Nils Ahbel of Deerfield Academy gave a thought provoking presentation at the 2011 Anja S. Greer Conference on Secondary School Mathematics (held at Phillips Exeter Academy in Exeter, NH) on the history and potential future of the American High School mathematics curriculum. The Prezi that he used to illustrate his talk can be found here.
As I recall, his core points about the state of things today were that:
– our curriculum has remained largely unchanged for 119 years (witness the content of the textbook whose pages fill the number 8 in his prezi).
– the current goal of most high school curricula is to prepare students to take calculus, yet only around 8% of the student population ever seems to (eventually) pass a calculus course.
– as a society, we consistently depict mathematics and other quantitative topics as being un-intelligible, obscure, and/or arcane – yet every student will need to be able to decide for themselves on questions such as: are they on track with their retirement fund? Does data support or refute global warming? Is driving to the airport more or less risky than flying?
He then turned to ideas on how we might change this situtation:
– our syllabi are full. If we wish to add a topic, we almost always have to find one or more topics to drop in exchange.
– Instead of pursuing incremental change, it is more sensible to re-think our curriculum from the ground up. Begin by adding the topics that are most important to the futures of the students we are teaching.
– Calculus is still a useful and needed course of study, particularly for students going into the sciences and engineering, but why prepare 92% of students for a course they are not likely to complete or make use of?
– Exponential equations and statistics are currently and seem likely to continue to be the most relevant topics our students should master .
– The problems that most students will need to understand in this day and age involve: compound interest, present value, population growth, resource depletion, metabolic assimilation rates, descriptive statistics, understanding standard deviation, and supporting arguments with statistics.
Update 7/16/11: Some of these points are not new, as R. Wright pointed out in a comment below. Sheldon P. Gordon wrote about these and related issues in a 2005 paper titled “What’s Wrong With College Algebra?“, which is interesting to read.
Update 7/29/11: Video of the presentation is now available on YouTube:
Part 1
Part 2
Part 3
Part 4
MathMaine 
I’d like to add probability to the list in the last bullet. Especially expected value and relative risk. The airport example is one place where relative risk appears (and is misunderstood), but it’s kind of a silly one. Where people literally cannot function meaningfully without a decent understanding of relative risk in in making medical decisions. If this or that activity increases (or decreases) the risk of disease X, what does that mean?
I agree with your example, particularly when it comes to expected values. However, as I recall, Mr. Ahbel felt that the typical introduction to formal probability is not as relevant-seeming or approachable for students (when it comes to complex counting situations, etc.), however much can nevertheless be learned from using descriptive statistics to support or refute arguments. A video of his talk may appear under “Past Presentations” on his web site in the future.
What’s funny is this is the same problem for many years and yet we are unable to solve it. Here in our country, they kept on revising the curriculum, but still, the exam results are declining.
Almost all of the points you list remind me of “What’s Wrong with College Algebra,” by Sheldon Gordon: http://www.uupinfo.org/research/working/gordon.pdf
Thank you for the reference! I will add it to the posting.