Test Your Mathematics Skill

choi

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Do not peek at the answer at the lower right corner, which in the print of
report below is printed upside down. Here is hte question.
http://www.nytimes.com/imagepages/2010/04/15/us/15math_CA0.html

Note:
(a) parallelogram (n): "a quadrilateral with opposite sides parallel and
equal"

* quadrilateral (n): "a polygon of four sides"

(b) bisect (vt): "to divide into two usually equal parts"



--------------After you make an effort, read on.
Sam Dillon, U.S. Falls Short in Measure of Future Math Teachers. New York
Times, Apr. 15, 2010.
http://www.nytimes.com/2010/04/15/education/15math.html?scp=1&sq=schmidt%20mathematics&st=Search

My comment:
(a) How to solve the question presented in NYT.

Angle BAD = 60 degrees.

Thus angle ABC = 120 degrees.

Because both angles are bisected, angles MAB and MBA are 30 and 60 degrees, respectively--so are angles DMA and CMB, respectively. AND angle CBM will be 60 degrees.

Therefore, triangle CBM is equilateral. Also, triangle BAM is a 30-60-90* right triangle, whose sides have lengths of 1: (square root of 3): 2. See
Special right triangles
http://en.wikipedia.org/wiki/Special_right_triangles

* Pronounced "thirty sixty ninety."

Assign length of BC as "x." then
(a) CM = BM = x, and
(b) AM = (square root of 3) times x;
AB = 2x.

So the perimeter of the parallelogram is x + 2x + x + 2x, or 6x. It is given that the perimeter is "6 cm."

Consequently x = 1 cm.

(To be continued)   

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choi

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(b) The NYT report is based on

Andy Henion and Nicole Geary, MSU study: U.S. needs better-trained math
teachers to compete globally. Michigan State University, Apr. 15, 2010.
http://news.msu.edu/story/7714/

To read the study, click "U.S. TEDS-M Study" under the photograph of the
lead author, Prof. William H. Schmidt. In the new page, click "Breaking the
Cycle."

Note:
(i) TEDS-M is the acronym for "Teacher Education and Development Study in
Mathematics."
(ii) As its subjects of research, the study tests future teachers destined
to teach primary AND middle schools of 16 countries that includes US and
Taiwan, but not Hong Kong or China.
(iii) The study gives the years of primary and middle school (see page 10,
the number at the bottom of the page; Table of Contents and pages prior to
it are not numbered).
(iv) For a general concept, see

Middle school
http://en.wikipedia.org/wiki/Middle_school

Quote:

"The term junior high dates back to 1909 with the founding of Indianola
Junior High School in Columbus, Ohio.[1] The term middle school dates back
to 1950 in Bay City, Michigan.

In US: "The faculty [of junior high school] is organized into academic
departments that operate more or less independently of one another.

Also in US: "The middle school concept often involves a group of two to
eight teachers from different disciplines working as a team with the same
group of students of the same grade level, with each teacher teaching a
different subject. This format facilitates interdisciplinary units * * * The
middle school philosophy also advocates assigning students in each team to
a homeroom. * * * The middle school format has now replaced the junior high
format by a ratio of about ten to one in the U.S.

(v) To understand the study, please read
* the first page of executive summary (page 1);
* Report Organization (page 10);
* first three pages of Chapter 2 (pages 11 to 13), as well as Appendix C (
pages 51 and 52)

(vi) The findings of the study are awesome, from Taiwanese point of view, as
Taiwan ranks top in all tables, which is called "display" in this study. (
In Display 4 at page 13, the difference between Singapore (593) and Taiwan (
592) is meaningless.

(vii) In the Displays, "Mn" stands for "mean," whereas "se," "standard error
." See
Standard error (statistics)
http://en.wikipedia.org/wiki/Standard_error_(statistics)

pedagogical (adj): "of, relating to, or befitting a teacher or education"
www.m-w.com

【 在 choi 的大作中提到: 】
: Do not peek at the answer at the lower right corner, which in the print of
: report below is printed upside down. Here is hte question.
: http://www.nytimes.com/imagepages/2010/04/15/us/15math_CA0.html
: Note:
: (以下引言省略...)

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