Introduction

This report examines the mathematics results for New Zealand Year 5 students from TIMSS 2006/07.¹ Along with the report on New Zealand’s results for science (Caygill 2008), this report forms the beginning of a series of reports around New Zealand’s participation in TIMSS 2006/07. International findings for mathematics for TIMSS 2006/07 have been published by the IEA (Mullis, Martin & Foy, 2008). A separate international report on science was also published at this time (Martin, Mullis & Foy, 2008).

This report begins by examining trends in New Zealand mathematics achievement at the Year 5 level from 1994 to 2006. It then looks at New Zealand’s mathematics achievement in relation to other countries that participated in the study. An examination of the TIMSS assessment questions in relation to New Zealand’s mathematics curriculum is presented along with analyses of achievement by sub-groupings (such as gender and ethnicity) and background factors. Lastly, a statistical model that attempts to explain variations among students, classes, and schools, using the background information discussed in this report is also described.

Assessment of mathematics in TIMSS

The TIMSS assessment has two main dimensions: a dimension that describes the content or subject matter to be assessed; and a dimension that describes the cognitive processes used to answer the questions. The three content dimensions for mathematics are: number, geometric shapes and measures, and data display. The detail about the topic areas covered in these domains at each grade or year level assessed and a set of assessment objectives for each topic area are presented in the TIMSS 2007 assessment frameworks (Mullis, Martin, Ruddock, O’Sullivan, Arora, and Erberber, 2005). Briefly, each of the content areas is described in the frameworks as follows.

“The number content domain for the fourth grade includes understanding of place value, ways of representing numbers, and the relationships between numbers.” (p. 16).

“The geometric shapes and measures domain includes properties of geometrical figures such as lengths of sides, sizes of angles, areas, and volumes.” (p. 19).

“The data display content domain includes reading and interpreting displays of data.” (p. 21).

In order to answer questions in the TIMSS test correctly, as well as being familiar with the mathematics content, students need to draw on a range of cognitive skills. Also, in their lives outside and beyond school, students will need to do more than accurately recall a range of mathematic facts. This is acknowledged in the framework with three aspects to the cognitive dimension entitled knowing, applying, and reasoning. Briefly, each cognitive dimension is described in the framework as follows.

“The first domain, knowing, covers the facts, procedures, and concepts students need to know, while the second, applying, focuses on the ability of students to apply knowledge and conceptual understanding to solve problems or answer questions. The third domain, reasoning, goes beyond the solution or routine problems to encompass unfamiliar situations, complex contexts, and multi-step problems.” (p. 33).

Data collection

Each student was assessed in two timed sessions of 36 minutes, and answered a combination of mathematics and science questions. The assessment was a pencil-and-paper test containing both multiple-choice and constructed-response questions. Following this, students were given a questionnaire containing questions about themselves, their opinions about mathematics and science, their computer use and time spent on homework. Principals and teachers were also given questionnaires in order to gain further information about the context in which the mathematics teaching and learning take place. In New Zealand, the assessments and questionnaires were conducted in English.²

International participants in TIMSS

The number of participants in TIMSS at the Year 5 or grade 4 level has steadily increased since 1994, when 26 countries took part. In 2002, 25 countries and 3 benchmarking participants took part. Benchmarking participants are usually states or parts of countries and are not included in international averages. In 2006, the number of education systems participating at the middle primary level had risen to 37 countries and 7 benchmarking participants.

Technical information

A lot of information is gathered during the TIMSS administration and a number of techniques are applied when collecting and analysing the data. The 'TIMSS 2007 technical report' (Olson, Martin, & Mullis (Eds.), 2008) contains a detailed account of the procedures for scoring, translation of materials, sampling, survey operations, quality assurance, sampling weights, item analysis, scaling, and reporting. In addition, the 'TIMSS 2007 user guide for the international database' (to be published in early 2009) contains information on how to analyse the data. Brief details of the technical information are given in the definitions and technical notes at the end of this report.

TIMSS encyclopaedia

In order to provide a context in which the TIMSS results can be examined, TIMSS also publishes the 'TIMSS 2007 encyclopedia: a guide to mathematics and science education around the world' (Mullis, Martin, Olson, Berger, Milne, & Stanco (Eds.), 2008). This encyclopaedia contains short reports from each country describing mathematics and science education policies and practices in that country.

Footnotes

1. Internationally this cycle of the study is called TIMSS 2007. As southern hemisphere countries conducted the study first, towards the end of 2006, it is referred to as TIMSS 2006/07 throughout this report.
2. In 2002, tests and questionnaires were also translated into te reo Māori, but in order to make comparisons between each of the cycles, these students were excluded from analyses presented in this report.