What Do Math Teachers Need to Know About Their Students?
In 1920, James Overman wrote Principles and Methods of Teaching Arithmetic, a methods text aimed at preparing prospective elementary teachers.
In this text, Overman wrote: "The teacher of arithmetic needs to know two things about her pupils' 'abilities' in the fundamentals: (1) What types of examples they can handle successfully, and (2) how well they can handle them; that is, how accurately and how rapidly. The teacher needs to know both of these things if she is to make her teaching effective."
Has anything changed today, almost 100 years later?
 Do we see the word "arithmetic" much anymore?
 Do we still typecast all elementary teachers as being females?
 Are the two key things in mathematics still accuracy and rapidity?
 Are skills the current focus...or is it conceptual understanding with meaningful use of skills?
Overall, I do think things have changed in a positive direction...at last as to how teacher preparation programs are trying to educate future teachers.
But, jumping on my soap box, I do not think that enough effort has been made to educate the other stakeholders (parents, administrators, politicians, and even students). Thus, the visible disconnect between what mathematics teachers should be doing (and are capable of doing) and what state/federal requirements are forcing teachers to do.
This is why anyone can now be considered an "effective teacher," because the criteria keep shifting, often in measureable but meaningless directions.
