught to adopt a "growth mindset." A growth mindset is one in which children believe that abilities like intelligence can be improved over time. Conversely, a "fixed mindset" teaches that things like character, intelligence, and creative ability are largely static.
Unfortunately, mindset theory hasn't fared well in recent research that has attempted to replicate the original mindset studies. Frankly, all the social justice stuff bothers me less than the framework's unquestioning reliance on a theory that hasn't panned out in the decade since it was introduced. If this is typical of their approach, there's little chance that the new framework will be successful.
The first part of this sounds like a plan for a math class drawn up by people who failed math.
Everyone has agreed for decades that math needs to be made "relevant" by posing problems connected to the real world, and the new framework carries on this tradition.
If you look at a math textbook from the 19th century you'll see that this has actually been the case for centuries, and it's almost completely wrong. In the 19th century it would have been about how many bushels of oats a horse can eat, which was modernized in the 20th century to some conflict between apples and oranges.
The problem is the story part of the 'story problem' engages the wrong part of the imagination and only confuses everything. Keeping it as abstract as possible simplifies it and allows the student to find connections to the real world themselves through their own experiences, where worrying about how many apples are in a bucket limits the application to apples in a bucket, and then daydreaming about various other things you might do with apples or with buckets, pulling the mind in an entirely wrong direction.
Interesting. I always kind of liked story maths stuff but not for "practical applications" like apples in a bucket but general gesturing at wordly applications.
I hated trigo. Nothing would have made me liked it but, sure, do mention the careers for which it is central/important/relevant (architecture and construction in general, I presume? Artillery officers, maybe?)
I kinda liked stats and probas. The fact that they're central to applied economics would have sold me even more and certainly reinforced my interest (the fact that they're useful for gambling was enough of a sell point, tbh).
Amen, bro. "Ms. Ross selects three word problems to connect with the class’s current read-aloud of George, a novel by Alex Gino that shares the story of a 10-year-old transgender fourth grader and her struggles with acceptance among friends and family." This seems way too full of irrelevant information. What will be the arithmetic question? Whether the "word problems" are sufficiently woke? How many of the white male students will get them right, v how many of the "transgenders"? Is it something about the content of "George", or a prediction of how old "George" is now, given the publication date of the novel?
It reads like one of those trick questions with lots of detail about the plane crash, its location, and route with the ask "Where are the survivors buried?"
The big change in the framework is a move from tte traditional course sequence to integrated mathematics. https://en.m.wikipedia.org/wiki/Integrated_mathematics
I disagree. Sure, teach/learn math concepts in the abstract. But also teach/learn how to apply it to word problems. The ability to apply the abstract math to real world problems is the whole point, and students are not going to find those connections to the real world on their own.
Here's a vivid reaction to a similar ivory tower conflict,
https://www.gnxp.com/WordPress/2021/04/13/verwoerds-revenge/?utm_source=rss&utm_medium=rss&utm_campaign=verwoerds-revenge&utm_source=rss&utm_medium=rss&utm_campaign=verwoerds-revenge
Considering the myth of white privilege scam nonwhites simply can't get by, because they think all capitalism is kosher, no it can't exist because the jews run debt and then pour it in white coffers which then produces income, consumption and production. If the system collapses like it should of in 2008, white children would be starving at quite a high clip, especially formerly rich white children who's parents business died in the panic. What's worse is, is watching small farm towns die as agribusiness collapses, creating no food.
When will Kevin block this antisemitic troll?
Considering math and the Social justice scam have little to do.with one another, remove the people proposing this junk and eliminate them from society decisions at large. See, not hard.
Calculus is useless in everyday living as well. I prefer poly sci majors over business administration majors 7/10. The former has horse sense. The latter is for finance or medicine. Stop trying to force people with mediocre math skills to take calculus.
!?!?! I can't believe I'm in actual agreement with Shootie. Yes, calculus is more or less a waste of time in a high school setting ... and I say that as someone who majored in mathematics and taught at university for many years.
I'd replace calculus with probability and statistics if I had my druthers.
Does this imply that middle school students are currently taking calculus? It's absolutely wild if that's the case. I was stellar in math and there's zero chance I could have handled calc in 8th grade.
I didn't even know what calculus was in 8th grade, but my Indian (dot) immigrant classmate did and knew its importance.
I just made it to precalc and took calculus (3 semesters) at Community College. That was fine, and indeed pretty traditional before we allowed a bunch of Asian grinds to settle in these United States.
There aren't very many middle school students who take calculus, but there are some. Back when I was a middle-schooler, it wasn't even a possibility. But I was a math-oriented kid and in 7th grade my father let me have his college calculus textbook and I taught it to myself. And I know of a handful of people who learned calculus before they were 10 years old.
That said, I think that calculus is overemphasized in secondary education. Unless you go on to become a mathematician or scientist (here, at least, we'll include economists in that) you will probably never use it in real life. By contrast, statistics is useful to almost everybody in real life, yet few students take it. (Conflict of interest disclosure: I am an epidemiologist, so my life's work involves statistics.)
I agree 100%. People have a greater need for an understanding of statistics and probability than calculus. Or trigonometry, for that matter.
Ah. I made a post to the same effect before I saw yours, so needless to say I agree in spades with your statistics comment. I'd go further though and teach probability as well. People just don't seem to get how conditional probability works, in particular.
I don't believe story problems are universally dreaded. They are not interesting stories, I'll grant.
I loved story problems, and still do. The weirder and funnier, the better.
I don't remember weird, funny ones. You might have had a better book or a better teacher.
Re: "tracking". Back in the day, I was fast-tracked into advanced maths and learned with a smaller cohort of similar students, who got special attention and had a kind of group spirit because of it. I think this example shows how smaller classes and better teachers can help people to excel.
As for "slow-tracking", it would seem that if this was to be done, the small group, individual attention, and well-trained teachers would be an improvement. That is, to bring the students up to grade under the assumption that they could learn and just needed more help. Not basically dumping them into a "stupid ghetto."
I know that the fashion these days is to put all students of all levels together in classes, so children "learn acceptance" or something. But my own experience was that too often, these children/young adults constantly disrupt the class and drag the pace of learning to a halt. Instead of learning to love people with "developmental disabilities", I've just become impatient. (I'm sorry. I know it's wrong.)
Now, bear in mind that it's been a long, LONG time since I was in a grade school classroom, so I'm definitely out of touch.
My pre-algebra teacher was an unrepentant Minnesota Vikings fan in Wisconsin who loved Pi to 200+ decimals, & was fond of the expression "be right, be wrong, but don't be a can of corn".
My algebra teacher was a lesbian who loved BASIC programming language.
Honestly, I didn't have a better math teacher after 8th grade. My junior year pre-calc teacher & my first year stats professor were drunks, also.
I thought the common wisdom was that stats professors were drunks more often than not ... statistically speaking, that is 😉
Quite possibly.
The standard deviation of legal blood alcohol content is not enough for the true statistician.
The problem with slow tracking is that racist white teachers assumed because I wasn't, I was put into slow groups and had to fight my way out repeatedly to my natural position (top 5 in my grade).
I'm curious where you were located. I've read such stories, but never saw them. Where I grew up, Illinois, they lumped most students together and then put the few who did math effortlessly in the next level class.
A bit north of you, MN.
Ha! I had assumed you’d say something in the South. Serves me right for stereotyping.
Your description reminded me of a report I saw on, it might have been 60 Minutes, back in the 90s. If I had to guess I’d say it was Georgia, but I forget. They actually had two tracks in the school. One for Whites and one for Blacks. The classes for Blacks were referred to as “D” classes. I forget the official reason that was given, but the D obviously stood for dumb and everyone knew it. And they interviewed a Black mother who talked about having to fight over and over again to put her kid in the regular classes.
Anyway, it never ceases to amaze me the effort some people put into keeping this crap going.
Ah, also less anecdotally if you remove the 5% of troublemakers or dumb kids in a class the other 95% have significantly improved results. But you can't just abandon kids.
private schools...excuse me, "charter schools".
As a former teacher, I'm _strongly_ in favor of removing disruptive students from the classroom. The needs of the few don't outweigh the needs of the many and I think we've all had a history lesson in what happens when the needs of the few take precedence.
It can't be "troublemakers". In my experience in teaching math in an urban district, those were the kids that were often just "passed along". They learned that there was not a consequence to failure. I believe that if they were "taught at the level that they are at", something that my district "said" they believed in, they could succeed. However, when a plurality of students are testing at 2+ grades below level, there is not a teacher in the world that can teach 3-4 different classes at once, where some students don't act as if they want to learn.
But mathematics is something that, with enough study and practice, anyone can reach any level they want. It might take one student 20 years to "get" calculus, but they can get there.
Shouldn’t and mustn’t but we certainly could. Whether the calculation for overall “goodness” favors it is unclear.
My recollection of word problems was they usually involved more mundane everyday things like when two trains would meet and they didn’t guild the lilly with extraneous information like the names of the train conductors and how the carriages were decorated.
Exactly.
Kid's mental capacities for different things develop at different times and rates. Some may be ready for calculus at age 12 and others not until age 18, but they won't necessarily be greatly different in calculus ability at age 25 (say). IQ tests were originally a measure of this development rate, not "native" intelligence, whatever that is. Because of this variation in development rate, IQ or ability tests for kids do not necessarily measure invariant native ability. I am not sure that this characteristic of learning is fully appreciated. It may be that "[almost] anyone can learn math up to high levels", but they certainly can't all do it at age 5. This kind of variation in development rate seems to argue against rigid tracking, and maybe also for withholding teaching advanced topics until the majority are ready (although some may never be ready).
My recollection is that word problems frequently contained extraneous numerical information, for instance that the northbound train has 90 passengers and the southbound train has 70 passengers, as a deliberate exercise in learning how to distinguish relevant information from irrelevant information.
I would worry about math problems that incorporate sexism, racism, etc would cause some kids to become anxious, reducing their capacity to actually focus on the problem. No one wants to relive personal trauma on a math test. You can be inclusive in more positive ways.
One thing I noticed in my own child's math homework was a continued reliance on very culturally specific knowledge. He recently had an assignment in 6th grade that required knowledge of the scoring systems of both golf and American football. He was clueless about both (he is not a sporty kid), but at least I could help him. For many of his classmates, who are the children of East African immigrants, these would have been extremely confusing questions. It is one thing to merely mention something cultural, and another to require someone to know what par 3 means, or that yardage is gained or lost in a series of plays.
Yup, the problems should as anodyne as possible.
The true, unrealized -- and probably unrealizable -- goal of story problems is to get students to learn abstraction. In order to be good at solving real-world math problems, you have to be able to take such a problem, cast aside the various non-mathematical details, and reduce the problem down to its purely mathematical kernel, to which you can apply your math skills to solve.
In my experience, most people never really get to the point that they understand that abstraction process. Instead, they learn to take a story problem and apply a bunch of "rules" that don't make much sense to them, and grind out a result, without ever knowing why the approach they've been taught to take actually works. They learn a process, but not the meta-process.
I don't know if there is a way to teach this that works. So many ways have been tried without success that I think it's probably an insoluble problem. The New Math of the 1960s was very heavy on trying to teach abstraction, but the result was that students just ended up learning a bunch of different rote rules that they didn't understand any better (and that were less applicable to real-world problems).
As for calculus, while I think the majority of people don't need to know the mathematical details of calculus (no one, to my knowledge, uses integration by parts in the real world), the conceptual part of calculus is absolutely essential, because everything in the physical world operates by the rules of calculus. But teaching this doesn't go much beyond demonstrating how differentiation represents the rate of change of a value, and integration represents a cumulative sum of values. Just get those two concepts down, and the bulk of day-to-day, real-world physics becomes comprehensible.
+1, mostly.
It's not true that nobody uses integration by parts in the real world. I have had occasion to use it in my work--then again, most of what I do is statistical analysis. But nobody outside of people working in the mathematical or physical sciences would have occasion to do it.
Integration by parts to me is part of an elaborate exercise in puzzle solving. You might not have to solve that same kind of puzzle in your later work, but I think the mental activity is generalizable. It is useful for many to have sharp puzzle solving skills.
You need to know integration by parts so you can help your children with their math homework, thereby demonstrating that dad does know something after all.
You do IBP by hand!?!?! I would have thought that symbolic packages like Mathematica would have taken over long ago
There's a good reason why a rule-based approach is the norm instead of abstraction: These are timed tests. Big No-no.
Kevin, you've been snookered. The authors say they're not against high school calculus, but their proposed policy of not tracking means that for a student to take calculus the student would have to take two math classes in one year in order to complete the requirements to enter the Calculus class. In our district in Minnesota, the proponents of the 'California' plan leave out that particular piece of information. And since, due to budget cuts, there are less class periods in the day while the state requirements for English, Science, etc have stayed the same, it would be extremely difficult to take Calculus even for the students who wanted to do two math classes in one year just to get into the Calculus class.
I happily avoided taking any calculus ever.
I got my math in science classes long before it showed up in math classes.
Of course there was the one Chemistry prof. when I was in grad school who liked to go on about "dimensional analysis". It took the rest of the semester to convince the undergrads that that meant cancel the units.
The biggest problem with education is that we are letting theorists write all the guides. I know many of these types - they are set to a particular ideology in education (usually driven by their politics) and they refuse to abandon their theories when they prove ineffective or even counterproductive. Another good example is the introduction of "whole language" reading in the 1990s because it was supposedly more culturally relevant. Problem is, "whole language" reading sucked and led to poor performance, which has been shown again and again by scientific studies. Even Wikipedia declares Whole Language instruction to be discredited. Yet, I still know education theorists who are devoted to whole language instruction because it is tied to their social justice activism.
And I'm sorry, but what the heck is a math class doing reading aloud a novel about a transgender 4th grader? The same people who built this math plan would go absolutely berserk with rage if the example was word problems drawn from a conservative-leaning kids book being read in class.
Tracking is associated with higher success rates for those in the highest and middle tracks. If you stick a bunch of students who are behind their peers into one group by themselves they perform worse, all else being equal.
Not surprisingly, parents want their kids in the upper tracks. As someone who has taught two different Advanced Placement courses, I can assure you that many students in the classes I taught struggled not just with the material but with the workload, too. I remember meeting with a pair of relatively high-status parents before starting the year about whether their academically undistinguished son could be assured of at least a B. He got it, but barely, and mainly on the strength of completing his assignments.
Nowadays, the College Board wants as many kids in AP as they can sign up, which means that my AP classes have higher percentages of students who don't fully know what they're in for, and struggle mightily when they find out. It's the Peter Principle, high school version; the Lake Wobegon effect. All the students must be above average.
The curricula get stuffed with courses that experts think students need, while parents want their children in the most demanding courses, whether they have the abilities to justify those placements or not. The result is that school curricula are designed to please parents and experts, not serve the needs of students.
Imagine creating a math curriculum with all of the narratives of the conservative movement baked into the coursework presented. Liberals and progressives would be horrified. But somehow it's okay to bake all the narratives of the left into school work. It's a might makes right mentality. If you can get Democrats, the media, and academia all on the page - you just do what you damn well please.
The problem today is the conservative movement no longer forms a respectable opposition, so people just try to ignore them. Plus they have few ideas anyway.
I think math should be taught with politics left out completely. That's very easy to do.
You can teach math without politics in it. Teaching children, OTOH, requires imparting values, which are bound up in politics. Since schools are institutions dedicated to helping students learn to get along with each other, they impart values of tolerance and understanding. Even in math class.
Wokeness is the opposite of tolerance and understanding. It's about proclaiming the country is built on systemic racism and is best characterized as being white supremacist. It stereotypes whites as all having the defect of whiteness and white privilege. And if you oppose any of this thinking then you are declared a racist, and you should be silenced.
Perhaps the material used in math classes won't go this far, but who knows. Learning math should not include controversial political material.
Conservative word problem:
Q: Say 40,000 fake ballots from SE Asia are dumped in Arizona ballot boxes in Maricopa County to cancel the actual overwhelmingly winning pro-Trump vote. What percentage of bamboo in the paper of the ballots would be needed to throw out the Democratic votes?
A: None, we already know they're fake because they're marked Democrat.
The social science replicability crisis has yet to penetrate the mighty brains of school system admins.
i see math as apolitical. teach the kids that 2+2=×4 not 2+2=5.