Jeremy Kilpatrick

TL;DR: In this article, the authors identify a historical progression towards the achievement of mathematics for all: from schooling for all to arithmetic for all, to basic mathematics, to primary mathematics, secondary mathematics, mathematical modelling, and quantitative literacy for all.

TL;DR: Most mathematicians consider themselves, at least to some degree, to be both educators and researchers as mentioned in this paper. Yet few embrace or even respect the subject at the intersection of these fields: research in mathematics education.

TL;DR: The problem of assessing the mathematics pupils have learned has inevitably been intertwined with the questions of who should receive additional mathematics instruction and how that instruction should be managed as mentioned in this paper, and scholars appear to have begun the empirical inquiry into these questions from the perspective of psychology during the Renaissance, asking what mental abilities are, how they develop, and how they are differentially disposed across people and across the requirements of various disciplines.