What a beautifully written article, and one to which I can truly relate. I'm a fully bilingual/biliterate (Spanish-English) retired math teacher, who began in upper elementary and later moved up through the grades. .

And I always wondered about the very question of the role of language in their math learning.

One thing your article clearly brings home is the crucial role of conceptual understanding in learning math, which I was always careful to stress throughout my career. I think that's why my students always scored so well on state tests.

I recall an incident from early in my career when a district official was in my class checking to see how the students were doing in this bilingual setting. 5th-grader Irma was explaining division of fractions to him, when he came up with, "I don't understand."

To which Irma countered with, "Then let me put it another way..." I think about Irma's wonderful response, and I cannot help but cry. This incident occurred 54 years ago, and I'm crying right now.