# NMSSA 2018 Insights for Teachers: Maths and Statistics Publications

## Publication Details

This report is designed to support the teaching of mathematics and statistics in primary and intermediate classrooms. It draws on insights generated from the assessment of the mathematics and statistics learning area carried out by the National Monitoring Study of Student Achievement (NMSSA) in 2018.

The report is in two main parts. Part One introduces NMSSA and the NMSSA assessment of mathematics and statistics. Part Two presents practical inisghts related to three focus areas: spatial reasoning, fractions and percentages, and collaborative problem solving.

**Author(s):** Educational Assessment Research Unit, University of Otago and New Zealand Council for Educational Research.

**Date Published:** February 2020

## Summary

### What is NMSSA?

NMSSA is designed to assess student achievement across the New Zealand Curriculum (NZC) (Ministry of Education, 2007) at Year 4 and Year 8 in New Zealand English-medium state and state-integrated schools. Each year, nationally representative samples of students from 100 schools at each of these two year levels are assessed in one or more learning areas. The mathematics and statistics learning area was assessed in 2013 and again in 2018.

### The 2018 NMSSA mathematics and statistics assessment

To assess the Mathematics and Statistics learning area in 2018, the NMSSA project team developed a two-part assessment called the Mathematics and Statistics (MS) assessment.

The first part was a group-administered paper-and-pencil assessment, which was completed by up to 25 students in each school. It was made up of a mixture of multi-choice and short answer questions. Students completed one of 14 assessment forms which were carefully linked together using common items.

The second part of the assessment involved several 'in-depth' tasks, which were completed by up to six of the students who did the group-administered assessment in each school. Students were videoed while they worked on these tasks, usually in a one-to-one interview with a teacher assessor (TA). The tasks included a focus on students explaining their mathematical thinking, describing and applying problem-solving strategies, and collaborating with a partner.

### The NMSSA mathematics and statistics scale

NMSSA used students' responses to both parts of the 2018 assessment to construct a measurement scale-the mathematics and statistics (MS) scale^{1}.

Figure 1 shows the MS scale. The descriptors show how students' mathematics and statistics understandings increase in sophistication as the scale score increases and indicate the sorts of things students typically know and can do when they score at different parts of the scale. For example, a student scoring about 110 units on the scale would typically be able to do the things described at that level. They would generally find the skills and knowledge described lower on the scale more straightforward. The descriptors further up the scale would typically involve knowledge they were less clear about or skills they were unable to demonstrate consistently.

It is important to note that the scale descriptors represent the knowledge and skills that were measured by the assessment items and are not intended to represent the mathematics^{2} learning area in its entirety.

##### Figure 1: 2018 Mathematics and Statistics scale descriptors

### How did students do on the 2018 mathematics and statistics assessment?

Figure 2 shows Year 4 and year 8 students' achievement on the 2018 NMSSA mathematics and statistics assessment, by levels of the curriculum.

The 2018 study found that most Year 4 students (81 percent) achieved at or above curriculum Level 2, the expectation for the end of Year 4. In 2018, 45 percent of Year 8 students achieved Level 4 or above, the curriculum expectation for the end of Year 8.

The study also found that there was no significant change in achievement for Year 4 students between 2013 and 2018. For Year 8 students, however, there was a small statistically significant increase in average achievement.

##### Figure 2: Distribution of Year 4 and Year 8 students' scores on the Mathematics and Statistics (MS) scale in 2018

Note: The blurred lines in the graph show the boundaries between curriculum levels. The lines are blurred to indicate the uncertainty involved in defining precise boundaries.

## Footnotes

- For detailed information about the scale description, go to the report: NMSSA 2018: Maths and Statistics - Key Findings.
- In the remainder of this report, the term ' mathematics and statistics' has usually been shortened to 'mathematics' to support readability. This in no way lessens the importance of statistics as part of the mathematics and statistics learning area.

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