The following is a tentative list. All sources are available in English. For some, Hebrew translations are available.
Benezet, L. P. (1935-1936). The Teaching of Arithmetic I, II, III: The Story of an experiment. Journal of the National Education Association, 24(8), 241-244, 24(9), 301-303, 25(1), 7-8.
Brownell, W. A. (1947). The place of meaning in the teaching of arithmetic. The Elementary School Journal 47(5), 256-265
Bruner, J. S. (1960). Chapter 2: The importance of structure. In The Process of Education, pp. 17-32
Erlwanger, S. H. (1973). Benny’s conception of rules and answers in IPI mathematics. Journal of Children’s Mathematical Behavior, 1, 7-26.
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
Llewellyn, A. (2012). Unpacking understanding: the (re)search for the Holy Grail of mathematics education. Educational Studies in Mathematics, 81(3), 385-399.
Schroeder, T. L., & Lester, F. K,. Jr. (1989). Developing understanding in mathematics via problem solving. In P. R. Trafton & A. P Shulte (Eds.), New Directions for Elementary School Mathematics – 1989 Yearbook, (pp 32-42). NCTM
Herbst, P.G. (2002). Establishing a custom of proving in American school geometry: Evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics 49, 283–312. doi:10.1023/A:1020264906740
Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13(1). 16-30.
Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29-63.