This is what is wrong with so many US math curricula.

You probably know that in international comparisons,
US students don't do really well in math.

One reason for that can be found in comparing the typical math
curricula in those countries that do well, versus typical
curricula used in the USA.

The following article of mine is based on a report by William
Schmidt, Richard Houang, and Leland Cogan called A Coherent
Curriculum: The Case of Mathematics, which appeared in
Summer 2002 in American Educator.

Some differences that emerge are as follows. The US math
curricula tend to be

* not focused. No country in the world covers as many topics
as US in their mathematics textbooks. For example, in
Japan, eighth-grade textbooks have about 10 topics
whereas US books have over 30 topics.

* highly repetitive. The average duration of a topic in US is
almost 6 years (!) versus about 3 years in the best-
performing countries. Lots of spiraling and reviewing
is done. Like Schmidt says, "We introduce topics early and
then repeat them year after year. To make matters worse,
very little depth is added each time the topic is addressed
because each year we devote much of the time to reviewing

the topic."

* not very demanding by international standards, especially
in the middle-school. In the USA, students keep studying
basic arithmetic till 7th and 8th grade, whereas other
countries change to beginning concepts in algebra and
geometry.

* incoherent. The math books are like a collection of
arbitrary topics. Like Schmidt et al. say, "...in the United
States, mathematics standards are long laundry lists of
seemingly unrelated, separate topics."

What this means is that typically in the US, a math topic is
studied for a short time, and then the next one, and then the
next one, on and on. A good part of this short time is spent
reviewing previous year's knowledge. It follows that any
particular math topic is NEVER studied very deeply in any
given school year.

Also, during the school year, many topics are covered but not in
a coherent and logical order. Instead the topics tend to jump
here and there in somewhat of an arbitrary fashion.

So, the end result of following a curriculum that is like
hodgepodge and "inch deep and mile wide", by the end of eighth
grade US students are about two years behind their
counterparts in the best performing countries.


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CHART WHICH I CAN'T SHOW IN THE EMAIL
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I need you to click to my website to see these very revealing two
charts that show which topics are typically covered on which
grade, either in the States, or in the best performing countries.

I got a special permission from the main author of the
aforementioned report to reproduce these on my site.

You can continue reading the article there.

http://www.homeschoolmath.net/teaching/coherent-curriculum.php#chart

Sincerely,
Maria Miller