I am a fan of John Dewey, but I wonder about his attitude towards mathematics.
I say this because in his book, How We Think, I sense a dislike for the memorization needed to learn arithmetic.
He does not say as much about mathematics as he does other topics, but I found what he had to say about math in his work, Democracy and Education. You can read the one paragraph on mathematics in this book on this web page, but I will reproduce the main point below:
Dewey: “Mathematics is said to have … cultural value in its enlargement of the imagination in dealing with the most general relations of things; even religious value in its concept of the infinite and allied ideas. But clearly mathematics does not accomplish such results because it is endowed with miraculous potencies called values...."
I believe the paragraph above indicates a lack of respect for mathematics, but I leave that for you to decide.
Barzun Versus Dewey
The following quote is from page 67 of From Dawn to Decadence by Jacques Barzun: "...the work of art must by its order mirror the hierarchical order of the world, which is a moral order. Whether by intuition or convention, the artist must know how to convey this reality."
I believe mathematics, like art, reflects something special about the universe around us. In that sense, mathematics is endowed with miraculous "potencies" (Dewey's word) that reflect order and values immanent in the universe.
I have enormous respect for John Dewey, but he was never a mathematician, never connected with mathematics, and could not fathom the "religious value" (his words) of mathematics.
Plato Versus Dewey
In Plato's Republic, Book 7, Plato says,
"Then it would be fitting, Glaucon, to set this study down in law and to persuade those who are going to participate in the greatest things in the city to go to caluculation and to take it up, not after the fashion of private men, but to stay with it until they come to the contemplation of the nature of numbers with intellection itself, not pracicing it for the sake of buying and selling like merchants or tradesmen, but for war and for ease of turning the soul itself around from becoming to truth and being."
Plato believed the leaders of a great city should be well grounded in mathematics (calculation), in plane geometry, and solid geometry as well. Plato believed there was something special about mathematics that touched the soul and revealed truth.
I say that John Dewey not only had a beligerent attitude towards mathematics, he had a beligerent attitude toward religion. The basis of this second assertion lies in John Dewey's signing the Humanist Manifesto. Dewey was a great supporter and advocate for civil society and democracy, but I believe he could not see past his nose. He was a materialist and could not believe there was a purpose mathematics or to life beyond material and political accomplishments.
As much as Dewey valued democracy, no democracy can long flourish if it is based only upon the material, ignoring the spiritual dimension of humanity, which is the only reliable safe-guard for a civil society.
I believe John Dewey's negative attitude towards mathematics has been transferred to the colleges of education, transferred to the teachers trained with this negative attitude, and transferred into the elementary school curriculums across America, inflicting enormous damage upon the education of our children.