I'm unaware of Professor Conrad having an "axe to grind". AFAIU, he simply thinks that what Professor Boaler advocates is incorrect, and he sees fit to describe the myriad mistakes and misrepresentations in her research and advocacy.
He shares this outlook with many people, including those who believe that despite saying that she advocates for "equity", her agenda would actually lead to worse outcomes for many students, including low-income students who lack family resources to procure advanced mathematical education.
have a private reason for doing or being involved in something.
I have never met Professor Boaler, nor do I have any private/hidden agendas. Do you simply mean "someone who disagrees with" when you say "axe to grind"? If so, it's somewhat of a meaningless epithet. If you mean the normal definition, I'd be curious what evidence you have for that (related to Professor Conrad, or me).
Dr. Brian Conrad is a very vocal critic of the California Math Framework. He definitely has an axe to grind.
Dr. Jo Boaler is a British education author and Nomellini-Olivier Professor of Mathematics Education at the Stanford Graduate School of Education. Boaler is involved in promoting reform mathematics and equitable mathematics classrooms. She is the primary author of the California Math Framework.