https://scottaaronson.blog/?p=6146 Shtetl-Optimized The Blog of Scott Aaronson If you take nothing else from this blog: quantum computers won't solve hard problems instantly by just trying all solutions in parallel. Also, next pandemic, let's approve the vaccines faster! --------------------------------------------------------------------- << Two new talks and an interview An alarming trend in K-12 math education: a guest post and an open letter Today, I'm turning over Shtetl-Optimized to an extremely important guest post by theoretical computer scientists Boaz Barak of Harvard and Edith Cohen of Google (cross-posted on the windows on theory blog). In addition to the post below, please read--and if relevant, consider signing--our open letter about math education in the US, which now has over 150 signatories, including Fields Medalists, Turing Award winners, and Nobel laureates. Finally, check out our fuller analysis of what the California Mathematics Framework is poised to do and why it's such an urgent crisis for math education. I'm particularly grateful to my colleagues for their writing efforts, since I would never have been able to discuss what's happening in such relatively measured words. -Scott Aaronson --------------------------------------------------------------------- Mathematical education at the K-12 level is critical for preparation for STEM careers. An ongoing challenge to the US K-12 system is to improve the preparation of students for advanced mathematics courses and expand access and enrollment in these courses. As stated by a Department of Education report "taking Algebra I before high school ... can set students up for a strong foundation of STEM education and open the door for various college and career options." The report states that while 80% of all students have access to Algebra I in middle school, only 24% enroll. This is also why the goal of Bob Moses' Algebra Project is to ensure that "every child must master algebra, preferably by eighth grade, for algebra is the gateway to the college-prep curriculum, which in turn is the path to higher education." The most significant potential for growth is among African American or Latino students, among whom only 12% enroll in Algebra before high school. This untapped potential has longer-term implications for both society and individuals. For example, although African Americans and Latinos comprise 13% and 18% (respectively) of the overall US population, they only account for 4% and 11% of engineering degrees. There is also a gap in access by income: Calculus is offered in 92% of schools serving the top income quartile but only in 77% of schools serving the bottom quartile (as measured by the share of students eligible for free or reduced-price lunch). Thus minority and low income students have less access to STEM jobs, which yield more than double the median salary of non-STEM jobs, and are projected to grow at a 50% higher rate over the next decade. Given these disparities, we applaud efforts such as the Algebra Project, the Calculus Project, and Bridge to Enter Advanced Mathematics that increase access to advanced mathematical education to underserved students. However, we are concerned by recent approaches, such as the proposed California Math Framework (CMF) revisions, that take the opposite direction. See this document for a detailed analysis and critique of the CMF, but the bottom line is that rather than trying to elevate under-served students, such "reforms" reduce access and options for all students. In particular, the CMF encourages schools to stop offering Algebra I in middle school, while placing obstacles (such as doubling-up, compressed courses, or outside-of-school private courses) in the way of those who want to take advanced math in higher grades. When similar reforms were implemented in San Francisco, they resulted in an "inequitable patchwork scheme" of workarounds that affluent students could access but that their less privileged counterparts could not. The CMF also promotes trendy and shallow courses (such as a nearly math-free version of "data science") as recommended alternatives to foundational mathematical courses such as Algebra and Calculus. These courses do not prepare students even for careers in data science itself! As educators and practitioners, we have seen first-hand the value of solid foundations in mathematics for pursuing college-level STEM education and a productive STEM career. While well-intentioned, we believe that many of the changes proposed by the CMF are deeply misguided and will disproportionately harm under-resourced students. Adopting them would result in a student population that is less prepared to succeed in STEM and other 4-year quantitative degrees in college. The CMF states that "many students, parents, and teachers encourage acceleration beginning in grade eight (or sooner) because of mistaken beliefs that Calculus is an important high school goal." Students, parents, and teachers are not mistaken. Neither is the National Society of Black Engineers (NSBE), which set in 2015 a goal to double the number of African American students taking calculus by 2025. Calculus is not the only goal of K-12 math education, but it is important for students who wish to prepare for STEM in college and beyond. We agree that calculus is not the "be-all and end-all" of high-school mathematics education. In particular, we encourage introducing options such as logic, probability, discrete mathematics, and algorithms design in the K-12 curriculum, as they can be valuable foundations for STEM education in college. However, when taught beyond a superficial level (which unfortunately is not the case in the CMF "data science" proposals), these topics are not any easier than calculus. They require the same foundations of logic, algebra, and functions, and fluency with numbers and calculations. Indeed, the career paths with the highest potential for growth require more and deeper mathematical preparation than ever before. Calculus and other mathematical foundations are not important because they are admission requirements for colleges, or because they are relics of the "Sputnik era". They are important because they provide fundamental knowledge and ways of thinking that are necessary for success in these fast growing and in-demand fields. We also fully support incorporating introductory data analysis and coding skills in the K-12 curriculum (and there are some good approaches for doing so). But we strongly disagree with marketing such skills as replacing foundational skills in algebra and calculus when preparing for 4-year college degrees in STEM and other quantitative fields. These topics are important and build on basic math foundations but are not a replacement for such foundations any more than social media skills can replace reading and writing foundations. Given the above, we, together with more than 150 scientists, educators, and practitioners in STEM, have signed an open letter expressing our concerns with such trends. The signatories include STEM faculty in public and private universities and practitioners from industry. They include educators with decades of experience teaching students at all levels, as well as researchers that won the highest awards in their fields, including the Fields Medal and the Turing Award. Signers also include people vested in mathematical high-school education, such as Adrian Mims (founder of The Calculus Project) and Jelani Nelson (UC Berkeley EECS professor and founder of AddisCoder) who have spearheaded projects to increase access to underserved populations. We encourage you to read the letter, and if you are a US-based STEM professional or educator, consider signing it as well: https://bit.ly /mathedletter Unfortunately, in recent years, debates on US education have become politicized. The letter is not affiliated with any political organization, and we believe that the issues we highlight transcend current political debates. After all, expanding access to mathematical education is both socially just and economically wise. --------------------------------------------------------------------- Note: The above guest post reflects the views of its authors, Boaz Barak and Edith Cohen. Any comments below by them, me, or other signatories reflect their own views, not necessarily those of the entire group. -SA Email, RSSEmail, RSS Follow This entry was posted on Friday, December 3rd, 2021 at 9:59 am and is filed under Announcements. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site. 11 Responses to "An alarming trend in K-12 math education: a guest post and an open letter" 1. Boaz Barak Says: Comment #1 December 3rd, 2021 at 10:04 am Thank you Scott for posting this! I've also wrote about this on Twitter https://twitter.com/boazbaraktcs/status/ 1466799615349608452?s=20 I hope this can make a positive change towards increasing access to advanced math education to more students. 2. Boaz Barak Says: Comment #2 December 3rd, 2021 at 10:21 am Also, the "Bridge to Enter Advanced Mathematics" (BEAM) project is currently having a 10x match program for new donors (and px match for returning donors). If you want to support projects that make a real difference in expanding access to math, take a look at https://www.beammath.org/donate Another project worth supporting is (co signer) Adrian Mims' calculus project https://secure.actblue.com/donate/ thecalculusproject 3. Wolfgang Richter Says: Comment #3 December 3rd, 2021 at 1:09 pm Scott thanks so much for posting this! I consider Computer Science to be on the tree of mathematics, and wondered if you do too? Mathematics just encompasses so much of all that everyone does today! I definitely do not want to see any steps back in math education, and would much rather see steps forward. 4. DavidM Says: Comment #4 December 3rd, 2021 at 1:20 pm Linked indirectly from that document: https://www.mathpathsf.com/ eighth-grade/ They're mad, these Americans. Can it really be true that in the world capital of progressivism people who would presumably talk your ears off about equity and social justice have created a system that allows kids to test out of easy classes, but only if they went to a private school or could afford to pay for an accredited course? 5. Scott Says: Comment #5 December 3rd, 2021 at 1:27 pm Wolfgang Richter #3: CS is famously a hybrid field, with some aspects that are fundamentally math, some aspects that are actually empirical science, and some aspects that are engineering or even art--united only by the shared interest in computation. You even see that in university organization: CS departments are sometimes part of arts and sciences colleges, sometimes part of engineering colleges, and sometimes even adjoined to math departments. I've personally worked or studied at universities with all three arrangements. 6. DR Says: Comment #6 December 3rd, 2021 at 2:08 pm I keep hearing about "Why Calculus?" in connection with high school math. My response is always, why a one-size-fit-all? Different people might want different things in their child's education. They are all right, for THEIR respective kids. I think the bigger question everyone is hesitant to ask, is why there is a one-size-fit-all solution. I think that is the right question. 7. Stefan Krastanov Says: Comment #7 December 3rd, 2021 at 2:48 pm I do not believe this set of signatories is what would give credence to this letter. University professors are good researchers and in some cases they are even be good college instructors, but they are very rarely good K12 instructors. At least in my experience of organizing K12 outreach events on university campuses. It would be much easier to convince me this is indeed a worrying trend if I see K12 educators and researchers studying K12 education and child development sign this letter. Otherwise some kind of logical fallacy is creeping in. My (admittedly flawed and biased) reading of the new CA plan says "gifted programs are fine, but we need to focus on the basics in a way that works for all K12 students". Lifting all boats, etc etc. 8. Jr Says: Comment #8 December 3rd, 2021 at 3:06 pm I am skeptical that there is some great benefit to be gained by trying to extend how many minority students take advanced math courses. In particular, the framing contributes to a major problem in western society today, where underperformance of minority groups is seen as a sign of societal oppression, instead of a reason for the minority group to assimilate better. 9. Scott Says: Comment #9 December 3rd, 2021 at 3:29 pm Stefan Krastanov #7: My (admittedly flawed and biased) reading of the new CA plan says "gifted programs are fine, but we need to focus on the basics in a way that works for all K12 students". Lifting all boats, etc etc. Alas, that's indeed a flawed and biased reading! Joanne Boaler, the architect of the new CA plan, has gone on record wanting to do away with gifted programs and academic acceleration entirely; she does not regard them as "fine." And if you want to focus on basics in a way that works for all students--well, what could be more basic than algebra? University professors are good researchers and in some cases they are even be good college instructors, but they are very rarely good K12 instructors ... It would be much easier to convince me this is indeed a worrying trend if I see K12 educators and researchers studying K12 education and child development sign this letter. Among our drafters are people like Boaz Barak, Jelani Nelson, Adrian Mims, and yours truly, all of whom have been directly involved in various kinds of K-12 outreach. By contrast, the new California math framework seems to have been developed entirely by ed-school types, without meaningful input of any kind from STEM professionals. And that seems directly related to why the framework document is so wilfully oblivious to what students pursuing STEM degrees in college will actually need as preparation. 10. arcana Says: Comment #10 December 3rd, 2021 at 4:34 pm The California plan is bad IMO but it the problem is very complicated to solve and I'm not sure the signatories deal with that at all. Every child can't and shouldn't master algebra by 8th grade. Not that it matters since no existing form of modern education could achieve that anyway. First we shouldn't be teaching a ton of standardized math until ~11 anyway. This strongly results in a perhaps majority of people who think they are "bad at math". They strongly believe they aren't and can't be good at it. Even Scott Siskind famously can't believe he could be great at math. It is possible we could identify the causes of some kids having an aptitude for and more importantly an interest in accelerated math development but we haven't and force feeding math to people who aren't yet ready makes them hate it. Something similar operates on the infamous high school "english lit and text interpretation classes" although that problem is not nearly as critical. Having tools for emotional self-regulation, stronger executive function, and better abstract thinking would allow even kids who are not ideal candidates for mathematical acceleration to at least avoid deeply ingrained anti-math thoughts. Additionally there is strong evidence that students wouldn't particularly suffer by removing standardized mandatory math classes during elementary school. And you could still allow kids who are talented at or enjoy math to take early advanced courses. One size fits all math education is terrible inherently and our current implementations are extra bonus bad. 11. Boaz Barak Says: Comment #11 December 3rd, 2021 at 4:40 pm This is now on Hacker News as well https://news.ycombinator.com/ item?id=29432816 Leave a Reply Comment Policy: All comments are placed in moderation and reviewed prior to appearing. Comments can be left in moderation for any reason, but in particular, for ad-hominem attacks, hatred of groups of people, or snide and patronizing tone. Also: comments that link to a paper or article and, in effect, challenge me to respond to it are at severe risk of being left in moderation, as such comments place demands on my time that I can no longer meet. You'll have a much better chance of a response from me if you formulate your own argument here, rather than outsourcing the job to someone else. I sometimes accidentally miss perfectly reasonable comments in the moderation queue, or they get caught in the spam filter. If you feel this may have been the case with your comment, shoot me an email. You can now use rich HTML in comments! 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