## Mathematics for Grades 4 and 8: Trends Over Three Time Points

### Cognitive Subscales

Table 11a. Change in average mathematics cognitive domain scores of 4th-grade students, by education system: 2007-2015 and 2011-2015
Education system Average cognitive domain score Change in average cognitive domain score1
2007 2011 2015 Score difference: 2007 to 2015 Score difference: 2011 to 2015
Knowing Applying Reasoning Knowing Applying Reasoning Knowing Applying Reasoning Knowing Applying Reasoning Knowing Applying Reasoning

Average score is higher than U.S. average score at the .05 level of statistical significance.

Average score is lower than U.S. average score at the .05 level of statistical significance.

― Not available.

# Rounds to zero.

*p<.05. Change in average scores is significant at the .05 level of statistical significance.

1 The change in average score is calculated by subtracting the 2007 or 2011 estimate, respectively, from the 2015 estimate using unrounded numbers.

2 National Defined Population covers 90 to 95 percent of the National Target Population in 2015.

3 Met guidelines for sample participation rates only after replacement schools were included in 2015.

4 Nearly satisfied guidelines for sample participation rates after replacement schools were included in 2015.

5 National Defined Population covers less than 90 percent of the National Target Population (but at least 77 percent) in 2015.

6 The number in parentheses indicates years of school not grade in schooling.

7 National Target Population does not include all of the International Target Population in 2015.

8 Reservations about reliability because the percentage of students with achievement too low for estimation exceeds 15 percent but does not exceed 25 percent in 2015.

9 Did not satisfy guidelines for sample participation rates in 2015.

NOTE: Education systems are ordered by 2015 average score in reasoning. Education systems that are not countries are designated by the appended three-letter international abbreviation for their country. Participants that did not administer TIMSS at the target grade are not shown; see the international report for their results. For cross-education system trend tables, data are shown for the first available and most recent year; 1995 is the first year for the overall mathematics scale and benchmark data and 2007 is the first year for the content and cognitive subscales. Participants that only participated in one of the three time points are also excluded. U.S. state data are based on public school students only. For TIMSS 2015, Norway revised its assessed population to students in their 5th and 9th years of schooling to obtain better comparisons with Sweden and Finland. However, in previous TIMSS cycles Norway assessed students in their 4th and 8th years of schooling, which were defined as 4th and 8th grades but have been redefined as 3rd and 7th grades because year 1 in Norway is now considered the equivalent of a year of kindergarten. To maintain trend with previous TIMSS cycles, in 2015 Norway also collected data from students in their 4th and 8th years of schooling, which is used in trend tables. Trend results for Kuwait do not include private schools. Trend results for Lithuania do not include students taught in Polish or in Russian.

For 2007, Georgia and Lithuania had a National Target Population that did not include all of the International Target Population; the United States, Ontario-CAN, and Quebec-CAN had a National Defined Population that covered 90-95 percent of the National Target Population; Denmark and the United States met guidelines for sample participation only after replacement schools were included; the Netherlands and Dubai-UAE nearly satisfied guidelines for sample participation rates after replacement schools were included; and Dubai-UAE tested the same cohort of students as other education systems, but later in the assessment year at the beginning of the next school year.

For 2011, Georgia, Kuwait, Lithuania, and Florida-USA had a National Target Population that did not include all of the International Target Population; Croatia, Denmark, Hong Kong-CHN, Kazakhstan, Lithuania, Qatar, Serbia, Singapore, and the United States had a National Defined Population that covered 90-95 percent of the National Target Population; Florida-USA had a National Defined Population that covered less than 90 percent of the National Target Population (but at least 77 percent); the Netherlands and Northern Ireland-GBR met guidelines for sample participation rates only after replacement schools were included; and Norway (4) nearly satisfied guidelines for sample participation rates after replacement schools were included. In Oman in 2011, there were reservations about reliability because the percentage of students with achievement too low for estimation exceeded 15 percent but did not exceed 25 percent; in Kuwait and Morocco there were reservations about reliability because the percentage of students with achievement too low for estimation exceeded 25 percent.

The standard errors for the estimates shown in this table are in table 11b available at http://nces.ed.gov/timss/timss2015/timss2015_table11b.asp.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007, 2011, and 2015.

Korea, Republic of 614 600 603 627 595 619 13 * -5 16 *
Singapore2 625 597 584 629 602 588 631 619 603 5 23 * 19 * 2 17 * 15 *
Hong Kong-CHN3 622 606 596 619 597 589 618 621 600 -4 14 * 4 -1 23 * 11 *
Japan 567 570 569 590 579 592 601 589 595 35 * 19 * 26 * 11 * 10 * 3
Chinese Taipei-CHN 586 574 571 599 593 577 620 593 576 35 * 19 * 5 21 * # -2
Russian Federation 539 549 544 541 539 548 556 566 570 18 * 18 * 26 * 16 * 27 * 22 *
Kazakhstan 503 499 501 546 541 553 43 * 42 * 52 *
Northern Ireland-GBR4 580 565 538 582 575 550 2 11 * 12 *
Denmark2, 3 514 527 525 531 539 543 536 538 548 22 * 11 * 22 * 5 -1 5
Czech Republic 472 493 491 502 512 523 519 528 544 48 * 35 * 52 * 17 * 16 * 21 *
Netherlands3 528 540 537 537 540 543 521 531 543 -8 * -10 * 6 -17 * -10 * #
Sweden2 483 506 519 489 507 520 501 521 542 18 * 16 * 22 * 12 * 14 * 22 *
Finland 548 544 546 530 536 540 -18 * -8 * -5
England-GBR 546 542 539 552 542 531 554 544 540 8 3 1 2 2 9
Belgium (Flemish)-BEL3 564 546 532 554 544 536 -10 * -2 4
Lithuania2 520 540 529 525 540 536 534 538 536 14 * -3 7 8 * -2 -1
Ireland-GBR 539 529 510 554 549 535 15 * 20 * 26 *
Germany 515 530 530 524 528 532 524 515 535 9 * -15 * 5 # -13 * 3
Portugal2 531 534 531 548 540 532 17 * 6 1
United States2, 3 541 524 525 556 539 525 547 537 531 6 13 * 6 -8 * -2 5
Hungary 511 506 510 519 513 514 532 526 529 21 * 20 * 20 * 13 * 13 * 15 *
Slovenia 498 502 504 510 514 516 517 521 524 19 * 19 * 20 * 7 * 7 * 8 *
Australia 511 522 516 516 519 513 509 521 523 -2 -1 7 -7 2 10 *
Serbia5 520 511 514 513 521 517 -7 10 * 2
Slovak Republic 492 496 499 506 505 511 491 497 515 -1 1 17 * -16 * -9 5
Croatia 495 484 492 502 499 507 8 * 15 * 15 *
Norway (4)6 459 475 486 487 499 501 479 495 506 20 * 20 * 20 * -8 -4 5
New Zealand 484 493 502 476 490 490 475 497 504 -8 * 4 2 -1 7 * 13 *
Italy2 512 499 511 510 506 505 511 504 503 -1 5 -8 1 -2 -3
Spain2 482 483 483 505 505 502 23 * 22 * 19 *
Turkey 475 469 462 491 482 466 17 * 13 * 5
Chile 455 463 469 449 462 466 -7 # -3
Georgia7 445 430 433 449 447 450 466 461 452 21 * 31 * 19 * 16 * 14 * 1
Bahrain2 438 431 439 453 450 447 15 * 19 * 8 *
United Arab Emirates 437 430 434 453 452 445 16 * 22 * 11 *
Qatar 411 411 416 444 434 431 33 * 23 * 15 *
Iran, Islamic Republic of 404 397 401 435 427 423 429 435 426 25 * 38 * 26 * -6 7 4
Oman 380 382 391 422 428 420 43 * 46 * 29 *
Saudi Arabia8 409 405 412 374 382 383 -36 * -23 * -29 *
Morocco 320 332 347 377 375 379 57 * 43 * 32 *
Kuwait8 343 330 329 326 322 306 -16 * -8 -23 *
Benchmarking participants
Quebec-CAN9 519 516 523 536 529 534 542 533 536 23 * 17 * 14 * 6 3 2
Florida-USA7 568 542 523 555 545 534 -13 * 3 11
Ontario-CAN 498 513 526 510 521 522 505 513 524 7 # -2 -5 -8 3
Dubai-UAE 454 436 441 472 465 464 514 510 507 60 * 74 * 66 * 42 * 45 * 44 *
Abu Dhabi-UAE2, 8 418 413 418 418 422 414 # 9 -5