From their website: “The National Council of Teachers of Mathematics is a public voice of mathematics education supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development and research.”
In 1989, the NCTM published Curriculum and Evaluation Standards (usually called the NCTM Standards), which is credited or blamed, depending on your view, with setting off the latest round in the Math Wars. The NCTM Standards were revised in 2000 with the publication of Principles and Standards for School Mathematics (usually referred to as PSSM). This was followed in 2006 by Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (aka, the Focal Points).
So what is the issue? Standards are good, right? And true, the NCTM Standards pushed most states to establish standards for their jurisdictions. However, when standards are poorly written or when something is presented as a standard and is really something else, or curriculum developers interpret them poorly (or interpret them to fit their own needs and aims), do you know what you get? POOR CURRICULUM! And POOR PRIORITIES!
To start, let us talk about priorities, i.e., how much time we spend on each topic. When I was in elementary school (during the dark ages of the sixties), we had books called Arithmetic. I guess the NCTM now covers this under the heading “Number and Operations.” In fact, you would be hard pressed to find the word arithmetic in their standards documents. I scanned the PSSM Executive Summary and found nary a mention of the word. http://www.nctm.org/uploadedFiles/Math_Standards/12752_exec_pssm.pdf
So how much time does the NCTM suggest I spend on “Number (no “s”) and Operations?” From the Executive Summary of PSSM (chart on page 4), I should spend about 30% of the time (between PreK and second grade), and about 26% of the time (between third and fifth grade). Really, when I am learning to count and add and multiply, I only need to spend a third or less of my time!
Where else should I be spending my time? For preK to second grade, I should spend 8% of my time on algebra, 29% on geometry, 20% on measurement, and 13% on “Data Analysis and Probability.” For third to fifth grade, I should spend 16% of my time on algebra, 25% on geometry, 20% on measurement, and 13% on “Data Analysis and Probability.”
Data Analysis and Probability??? Now you know why your student is so good at making those bar charts! Maybe they can figure the odds of the Giants winning this weekend? I will predict there is a high probability that many of those students can’t multiply and divide at the end of fifth grade.
So have times changed? Or have our standards changed? Or are we trying to cram too much (too much superfluous material, to early) into too little time. If I consider algebra to be arithmetic, I should (according to the NCTM) be spending only about 42% of my time on arithmetic between third and fifth grade.
The chart on page eight from the link below shows one math professor’s analysis of how much time is spent on various topics in fifth grade according to various source documents. When he was in fifth grade (1956), he spent about 85-90% of his time on arithmetic and the rest on everything else.
http://www.math.jhu.edu/~wsw/ED/wsw.ppt (you may have to double click)Source: website of W. Stephen Wilson, Professor of Mathematics, Johns Hopkins University, from Leading Minds K-12 Math Education Forum, April 24, 2008 http://www.math.jhu.edu/~wsw/
Ah, no wonder I can’t add and subtract and multiply and divide! I am only spending half as much time as my grandparents did, and about 60% of the time my competition in Singapore does (42%/70%).
As a check point, I did a similar study of my daughter’s fourth grade EDM home work book. I got about 55% for time spent on arithmetic, 14% on data/ estimation/ statistics/ probability, and 31% geometry/measurement.
So maybe part of the problem is that we are not spending enough time on the basics. Remember, if you want to teach other stuff, something has to get dropped. So what if it is just basic arithmetic! But the EDM Teacher’s Reference Manual Grades 1-3 says “Children need a mathematics curriculum that is rigorous and balanced and that: … Explores a broad mathematics spectrum, not just basic arithmetic…”
I am reminded of a line from a semi-famous movie that says “Let us redefine progress to mean that just because we can do a thing, it does not necessarily mean we must do that thing.” Just because the Everyday Math philosophy says our children can learn many things, does not mean they must learn many things at the cost of learning important things well.
Okay, you got me, it was Star Trek IV: The Undiscovered Country.
Up next: more alphabet soup.