Searching for the Truth About
the TIMSS 4th Grade Math Test

Did The United States Deserve
the "Above Average" Ranking?

by Bill Quirk (E-Mail:

Although the United States ranked below the "international mean" for the TIMSS 8th grade math test  and near the bottom for the TIMSS 12th grade math test, our 4th graders appeared to save the day with an "above average"  performance.  But a careful reading of TIMSS documentation  casts serious doubt on the validity of this apparently positive result.

The TIMSS 4th Grade Math Test: Background Information

United States 100, Singapore 74

No, this doesn't refer to test results, it's the percentage of TIMSS  test questions that each country considered relevant to their 4th grade curriculum.  Only 74% of the 4th grade math  test questions were "considered appropriate" by  Singapore, while 100% were approved by the United States. The percentage for Korea was even lower at 43%.   Yet Singapore and Korea ranked first and second on the TIMSS 4th grade math test, scoring "significantly higher" than the United States.4

It's clear that there was a "constructivist" vs. "traditional" battle over the development of the pool of questions for the TIMSS 4th grade math test.  Even with such weak criteria as "appropriate for at least 70% of the countries" and "recommended for deletion by less than 30% of the countries", the total number of acceptable test questions was continually found to be inadequate. Finally, due to "very tight deadlines for test production", The Educational Testing Service (United States) and SRI International (United States) were both both hired to add test items.5

Above Average?  It's All Relative!

For the 8th grade math test, 20 nations scored "significantly higher" than the United States. Only 12 of these nations competed at the 4th grade level, and 11 of them again scored higher than the United States.6  What happened to the other 8 "significantly higher" nations?   It's never explained.  But  perhaps they didn't like test questions that were 100% approved only by the United States. Whatever the reason, the fact that they were missing clearly helped to boost the relative standing of the United States.

The Spin From the National Center for Education Statistics (NCES)

"TIMSS is a fair comparison of achievements for several reasons. First, the test was jointly developed and carefully reviewed by the participating countries to ensure that the items reflected curriculum topics considered important in all countries, and did not over-emphasize the curriculum content taught in only a few.  Second, international monitors carefully reviewed nations' adherence to guidelines to ensure that significant numbers of students were not excluded from the test process for any reason".7

The Truth About Exclusions: The United States excluded  412 fourth grade students, more than any other nation.  Canada, also mesmerized by constructivism,  was next with 268.  The other 24 nations excluded a combined total of 804 fourth graders.  The seven nations that scored "significantly higher" than the United States had a combined total of  11 exclusions, with none for the three highest scoring countries, Singapore, Korea, and Japan.8

"ARE U.S. FOURTH-GRADE TEACHERS BETTER TRAINED THAT THEIR COLLEAGUES IN OTHER TIMSS COUNTRIES?   The profile of a typical U.S. teacher of fourth graders is similar to that of teachers in most other TIMSS countries: a woman at least 40 years old with more than 10 years of teaching experience. However, teachers of U.S. fourth graders have more university training than their counterparts in most TIMSS countries." 9 (Caps and bold emphasis in the original)

The Truth About Teacher Training: There was no mention of education in mathematics.

The Spin From the TIMSS International Study Center, Boston College

"Before giving results, I believe that it is important to note that the TIMSS study was conducted  with great attention to quality at every step of the way.  Rigorous procedures were designed specifically to translate the tests, and numerous regional training sessions were held in data collection and scoring.  Quality control monitors observed testing sessions (emphasis added) and reported back to the International Study Center at Boston College". 10  - Dr. Albert Beaton, TIMSS Study Director

The Truth About Test Observations:

What About Test Security?

Although there were many lip service efforts at test security, the TIMSS documentation make it clear that anyone who wanted an advance copy of the test would have no difficulty getting it:

Defects With Booklets and Supplies, But Probably Not in the United States

Difficulties With Translation, But Not in the United States

The TIMSS 4th grade math test was prepared in the United States and then translated from English (United States version) into 17 additional languages for the 26 participating countries.  Although the TIMSS documentation shows that serious efforts were made to ensure accurate translations and appropriate cultural adaptations, it's clear that these efforts weren't totally successful and probably couldn't be totally successful, particularly when one considers the limited resources used, the complex subtlety of cultural adaptation, and the lack of precision in the source English version..

Never Mind Translation, What Does It Mean in English?

Here are examples of ambiguous TIMSS 4th grade questions.  These are "free response", not multiple choice questions. (See Reference 3 for all TIMSS 4th grade math questions)

Question T2:  What is the smallest whole number that you can make using the digits 4, 3, 9, and 1?  Use each digit only once.

The expected answer is the 4-digit number 1349.  But notice that the question didn't request a 4-digit number.  How about 1 = 9 - (4 + 3 +1)?  The answer "1" is given the incorrect response code of  71, and listed as the second possible "incorrect response".

Question U5:  Addition Fact: 4+4+4+4+4 = 20.  Write this addition fact as a multiplication fact.

The expected answer is 4x5 = 20 or 5x4 = 20.  The answer 2x10 = 20 or 10x2 = 20 is given the incorrect response code of  72, and listed as the third possible "incorrect response".

Question S3:  Julie put a box on a shelf that is 96.4 centimeters long.  The box is 33.2 centimeters long.  What is the longest box she could put on the rest of the shelf.

The expected answer is 96.4- 33.2 = 63.2 (with no mention of centimeters).  But since there is no information given about the width of the shelf or the width of boxes, the most that can be said is that the length of "the longest box" is greater than or equal to 63.2 cm, and it could even be greater than 96.4 cm.  Since a written response was required, the good student might have looked for more than a simple subtraction.  Only 26% of 4th graders got the "right answer".

Searching For the Math

Beyond the lack of precision in the statement of questions, the children from many countries must have been puzzled by the non-math questions involving "eyeball" estimation, pattern recognition, and "probability". (See Reference 3 for all TIMSS 4th grade math questions)

Question K5:  About how long is this picture of a pencil?

Note that "measurement instruments (such as graduated rulers or protractors) were NOT permitted for any of the student populations because several items called for estimation (Cap is original, bold emphasis added)".25   The "picture of the pencil" actually measures 9.2 cm (using a "measuring instrument.).  The answer choices were 5 cm, 10 cm, 20 cm, and 30 cm.

Question L4:  These shapes are arranged in a pattern. (Graphic shows a left-to-right string of symbols as follows: 1 Circle, 1 Triangle, 2 Circles, 2 Triangles, 3 Circles, 3 Triangles)
Question: What set of shapes is arranged in the same pattern?  (Four answer patterns use stars and squares instead of circles and triangles).

Question S5:  Here is a paper clip  (graphic of a paper clip is given, with the word "Length" written below and arrow heads pointing to the left and right to the ends of the paper clip image).
The question: How many lengths of the paper clip is the same as the length of this line. (A straight line is shown below the statement of the question).  The paper clip actually measures 1 inch, and the line measures  4.5 inches.  Correct answers were 4, 5, and any number between 4 and 5.5 (Yes that's right, not 3.5 to 5.5).  Note that this is an example of multiple right answers.

Question T5:  Craig folded a piece of paper in half and cut out a shape (a picture of a folded page is given with a rough image of the number 3 shown as cut out of the folded edge). The student is asked "to draw a picture to show what the cut-out shape will look like when it is opened up and flattened out."  Multiple correct answers included a drawing of  "the cut-out shape" and drawing of "the remaining piece of paper".

Question U2:  Write a fraction that is larger than 2/7. Multiple correct answers included 3/8.

Question L2:  There is only one red marble in each of these bags (graphic shows 3 bags, one labeled 10 marbles, one labeled 100 marbles, and one labeled 1000 marbles).  Question: Without looking in the bags, you are to pick a marble out of one of the bags.  Which bag would give you the greatest chance of picking the red marble?

 Yes, it's trivial, but only if you have previously seen questions of this type and understand  the concept of "chance".  Internationally, only 51% of 4th graders answered correctly.

Somewhere in the Directions it Said "No Calculators"!

If calculators were allowed, many TIMSS 4th grade math questions would be trivial: After an apparently bitter debate, it was decided that calculators would not be permitted for the TIMSS 4th grade math test.26

What a moral dilemma for the constructivist brethren in the United States!  Their first commandment is "calculators in kindergarten".  The second is "the child shall use the calculator whenever the child thinks such use is appropriate".  Now, for this one test, they were expected to deny these fundamental beliefs.

We assume that Test Administrators in the United States did the right thing.  Of course, with no quality control monitor observations in the United States, we'll have to rely on faith.

 TIMSS Documentation

Reference 1.  TIMSS Technical Manual, Volume 1: Design and Development
Reference 2.  TIMSS Quality Assurance in Data Collection
Reference 3.  TIMSS Released Item Sets  - Set for Population 1 (Third and Fourth Grades)
Reference 4:  TIMSS Mathematics in the Primary School Years
Reference 5.  A TIMSS Primer:  (Fordham Report by  Harold W. Stevenson)
Reference 6:  TIMSS Primary School Years News, Statement by Dr. Albert Beaton
Reference 7:  US TIMSS Steering Committee Members
Reference 8:  Pursuing Excellence NCES  (Study of 4th Grade TIMSS)

Numbered References: (See Superscript Numbers in Text)

1. Reference 4, Pages A-13 through A16 in Appendix A
2. Reference 1, Pages 3-4 through 3-9
3. Reference 7, Page 2
4. Reference 4, Pages B2 and B3 in Appendix B
5. Reference 1, Pages 2-3 through 2-6
6. Reference 5, Tables 3 and 5  (Pages 11 and 15 in hardcopy)
7. Reference 8, Chapter 1, Special Notes On The Test Scores
8. Reference 4, Page A-14 in Appendix A
9. Reference 8, Chapter 2, Are U.S. Fourth-grade Teachers Better Trained?
10. Reference 6, Page 1
11. Reference 2, Page 3-1
12. Reference 1, Page 3-1
13. Reference 2, Page 3-8
14. Reference 2, Page 4-2 and 4-3.
15  Reference 2, Page 4-4
16. Reference 2, Page 4-4
17. Reference 2, Page 4-6
18. Reference 2, Page 3-10
19. Reference 2, Page 4-5
20. Reference 2, Page 4-9
21. Reference 2, Page 1-5
22 .Reference 1, Page 8-3
23. Reference 2, Page 3-10
24. Reference 2, Page 3-10
25. Reference 1, Page 2-19
26. Reference 1, Page 2-19
Copyright 1998-2011 William G. Quirk, Ph.D.