Googling "California CMF" led me to a clearly biased article with text like: Clearly that's talking past the point of opposition in bad faith, since I have a hard time believing many educators are...
Googling "California CMF" led me to a clearly biased article with text like:
The debates over math instruction have been mired in misinformation and marred by melodrama ...
Advocating for a math framework that centers on equity and meaningful opportunities for all California students is not controversial.
Clearly that's talking past the point of opposition in bad faith, since I have a hard time believing many educators are actually opposing a framework because it favors equality or opportunity for all...
Diving further, I ran across this site by Brian Conrad, Professor of Mathematics and Director of Undergraduate Studies in Math, Stanford University: https://sites.google.com/view/publiccommentsonthecmf/ with gems like:
"When I read the new CMF posted in mid-March, I encountered a lot of assertions that were hard to believe and were justified via citations to other papers. So I read those other papers. To my astonishment, in essentially all cases, the papers were seriously misrepresented in the CMF. Some papers even had conclusions opposite to what was said in the CMF"
Anyway, personal opinions: a course on data literacy sounds great and is more applicable to real-life than algebra. California / the US don't let children specialize, which leads to these weird either-or situations; if you're pursuing certain subfields of STEM, you need a strong grasp of calculus, linear algebra, and differential equations to understand many basic concepts from first principles. For other subfields and non-STEM fields, there's effectively zero benefit to learning calculus and something like data literacy is far more valuable (e.g. how to interpret data and detect misleading conclusions). There shouldn't be one track for all students, and if perhaps there isn't time to teach these valuable concepts to students, we need to reevaluate the entire structure of education, not mess up math in isolation.
I'm learning several years out of an engineering degree and Masters, that the math I wished I did more of and am now self teaching is statistics. We should teach everyone 5x more probability and...
I'm learning several years out of an engineering degree and Masters, that the math I wished I did more of and am now self teaching is statistics. We should teach everyone 5x more probability and statistics than we do now.
Also when it comes to actually doing maths, starting by writing proofs and basic logic would have been a dream for me. (I am very first principles / start with a blank sheet of paper and some axioms).
I didn't touch anything related to mathematics at university, but at my school the class with by far the highest fail rate overall was Introductory Statistics. It was (and presumably still is) a...
I didn't touch anything related to mathematics at university, but at my school the class with by far the highest fail rate overall was Introductory Statistics. It was (and presumably still is) a core unit for a lot of different degrees, and in my last year there the pass rate was so low that they ended up having to split it in half so people could take it across two semesters. We are talking people who were ordinarily pretty handy with maths skills, but that class used to turn people into a dribbling mess by week 5.
For reference, I'm a grad student in statistics. My own personal belief is that the entire way we teach introductory statistics should probably be overhauled. The specific curriculum should depend...
For reference, I'm a grad student in statistics. My own personal belief is that the entire way we teach introductory statistics should probably be overhauled. The specific curriculum should depend largely on a person's major, which is already often the case (psychology majors learn different material than engineering majors in their statistics classes) but I find that people typically come out of these classes barely understanding the basic definitions and meaning of concepts, which is likely the underlying reason the subject seems hard.
Honestly I also think emphasis should be put on the fact that universities have statistical consulting services for researchers and that no one should hesitate or feel embarrassed if they want or need help with statistical design or analysis. Just like you wouldn't expect someone who doesn't have years of study or experience in your field to be that great at it, statisticians don't expect non-statisticians to be great at statistics and we'd much rather have people consult with us than try to wing it, which often results in crappy research.
That being said, everyone should have a grasp of certain basic fundamentals. I'd err on the side of focusing more on interpretation of data and statistical results than application of statistical methods since nearly everyone needs to interpret research at some point but few people will actually be doing research themselves.
In the end, I do wish there were more emphasis on statistics in schools, but it is also worth noting that calculus and the like is an integral (pun not intended) part of the building blocks of the field and that you can't really understand statistics on any sort of deep level unless you understand calculus and all its prerequisites.
I work in the data space. You would not believe the amount of people at all levels of society who simply fail to grasp how statistics and data works is unreal. Even basic averages can baffle some...
data literacy
I work in the data space. You would not believe the amount of people at all levels of society who simply fail to grasp how statistics and data works is unreal.
Even basic averages can baffle some folks, it's really harrowing how weak our maths skills are.
My doc and I talked about it during a session, our conclusion is that HS Math education should cover: Algebra (they're starting basics as early as K now, which is great) Geometry/Trig...
My doc and I talked about it during a session, our conclusion is that HS Math education should cover:
Algebra (they're starting basics as early as K now, which is great)
Geometry/Trig
Logic/Statistics
Finance
Programming (thats right, mandatory programming classes)
Calculus and the like can be saved for post-secondary, where it belongs. It's so impracticle outside of deep STEM.
For those interested, these are the general HS graduation requirements in the US by state: https://reports.ecs.org/comparisons/high-school-graduation-requirements-2023-04 And specific math...
For those interested, these are the general HS graduation requirements in the US by state:
The majority of states require Algebra I. Most require 3 years of math, usually offering Algebra I, Geometry, and Algebra II as the easiest path to fulfill this requirement. I count only 8 states that require personal finance, and no direct reference to statistics or logic (though statistics might be available to fulfill a 4-year math requirement).
On the other hand, no state in the US requires Calculus for graduation (individual schools notwithstanding). Table 3 in the 2nd link.
I think it’s fine to offer Calculus as an optional 4th-year class for those that know they’re headed into STEM.
(I just skimmed these links, so feel free to correct me if I’m misrepresenting.)
Math is funny, in the sense that it's so necessary for us to understand but it's embedded into our culture (to some degree) that we should be afraid of it and avoid it whenever necessary....
Math is funny, in the sense that it's so necessary for us to understand but it's embedded into our culture (to some degree) that we should be afraid of it and avoid it whenever necessary. Students, especially underrepresented students, pick up on this and are very sensitive to math education -- they'll only learn it insofar as it applies to their day to day life. My experience with the situation is that if you let students choose between math and "not math" (say, data literacy), students will choose the not math course.
I don't think we should be finding alternatives for such fundamental courses. People will argue that Algebra 2 is not necessary for most students lives, but I dont think I've used my history courses at all, my philosophy courses are fun for parties, and arguably my English courses (beyond grammar) have been useless (though many arguments can be made here). I think all of these courses are important to forming who I am today and my understanding of the world, and I am very happy I did take them. I wish others would apply the same logic to math.
To start, some background about me: this subject is an "oddly specific" issue I've been passionate about for years (arguments for and against tracking and the like have been going on as long as I...
To start, some background about me: this subject is an "oddly specific" issue I've been passionate about for years (arguments for and against tracking and the like have been going on as long as I can remember). I have a degree in education (although my specialization was not math), I worked in a math department at a community college, and I'm a grad student in a math department at an R1 university.
On a personal level, I benefited greatly from tracking. In middle school I was bored out of my mind in all my classes except math, which was tracked-- it was the only class I liked because I felt like I was actually learning rather than of being forced to sit around doing busy work. For reference, I took Algebra I in the 7th grade and excelled at it. I have fond memories of math in school and it is only because I wasn't forced to move so slowly that I wanted to gauge my eyes out. I get mad when I mentally put myself into the shoes of a middle schooler who would be forced to wait a whole 2 years to learn material that they are capable of and want to learn at a younger age (not everyone hates math-- some of us love it). The whole idea this could happen is absurd.
It should be pretty obvious whose "side" I'm on. As someone who's studied education, I've seen the arguments, but they've always had about as much evidence to back them up as the "arguments" of the people who propose this new California policy (aka not much). Sadly, I would argue that, based on my experience in education academia, many of the researchers in the field of education are themselves mathematically illiterate and often have a bizarre level of disgust towards the subject. It is not only sad to see, but infuriating that they have political influence. Some of the research I've seen produced in the field of education is so bad that I feel confident saying that even my stats 101 students could call them out for blatant misrepresentation of the data. The fact that tenured professors get away with this is shameful-- absolutely shameful.
I get that there are systemic inequalities. Getting rid of opportunities for bright students (many of whom are underrepresented minorities) to learn more rigorous math at an earlier age simply will not help solve the problem they're trying to solve and instead will cause damage. The article and Brian Conrad's site linked by @miyu provides good evidence that the whole premise of forcing 9th grade Algebra I is bullshit. I highly recommend exploring Conrad's website if you want an idea of the quality of "research" I saw when I was an undergrad studying education.
To be clear, not all research in education is bad. But the bad research is really bad, "peer reviewed" my ass. Clearly there are enough incompetent researchers that bullshit gets passed peer review and published in "reputable" journals.
I left education because I've decided I'm done with the idiocy that permeates the field. It's just not worth the stress.
I'm much happier working in a place where I don't feel like an outcast because I believe in the value of mathematical rigor.
Sorry for the rant. I've been waiting years to get this off my chest.
Wow, that’s worse than I thought. I’m bewildered by the claim that removing tracking improves equity, it seems quite obvious to me that those with means would hire a private math tutor to get...
Wow, that’s worse than I thought. I’m bewildered by the claim that removing tracking improves equity, it seems quite obvious to me that those with means would hire a private math tutor to get ahead anyways which will only widen the gap.
I may not have come from enough money for my family to hire a private tutor for several years of math, but I know my family and I would’ve found a way to get ahead: math has always been my favorite (or related to my favorite) subject, and we likely would’ve used some amalgamation of Khan Academy and IXL or similar. I did it before to skip up to the next track, I’d do it again in a heartbeat.
This feels suspiciously similar to the claims about how we’ll have fewer COVID cases if we stop testing people for COVID. People will fail math less often if you stop teaching it!
Googling "California CMF" led me to a clearly biased article with text like:
Clearly that's talking past the point of opposition in bad faith, since I have a hard time believing many educators are actually opposing a framework because it favors equality or opportunity for all...
Diving further, I ran across this site by Brian Conrad, Professor of Mathematics and Director of Undergraduate Studies in Math, Stanford University: https://sites.google.com/view/publiccommentsonthecmf/ with gems like:
Anyway, personal opinions: a course on data literacy sounds great and is more applicable to real-life than algebra. California / the US don't let children specialize, which leads to these weird either-or situations; if you're pursuing certain subfields of STEM, you need a strong grasp of calculus, linear algebra, and differential equations to understand many basic concepts from first principles. For other subfields and non-STEM fields, there's effectively zero benefit to learning calculus and something like data literacy is far more valuable (e.g. how to interpret data and detect misleading conclusions). There shouldn't be one track for all students, and if perhaps there isn't time to teach these valuable concepts to students, we need to reevaluate the entire structure of education, not mess up math in isolation.
I'm learning several years out of an engineering degree and Masters, that the math I wished I did more of and am now self teaching is statistics. We should teach everyone 5x more probability and statistics than we do now.
Also when it comes to actually doing maths, starting by writing proofs and basic logic would have been a dream for me. (I am very first principles / start with a blank sheet of paper and some axioms).
I didn't touch anything related to mathematics at university, but at my school the class with by far the highest fail rate overall was Introductory Statistics. It was (and presumably still is) a core unit for a lot of different degrees, and in my last year there the pass rate was so low that they ended up having to split it in half so people could take it across two semesters. We are talking people who were ordinarily pretty handy with maths skills, but that class used to turn people into a dribbling mess by week 5.
For reference, I'm a grad student in statistics. My own personal belief is that the entire way we teach introductory statistics should probably be overhauled. The specific curriculum should depend largely on a person's major, which is already often the case (psychology majors learn different material than engineering majors in their statistics classes) but I find that people typically come out of these classes barely understanding the basic definitions and meaning of concepts, which is likely the underlying reason the subject seems hard.
Honestly I also think emphasis should be put on the fact that universities have statistical consulting services for researchers and that no one should hesitate or feel embarrassed if they want or need help with statistical design or analysis. Just like you wouldn't expect someone who doesn't have years of study or experience in your field to be that great at it, statisticians don't expect non-statisticians to be great at statistics and we'd much rather have people consult with us than try to wing it, which often results in crappy research.
That being said, everyone should have a grasp of certain basic fundamentals. I'd err on the side of focusing more on interpretation of data and statistical results than application of statistical methods since nearly everyone needs to interpret research at some point but few people will actually be doing research themselves.
In the end, I do wish there were more emphasis on statistics in schools, but it is also worth noting that calculus and the like is an integral (pun not intended) part of the building blocks of the field and that you can't really understand statistics on any sort of deep level unless you understand calculus and all its prerequisites.
I work in the data space. You would not believe the amount of people at all levels of society who simply fail to grasp how statistics and data works is unreal.
Even basic averages can baffle some folks, it's really harrowing how weak our maths skills are.
My doc and I talked about it during a session, our conclusion is that HS Math education should cover:
Algebra (they're starting basics as early as K now, which is great)
Geometry/Trig
Logic/Statistics
Finance
Programming (thats right, mandatory programming classes)
Calculus and the like can be saved for post-secondary, where it belongs. It's so impracticle outside of deep STEM.
For those interested, these are the general HS graduation requirements in the US by state:
https://reports.ecs.org/comparisons/high-school-graduation-requirements-2023-04
And specific math requirements by state (old, from 2007):
https://files.eric.ed.gov/fulltext/ED535222.pdf
The majority of states require Algebra I. Most require 3 years of math, usually offering Algebra I, Geometry, and Algebra II as the easiest path to fulfill this requirement. I count only 8 states that require personal finance, and no direct reference to statistics or logic (though statistics might be available to fulfill a 4-year math requirement).
On the other hand, no state in the US requires Calculus for graduation (individual schools notwithstanding). Table 3 in the 2nd link.
I think it’s fine to offer Calculus as an optional 4th-year class for those that know they’re headed into STEM.
(I just skimmed these links, so feel free to correct me if I’m misrepresenting.)
Math is funny, in the sense that it's so necessary for us to understand but it's embedded into our culture (to some degree) that we should be afraid of it and avoid it whenever necessary. Students, especially underrepresented students, pick up on this and are very sensitive to math education -- they'll only learn it insofar as it applies to their day to day life. My experience with the situation is that if you let students choose between math and "not math" (say, data literacy), students will choose the not math course.
I don't think we should be finding alternatives for such fundamental courses. People will argue that Algebra 2 is not necessary for most students lives, but I dont think I've used my history courses at all, my philosophy courses are fun for parties, and arguably my English courses (beyond grammar) have been useless (though many arguments can be made here). I think all of these courses are important to forming who I am today and my understanding of the world, and I am very happy I did take them. I wish others would apply the same logic to math.
To start, some background about me: this subject is an "oddly specific" issue I've been passionate about for years (arguments for and against tracking and the like have been going on as long as I can remember). I have a degree in education (although my specialization was not math), I worked in a math department at a community college, and I'm a grad student in a math department at an R1 university.
On a personal level, I benefited greatly from tracking. In middle school I was bored out of my mind in all my classes except math, which was tracked-- it was the only class I liked because I felt like I was actually learning rather than of being forced to sit around doing busy work. For reference, I took Algebra I in the 7th grade and excelled at it. I have fond memories of math in school and it is only because I wasn't forced to move so slowly that I wanted to gauge my eyes out. I get mad when I mentally put myself into the shoes of a middle schooler who would be forced to wait a whole 2 years to learn material that they are capable of and want to learn at a younger age (not everyone hates math-- some of us love it). The whole idea this could happen is absurd.
It should be pretty obvious whose "side" I'm on. As someone who's studied education, I've seen the arguments, but they've always had about as much evidence to back them up as the "arguments" of the people who propose this new California policy (aka not much). Sadly, I would argue that, based on my experience in education academia, many of the researchers in the field of education are themselves mathematically illiterate and often have a bizarre level of disgust towards the subject. It is not only sad to see, but infuriating that they have political influence. Some of the research I've seen produced in the field of education is so bad that I feel confident saying that even my stats 101 students could call them out for blatant misrepresentation of the data. The fact that tenured professors get away with this is shameful-- absolutely shameful.
I get that there are systemic inequalities. Getting rid of opportunities for bright students (many of whom are underrepresented minorities) to learn more rigorous math at an earlier age simply will not help solve the problem they're trying to solve and instead will cause damage. The article and Brian Conrad's site linked by @miyu provides good evidence that the whole premise of forcing 9th grade Algebra I is bullshit. I highly recommend exploring Conrad's website if you want an idea of the quality of "research" I saw when I was an undergrad studying education.
To be clear, not all research in education is bad. But the bad research is really bad, "peer reviewed" my ass. Clearly there are enough incompetent researchers that bullshit gets passed peer review and published in "reputable" journals.
I left education because I've decided I'm done with the idiocy that permeates the field. It's just not worth the stress.
I'm much happier working in a place where I don't feel like an outcast because I believe in the value of mathematical rigor.
Sorry for the rant. I've been waiting years to get this off my chest.
Wow, that’s worse than I thought. I’m bewildered by the claim that removing tracking improves equity, it seems quite obvious to me that those with means would hire a private math tutor to get ahead anyways which will only widen the gap.
I may not have come from enough money for my family to hire a private tutor for several years of math, but I know my family and I would’ve found a way to get ahead: math has always been my favorite (or related to my favorite) subject, and we likely would’ve used some amalgamation of Khan Academy and IXL or similar. I did it before to skip up to the next track, I’d do it again in a heartbeat.
This feels suspiciously similar to the claims about how we’ll have fewer COVID cases if we stop testing people for COVID. People will fail math less often if you stop teaching it!