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Some of the proposals I’ve seen for AI applications that are supposed to help students learn mathematics are deeply flawed, because they fail to take into account a fundamental principle of learning, a principle that applies to all education and training activities that are intended to develop proficiency and

The first Real Algebra blog explained the need for a widely effective solution to the problem of learning the course of mathematics starting with algebra and continuing through calculus. Other blogs discussed the importance of developing conceptual understanding and how to do that, and why it is essential to provide

In Real Algebra blogs #1 and #2, we addressed the need for a program that makes algebra and other grade 7-12 math topics accessible to many more students.  We also discussed some of the characteristics of such a program, focusing the development of conceptual understanding.  This third blog deals with

Real Algebra, Blog #2 In the previous blog I talked about the importance of providing a reliable route to success in math, and specifically in algebra, for all students.  Such a route does not currently exist.   There are three fundamental flaws in existing algebra curricula: • They do not effectively get

In the United States, the journey of students as they attempt to learn mathematics from preschool through 12th grade is akin to Napoleon’s “march to Moscow.”

I’m reading a book by a well-known edtech leader about AI. He’s a person whose opinion I respect, and he sees a great deal of potential in Generative AI,  appropriately so. He starts the book by describing how he had used AI to help his 11-year-old daughter write

This is an update on my professional activities for my past and present colleagues, and anyone else who might be interested. Today, which happens to be my birthday, I completed what I believe is my final consulting project for Age of Learning: a knowledge map for the mastery of algebraic

It’s funny how one can work in a field for many years and in many contexts and discover that some of the most basic concepts of that field are not clearly elucidated.  Let’s consider the concepts of “student” and “teacher.” Everybody knows what a student is—it’s