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4
MATHEMATICS CONCEPTS
MATHEMATICS ITEMSMATHEMATICS CONCEPTSMATHEMATICS ITEMS
The
Mathematics Concepts and Mathematics Items
book contains the released TIMSS mathematics assessment items. These are the released items from the 1995 and 2003 assessments (as distinct from the secure items, which are kept conﬁdential so that they may be used in subsequent cycles to monitor trends).
Guide to Using the
Mathematics Concepts and Mathematics Items
Materials
The materials contained in this book can be used in a number of ways as a tool to assist teachers in making a formative assessment of student knowledge and skills. Some of these ways include the following:
Teacher-designed formative assessments.
A teacher might, for example, decide to examine how well his or her class knows facts and procedures. In such a case, the ﬁrst step would be to review the questions in
Mathematics Concepts and Mathematics Items
, selecting the ones of interest. Ready-to-use versions of these items can be found in the
Mathematics Items
book. Teachers can print these items or present them to students on an overhead. Student responses can be scored by referring to the appropriate page in
Mathematics Concepts and Mathematics Items
. Teachers can also compare the overall percentage of students responding correctly to the international benchmark for that item.
Feedback on teaching.
To the extent that the items coincide with concepts taught, the teacher might follow the same process to gain rapid feedback on the success of the teaching episode.
Understanding misunderstandings.
Again, a teacher might decide to examine the incorrect or partially correct responses of the class for insight into any general misunderstandings, with a view to re-teaching a particular topic or skill.
Identifying individual difﬁculties.
In the same way, the teacher might use the items to identify particular difﬁculties experienced by individual students, as the basis for some remedial teaching or focused practice.
18675.0206
33
Guide to the Content and Layout of This Book
This book contains the released items from both TIMSS 1995 and TIMSS 2003. Due to slight revisions in terminology and released information between cycles, the format for the items in each cycle differs slightly. Each item appears on a single page and is accompanied by a number of descriptors.
1995 Content Domains
:ã Whole numbersã Fractions and proportionalityã Measurement, estimation, and number senseã Data representation, analysis, and probabilityã Geometry ã Patterns, relations, and functions
2003 Content Domains
:ã Patterns and Relationshipsã Data ã Geometryã Measurementã Number
1995 Cognitive Domains
:ã Knowingã Performing routine proceduresã Using complex proceduresã Solving problems
2003 Cognitive Domains
:ã Knowing facts and proceduresã Using conceptsã Solving routine problemsã ReasoningTake a look at
Which number is it
, the name given to the ﬁrst 1995 item in this book. As speciﬁed in boxes at the top of the page, the content domain for this item is
whole numbers
and the cognitive domain is
using complex procedures
. Looking at
Symbolic linear equation of magazines
, the ﬁrst item from TIMSS 2003 (page 73), the content domain (
patterns and relationships
) and the cognitive domain (
solving routine problems
) are also accompanied by the main topic (
equations and formulas
).
International item numbers
identify each item. This number appears just below the item box.
Correct answers
are shown beneath each item. These correct answers take two forms:ã
Letter code
. This form is used for the correct response on multiple-choice items.
Which number is it
provides an example of the letter code type—the correct answer is D. ã
Scoring guide
. This form is used to assist in scoring write-in responses.
Complete number sentence (S2)
further along in the
Whole Numbers
domain (page 13), provides an example of the scoring guide approach, indicating the general nature of correct and incorrect responses. In some cases, partial credit may be awarded and these items will provide guidelines for fully correct, partially correct, and incorrect responses.
Sample student responses
are provided for TIMSS 2003 extended response items. An example of an actual U.S. fourth-grade student’s response is provided for each scoring category. See Item M031249 on page 76.
International benchmarks
are provided in a table next to each item. These consist of statistics on the percentage of students in each country who answered the question correctly. The countries are ordered in terms of this percentage. The international average is included as well, and this display also indicates which countries scored signiﬁcantly higher, signiﬁcantly lower, and not signiﬁcantly different from this international average
.
TIMSS 1995 4th-Grade Mathematics Concepts and Mathematics Items
Content DomainCognitive Domain
Overall Percent Correct
3
When you subtract one of the numbers below from 900, theanswer is greater than 300. Which number is it? A. 823B. 712C. 667D. 579
Country average vs. International average:
Higher
Not different OLower
Correct Response:DWhole Numbers
Using Complex Procedures
Which number is it
Item Number: I3
Korea 82
Czech Republic 74
Hong Kong 74
Hungary 74
Slovenia 72
Japan 71
Netherlands 70
Austria 65
O
Ireland 62
O
Singapore 62
O
Latvia (LSS) 61
O
International average57
United States 57
O
Scotland 56
O
Thailand 54
O
Canada 53
O
Cyprus 52
O
Greece 52
O
Israel 52
O
Australia 51
O
England 48
Iceland 47
O
New Zealand 47
O
Norway 43
Portugal 40
Iran, Islamic Rep. 39
Kuwait 34
Correct Response:C
Overall Percent Correct
4
TIMSS 1995 4th-Grade Mathematics Concepts and Mathematics Items
What is 3 times 23
Item Number: I4
Country average vs. International average:
Higher
Not different OLower
Netherlands 98
Czech Republic 97
Hungary 96
Japan 96
Hong Kong 95
Latvia (LSS) 95
Slovenia 95
Austria 94
Singapore 93
United States 90
England 89
O
Ireland 87
O
Australia 86
O
Greece 86
O
Korea 86
O
Canada 85
O
Scotland 85
O
International average84
Cyprus 82
O
Norway 82
O
Iceland 80
O
Israel 80
O
Portugal 80
O
New Zealand 78
O
Iran, Islamic Rep. 73
Thailand 54
Kuwait 12
What is 3 times 23? A. 323B. 233C. 69D. 26
Content DomainCognitive DomainWhole Numbers
Performing Routine Procedures

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