Helping Students to Learn Mathematics (aka develop a mathematical mind )

Barbara Oakley wrote about her life of learning and how she overcame problems learning mathematics.
http://nautil.us/issue/40/learning/how-i-rewired-my-brain-to-become-fluent-in-math-rp

What an interesting read.

(She and Professor Terrence Sejnowski run the online course at https://www.coursera.org/learn/learning-how-to-learn)


Key points of the article:
Conceptual understanding during learning process - balance it with developing mastery and fluency.
This development of mastery and fluency must be involve active learning by the learner.

Repetition, memorization, and practice, and chunking of knowledge as in "....building well-ingrained chunks of expertise through practice and repetition was absolutely vital ...."
Experts were so because they were fluent, and had "....rote learning that emphasized the ability to think flexibly and quickly."

And her experiences in learning the Russian language very effectively were replicated in her own transformation from being a language person into a professor of engineering!
And she wrote this. "Language, math, and science, as with almost all areas of human expertise, draw on the same reservoir of brain mechanisms."


Some related articles about learning of mathematics

PBS : https://www.pbs.org/wgbh/misunderstoodminds/mathbasics.html
        : PBS Video on Misunderstood Minds
Montessori : https://www.montessoriservices.com/ideas-insights/building-the-mathematical-mind

Jump Math : https://jumpmath.org/jump/us,
                     AMS article by John Mighton http://www.ams.org/notices/201402/rnoti-p144.pdf
                   What barriers prevent students from paying attention and being engaged in math lessons?                      Research  https://jumpmath.org/jump/us/supporting_research