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religion-is-a-mental-illness · 7 months

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By: Brian Conrad

Published: Oct 2, 2023

When I decided to read every word of California’s 1,000-page proposal to transform math education in public schools, I learned that even speculative and unproved ideas can end up as official instructional policy. In 2021, the state released a draft of the California Mathematics Framework, whose authors were promising to open up new pathways into science and tech careers for students who might otherwise be left behind. At the time, news reports highlighted features of the CMF that struck me as dubious. That draft explicitly promoted the San Francisco Unified School District’s policy of banishing Algebra I from middle school—a policy grounded in the belief that teaching the subject only in high school would give all students the same opportunities for future success. The document also made a broad presumption that tweaking the content and timing of the math curriculum, rather than more effective teaching of the existing one, was the best way to fix achievement gaps among demographic groups. Unfortunately, the sheer size of the sprawling document discouraged serious public scrutiny.

I am a professional mathematician, a graduate of the public schools of a middle-class community in New York, and the son of a high-school math teacher. I have been the director of undergraduate studies in math at Stanford University for a decade. When California released a revised draft of the math framework last year, I decided someone should read the whole thing, so I dove in. Sometimes, as I pored over the CMF, I could scarcely believe what I was reading. The document cited research that hadn’t been peer-reviewed; justified sweeping generalizations by referencing small, tightly focused studies or even unrelated research; and described some papers as reaching nearly the opposite conclusions from what they actually say.

The document tried hard to convince readers that it was based on a serious reading of neuroscience research. The first chapter, for example, cited two articles to claim that “the highest achieving people have more interconnected brains,” implying that this has something to do with learning math. But neither paper says anything about math education.

The CMF is meant only to guide local districts, but in practice it influences the choices they make about what and how to teach. Even so, the version ultimately adopted by the State Board of Education is likely to distort math instruction for years to come. Armed with trendy buzzwords and false promises of greater equity, California is promoting an approach to math instruction that’s likely to reduce opportunities for disadvantaged students—in the state and wherever else educators follow the state’s lead.

In my position at Stanford, I’ve heard from people around the country about the math preparation necessary to attain a variety of degrees and succeed in a range of careers. A solid grounding in math from high school—which traditionally has included two years of algebra, a year of geometry, and then, for more advanced students, other coursework leading up to calculus—is a prerequisite for a four-year college degree in data science, computer science, economics, and other quantitative fields. Such a degree is, in turn, the price of entry for jobs not only in the sciences and Silicon Valley but also in a number of seemingly distant fields. A data scientist at a company that makes decisions about how and when to store, freeze, and transport food once told me that he and his crew “could not do our jobs” without fluency in areas of college-level math that require previous mastery of the basics.

Without overtly saying so, California is building off-ramps from that kind of math. The CMF pitches relatively new courses, branded as “data science,” both as an alternative to a second year of algebra and as an entry point into fast-growing career fields. But the course name is something of a misnomer.

In private industry and higher ed, data science describes a powerful synthesis of computer science, mathematics, and statistics that seeks to extract insights from large data sets. It has applications in industries as varied as health care, retail, and, yes, food-supply logistics. The ability to do actual data science rests on math skills that have been taught for eons. Data literacy would be a better name for the most widely taught high-school data-science classes, which were developed by UCLA’s statistics department and my own university’s Graduate School of Education. To be sure, schools should be teaching citizens enough about statistics and data to follow the news and make educated financial and health decisions. Many parts of the math curriculum can be illustrated with engaging contemporary data-oriented applications. But much as a music-appreciation course won’t teach you how to play a piano, data literacy is not data science.

Advocates of the new courses have suggested that they produce better outcomes for groups, such as girls and students of color, that are traditionally underrepresented in mathematics. But proponents should own up to the downstream effects: In practice, steering sophomores and juniors away from Algebra II forecloses the possibility of careers in certain fast-growing quantitative fields—which would seem to do the opposite of promoting equity. Many schools in Europe and Asia separate students into different career paths early on in their education, but a key goal of the American system has been to help students keep their options open. In other contexts, the CMF is notably skeptical of efforts to group students in math class according to ability, out of a fear that disadvantaged students will be placed in low-expectation tracks that they can never escape. But for some reason, shunting them away from advanced math is portrayed as progress. The STEM fields won’t increase their diversity through math classes that contain very little math.

Ultimately, I ended up submitting 170 pages of documentation about extensive flaws in the CMF draft that I read. I was hardly the only one finding fault. A multiracial national coalition of more than 1,700 quantitative experts from higher education and industry strongly objected to the early drafts. Faculty in the University of California and California State University systems wrote letters warning state officials against prematurely steering students away from algebra-intensive academic and career options. UC administrators had begun to allow data-literacy courses to fulfill Algebra II admissions requirements, but a faculty working group representing all campuses in the system voted unanimously this summer to reverse that policy.

Before the State Board of Education in California approved the third version of the CMF in July, officials did try to address some of its flaws. Although school officials in San Francisco had largely ignored parents who questioned the district’s policy against offering Algebra I in middle school, critics refused to give up, and for good reason. A recent working paper from three Stanford researchers indicates that the San Francisco Unified School District’s decade-long experiment was a bust. The percentage of Black and Latino students taking advanced math courses did not increase. Some students who would otherwise have studied calculus as high-school seniors were unable to do so. The kids who succeeded in reaching calculus typically did so through extracurricular measures, such as summer classes. Later CMF drafts quietly removed the mention of the SFUSD policy while still generally endorsing the ideas behind it.

Meanwhile, the ideas that animate the CMF—particularly its endorsement of data-literacy classes as a substitute for math and its suggestion that large swaths of the traditional high-school math curriculum are obsolete—are popping up in other states. In Ohio, for example, a menu of alternative math “pathways” in high school has been touted as providing entry into a variety of appealing and lucrative careers. But the pathways labeled for data science and computer science remove many Algebra II skills; the fine print reveals that the pathways are inadequate for students who might want college degrees in those fields. School officials in Middletown, Connecticut, have proposed to revamp the traditional calculus track by scaling back on preparations for eighth-grade Algebra I and introducing mash-up algebra-and-geometry courses that would magically pack three years of instruction into two.

Unfortunately, not every state has a critical mass of academic experts and private-sector tech practitioners to push back when school systems try to rebrand an inferior math education as something new and innovative. The students who are most reliant upon public schools are the most harmed when districts embrace policies based on superficial appeals to equity or false promises about future job opportunities. When only the children of families with resources beyond the public schools are gaining preparation for the lucrative degrees and secure jobs of the future, public education is failing in a primary duty.

Brian Conrad is a mathematics professor and the director of undergraduate mathematics studies at Stanford University.

[ Via: https://archive.md/OuKIa ]

Nothing good comes of lowering standards or encouraging students to opt out of challenge.

A class in Math Appreciation is not not a substitute for Math.

#Brian Conrad #corruption of education #mathematics #math #maths #ideological corruption #ideological capture #equity #math equity #math education #low expectations #bigotry of low expectations #math appreciation #religion is a mental illness

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milkamilkamoo · 1 year

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Sometimes the learning process does not allow us to be organized.

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drafthorsemath · 9 months

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I gotta rant about the state of math education for a minute. I say this as a math educator with a math PhD who currently works to create digital math content and assessments (primarily for high school and college level). We have to do better for students and the way we're attempting to do that is mostly garbage because of publishing companies.

I currently work for two educational publishers who will remain unnamed. They're competitors and I think it's funny that I and one other person I know work for both of them.

Anyway, company M, who I primarily work for, is finding that students are using fewer of their tools and appear to just guess when they don't know an answer instead of attempting and getting feedback. Instead of figuring out what would actually help students, this company is taking a more bare bones approach to authoring math assessment tools going forward, firing authors (the team I was on used to have over 20 people at any given time and now there are 4 of us), and then complaining how we can't keep up with authoring new content. The problem is that they are not offering a wider variety of content for different types of learners, but they don't want to hear that. They write a textbook, make online homework and study guides for it, and call it good. That's not nearly enough, but they don't want to invest in getting better.

This week I started training for a new part time job at company C to try to make a little more money and they are trying to do a better job. They want higher student engagement, fewer assessments, and for students to explore a topic instead of traditional lectures. Great. Research supports a more interactive approach to learning. Except their idea of student engagement and interaction solely focuses on extroversion: reading, writing, conversing, analyzing, actively listening, group work, sharing with the class, and more. And none of it has the options of being done alone. On top of this, they do not address disabilities and are only just starting to realize they need different content for multilingual learners.

Some students can actually read and learn and do not need to interact. Some students are anxious to interact. I've seen it. I've had a student stuttering just trying to talk in class to ask a question, and making her come to the board? Why? For what purpose? Said student was already doing well in class and she simply wrote everything out. I had multiple students who were combat veterans; one in particular who had a brain injury and needed a lot of repetition. Having a lot of approaches in a 50 minute class would have been overwhelming for him since he needed clear examples and lots of independent practice. He thrived in my office hours. Forcing this model will not help these students. While I think there are some good things about this versus just using a digital textbook, I take issue with the approach because it is still forcing students to all learn the same way. It's a different way of learning than using a textbook, but there is no room for flexibility.

Look, I know that it's impossible to teach a classroom of students in a way that gives each enough time and resources to perfectly meet their needs. I taught at a university for 8 years. I've tutored students in grades 3-12 for over a decade. This is not me bashing teachers, lecturers, or professors. I know they are simply limited to what math ed materials are on the market and what they write themselves. (Thinking of Dr. Bell who wrote his own book for Modern Algebra because he hated every book on the market.) I just get frustrated when everyone (publishers) tries to push new teaching styles and tools, saying "there are multiple approaches to suit multiple learners." If each student must go through and master each approach, how is that any better than saying they must all master this one approach?

I'm just a frustrated math lady. Also, this has reminded me of the time many years ago when I had an anon who would ask for math homework help in my inbox because they had no where else to go. That was also before we had DMing on tumblr. Thinking of you today, Stats Anon.

#math #math education #about me #math publishing #so many educators out there trying their best and the materials they have to work with are just not enough #the answer to this is probably increase funding for education

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mathhombre · 3 months

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Deborah Loewenberg Ball

@jstor has a great series on intellectual humility, and I thought it was interesting that they interviewed a math teacher educator for a math part. Dr. Ball is definitely one of the national leaders on teacher education in general, and did a lot of great work on math education when she was researching.

A colleague and I have a bit of an ongoing joke about how is she going to bring up Shea, because she always does...

This is a fairly well known story. Giggle.

But great interview, with links to lots of great articles because it's JSTOR. The main point is about how math is a good place to learn these things, but gets at the barriers that come from school being racialized and gendered.

#math education #interview #intellectual humility

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sailing-the-cylindrical-sea · 1 year

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Calculus Made Easy, by by Silvanus P. Thompson, 1910. Full text available online.

Love this book. I read it after already learning calculus, but I learned a lot about how to teach a complicated subject in an approachable way.

#mathematics #mathisfun #calculus #education #math education

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wielsonf · 5 months

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why qualitative research matters to teaching (mathematics)

the pioneer cohort of ed.d. and ph.d. educ at ateneo gbseald with dr. ma. assunta "achoot" cuyegkeng / screengrabs from markkie aribon and lavi subang of ed.d.

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i told the internet about why i am where i am now in a previous post. now, i am ready to share what invaluable knowledge i've got from one of my courses so far.

during my undergrad and graduate studies, just pen and paper is mostly sufficient to create new ideas, problems, and solutions, and do research in math, but that's not the only concern i have with life and work.

for the past half a decade or so, peers and i saw a decline in the perceived quality of students in calculus at the university of the philippines los banos. what was supposed to be tackled in senior high school, like algebra, trigonometry, and precalculus especially for those from stem track, wasn't adequately done so. when introduced to fundamental calculus concepts, they do understand the notion of limit, how lines and derivatives intertwine and entangle, and why area is an integral, but when it comes to crafting solutions and answering problems, this inadequacy becomes apparent.

in turn, it becomes necessary for us to ask why this is the case? how do teachers influence their students' calculus learning and what are they doing to adapt? has existing policies done us (dis)service in the philippine (math) education? and, why is everybody and nobody at fault here?

just thinking about possible solutions is not enough. we need to get our hands dirty, wreck some established norms, and possibly hurt some feelings in the process. qualitative research, i learned, has some of the answers.

as i mentioned in a previous post,

for this course, i posed this question: how do teachers facilitate collegiate calculus learning through creative interventions?

in an attempt to answer this question, i had to look back at what is happening and what research tells us about calculus learning.

for one, most mathematics learning theories are based on existing ones from classical learning theories, like constructivism, positivism, and behaviorism. since the start of the 21st century, one of the main motivations of mathematics education research is rationalizing a theory for mathematics in consideration of its unique nature as a subject matter.

next comes becoming aware of challenges and factors in teaching and learning calculus, how do teachers intervene, and how important their role is.

as of yet, i think the question can't be answered by a simple survey, answered using a likert scale. we have to go on the ground and diligently ask calculus teachers and instructors in college the existing literature still resonate with the challenges they face and what they do about them in order to help their students. the quality of administration and prestige of the institutions they serve affect their students, but in reality, educators are at the frontline facing the students and implementing interventions as they go along day by day. their experience is a vital part of understanding the problem.

we should break down such a complex question into easily digestible and directly answerable ones that help us understand sac (structures-agency-culture): ask where the teachers come from, what kind of pool do they dive in to teach calculus, what restrictions they are put in, what the students are like, what they do to help the children [sic], and in what way do their interventions affect the students.

with the pisa results just released, now more than ever, we need to act as fast as we can to implement changes from the ground up.

why are we, everyone at school, so miserable in one way or another? this, i can definitely say, is my magnum opus.

i will die on this hill.

#education #critical realism #math #mathed #math education #philippines

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futurebird · 5 months

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For math teachers ONLY

Here is a simple trick to seem like a hot shot when teaching about exponentials. It’s easy to memorize a boatload of digits from e.

First you just need to know the first two. can’t help you there, but you know it’s 2.7 right?

Ok now only two more things will get you 14 digits deep. 1. a year 2. a triangle

Imagine a Webster’s Dictionary but it’s an isosceles right triangle: half is missing because Andrew Jackson burned it.

2.7 1828 1828 45-90-45

If you want 11 more digits … after the half burned dictionary now a more happy image. Michael Jordan! he stands arms out making everything better. He turns around exactly five times healing the world. “‘28 was a bad year” he says in a deep voice but what he says next is drowned out by the jet plane … you only catch the last words “… bad luck”

2.7 1828 1828 45-90-45 23 (5 360s) “28 … 747 … 13”

#math #math education #exponential

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dodecalemma · 1 year

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It is abundantly clear to me that the person who said this (Bob Hughes) does not understand math education and it’s a shame he’s the one heading the over 1 billion dollar effort to “improve” it.

#this makes me sad #what do you think?#will Id later #undescribed #math education #mathblr #mathematics #education #math #bill gates #I have such a long criticism of this plan #but I don’t know if I should put it on tumblr #send an ask if you’re interested to hear more about what I think of this

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art-of-mathematics · 2 years

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Your blog intro brings to mind the best line I’ve ever read as someone trying to change how mathematics classrooms and curriculum are approached. From Paul Lockhart’s A Mathematician’s Lament, “We’re killing people’s interest in circles for god’s sake!”

Anyways, as someone with similar specific interests and passions, wanted to thank you for the serendipitous encounter your blog has brought to my life, it was especially enchanting on a day like today.

Thank you for approaching me via the askbox - I am glad my blog could give you something enchanting.

Lockhart's Lament is brilliant! And I agree, the curricula are destroying education for memorization's sake - also, and especially the math field suffers under the rhetorics current "education sytems" are handled/led: "Understand nothing. Don't question. Just do what you are told." Curiosity is not just important for STEM and the arts, it's also essential for a maintaining healthy human aspects and functional co-existence. It's, much like creativity as well as compassion, the driving aspects why mankind could even come that far. Would mankind ever have survived so long with a severe reduction or even lack of curiosity (and an elevated drive by fear and avoiding?), or by morbidly elevated drive by egoism and not wanting to try anything new? I doubt it. Curiosity, creativity and compassion are three sides of one and the same (manifold-)medal, so to speak. Are they almost gone, the "scale" is out of balance - fear, comfort and hate become primary driving motivations - suffers the individual then the accompanied society suffer as well - and the loop leads back: downwards spiral. Morbid individuals and morbid groups go hand in hand.

If you give the individual hope again they can restore their own inner "flame", so to speak.

I have witnessed very often how much spark people get in their eyes when I make them realize interesting things by themselves - the eureka-moments they get - it's a very fascinating thing.

It reminds me of futility of life: People tend to fear or hate the idea that life might be futile, because they value nothingness as a lack of something. But what does a futile life lack? A pressure to achieve a pre-defined sense? Why should meaninglessness of life be considered so bad if one can create meaning all by oneself? Re-valuation requires a perspective shift - like seeing the bright side of darkness, so to speak. And seeing the neutral ("futile") reality as an empty notebook, and an opportunity to create the most wonderful playground all by yourself. I think people are confused and helpless because they can't set something helpful against unpleasant topics suh as futility. I have smashed some people's beliefs already, but afterwards thes were thankful for the perspective I have stated.

That is what curiosity induces:

"We stand on the shoulders of giants, not in fear but in wonder."

Or as a quote attributed to Marie Curie goes:

"Nothing in life is to be feared, but to be understood. Now is the time to understand more so that we can fear less."

Also: I remember Martin Luther King's quote:

"Darkness cannot drive out darkness, only light can do that. Hate cannot drive out hate, only love can do that." Strength to Love, 1963

As for "love", I would like to hint towards the connection between love and compassion, and compassion and curiosity:

Curiosity not just indicates an interest in topics, but also interest in other people, and an interest in thinking about the impact of one's own actions and words on other people.

Thus, to come back to King's quote: Hate cannot drive out hate, but compassion and understanding can. We might not be able to understand each other's viewpoints- but we can try to understand each other.

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Curiosity serves many functions:

It satisfies natural interest. It lets us expand our minds. It gives us insights. It makes us wonder. It might give us awe and inspiration, and fuel us to challenge the status quo.

But it might also enable a more functional co-existence with other people, as it might also increase authentic interaction with others.

Curiosity might also help restore a better own inner harmony with oneself.

Sooo, I am sorry I indulged into a semi-sentimental rant.

(I am also really thankful that you encountered me - and shared your thoughts. I am glad you have similar interests and passions. )

#sandtripper #curiosity #math ed #math education #education #education system #creativity

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