Here are various articles, currently in no particular order, that we think might be useful to people doing Lesson Study or just thinking about teaching or mathematics. There are also blog posts that may be of interest on this website; some of the most-commonly useful are referenced here.
Teaching Math through Problem Solving, by Tom McDougal and Akihiko Takahashi. Reprint of published article.
Learning Goals Should Describe Cognitive Change, by Tom McDougal. Blog post on this site.
Teaching Mathematics Conceptually: An Example, by Roger Howe. Focuses on place value.
It’s Not the Teacher’s Job to Teach the Students, by Tom McDougal. Blog post on this site.
Fractions as Numbers vs. Fractions as Ratios, by Tom McDougal. Blog post on this site.