Chapter 13: The TIMSS 2007 International Benchmarks of ...

Ina V.S. Mullis, Ebru Erberber, And Corinna Preuschoff

Description

Chapter 13
The TIMSS 2007 International
Benchmarks of Student Achievement
in Mathematics and Science
Ina V.S. Mullis, Ebru Erberber, and Corinna Preuschoff
13.1 Overview
it is important for users of the ti MSS achievement results to understand what
the scores on the ti MSS mathematics and science achievement scales mean.
t hat is, what does it mean to have a scale score of 513 or 426? t o describe
student performance at various points along the ti MSS mathematics and
science achievement scales, ti MSS 2007 used scale anchoring to summarize
and describe student achievement at four points on the mathematics and
science scales—a dvanced international Benchmark (625), h igh international
Benchmark (550), intermediate international Benchmark (475), and Low
international Benchmark (400). f or the description of performance at the
international benchmarks please see TIMSS 2007 International Mathematics
Report (Mullis, Martin, & f oy, 2008) and TIMSS 2007 International Science
Report (Martin, Mullis, & f oy, 2008).
t his chapter describes the scale anchoring procedures that were applied
to describe student performance at these benchmarks. information about
the ti MSS 2007 achievement scales and details about the methods used
for scaling were presented in c hapter 11. in brief, scale anchoring involves
selecting benchmarks (scale points) on the ti MSS achievement scales to
be described in terms of student performance and then identifying items
that students ...

Sujets

• Mathematics of Information Technology and Complex systems
• Science en Chine
• Exhibition (GO Transit)
• Tatooine
• Succès (homonymie)
• Eagles de Boston College

Informations

• Publié par: Nufeng
• Nombre de lectures: 71
• Langue: English

Extrait

Chapter 13

e TIMSS 2007 International Benchmarks of Student Achievement in Mathematics and Science

Ina V.S. Mullis, Ebru Erberber, and Corinna Preuschoff

13.1

Overview

î ïŝ ïôâ ô ûŝéŝ ô é îŚŚ âçïééé éŝûŝ ô ûéŝâ wâ é ŝçôéŝ ô é îŚŚ âéâïçŝ â ŝçïéçé âçïééé ŝçâéŝ éâ. â ïŝ, wâ ôéŝ ï éâ ô âé â ŝçâé ŝçôé ô 5 ô 46? ô éŝçïé ŝûé éôâçé â âïôûŝ ôïŝ âôG é îŚŚ âéâïçŝ â ŝçïéçé âçïééé ŝçâéŝ, îŚŚ  ûŝé ŝçâé âçôïG ô ŝûâïzé â éŝçïé ŝûé âçïééé â ôû ôïŝ ô é âéâïçŝ â ŝçïéçé ŝçâéŝ—àâçé îéâïôâ béçâ (65), HïG îéâïôâ béçâ (55), îééïâé îéâïôâ béçâ (45), â Lôw îéâïôâ béçâ (4). Fô é éŝçïïô ô éôâçé â é ïéâïôâ éçâŝ éâŝé ŝééTIMSS  International Mathematics Report(ûïŝ, âï, & FôY, ) âTIMSS  International Science Report(âï, ûïŝ, & FôY, ). ïŝ çâé éŝçïéŝ é ŝçâé âçôïG ôçéûéŝ â wéé âïé ô éŝçïé ŝûé éôâçé â éŝé éçâŝ. îôâïô âôû é îŚŚ  âçïééé ŝçâéŝ â éâïŝ âôû é éôŝ ûŝé ô ŝçâïG wéé éŝéé ï Câé . î ïé, ŝçâé âçôïG ïôéŝ ŝééçïG éçâŝ (ŝçâé ôïŝ) ô é îŚŚ âçïééé ŝçâéŝ ô é éŝçïé ï éŝ ô ŝûé éôâçé â é ïéïYïG ïéŝ â ŝûéŝ ŝçôïG â é âçô ôïŝ (é ïéâïôâ éçâŝ) çâ âŝwé çôéçY. é ïéŝ, ŝô ïéïïé, âé Gôûé Y çôé ôâï wïï éçâŝ ô éïéw Y âéâïçŝ â ŝçïéçé éxéŝ. Fô îŚŚ , é Śçïéçé â âéâïçŝ îé Réïéw Côïéé çôûçé é éïéw. é çôïéé ééŝ éxâïé é çôé ô

TIMSS & PIRLS InTeRnaTIonaL STudy CenTeR, LyNCH ŚCHOOL OF EDUCàîON, bOŚON COLLEgE

339

340

chapter 13: The TIMSS 7 International Benchmarks of Student Achievement in Mathematics and Science

éâç ïé â ééïé é ï ô âéâïçŝ ô ŝçïéçé ôwéGé â/ô ŝï éôŝâé Y ŝûéŝ âŝwéïG é ïé çôéçY. éY é ŝûâïzé é éâïé ïŝ ô ïé çôééçïéŝ ï â ïé éŝçïïô ô âçïééé â éâç ïéâïôâ éçâ. ïŝ ôçéûé éŝûé ï â çôé-éééçé ïééâïô ô é âçïééé éŝûŝ â çâ é çôŝïéé ï ïG ô é îŚŚ  âéâïçŝ â ŝçïéçé âéwôŝ. é ïé-Y-ïé éŝçïïôŝ ééôé âŝ â ô é ŝçâé âçôïG ôçéûéŝ âé ôïé ï àéïx F.

13.2

 History of Identifying the International Benchmarks

îéïYïG é ŝçâé ôïŝ ô ŝéé âŝ ïéâïôâ éçâŝ ïïïâY wâŝ â çâéGé ô îŚŚ ï é çôéx ô éâŝûïG éŝ. Fô é îŚŚ 5 â  âŝŝéŝŝéŝ, é ŝçâéŝ wéé âçôé ûŝïG éçéïéŝ. â ïŝ, é ŝçâé âçôïG ââYŝïŝ wâŝ çôûçé ûŝïG é ô  éçé    ( éçéïé), é ô Qûâé (5 éçéïé), é ô Hâ (5  éçéïé), â é bôô Qûâé (5 éçéïé). Hôwéé, wï ïéé âïçïâïG çôûïéŝ ï éâç îŚŚ çYçé â ïéé âçïééé ô çôûïéŝ âïçïâïG ï éïôûŝ çYçéŝ, é éçéïé ôïŝ â çâGé éwéé 5 â . î âïG ô éôïG é éŝûŝ ô îŚŚ , ï wâŝ çéâ â îŚŚ ééé â ŝé ô ôïŝ ô ŝéé âŝ éçâŝ, â wôû ô çâGé ï é ûûé, â wôû ôô ŝéŝïé, â â wéé ŝïïâ ô é ôïŝ ûŝé ï . àé ûç çôŝïéâïô, â ŝé ô ôû ôïŝ wï éqûâ ïéâŝ ô é âéâïçŝ â ŝçïéçé âçïééé ŝçâéŝ wâŝ ïéïïé ô é ûŝé âŝ é ïéâïôâ éçâŝ, âéY 4, 45, 55, â 65. éŝé ôïŝ wéé ŝééçé ô é âŝ çôŝé âŝ ôŝŝïé ô é éçéïé ôïŝ âçôé ï  â é éïG Gâé (ï.é., ô  éçé wâŝ 66 ô âéâïçŝ â ŝçïéçé, ô Qûâé wâŝ 555 ô âéâïçŝ â 55 ô ŝçïéçé, ô Hâ wâŝ 4 ô âéâïçŝ â 4 ô ŝçïéçé, â bôô Qûâé wâŝ 6 ô âéâïçŝ â 4 ô ŝçïéçé). é éwY éïé éçâ ŝçâé ôïŝ wéé ûŝé âŝ é âŝïŝ ô é ŝçâé âçôïG éŝçïïôŝ ï îŚŚ  â âGâï ï îŚŚ .

1 The description of the scale anchoring procedure was adapted from Kelly (1999), and Gregory and Mullis (2000).

620–630

Advanced Benchmark

chapter 13: The TIMSS 7 International Benchmarks of Student Achievement in Mathematics and Science

13.3

Identifying the Students Achieving at the International Benchmarks

Range Around Each International Benchmark and Number of Students Within Each Range – Science

5732 5639

2981 2767

620–630

545–555

470–480

High Benchmark

Intermediate Benchmark

Low Benchmark

395–405

Exhibit 13.2

395–405

2950 6393

Range of Scale Scores Fourth Grade Eighth Grade

470–480

5091 8366

3151 6969

545–555

6321 6749

5243 7649

13.4

The Scale Anchoring Criteria

Range Around Each International Benchmark and Number of Students Within Each Range – Mathematics Intermediate High Advanced Low Benchmark Benchmark Benchmark Benchmark

Range of Scale Scores Fourth Grade Eighth Grade

Exhibit 13.1

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é ïŝ ŝé ï é ŝçâé-âçôïG ôçéûé wâŝ ô ïéïY ôŝé ŝûéŝ ŝçôïG â é ïéâïôâ éçâŝ. FôôwïG é ôçéûé ûŝé ï éïôûŝ îEà ŝûïéŝ, ŝûéŝ ŝçôïG wïï ûŝ â ïûŝ 5 ŝçâé ŝçôé ôïŝ ô éâç éçâ wéé ïéïïé ô é éçâ ââYŝïŝ. é ŝçôé âGéŝ âôû éâç ïéâïôâ éçâ â é ûé ô ŝûéŝ ŝçôïG ï éâç âGé â é ôû â éïG Gâéŝ ô âéâïçŝ âé ŝôw ï Exïï . â ô ŝçïéçé ï Exïï .. é âGé ô ûŝ â ïûŝ 5 ôïŝ âôû â éçâ ïŝ ïéé ô ôïé â âéqûâé ŝâé ï éâç Gôû, Yé é ŝâ éôûG ŝô â éôâçé â éâç éçâ âçô ôï ïŝ ŝï ïŝïGûïŝâé ô é éx. é ââ ââYŝïŝ ô é ŝçâé âçôïG wâŝ âŝé ô éŝé ŝûéŝ ŝçôïG â éâç éçâ âGé.

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HâïG ïéïïé é ûé ô ŝûéŝ ŝçôïG â éâç éçâ âçô ôï, é éx ŝé wâŝ ééïïG wïç âïçûâ ïéŝ âçôé â éâç ô é âçô ôïŝ. à ïôâ éâûé ô é ŝçâé âçôïG éô ïŝ â ï Yïéŝ éŝçïïôŝ ô é éôâçé éôŝâé Y ŝûéŝ éâçïG éâç ô é éçâŝ ô é îŚŚ âéâïçŝ â ŝçïéçé âçïééé ŝçâéŝ, â â éŝé éŝçïïôŝ ééç éôŝâY

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chapter 13: The TIMSS 7 International Benchmarks of Student Achievement in Mathematics and Science

ïéé âççôïŝéŝ Y ŝûéŝ éâçïG éâç ŝûççéŝŝïéY ïGé éçâ. é ôçéŝŝ éâïŝ é éïéâïô ô ŝéŝ ô ïéŝ â ŝûéŝ â éâç ïéâïôâ éçâ âé éY ïéY ô âŝwé çôéçY â â ïŝçïïâé éwéé ôé éçâ â é éx. Cïéïâ wéé âïé ô ïéïY é ïéŝ â wéé âŝwéé çôéçY Y ôŝ ô é ŝûéŝ â â âïçûâ éçâ, û Y éwé ŝûéŝ â é éx ôwé éçâ. î ŝçâé âçôïG, é âçô ïéŝ ô éâç ôï âé ïéé ô é ôŝé â ïééïâé éwéé âjâçé âçô ôïŝ (é.G., éwéé é àâçé â é HïG îéâïôâ béçâŝ). ô éé ïŝ Gôâ, é çïéïâ ô ïéïYïG é ïéŝ ûŝ âé ïô çôŝïéâïô éôâçé â ôé â ôé éçâ. ééôé, ï âïïô ô â çïéïô ô é éçéâGé ô ŝûéŝ â â âïçûâ éçâ çôéçY âŝwéïG â ïé, ï âŝô wâŝ éçéŝŝâY ô ûŝé â çïéïô ô é éçéâGé ô ŝûéŝ ŝçôïG â é éx ôwé éçâ wô çôéçY âŝwé â ïé. Fô ûïé-çôïçé ïéŝ, é çïéïô ô 65 éçé wâŝ ûŝé ô é éçâ, ŝïçé ŝûéŝ wôû é ïéY (âôû wô ïŝ ô é ïé) ô âŝwé é ïé çôéçY. é çïéïô ô éŝŝ â 5 éçé wâŝ ûŝé ô é éx ôwé éçâ, éçâûŝé wï ïŝ éŝôŝé ôâïïY, ŝûéŝ wéé ôé ïéY ô âé âŝwéé é ïé ïçôéçY â çôéçY. à ŝôéwâ éŝŝ ŝïç çïéïô wâŝ ûŝé ô çôŝûçé-éŝôŝé ïéŝ, éçâûŝé ŝûéŝ âé ûç éŝŝ ôŝŝïïïY ô GûéŝŝïG. Fô çôŝûçé-éŝôŝé ïéŝ, é çïéïô ô 5 éçé wâŝ ûŝé ô é éçâ wïôû âY ïŝçïïâïô çïéïô ô é éx ôwé éçâ. é çïéïâ ûŝé ô ïéïY ûïé-çôïçé ïéŝ â “âçôé” âé ôûïé éôw: Fô é Lôw îéâïôâ béçâ (4), â ûïé-çôïçé ïé âçôé ï • à éâŝ 65 éçé ô ŝûéŝ ŝçôïG ï é âGé âŝwéé é ïé çôéçY (éçâûŝé ïŝ wâŝ é ôwéŝ éçâ éŝçïé, éé wéé ô ûé çïéïâ). Fô é îééïâé îéâïôâ béçâ (45), â ûïé-çôïçé ïé âçôé ï • à éâŝ 65 éçé ô ŝûéŝ ŝçôïG ï é âGé âŝwéé é ïé çôéçY â

chapter 13: The TIMSS 7 International Benchmarks of Student Achievement in Mathematics and Science

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Léŝŝ â 5 éçé ô ŝûéŝ â é Lôw îéâïôâ béçâ âŝwéé é ïé çôéçY.

Fô é HïG îéâïôâ béçâ (55), â ûïé-çôïçé ïé âçôé ï • à éâŝ 65 éçé ô ŝûéŝ ŝçôïG ï é âGé âŝwéé é ïé çôéçY â • Léŝŝ â 5 éçé ô ŝûéŝ â é îééïâé îéâïôâ béçâ âŝwéé é ïé çôéçY. Fô é àâçé îéâïôâ béçâ (65), â ûïé-çôïçé ïé âçôé ï • à éâŝ 65 éçé ô ŝûéŝ ŝçôïG ï é âGé âŝwéé é ïé çôéçY â • Léŝŝ â 5 éçé ô ŝûéŝ â é HïG îéâïôâ béçâ âŝwéé é ïé çôéçY. ô ïçûé â ô é ïéŝ ï é âçôïG ôçéŝŝ â ôïé ïôâïô âôû çôé ôâïŝ â çôGïïé ôçéŝŝéŝ â ïG ô âé â âY ïéŝ âçô éxâçY, ïéŝ â é â ŝïGY éŝŝ ŝïGé ŝé ô çïéïâ wéé âŝô ïéïïé. é çïéïâ ô ïéïY ûïé-çôïçé ïéŝ â “âôŝ âçôé” wéé é ôôwïG: Fô é Lôw îéâïôâ béçâ (4), â ûïé-çôïçé ïé âôŝ âçôé ï • à éâŝ 6 éçé ô ŝûéŝ ŝçôïG ï é âGé âŝwéé é ïé çôéçY (éçâûŝé ïŝ wâŝ é ôwéŝ éçâ ô ûé çïéïâ wéé ûŝé). Fô é îééïâé îéâïôâ béçâ (45), â ûïé-çôïçé ïé âôŝ âçôé ï • à éâŝ 6 éçé ô ŝûéŝ ŝçôïG ï é âGé âŝwéé é ïé çôéçY â • Léŝŝ â 5 éçé ô ŝûéŝ â é Lôw îéâïôâ béçâ âŝwéé é ïé çôéçY.

Fô é HïG îéâïôâ béçâ (55), â ûïé-çôïçé ïé âôŝ âçôé ï • à éâŝ 6 éçé ô ŝûéŝ ŝçôïG ï é âGé âŝwéé é ïé çôéçY â

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chapter 13: The TIMSS 7 International Benchmarks of Student Achievement in Mathematics and Science

• Léŝŝ â 5 éçé ô ŝûéŝ â é îééïâé îéâïôâ béçâ âŝwéé é ïé çôéçY. Fô é àâçé îéâïôâ béçâ (65), â ûïé-çôïçé ïé âôŝ âçôé ï • à éâŝ 6 éçé ô ŝûéŝ ŝçôïG ï é âGé âŝwéé é ïé çôéçY â • Léŝŝ â 5 éçé ô ŝûéŝ â é HïG îéâïôâ béçâ âŝwéé é ïé çôéçY. ô é çôééY ïçûŝïé ô â ïéŝ, ïéŝ â é ôY é çïéïô â â éâŝ 6 éçé ô é ŝûéŝ âŝwéé çôéçY (éGâéŝŝ ô é éôâçé ô ŝûéŝ â é éx ôwé ôï) wéé âŝô ïéïïé. é éé çâéGôïéŝ ô ïéŝ wéé ûûâY éxçûŝïé, â éŝûé â â ô é ïéŝ wéé ââïâé ô ïô é éŝçïïôŝ ô ŝûé âçïééé â é âçô ééŝ. à ûïé-çôïçé ïé wâŝ çôŝïéé ô é “ôô ïïçû” ô âçô ï éŝŝ â 6 éçé ô ŝûéŝ â é ââçé éçâ âŝwéé é ïé çôéçY. Dïéé çïéïâ wéé ûŝé ô ïéïY çôŝûçé-éŝôŝé ïéŝ â “âçôé.” à çôŝûçé-éŝôŝé ïé âçôé â ôé ô é ïéâïôâ éçâŝ ï â éâŝ 5 éçé ô ŝûéŝ â â éçâ âŝwé é ïé çôéçY. à çôŝûçé-éŝôŝé ïé wâŝ çôŝïéé ô é “ôô ïïçû” ô âçô ï éŝŝ â 5 éçé ô ŝûéŝ â é ââçé éçâ âŝwéé é ïé çôéçY.

13.5

Identifying the Anchor Items at Each International Benchmark

Fô é ŝûéŝ ŝçôïG ï é âGé âôû éâç ïéâïôâ éçâ, é éçéâGé ô ôŝé ŝûéŝ â âŝwéé éâç ïé çôéçY wâŝ çôûé. ô çôûé éŝé éçéâGéŝ, ŝûéŝ ï éâç çôûY wéé wéïGé ô çôïûé ôôïôâ ô é ŝïzé ô é ŝûé ôûâïô ï â çôûY. ôŝ ô é îŚŚ  ïéŝ wéé ŝçôé -ôï ô â çôéç âŝwé â  ôïŝ ô ôé âŝwéŝ. Fô éŝé ïéŝ, é éçéâGé ô ŝûéŝ â éâç éçâ wô âŝwéé éâç ïé çôéçY wâŝ çôûé. Fô éâïéY éw çôŝûçé-éŝôŝé ïéŝ ŝçôé ô âïâ ô û çéï, éçéâGéŝ wéé çôûé ô é ŝûéŝ éçéïïG û çéï. é çïéïâ éŝçïé âôé wéé âïé ô ïéïY é ïéŝ â âçôé, âôŝ âçôé, â é ôY é 6 ô 65 éçé çïéïâ. Fô âéâïçŝ â é ôû Gâé  ïéŝ âçôé,  âôŝ âçôé,

chapter 13: The TIMSS 7 International Benchmarks of Student Achievement in Mathematics and Science

â 4 é é 6 ô 65 éçé çïéïâ. à é éïG Gâé, 5 âéâïçŝ ïéŝ âçôé,  âôŝ âçôé, â 6 é é 6 ô 65 éçé çïéïâ. Fô ŝçïéçé  ïéŝ âçôé, 6 âôŝ âçôé, â 4 é é 6 ô 65 éçé çïéïâ â é ôû Gâé. à é éïG Gâé 5 ŝçïéçé ïéŝ âçôé, 6 âôŝ âçôé, â 4 é é 6 ô 65 éçé çïéïâ, éŝéçïéY. bôâéïG é âçô çïéïâ ô éâç éçâ ô ïçûé ïéŝ ééïG é éŝŝ ŝïGé çïéïâ, éâé é Śçïéçé â âéâïçŝ îé Réïéw Côïéé ô ûŝé â ô é ïéŝ ïçûé ï é îŚŚ  âŝŝéŝŝé ô çââçéïzé éôâçé â éâç éçâ. Eé ôûG éŝé ïéŝ ï ô éé é 65 éçé âçôïG çïéïâ, éY wéé ŝï ïéŝ â ŝûéŝ ŝçôïG â é éçâŝ â â ïG éGéé ô ôâïïY ô âŝwéïG çôéçY. Exïï . éŝéŝ é ûé ô âéâïçŝ ïéŝ Y çôé ôâï â âçôé â éâç ïéâïôâ éçâ â é ôû Gâé. Exïï .4 éŝéŝ é çôéŝôïG ïôâïô ô é éïG Gâé. Exïï .5 â Exïï .6 éŝé é ûé ô ŝçïéçé ïéŝ Y çôé ôâï â éâç ïéâïôâ éçâ â ôû â é éïG Gâéŝ, éŝéçïéY.

Exhibit 13.3

Number of Items Anchoring at Each International Benchmark by Content Domain – Fourth Grade Mathematics*

Too Intermediate High Advanced Low (400) Difficult Total (475) (550) (625) to Anchor Number6 15 36 30 4 91 Geometric Shapes 5 13 20 18 4 60 and Measures Data Display3 11 – 269 3 Total 14 39 65 51 8 177 * Following the item review, 2 items were deleted out of 179 items in the mathematics fourth grade test, resulting in 177 items (see Chapter 10 for more details on the item review process).

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chapter 13: The TIMSS 7 International Benchmarks of Student Achievement in Mathematics and Science

Exhibit 13.4

Number of Items Anchoring at Each International Benchmark by Content Domain – Eighth Grade Mathematics*

Too Intermediate High Advanced Low (400) Difficult Total (475) (550) (625) to Anchor Number5 17 24 14 3 63 Algebra29 26 1 7 1 64 Geometry22 17 – 7 1 47 Data and Chance403 9 19 8 1 Total 9 40 94 65 6 214 * Following the item review, 1 item was deleted out of 215 items in the mathematics eighth grade test, resulting in 214 items (see Chapter 10 for more details on the item review process).

Exhibit 13.5

Number of Items Anchoring at Each International Benchmark by Content Domain – Fourth Grade Science*

Too Intermediate High Advanced Low (400) Difficult Total (475) (550) (625) to Anchor Life Science15 20 7 17 12 71 Physical Science28 15 7 9 5 64 Earth Science4 3511 13 1 6 Total 15 32 54 48 21 170 * Following the item review, 3 items were deleted out of 174 items in the science fourth grade test, resulting in 171 items. Also, 1 two- part item was combined to form a single item, further reducing the number of items to 170 (see Chapter 10 for more details on the item review process).

Exhibit 13.6

Number of Items Anchoring at Each International Benchmark by Content Domain – Eighth Grade Science*

Too Intermediate High Advanced Low (400) Difficult Total (475) (550) (625) to Anchor Biology26 25 11 752 11 Chemistry3 4 7 4111 16 Physics5414 24 12 2 2 Earth Science- 6 17 12 5 40 Total 7 23 68 77 35 210 * Following the item review, 4 items were deleted out of 214 items in the science eighth grade test, resulting in 210 items (see Chapter 10 for more details on the item review process).

13.6

Experts Review Anchor Items by International Benchmark and Content Domains to Develop the Descriptions of Achievement

HâïG ïéïïé é ïéŝ â âçôé â éâç ô é ïéâïôâ éçâŝ, é éx ŝé wâŝ ô âé é ïéŝ éïéwé Y é îŚŚ  Śçïéçé â âéâïçŝ îé Réïéw Côïéé ô ééô éŝçïïôŝ

chapter 13: The TIMSS 7 International Benchmarks of Student Achievement in Mathematics and Science

ô ŝûé éôâçé. î éââïô ô é éïéw Y é ééŝ ô é îŚŚ  Śçïéçé â âéâïçŝ îé Réïéw Côïéé, é âéâïçŝ â ŝçïéçé ïéŝ, éŝéçïéY, wéé ôGâïzé ï ïéŝ Gôûé Y ïéâïôâ éçâ â wïï éçâ, é ïéŝ wéé ŝôé Y çôé âéâ â é Y é âçôïG çïéïâ éY é - ïéŝ â âçôé, ôôwé Y ïéŝ â âôŝ âçôé, ôôwé Y ïéŝ â é ôY é 6 ô 65 éçé çïéïâ. é ôôwïG ïôâïô wâŝ ïçûé ô éâç ïé: çôé âéâ, ôïç âéâ, çôGïïé ôâï, âxïû ôïŝ, âŝwé éY, ééâŝé ŝâûŝ, éçé çôéç â éâç éçâ, â ôéâ ïéâïôâ éçé çôéç. Fô çôŝûçé-éŝôŝé ïéŝ, é ŝçôïG Gûïéŝ wéé ïçûé. é îŚŚ & PîRLŚ îéâïôâ ŚûY Céé ŝâ çôéé é îŚŚ  Śçïéçé â âéâïçŝ îé Réïéw Côïéé ô â ôû- âY ééïG ï KâôŝïûG, âïwâ. é wô ïôé ï çôéïG é ŝçâé âçôïG ô é ïéâïôâ éçâŝ çôŝïŝé ô éé âŝŝ: () wô ôûG éâç ïé ï éâç ïé â âïé â â ŝô éŝçïïô ô é ôwéGé, ûéŝâïG, â/ô ŝïŝ éôŝâé Y ŝûéŝ âŝwéïG é ïé çôéçY; () âŝé ô é ïéŝ â âçôé, âôŝ âçôé, â é ôY é 6 ô 65 éçé çïéïô, ééô â éŝçïïô (ï éâïé â ŝûâY ô) ô é éé ô âéâïçŝ ô ŝçïéçé ôïçïéçY éôŝâé Y ŝûéŝ â éâç ô é ôû ïéâïôâ éçâŝ ô ûïŝ ï é îŚŚ  ïéâïôâ éôŝ; â () ŝééç éxâé ïéŝ â ŝûôé â ïûŝâé é éçâ éŝçïïôŝ ô ûïŝ ôGéé wï é éŝçïïôŝ.

References géGôY, K. D. & ûïŝ, î. V. Ś. (2000). DéŝçïïG ïéâïôâ éçâŝ ô ŝûé âçïééé. î . O. âï, K. D. géGôY, & Ś. E. Śéé (Eŝ.),TIMSS 1999 technical report. Céŝû Hï, à: îŚŚ & PîRLŚ îéâïôâ ŚûY Céé, bôŝô CôéGé. KéY, D. L. (999).Interpreting the ird International Mathematics and Science Study (TIMSS) achievement scales using scale anchoring. Uûïŝé ôçôâ ïŝŝéâïô, bôŝô CôéGé, Céŝû Hï, à.

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