Boaler, Wolfram, (Musk?), and the Battle for School Mathematics
Recently stories have appeared in the mainstream news of Dr Jo Boalers academic integrity have made the news again. Even Elon Musk weighed in:
First of all I’ve been a fan of Boalers work for years. Her 2015 book Mathematical Mindsets was deeply powerful because it talked a lot about how to help students (and teachers!) get past failure as a fault, and instead be able to use it for good. Her prominence grew from mostly math-centric to mainstream with her assistance in the latest California Math Framework as well as a lot of work at youcubed.org doing data-science-in-schools work. As an adjunct professor at Fresno Pacific University for the last 11 years teaching a variety of Curriculum and Instruction courses and even created a Data Science for Math Educators course, I’ve used much of her work in various capacities.
There has always been criticism both of her and the fact that she hasn’t actually worked in schools much as a regular teacher, but has had a lot of influence on what classroom teachers ‘should’ be doing. I admit there are far too many armchair educators that tell teachers what they should and shouldn’t be doing. Even as someone who was in the classroom for 10 years but now has been out of it for 9, I shouldn’t be saying what best practice is right now either.
However with the recent attacks on Dr Boaler around wrong interpretation of studies that she espouses in her books, she published a statement rebutting some of the claims and/or choosing to ignore others. If the citation errors mentioned have been checked by others, then it’s done and we can move on — but those accusing have no further credence.
https://www.youcubed.org/wp-content/uploads/2024/04/Boaler-Statement-4.8.24.pdf
But this is bigger than Dr Boaler. She’s mainly become a target because the headlines about the CA Math framework talk about it removing Calculus as a goal or Algebra for 8th graders. This isn’t entirely true. What it aims to do instead is for students who probably wouldn’t race to calculus anyway, to shore up their foundational knowledge and then have room to give them exposure to mathematical skills such as in Data Science that would be useful for a variety of careers. Things like modeling, some programming, how AI works etc.
This is all well and good, but I still do think misses the mark. As my mentor Chris Brownell and his co-author of Math Recess Sunil Singh has been writing about for years, School Math is broken in general because the subjects taught (multiplying polynomials anyway?!) are largely irrelevant in an age where computers can do calculation, and students should be focusing on content and knowledge.
In 2021 I read Conrad Wolfram’s book The Maths Fix — a culmination of ideas he has been talking about for a long time to make math in schools computation based. He has developed a George Polya-esque problem solving guide available here. (computerbasedmath.org). This post was inspired partly by reading a recent post of his about the US Math Wars between mathematicians(like him)and educators (like Dr Boaler).
Many of those attacking Dr. Boaler are of the mindset, “it worked for me, she’s trying to take math achievement away from kids!”. And while they’re not all wrong, Algebra skills are essential. Yes, students who fail algebra 1 are strongly correlated to not graduating high school, but it seems there are definitely some lurking variables there such as income, parent education levels etc.
Math — for a job or future jobs?
At the end of the day, those who want to do things like help kids focus on conceptual things, use math as a tool for life skills (the Common Core 8 mathematical practices, learn from failure etc) and those who want to teach it as something to invent the future. All of the AI tools etc of the past few years is only possible because of advances in true computer science modeling, statistics, and the humble correlation coefficient aka slope in Algebra I.
For the last 8 years I’ve worked a lot in the realm of machine readable standards via the CASE specification and various companies like ACT, a workforce skills company Empath and now early education provider Frog Street. Across the gamut truly of cradle to gray, it’s clear to me that every industry thinks they’re doing something unique when they connect skills(knowledge) and competencies (what someone can do in a job) to accomplish a task. In PK-12 we call these Crosswalks between state standard frameworks or progressions when the ideas are connected within the same math framework. In Workforce we call them skills taxonomies, sometimes ‘crosswalks and progressions’ are just called ‘groupings’/pre-requisites — that is groups of skills that are dependent on one another — such as if you know ReactJS you also must know some javascript.
I feel we can keep the existing math standards from most states, but need to do a better job both being explicit about what identifiable current workforce skills they match with as well as aim for the skills we don’t know about yet. That is, keep polynomials but more important for students to know how to use them to model and the limitations of that.
As an example, I used hundreds of skills from the Open Skills Network as a foundation and used Natural Language Processing techniques to find skills that would be enabled when a student really understood the high school algebra standard A.REI.10 “Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).” After some editing, it came up with these skills:
- Use Mathematical Reasoning: This skill involves using mathematical reasoning, which is integral to understanding equations and their graphical representations.
- Data Analysis Task Information Access: Involves accessing information necessary for data analysis tasks, which could encompass understanding graphical data representations.
- Data Analysis Task Information Collection: This skill pertains to collecting information for data analysis tasks, possibly including the interpretation of graphs.
- Problem Solving with Mathematical Techniques: This skill involves solving problems using mathematical techniques, which are crucial for interpreting equations and their graphs.
- Data Visualization: Creating graphical representations of data is directly related to understanding the graphical interpretation of equations.
- Data Science: At a basic level, this skill includes understanding data analysis and possibly the graphical representation of data sets or equations.
- Programming: Writing and understanding code for data analysis may involve dealing with mathematical equations and their visual representations.
Conclusion
Obviously perhaps I’m a proponent of Data Science not replacing the high school courses, but being integrated into the content standards of states and training for teachers to think not just as educators but mathematicians.
I don’t think vilifying Dr Jo Boaler’s work on the CA Math Framework is justified for the reasons mentioned above — ie, it’s not just about ‘slowing down math course progression’ but about making math more relevant for students. The gap between school mathematics and what’s actually needed is too large, and a way to determine the truly most important math standards and what’s needed is figuring out which skills have historically and presently translate to emerging workforce skills, particularly those around training and using artificial intelligence models.
