Mathematical mindsets

What Hacker News says

1. BeldinOct 2019
   I would recommend "The Number Devil" [1] for children (from 11 on) and adults alike.

   It's a zany story, but in that respect it provides a refreshing intro into some math concepts.

   In that vein, I also recommend "mathematical mindsets" [2]. A colleague developed a course inspired by this book. Though I only witnessed a tidbit, it radiated with the "new perspective/ new insights / gained understanding" that you'd get from the Feynman lectures.

   Sidenote: neither is "now you know how all of maths work", but neither is Feynman thaf (foot physics). More importantly, all of them help you gain a new perspective on things.

   [1] eg. https://www.bol.com/nl/p/the-number-devil-a-mathematical-adv...

   [2] eg. https://books.google.nl/books/about/Mathematical_Mindsets.ht...

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2. mklAug 2018
   That may be a bad reference, but there are lots of studies about this. See the book Mathematical Mindsets by Jo Boaler for many references.
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3. ProjectibogaMar 2024
   Boaler has drawn praise from many educators for advocating for math instruction that, broadly, emphasizes real-world applications, de-emphasizes memorization, and aims to reduce gender and racial disparities. It is a vision she’s laid out in popular books like Mathematical Mindsets and Limitless Mind, and through Youcubed, a Stanford research center that she co-founded to provide free teaching resources. Education Week recently named her one of the country’s most influential scholars.

   The complaint reportedly filed on Wednesday lands as Boaler has drawn criticism for how her stances have affected math education in California and across the nation. For example, she praised San Francisco schools for adopting a policy of not teaching algebra during middle school. A decade later, the district is undoing that policy, following research showing that it did not reduce racial disparities as hoped.

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4. rahimnathwaniApr 2022
   My objections to Jo Boaler's recommendations are mainly related to the content covered in chapters 6 and 7 of her book (Mathematical Mindsets). Not all of it is wrong. But some of the things she's written in that book, and in the intro the California Math Framework 2021 is wrong-headed:

   1. She claims that studies show that detracking improves student outcomes for all students, including the strongest. The cited studies mix a number of interventions, so it's impossible to draw the conclusion that detracking caused the increase in performance.

   2. She attacks a straw man when she talks about the 'elitist construction of math'. I don't believe her characterisation that many/most people believe that math ability is genetic.

   3. The talk of open-ended 'Low floor, high ceiling' tasks sounds nice in principle. But I challenge you to come up with a task that would work for people spanning 5 grade levels's of math ability (like the 6th graders at several schools in the Bay Area), and that a median California math teacher could supervise effectively.

   4. No, there's no rule that says, if you group kids by ability, you can't provide differentiated instruction within each classroom.

   5. If high school math achievement is used as a gatekeeper for college admissions, and this reinforces inequity, the answer cannot be to hold some students back. Rather, we should improve early math education so that people can all progress. Even if it's true that folks who study calculus in high school end up studying it again in college, this doesn't indicate they didn't benefit from that high school exposure.

   6. The five strides of Equitable Math (https://equitablemath.org/) (recommended in the California Math Framework 2021, Chapter 2), is NOT a good guide to improving math teaching. Its characterisation that every problem with math education is the cause of 'White Supremacy culture' is plainly wrong. Many of those problems exist in places like China, and it's hard to claim that's also a result of white supremacy. I highly recommend reading Stride 1 on that web site.

   7. She pushed some changes at San Francisco Unified School District, the main one of which was moving Algebra I from 8th grade to 9th grade. She and the district claimed great success, and published some misleading stats. I won't go into the reasons why those stats are misleading here. But just look at what happened to those students when it came time to take the SAT. The first cohort of students who did algebra in 9th grade had a 10% lower pass rate on the Math SAT than did the previous cohort (61%, down from 66%). This is on the public record: you can request the aggregate data from CA Dept Ed (it used to be online, but they took down the page, as they don't care about SAT results now that UC doesn't look at them).

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