B REAKING THE C YCLE - Michigan State University

APPENDIX B

Example Items from the Primary Mathematics Knowledge and Mathematics Pedagogy
Knowledge Assessment

Indicate whether each of the following statements is true for the set of all whole numbers
a, b and c greater than zero.

Check one box in each row.

A. a – b = b – a True Not True
B. a ÷ b = b ÷ a
C. (a + b) + c = a + (b + c) 1 2
D. (a – b) – c = a – (b – c) 1 2
1 2
1 2

The area of each small square is 1 cm2.

What is the area of the shaded triangle in cm2? Check one box.

A. 3.5 cm2 1
B. 4 cm2 2
C. 4.5 cm2 3
D. 5 cm2 4

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When teaching children about length measurement for the first time, Mrs. [Ho] prefers to
begin by having the children measure the width of their book using paper clips, then again
using pencils.
Give TWO reasons she could have for preferring to do this rather than simply teaching the
children how to use a ruler?
Reason 1:
Reason 2:

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Example Items from the Lower Secondary Mathematics Knowledge and Mathematics
Pedagogy Knowledge Assessment
On the figure, ABCD is a parallelogram, ∠BAD = 600 , AM and BM are angle bisectors of
angles BAD and ABC respectively. If the perimeter of ABCD is 6 cm, find the sides of
triangle ABM.
Write your answers on the lines below.

AB = _______cm
AM = _______cm
BM = _______cm

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Prove the following statement:

If the graphs of linear functions

f (x) = ax + b and g(x) = cx + d

intersect at a point P on the x-axis, the graph of their sum function

(f + g)(x)

must also go through P.

A mathematics teacher wants to show some students how to prove the quadratic formula.

Determine whether each of the following types of knowledge is needed in order to
understand a proof of this result.

Check one box in each row.

Needed Not needed

A. How to solve linear equations. 12

B. How to solve equations of the form x2 = k , where 1 2
k >0.

C. How to complete the square of a trinomial. 12

D. How to add and subtract complex numbers. 12

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APPENDIX C

Display C1. Distribution of Primary Future Teachers’ Mathematics Knowledge
Scaled Scores1 by Country.

Country Mathematics Knowledge Mn (se)

Taiwan 623 (4.2)
Singapore 590 (3.1)
Switzerland 543 (1.9)
Russian Federation 535 (9.9)
Thailand 528 (2.3)
United States-Private 526 (3.6)
Norway 2 519 (2.6)
United States-Public 518 (4.1)
Germany 510 (2.7)
Poland 490 (2.2)
Malaysia 488 (1.8)
Spain 481 (2.6)
Botswana 441 (5.9)
Philippines 440 (7.6)
Chile 413 (2.1)
Georgia 345 (3.9)

100 200 300 400 500 600 700 800
Percentiles of Performance 95th
5th
25th 75th

95% Confidence Interval for Average (±2SE)

Significantly above the U.S. - Public
Not significantly different from the U.S. - Public

Significantly below the U.S. - Public

Display C2. Distribution of Primary Future Teachers’ Mathematics Pedagogy
Knowledge Scaled Scores1 by Country.

Country Mathematics Pedagogy Knowledge Mn (se)

Singapore 593 (3.4)
Taiwan 592 (2.3)
Norway 2 545 (2.4)
United States-Private 545 (3.1)
United States-Public 544 (2.5)
Switzerland 537 (1.6)
Russian Federation 512 (8.1)
Thailand 506 (2.3)
Malaysia 503 (3.1)
Germany 502 (4.0)
Spain 492 (2.2)
Poland 478 (1.8)
Philippines 457 (9.7)
Botswana 448 (8.8)
Chile 425 (3.7)
Georgia 345 (4.9)

100 200 300 400 500 600 700 800

Percentiles of Performance

5th 25th 75th 95th

95% Confidence Interval for Average (±2SE)

Significantly above the U.S. - Public
Not significantly different from the U.S. - Public

Significantly below the U.S. - Public

Notes.

1All scale scores are based on the preliminary data released by the IEA to the National Research Coordinator
in each participating country.

2Norway estimate based on a sample of both generalists and those generalists specializing in mathematics.

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Display C3. Distribution of Lower Secondary Future Teachers’ Mathematics
Knowledge Scaled Scores1 by Country.

Country Mathematics Knowledge Mn (se)

Taiwan 667 (3.9)
Russian Federation 594 (12.8)
Singapore 570 (2.8)
Poland 540 (3.1)
Switzerland 531 (3.7)
Germany 519 (3.6)
United States-Private 512 (16.3)
United States-Public 505 (9.7)
Malaysia 493 (2.4)
Thailand 479 (1.6)
Oman 472 (2.4)
Norway 2
Philippines 444 (2.3)
Botswana
Georgia 442 (4.6)
Chile 441 (5.3)
424 (8.9)
354 (2.5)

100 200 300 400 500 600 700 800

Percentiles of Performance

5th 25th 75th 95th

95% Confidence Interval for Average (±2SE)

Significantly above the U.S. - Public
Not significantly different from the U.S. - Public

Significantly below the U.S. - Public

Display C4. Distribution of Lower Secondary Future Teachers’ Mathematics
Pedagogy Knowledge Scaled Scores1 by Country.

Country Mathematics Pedagogy Knowledge Mn (se)

Taiwan 649 (5.2)
Russian Federation 566 (10.1)
Singapore 553 (4.7)
Switzerland 549 (5.9)
Germany 540 (5.1)
Poland 524 (4.2)
United States-Private 505 (13.0)
United States-Public 502 (8.7)
Thailand 476 (2.5)
Oman 474 (3.8)
Malaysia 472 (3.3)
Norway 2 463 (3.4)
Philippines 450 (4.7)
Georgia 443 (9.6)
Botswana 425 (8.2)
Chile 394 (3.8)

100 200 300 400 500 600 700 800

Percentiles of Performance

5th 25th 75th 95th

95% Confidence Interval for Average (±2SE)

Significantly above the U.S. - Public
Not significantly different from the U.S. - Public

Significantly below the U.S. - Public

Notes.

1All scale scores are based on the preliminary data released by the IEA to the National Research Coordinator
in each participating country.

2Norway estimate based on a sample of both generalists and those generalists specializing in mathematics.

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This report presents the United States results from an international study
of mathematics teacher preparation for the elementary or lower secondary
(middle) grades. The Teacher Education and Development Study in
Mathematics (TEDS-M) was sponsored by the IEA and conducted in 16
countries: Botswana, Chile, Germany, Georgia, Malaysia, Norway, Oman,
the Philippines, Poland, the Russian Federation, Singapore, Spain,
Switzerland, Taiwan, Thailand, and the United States.
Potential future teachers near the end of their programs completed a
survey about their background, learning opportunities, and an assessment
of their mathematics knowledge and their knowledge of mathematics for
teaching. Involved in the US were nearly 3300 future teachers from over
80 public and private colleges and universities in 39 states.!

Center for Research in Mathematics and Science Education
College of Education

Additional copies of this report can be downloaded at http://usteds.msu.edu