"Reshaping Assessment"

"A Core Curriculum", NCTM (1992), page vii

Analysis of students' written work remains important. However, single-answer paper-and-pencil tests are often inadequate to assess the development of students' abilities to analyze and solve problems, make connections, reason mathematically, and communicate mathematically. Potentially richer sources of information include student-produced analyses of problem situations, solutions to problems, reports of investigations, and journal entries. Moreover, if calculator and computer technologies are now accepted as part of the environment in which students learn and do mathematics, these tools should also be available to students in most assessment situations.

Let's analyze this innocuous looking statement from the preface of A Core Curriculum.

"Single-answer paper-and-pencil tests are often inadequate." – Why? What's the evidence for this statement?

"Student-produced analyses of problem situations" – What does this mean?

"solutions to problems" – Exactly how is this different from a "single-answer paper-and-pencil test"?

"Reports of investigations" – What exactly is a high school student qualified to "investigate"? Certainly, the occasional research project may be helpful and even desireable, but for the most part traditional techniques are a much more efficient method for imparting mathematical knowledge than student investigations. Of course, the premise of NCTM math is that this statement is not true. Fine, what evidence supports the thesis that student investigations are more efficient? I've never seen any.

"journal entries" – too stupid for words.

Most interesting of all is the last sentence. "IF calculator and computer technologies are now accepted . . . these tools should be available." They are using the very statement for which they are attempting to provide justification as their hypothesis. Nice.

In summary, what evidence supports the counter-intuitive notions that (a) high school students can handle complex, multi-step, open-ended (often ill-posed) investigations and (b) this is the best way to teach basic mathematical concepts?