Christian Party

The Truth About Calculus

	Hedrick Smith,"Rethinking America", July 15, 1995 points out that 6% of U.S. and 40% of German and 94% of Japanese students study calculus in high school.
	The US Department of Education reports that 10.1% of US high school graduates take calculus http://nces.ed.gov/pubsold/CoE95/26-01.html
	SAT Scores are down 98 points since 1960.
	Educators Who

John Muir High

Several years ago it was
published that, after declining year-by-year, no one had received a 3
or better on the College Board exam for AP Calculus, two 2s and four
1s so I took it upon myself to get the full grade distribution
(available under California's FOIA law). It took four or five months
but I finally succeeded in doing so. It turns out that 23 students
took the class and the distribution was pretty easy: 19 As and 4 Bs,
and absolute disconnect

100% of Japanese "exposed" to Calculus

Most of the teachers we interviewed indicated that the goal of instruction is exposure, not mastery. Although most Japanese high school students are exposed to calculus, Japanese teachers indicated that they did not expect all their students to understand calculus. When asked, �What percentage of students, in your experience, are able to do calculus problems and understand calculus?�, one teacher said:

About 20 percent of students are able to both do and understand. Almost all students are able to do calculus, although they may not understand it. I am referring to science students here. As for the humanities students, all those that have taken math are able to do calculus, whether or not they understand it. But very few students understand the concept of change in calculus. That is why I think that there is an element of the horse learning to pull out the card when hearing two thumps. I do not think that this is a good way to teach math. I dislike this immensely. But I forget that and teach.

Retention (genkyutomeoki) is rarely practiced in Japanese schools, particularly during the compulsory years, or even during senior high school. In fact, one senior high school teacher could not recall a time in his entire teaching career when a student was retained. Other senior high school teachers reported �one case every 4 or 5 years.�

Instead of retaining students, Japanese teachers are encouraged by administrators to provide extra instruction in basic skills (fushinsya shido) to students having trouble meeting minimum school standards. This may involve the teachers spending time with students outside of class or providing remedial homework assignments during the summer or winter vacations. In spite of these efforts, some students still perform poorly on examinations. In these cases, Japanese teachers reported practicing what they call �letting the student put on a pair of geta (Japanese elevated wooden clogs)�. This expression refers to giving students extra points for good effort.

http://www.ed.gov/pubs/JapanCaseStudy/chapter2c.html

4% of US High school students take calculus

96% of Japan's students, 70% of Germany's students, and only 4% of US students take calculus in high school, another key factor conveniently overlooked in this report

http://fathersmanifesto.net/depted.htm

82% of Japanese high school students take calculus

Yoshihiko Hashimoto, Yokohama National University

Changes in mathematics education are currently taking place in Japan. The school week is changing from six days to five days per week to allow children to develop "competency for positive living." Changes in Japan seem to occur approximately every ten years, although the mathematics content over the last 30 years has been relatively stable. Reform is based on tradition and varies according to the times. Since 1994, Japan has had a "core and optional modules" model for upper secondary school mathematics. An overall objective of the entire curriculum is to foster students' abilities to think mathematically. "Open" methods of teaching - open process, using different ways to solve a problem; open-ended where problems have multiple correct answers; and open problem formulation where students pose new mathematical problems can help meet this objective. Traditionally, one important feature of learning mathematics was to develop the ability to calculate rapidly.

Miho Ueno
Tokyo Gakugei University Senior High School

The goal of mathematics education might be seen as learning the basic idea of calculus by the time students graduate from high school. Beginning calculus is taken by 82 percent of high school students in a traditional mathematics program. It is often difficult to implement a new course of study due to factors such as a lack of teachers in a small school system, which limits the courses offered to those needed for college entrance, or to a lack of technology. Thus, the intended curriculum may not get implemented.

The results of the Third International Mathematics and Science Study (TIMSS) indicated that Japanese students disliked mathematics. The new course of study addresses this by stressing mathematical activities aimed at helping students appreciate the importance of mathematical approaches and ways of thinking. What matters is finding principles in given phenomena in the world and finding materials that will allow students to use mathematics spontaneously. Reform should be realized through teachers' attempts to enrich the contents of the prescribed curriculum.

http://mathforum.org/pcmi/int2001report/page47.html

"6 percent [US students] study calculus (Sudo, 1989)"

The Japanese assume that learning is the product of effort, perseverance, and

self-discipline rather than of ability. The schools have no ability grouping in the

elementary and junior high schools and virtually no individualized classroom instruction

(Becker, et al., 1990). All children go through junior high school, and 94% of Japanese

youth attend high school. Close to a third of the graduates continue on to higher

education (Reischauer, 1988). Those who graduate have the equivalent of three to

four years more schooling than U.S. graduates do. Japanese graduates have all studied

calculus, physics, and chemistry. Fewer than half of U.S. students take a year of

physics and chemistry, and only 6 percent study calculus (Sudo, 1989).

http://www.gphillymath.org/ExempPaper/TeacherPresent/Mastrull/SMastrull.pdf

http://www.nsf.gov/statistics/nsf99338/access/c2/c2s3.htm#note3
Aside from her use of the NELS data, Kim also cites other statistics concerning the disadvantages facing some Asian ethnic groups. These include high school dropout rates around 50 percent for schools with high concentrations of Southeast Asians and high dropout rates for Filipinos (46 percent) and Samoans (60 percent) in 1992. The median family income in 1990 for all Asian Americans was $41,241 but only $14,327 for Hmongs, $18,126 for Cambodians, and $23,101 for Laotians.

PISA

In 2006, the average U.S. score in mathematics
literacy was 474 on a scale from 0 to 1,000, lower
than the OECD average score of 498 (tables 3 and
C-7). Thirty-one jurisdictions (23 OECD jurisdictions
and 8 non-OECD jurisdictions) had a higher average
score than the United States in mathematics literacy
in 2006. In contrast, 20 jurisdictions (4 OECD
jurisdictions and 16 non-OECD jurisdictions) scored
lower than the United States in mathematics literacy
in 2006.

High Drop Out Rate in US

Between 1972 and 1995, the number of 18 year olds in the U.S. population decreased from 3,927,000 to 3,745,000 and the number of high school graduates decreased from 3,001,000 to 2,553,000, which means that the percent of 18 year olds who graduated from high school decreased from 76.4% to 68.2% in 23 years, while the percent of Japanese 18 year olds in high school remained consistent, at 94%.

Japanese teachers thus teach calculus to their citizens at a rate which is 12.8 times greater than the rate at which American teachers teach calculus to American citizens.

	1972	1995	Difference
Number of 18 year olds	3,927,000	3,745,000	-182,000
Number of high school graduates	3,001,000	2,553,000	-448,000
Percent of 18 year olds graduating from high school	76.4%	68.2%	-8.2%
Percent of high school graduates taking calculus	4.3%	10.1%	1.9%
Number taking calculus	129,043	257,853	128,810
Percent of 18 year olds taking calculus in the US	3.3%	6.9%	0.9%
Percent of 18 year olds taking calculus in Japan	-	88.4%
Ratio Japan:US		12.8X

	We agree with Charles A Fuller!
	Correlating standardized test scores with incomes and college grades.
	Download the spreadsheet with references from population18to24.xls
	and sat.xls
	SAT Graphs
	For 1960 SAT scores
	For 1995 SAT scores, http://nces.ed.gov/pubs/ce/c9622a01.html
	SAT Scores 1966-1999

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Modified Friday, July 08, 2011