Summary

Along with children from over 60 countries, New Zealand’s Year 5 students took part in the 2010/11 cycle of the Trends in International Mathematics and Science Study (TIMSS 2010/11). This study measures trends in mathematics and science achievement in Years 5 and 9 and identifies effective instructional practices from around the world. After every cycle of TIMSS, some of the test questions are released to the public while some are kept confidential to help measure trends from one cycle to the next.
This booklet contains a selection of TIMSS 2010/11 test questions from the three mathematics content domains. It includes examples of questions where New Zealand Year 5 students did better than the international average and examples where they did worse. For those questions where New Zealand students struggled, suggested resources are provided for use in the classroom for teaching the topics these questions relate to. This booklet is intended as a resource for Year 5 mathematics teachers.

The TIMSS content and cognitive domains

The assessment in TIMSS is organised around a content domain and a cognitive domain. Details of these domains are published in the TIMSS 2011 assessment frameworks (Mullis et al., 2009). The content domain for Year 5 (Grade 4) mathematics has three areas: number, geometric shapes and measures, and data display. These three content areas relate to the strands of the New Zealand Mathematics and Statistics Curriculum: number and algebra, geometry and measurement, and statistics. These strands are themselves combinations of five strands from the previous Mathematics Curriculum (number, algebra, measurement, geometry, and statistics).
The cognitive domain for mathematics is made up of three areas that describe the thinking processes students must use as they engage with the content: knowing, applying, and reasoning.

In the content domain, New Zealand Year 5 students did better at data display questions and worse at number and geometric shapes and measures questions in 2010/11. In the cognitive areas, our students did better at tasks that required them to apply their knowledge and use their reasoning and worse at questions that required them to demonstrate their knowledge of mathematical concepts, procedures, and facts.

The questions (and accompanying score points) in the TIMSS test were not evenly distributed across all content and cognitive areas. The distribution reflects the content and cognitive emphasis of the curricula of the participating countries. In the mathematics content areas at Year 5, the most emphasis was on number, followed by geometric shapes and measures. Note that the content area in which New Zealand Year 5 students showed the greatest strength, data display, had the least number of questions.

Time spent on content and cognitive areas in New Zealand classrooms.

On average, New Zealand Year 5 teachers indicated that they spent two-thirds of their mathematics teaching time in the school year on number and algebra (including computation with whole numbers, fractions, decimals, and pre-algebraic concepts, including number patterns). Sixteen percent of mathematics teaching time was spent on geometric shapes and measures (including two- and three-dimensional shapes, length, area and volume) and 14 percent on data display (including reading, making, and interpreting tables and graphs). On average, three percent of teachers’ time was spent on general topics other than those three.
According to teachers, the cognitive emphasis in their lessons was on getting students to explain answers (69% in every or almost every lesson) and work problems (individually or with peers) with teacher guidance (59% in every or almost every lesson), rather than on memorising rules, procedures and facts (12% in every or almost every lesson).

Test curriculum matching analysis

When developing TIMSS 2010/11, every effort was made to ensure the widest possible coverage of the mathematics and science curricula in each country. However, inevitably the TIMSS 2010/11 tests were not a perfect match for every curriculum, and so some questions fell outside the scope of what the children had covered in class. To address this issue, each country was asked to indicate which questions on the tests were inappropriate for their curriculum. Those questions in which New Zealand students did worse than the international average and were mismatches for the New Zealand curriculum have not been included in this booklet.
How is the information in this booklet presented?
Each question in the three mathematics content areas gives the question, label and item number, the content and cognitive domain it relates to, the expected answer (and in some cases typical wrong answers), and a table with a selection of countries’ results for comparison. This table shows the percentage of students who correctly answered the question and achieved the maximum number of points. The number/s of the released booklets in which the questions can be found are also mentioned in the table.

Benchmarks

In the body of the test above each set of questions, the benchmarks to which the questions are anchored are included. These benchmarks link student performance on the TIMSS mathematics scale to performance on mathematics questions and describe what students can typically do at set points on the mathematics achievement scale. More information about the benchmarks can be found in Mullis et al. (2012).