Note: the publisher sent a copy for review but all opinions are my own.
“How this plays out affects us, our children and society profoundly. Allow maths education to continue in its current mould, and we will increasingly remove most students’ opportunities for success in a wide range of fields: the AI age requires more, different, computer-augmented computational thinking for human empowerment, not more of the same maths.”
Wolfram’s central message is one of change and empowerment. He reaches out to anyone who cares about math education or education in general— not just teachers and policy makers, but parents, students, employers, and the educational community at large. This book is a powerful, passionate, and critical analysis of the current system and a vision of what math education should be. Central to math education is empowerment of the learner— and this consistent theme is present throughout Wolfram’s vision as he articulates the “fix” for math education.
Having not known much about Conrad Wolfram before reading this book (come to find out he is arguably one of the most important thinkers and innovators in mathematics), I was pleased to see how closely his reimagining of math education aligned with other critical thinkers in the field as well as research, evidence, and effective educational practices and theory. I found many similarities with Jo Boaler’s essential work in math education, as well as Alfie Kohn’s insights.
The fix that he proposes follows effective educational design (“backwards design”) where, after examining the purpose, he delves into outcomes or standards. Overall, the goals of transfer are apparent, as is the foundational belief that students need to be engaged in real-world math— this can happen through open-ended questioning and using real-world technology and not made-for-education technology. While only discussed briefly, it’s easy to see how this would result in much higher engagement from students— who in the current system question how math will help them in real life and rarely, if ever, find a satisfactory answer to that question as they stare down endless sets of decontextualized practice problems. He critically identifies, “This confusion between calculating as a means to a problem-solving end and as an end in itself is the central and fundamental misunderstanding at the heart of today’s math education crisis.”
Instead, Wolfram argues for a constructionist approach, even a project-based one, where there are “actual problems solved by real people in the real world with today’s technology”, and where computational literacy is not solely the purview of math teachers. However, he doesn’t neglect the necessity of scaffolding, careful curation, and skill development that would give students the ability to do well in a problem-based setting. This is a critical point because many iterations of project-based learning fail students on this level.
Those looking to affect change in the way that Wolfram describes will find solidarity in his struggle to develop and refine his ideas. Because he and his team went through the process of designing a computational subject curriculum, they can sympathize with teachers and recognize the ins and outs of curriculum design and pedagogy. However, he makes several important points that should not go unnoticed— for example, that much of the uses of technology in the classroom at present are computer assisted and not computer based— a very important distinction that educators and curriculum developers need to examine closely.
Wolfram is particularly perceptive when it comes to assessment— the seemingly unavoidable determinant of modern education. “. . . [Yet] in the modern concept of exam legitimacy, questions set up for easy reproducibility of quantitative scoring trump questions that more accurately simulate real life, but are harder to mark . . . when in real life did you pick from 4 or 5 answers, one of which you knew “has to be” right?” Rather, Wolfram calls for more complex but better aligned assessment: “ . . . questions which need explanation and judgement calls can be much more representative and therefore legitimate and fairer tests of the student’s ability at the real-life subject, even if working out who did better and worse needs more complexity to achieve acceptable reproducibility.” This might make many in the education field uncomfortable with the task, but anyone who has suffered at the hands of standardized testing and recognizes the deleterious role that it plays will also recognize the validity of what he calls for.
I found Wolfram to be particularly insightful and even motivational in his discussion of the profound implications of a computational subject— or lack of one— for individuals and society. His powerful, passionate expression communicates the urgency of a computational subject in today’s “post-truth” society. In his view, “Those poorly educated in the rich computational thinking I talk about more easily succumb to that megaphone [of misinformation or mis-understanding]. They can be blinded by quantitative certainties or bamboozled by the aura of computational complexity. They can confuse abstract representation with the reality it was supposed to be representing, even when the two have diverged.” He even goes so far as to say that most people are “easily misled” and perhaps even “no longer believe any logic.” The critical implication of the failure of our calculation-based math education upon society is continuously, powerfully, and necessarily reiterated.
I do wish that Wolfram would have included a deeper discussion of how computation-based math improves equity for students, beyond just a selling point. He does point out that certain key aspects of math education, such as the qualitative experience of the concepts of cause versus correlation, usefulness and reliability of models and algorithms, or understanding bias, “cause a ‘computational divide’ between those who are empowered with computers and those who aren’t: having a computer and being able to work it doesn’t mean you can effectively apply computation or think computationally.” His comparison of the historical power of literacy to the power of computational literacy for the present and the future is important, however his discussion does not go much beyond these points. The bridge that computational thinking and education can provide for many students who are traditionally disadvantaged when it comes to calculation-based math is a critical— and one that Wolfram, while covering a great many other aspects— sort of skims over.
In the end, Wolfram’s carefully thought out arguments show incredible amounts of hard work and dedication. His rare vision and clarity for where math education needs to go in order to empower and engage students and prepare them for the kinds of logical and computational thinking that is so necessary, both now and in the future, is perceptive and compelling.