The article doesn't make it clear if (1) this is just a lone admin submitting a bad proposal that is ultimately dead on arrival or (2) this framework is seriously being consideration as policy. I won't hide my feelings that this is a bad idea--prodigies exist.
And that's not just a proposal from some rando, it's a DoE policy. It seems to be an ideological trends of destroying advanced education so that "equity" ideologies can feel good about it.
Prodigies absolutely exist. But this proposal is also so woefully uninformed as it rejects a basic fact: some folk are more intelligent than others. We don't know why -- it's both nature and nurture -- but we know it exists because humanity has observed it since forever.
Equity in education isn't to see a kid that's doing well and think, "well fuck that kid, we'll just make him bored out of his mind and ultimately become disinterested as we force them to sit through another year of class on a subject they already mastered."
Rather, it's simply to redirect resources (read: money to hire more teachers so there's a smaller student to teacher ratio) to the schools whose students are achieving the least. And teachers are the ones that get to make that determination.
California has really been pushing the idea that all their students are equal, while quietly opening more charter and magnet schools to support the students that are "more equal than others", it's just plain inefficient to split the levels of student achievement into completely separate campuses instead of just different classes.
Providing resources to students who need it is definitely important, and it is equally important not to stand in the way of the next Newton, Euler, or Einstein
Of course I disagree with the proposal in the post, but I wonder... how much real encouragement did Newton, Euler and Einstein get (or need) when they were young? Could anybody have stood in their way? Ramanujan got as little encouragement as one could imagine but still ended up as one of the greatest mathematicians of his time - but on the other hand, maybe he would have been even greater if he had had more opportunities.
Ramanujan was motivated by his deeply held spiritual beliefs and then later adopted and mentored by G.H.Hardy. Perhaps you mean before all that? I imagine there are 100 Ramanujans we've never heard of.
Looks like the "State Board of Education appointed 20 members to the Mathematics Curriculum Framework and Evaluation Criteria Committee (Mathematics CFCC) to assist in the development of the Mathematics Framework." Looks like this is more than just a rouge admin, unfortunately.
It is nice.
Next step to remove The Fields Medal and Clay Research Award.
Those gentlemens (Fourier, Hamilton, Leibniz and Sir Isaac Newton) crying in their grave.
Not just California and not just under the banner of "equity" either. The push for equity (meaning equality of outcomes as opposed to equality of opportunity) comes under many different brands - social justice, critical race theory (CRT), diversity/equity/inclusion (DEI), cultural competence, cultural responsiveness, and so on. Activists across the country have been pushing these agendas for years, building up to this point where any difference in performance or talent or potential is erased.
you realize that all your references are to second-order sources, right? fox news, usa today, and reason.com are all going to filter their information with opinion.
some primary sources (like the actual proposal being discussed here [0] ) might help to make a stronger case.
This proposal seems to me like it's centered around a false dichotomy:
- Acknowledge the presence of natural talent, put naturally talented kids into advanced levels of math, and create inequity.
- Denounce the belief in natural talent, keep all kids at one level of learning, and help resolve inequity issues.
It doesn't seem to leave any space for kids who are just more interested in math or more dedicated to their pursuit of mastering it, as well as kids who have little to no interest in math and are not as dedicated to their pursuit of mastering it. I can't see the potential gains of this proposal outweighing the results of stifling the ability of many kids to explore the areas of academia that they're interested in. Isn't that one of the most beneficial aspects of the learning experience?
Even worse is that nowhere in the doc is suggestion that low performing students might do better if they were given more schooling! Instead it proposes teaching English and social studies during math lessons (but not vice. versa)
Isn't gym class already at the end-point of removing rigor?
It's generally not separated into tracks by ability, it's widely regarded as easy filler, and anybody with any serious interest in athletics does their real training outside of class. It's less "Why stop at math?" than "Please stop at gym!"
The same reason the math club can still do pentagon-inscribed-in-an-ellipse problems. (But I'm not actually convinced that the math equivalent of after-school weightlifting would be the actual result, rather than just the families that can afford it fleeing to private schools.)
Rather than running with a click-baity title, I'd encourage readers to look at the proposal, particularly the introduction: https://www.cde.ca.gov/ci/ma/cf/
Don't walk away from this thread assuming the authors are trying to dumb down math education without reason.
Instead, I'd encourage you to think about a few questions:
- Does raising the average math competency of all students outweigh the possible benefits of catering to a select few?
- Is it the school's (and thus, the government's) obligation to develop a hypothetical gifted student?
- If you're a student not enrolled in an advanced course (when one exists) do you assume that you're "not a math person"?
> Does raising the average math competency of all students outweigh the possible benefits of catering to a select few?
This assumes that advanced courses harm students not enrolled in them. I don't see why that should be the case, and would like to see some evidence for this dichotomy you presented.
If you have 3 teachers, and they A) each teach classes that are composed of 20 regular and 10 gifted students, or B) 2 of them teach classes of 30 regular students, and one teaches 30 gifted students, is B) "catering to a select few"? If so, which select few? Both regular and gifted students receive education adjusted to their abilities, so are they not both being catered to?
One of several examples mentioned in the proposal:
> Burris, Heubert & Levin (2006) followed students through middle schools in the district of New York. In the first three years, the students were in regular or advanced classes, in the following three years all students took the same mathematics classes comprised of advanced content. In their longitudinal study the researchers found that when all students learned together the students achieved more, took more advanced courses in high school, and passed state exams a year earlier, with achievement advantages across the achievement range, including the highest achievers (Burris, Heubert & Levin, 2006).
If having no advanced courses is best for everyone, as that study claims, then there's no need to think about those questions you raised, is there? There's no dilemma, since both gifted and ordinary students are best served by the same kind of program.
> If having no advanced courses is best for everyone, as that study claims, then there's no need to think about those questions you raised, is there?
You are correct, and that’s probably why the intro to the framework, while it mentions equity concerns on this issue, breezes past them fairly quickly and spends a lot more focus on the evidence of more universal problems with the existing tracking approach.
The framework’s position is not “tracking is segregation that enables serving more able (or white and asian) students better” but “tracking is segregation that is a pedagogical disservice to students across tracks”.
The DoE proposal talks around it but explains that low performers do better when high performers tutor them in small group projects, because teachers can't teach a whole class.
What it doesn't say is to let that happen but then also split into groups for ability-customized lessons.
If high performers are expected to tutor low performers, then the high performers ought to be paid a salary by the school. Otherwise, such an expectation of work cannot be expected. The teachers are being paid to do a job, they are the oned who are responsible for doing the job.
If this passes and the characterization of this bill is true, I think we should expect to see a further divide between private and public schooling outcomes.
The actual framework is here[0], the discussion of detracking in the context of advanced students starts on page 15 of the introduction.
The Reason article is huperventilating culture-war flamebait. While equity is a concern raised innregard to detracking and elsewhere in the framework its not the centerpiece of the rationale for detracking; there is a wide variety of evidence cited for tracking being associated with undeisrable results across the spectrum of ability-as-tracked.
Nor is the approach recommended by the framework in place of classical tracking “everyone regardless of ability is stuck with the same material”, it calls for variation within the same framework for students with differing ability.
(My biggest concern with this as a general approach—though its also an approach already in use lots of places and one which played a positive factor in out school selection for our son—is that it seems to be a much harder approach calling for more teacher skill to implement in practice.)
>>My biggest concern with this as a general approach—though its also an approach already in use lots of places and one which played a positive factor in out school selection for our son—is that it seems to be a much harder approach calling for more teacher skill to implement in practice.
Not only calling for more teacher skill, but also potentially requiring for more teachers (or assistants) in the classroom to implement this approach effectively, with no corresponding increase in education budgets beyond ad-hoc/one-time stimulus budget injections.
I agree that that Reason article is very flamebait. I also agree that math should be made accessible to all students and that we shouldn't effectively be determining kids' future in math when they're in sixth grade. Everyone should be able to find the "joy" of math.
Where I disagree is in the proposed methods, though I don't know what the "right" answer would be. The idea of a completely homogenous experience for all middle schoolers is what I experienced in going to a smaller middle school. There was only one track, and as one of those "good at math" kids, it was A+ all day with essentially no effort. As a result, I built exactly zero study skills and most classes were me getting my work done quickly and then twiddling my thumbs waiting for others in the class to catch up.
I didn't actually didn't find any joy in math until taking Calculus in high school. That was the first time I felt truly challenged, and the lack of study skills made it an initially painful experience. Finding success in discovering the concepts and eventually mastering them was exciting.
Even though it's been 30 years, I still remember the exact moment that Calculus "clicked" for me. Everyone deserves that experience. The right solution should be one where all students get that, but I don't think the proposed framework provides that.
> Everyone should be able to find the "joy" of math.
There's the key difference in approach. Everyone should be able to, but not everyone will. Some people find joy in it, some people find it deathly boring. Some people are fabulous at it, some couldn't do it literally when their livelyhoods - and sometimes lives - depend on it. One approach is to enable those who benefit from it - and give those who do not something else, more fit to them. Each person get their equal sets of chances, but not everyone would take them, and not everyone will succeed.
Another - the "equity" - approach says everybody should have exactly the same result, whatever it costs. If somebody would benefit from a very deep math education, but others would not - nobody gets a deep math education, in order for nobody to be "left behind". Under the guise of "diversity and inclusion", the actual diversity - diversity of interests, capabilities and skills - gets suppressed, while enforced equality of the lowest common denominator replaces it.
The results of it would be disastrous. Lowest common denominator would never enable students that don't like math, but it would disable ones that could.
Could you outline in short where the nuances that Reason is missing are? I'm afraid life's too short to analyze a dozen on 60-page documents in bureaucratese... Is it correct that the authors reject the idea of diversity of skills among the students and support the idea that teachers should enforce equalization of achievement, regardless of skill, as Reason states?
There is evidence. I feel people started using "without evidence" as "I disagree with it" lately and it's just wrong. The evidence is outlined in the article and supported by my prior knowledge of how woke education works and what Reason is. I can not independently experience and evaluate everything in the world, so for some things I must rely on trusting other people to deliver the information. Reason is not perfect but usually reliable enough to not distort the information beyond recognition. So, if in a particular case it is claimed that they got it wrong, I'd like at least specific information about what they got wrong and why I should change my mind about them. Just saying "oh it's all wrong" and dumping link to a gigabyte of dense bureaucratic language is not going to convince anybody. Reason did the work of sifting through it and refining the conclusions. Maybe they did it wrong, in this case the right thing is to point out the mistakes, not to say "it's all just wrong, but I won't tell you where".
"we reject ideas of natural gifts and talents" this is the direct quote from the document. How is it okay for a government document to bluntly lie? Natural gifts and talents are not ideas, but facts. How is it okay to reject facts by falsely claim they are just ideas? What if it says we reject the idea of evolution or climate change?
I would love to see hard evidence that "natural gifts and talents are facts". Environment, circumstance, and chance are more than sufficient to explain differences in performance, and I have yet to see any hard science that proves one way or the other.
My siblings (multiple genders and genetic histories, same parents and schools) had very different levels of success in academics. How does that fit your theory?
I don't have a theory - I was pointing out our lack of concrete insight into the processes that drive performance. Literally, we do not know how cognition works, so any concept we have regarding its management is based on a set of assumptions and approximations.
Going to the same school and having the same parentage does not mean you have the same experience. Heck, you could be twins, raised identically at identical schools and with absolute equity, and you'd have differing experiences (leading to differences in perspective and subsequently differences in thinking).
To be clear: I am not saying I know either way, but I also reject any notion based on the assumption that we have a strong grasp on how minds work. As such, it would behoove us to implement strategies that are not subject to strong feedback loops - that might have an amplifying effect on the initial conditions of a human life.
> "we reject ideas of natural gifts and talents" this is the direct quote from the document.
It’s a dishonestly-presented decontextualized excerpt from the middle of a sentence, excluding the thesis of the sentence and references. The full sentence is: All students deserve powerful mathematics; we reject ideas of natural gifts and talents (Cimpian et al, 2015; Boaler, 2019) and the “cult of the genius” (Ellenberg, 2015). They aren’t rejecting the idea that gifts and talents exist, they are denying particular ideas about natural gifts and talents, specifically, that the ideas, silent and expressed, among educators that natural gifts and talents are the critical determinants of individual success in mathematics (this is explored in fairly extensive detail in the paragraphs preceding the bulleted list the excerpt draws a tiny piece out of one bullet point from) and justify exclusionary gating on mathematics education.
The text literally said "we reject ideas of natural gifts and talents". You want to twist it to the opposite. There is no context here to make this dramatic turn. Even if the writer does not know how to finish a sentence, you are not authorized to fill the gap from -10000 to 10000. Maybe a government document is not intended for second guessing?
The proposed action here is to not separate "gifted" kids until grade 9. That seems pretty reasonable to me.
I don't think this is about true prodigies (don't they usually get picked up by universities?).
If you can separate students into winners and losers before grade 9, I think that's a strong indication that more resources need to be spent on the losers, not that we should be teaching the winners calculus before they reach HS (which I suspect is often more about the college admissions arms race than any love of learning or desire for knowledge)
The issue isn’t prodigies! The issue is that students will no longer be able to take calculus in high school. And that’s a big problem since it slows down students abilities to take advanced math in college, at a time where the amount of math needed by technical professions is only growing!
Perhaps 1% of graduating seniors are ready to skip calculus upon entering college. But that’s an important 1%! It includes all professional mathematicians, statisticians, data scientists, and most high level engineers!
>students will no longer be able to take calculus in high school
What leads you to this conclusion?
You can still take calculus without being designated a gifted student before you enter HS. In fact, isn't 12th grade calculus the standard without any acceleration?
It sounds like the report questions the rationale for targeting calculus, which seems like a healthy debate to me. Maybe some students would be better served by something else. However, I don't see anything to suggest that calculus is going anywhere.
> The issue is that students will no longer be able to take calculus in high school.
False. The Framework has a common 9/10 base designed to meet the legal two-year mandate and then a wider variety of advanced options than are currently typically offered for 11/12 which include Calculus+Trig, Data Science, and others.
The framework challenges the existing “every is trying to get to Calculus, the only difference is how quickly they skim everything else to get there” approach, not challenging the option for students to take Calculus in High School.
Reading chapter 8 of the framework, it does not seem that the curriculum described provides adequate preparation for technical courses at a college level. It lacks sufficient preparation in trigonometry (particularly identities) imaginary numbers, analytic geometry, nor does it provide adequate time for crucial techniques such as polynomial series in a 12th grade trig/calculus course.
52 comments
[ 3.3 ms ] story [ 93.9 ms ] threadAnd that's not just a proposal from some rando, it's a DoE policy. It seems to be an ideological trends of destroying advanced education so that "equity" ideologies can feel good about it.
Equity in education isn't to see a kid that's doing well and think, "well fuck that kid, we'll just make him bored out of his mind and ultimately become disinterested as we force them to sit through another year of class on a subject they already mastered."
Rather, it's simply to redirect resources (read: money to hire more teachers so there's a smaller student to teacher ratio) to the schools whose students are achieving the least. And teachers are the ones that get to make that determination.
Of course I disagree with the proposal in the post, but I wonder... how much real encouragement did Newton, Euler and Einstein get (or need) when they were young? Could anybody have stood in their way? Ramanujan got as little encouragement as one could imagine but still ended up as one of the greatest mathematicians of his time - but on the other hand, maybe he would have been even greater if he had had more opportunities.
https://www.cde.ca.gov/ci/ma/cf/
"...young people who aren't particularly adept at any academic discipline might pick up art, music, computers..."
Apart from California: Seattle is trying to get rid of its gifted education programs (https://reason.com/2020/03/26/seattles-school-system-has-beg...), Virginia is trying to eliminate accelerated math courses (https://www.foxnews.com/us/virginia-accelerated-math-courses...), San Francisco ended merit-based admissions at its highest performing school (https://www.sfchronicle.com/bayarea/article/S-F-school-board...), and more. Let's also not forget the corruption of school curricula to teach students activism and progressive politics, such as with Seattle's Ethnic Studies math program (https://reason.com/2019/10/22/seattle-math-oppressive-cultur...).
It's not just schools either. The adoption of DEI policies has been widespread, ranging from government agencies to private companies to nonprofits. For example, the National Education Association (NEA), the largest teacher's union and largest union in the US, holds explicit left-biased activist stances and officially advocates for social justice agendas (https://www.nea.org/advocating-for-change/racial-social-just...). Tech companies like Microsoft have set explicit race-based hiring goals that are illegal (https://www.usatoday.com/story/tech/2020/10/06/microsoft-div...). And Biden recently issued an executive order to implement equity programs across his administration (https://www.whitehouse.gov/briefing-room/presidential-action...).
some primary sources (like the actual proposal being discussed here [0] ) might help to make a stronger case.
[0] https://www.cde.ca.gov/ci/ma/cf/
- Acknowledge the presence of natural talent, put naturally talented kids into advanced levels of math, and create inequity.
- Denounce the belief in natural talent, keep all kids at one level of learning, and help resolve inequity issues.
It doesn't seem to leave any space for kids who are just more interested in math or more dedicated to their pursuit of mastering it, as well as kids who have little to no interest in math and are not as dedicated to their pursuit of mastering it. I can't see the potential gains of this proposal outweighing the results of stifling the ability of many kids to explore the areas of academia that they're interested in. Isn't that one of the most beneficial aspects of the learning experience?
Don't walk away from this thread assuming the authors are trying to dumb down math education without reason.
Instead, I'd encourage you to think about a few questions:
- Does raising the average math competency of all students outweigh the possible benefits of catering to a select few?
- Is it the school's (and thus, the government's) obligation to develop a hypothetical gifted student?
- If you're a student not enrolled in an advanced course (when one exists) do you assume that you're "not a math person"?
This assumes that advanced courses harm students not enrolled in them. I don't see why that should be the case, and would like to see some evidence for this dichotomy you presented.
If you have 3 teachers, and they A) each teach classes that are composed of 20 regular and 10 gifted students, or B) 2 of them teach classes of 30 regular students, and one teaches 30 gifted students, is B) "catering to a select few"? If so, which select few? Both regular and gifted students receive education adjusted to their abilities, so are they not both being catered to?
> Burris, Heubert & Levin (2006) followed students through middle schools in the district of New York. In the first three years, the students were in regular or advanced classes, in the following three years all students took the same mathematics classes comprised of advanced content. In their longitudinal study the researchers found that when all students learned together the students achieved more, took more advanced courses in high school, and passed state exams a year earlier, with achievement advantages across the achievement range, including the highest achievers (Burris, Heubert & Levin, 2006).
You are correct, and that’s probably why the intro to the framework, while it mentions equity concerns on this issue, breezes past them fairly quickly and spends a lot more focus on the evidence of more universal problems with the existing tracking approach.
The framework’s position is not “tracking is segregation that enables serving more able (or white and asian) students better” but “tracking is segregation that is a pedagogical disservice to students across tracks”.
What it doesn't say is to let that happen but then also split into groups for ability-customized lessons.
The Reason article is huperventilating culture-war flamebait. While equity is a concern raised innregard to detracking and elsewhere in the framework its not the centerpiece of the rationale for detracking; there is a wide variety of evidence cited for tracking being associated with undeisrable results across the spectrum of ability-as-tracked.
Nor is the approach recommended by the framework in place of classical tracking “everyone regardless of ability is stuck with the same material”, it calls for variation within the same framework for students with differing ability.
(My biggest concern with this as a general approach—though its also an approach already in use lots of places and one which played a positive factor in out school selection for our son—is that it seems to be a much harder approach calling for more teacher skill to implement in practice.)
[0] https://www.cde.ca.gov/ci/ma/cf/
Not only calling for more teacher skill, but also potentially requiring for more teachers (or assistants) in the classroom to implement this approach effectively, with no corresponding increase in education budgets beyond ad-hoc/one-time stimulus budget injections.
Where I disagree is in the proposed methods, though I don't know what the "right" answer would be. The idea of a completely homogenous experience for all middle schoolers is what I experienced in going to a smaller middle school. There was only one track, and as one of those "good at math" kids, it was A+ all day with essentially no effort. As a result, I built exactly zero study skills and most classes were me getting my work done quickly and then twiddling my thumbs waiting for others in the class to catch up.
I didn't actually didn't find any joy in math until taking Calculus in high school. That was the first time I felt truly challenged, and the lack of study skills made it an initially painful experience. Finding success in discovering the concepts and eventually mastering them was exciting.
Even though it's been 30 years, I still remember the exact moment that Calculus "clicked" for me. Everyone deserves that experience. The right solution should be one where all students get that, but I don't think the proposed framework provides that.
There's the key difference in approach. Everyone should be able to, but not everyone will. Some people find joy in it, some people find it deathly boring. Some people are fabulous at it, some couldn't do it literally when their livelyhoods - and sometimes lives - depend on it. One approach is to enable those who benefit from it - and give those who do not something else, more fit to them. Each person get their equal sets of chances, but not everyone would take them, and not everyone will succeed.
Another - the "equity" - approach says everybody should have exactly the same result, whatever it costs. If somebody would benefit from a very deep math education, but others would not - nobody gets a deep math education, in order for nobody to be "left behind". Under the guise of "diversity and inclusion", the actual diversity - diversity of interests, capabilities and skills - gets suppressed, while enforced equality of the lowest common denominator replaces it.
The results of it would be disastrous. Lowest common denominator would never enable students that don't like math, but it would disable ones that could.
read the actual proposal- it's a lot more nuanced than this makes it out to be
https://www.cde.ca.gov/ci/ma/cf/
"we reject ideas of natural gifts and talents" this is the direct quote from the document. How is it okay for a government document to bluntly lie? Natural gifts and talents are not ideas, but facts. How is it okay to reject facts by falsely claim they are just ideas? What if it says we reject the idea of evolution or climate change?
Going to the same school and having the same parentage does not mean you have the same experience. Heck, you could be twins, raised identically at identical schools and with absolute equity, and you'd have differing experiences (leading to differences in perspective and subsequently differences in thinking).
To be clear: I am not saying I know either way, but I also reject any notion based on the assumption that we have a strong grasp on how minds work. As such, it would behoove us to implement strategies that are not subject to strong feedback loops - that might have an amplifying effect on the initial conditions of a human life.
It’s a dishonestly-presented decontextualized excerpt from the middle of a sentence, excluding the thesis of the sentence and references. The full sentence is: All students deserve powerful mathematics; we reject ideas of natural gifts and talents (Cimpian et al, 2015; Boaler, 2019) and the “cult of the genius” (Ellenberg, 2015). They aren’t rejecting the idea that gifts and talents exist, they are denying particular ideas about natural gifts and talents, specifically, that the ideas, silent and expressed, among educators that natural gifts and talents are the critical determinants of individual success in mathematics (this is explored in fairly extensive detail in the paragraphs preceding the bulleted list the excerpt draws a tiny piece out of one bullet point from) and justify exclusionary gating on mathematics education.
I don't think this is about true prodigies (don't they usually get picked up by universities?).
If you can separate students into winners and losers before grade 9, I think that's a strong indication that more resources need to be spent on the losers, not that we should be teaching the winners calculus before they reach HS (which I suspect is often more about the college admissions arms race than any love of learning or desire for knowledge)
What leads you to this conclusion?
You can still take calculus without being designated a gifted student before you enter HS. In fact, isn't 12th grade calculus the standard without any acceleration?
It sounds like the report questions the rationale for targeting calculus, which seems like a healthy debate to me. Maybe some students would be better served by something else. However, I don't see anything to suggest that calculus is going anywhere.
False. The Framework has a common 9/10 base designed to meet the legal two-year mandate and then a wider variety of advanced options than are currently typically offered for 11/12 which include Calculus+Trig, Data Science, and others.
The framework challenges the existing “every is trying to get to Calculus, the only difference is how quickly they skim everything else to get there” approach, not challenging the option for students to take Calculus in High School.
(See Chapter 8 of the framework.)