NMSSA 2018: Mathematics and Statistics Publications
This report is designed to provide a succinct overview of key findings from the 2018 mathematics study. It is supplemented by a report focused on curriculum insights for teachers, a technical report and an online interactive statistical application. All reports and the interactive application can be found on the NMSSA (National Monitoring Study of Student Achievement) website.
Author(s): Educational Assessment Research Unit, University of Otago and New Zealand Council for Educational Research for the Ministry of Education.
Date Published: December 2019
The National Monitoring Study of Student Achievement (NMSSA) is designed to assess student achievement across the New Zealand Curriculum (NZC) at Year 4 and Year 8 in English-medium state and state-integrated schools. The study is organised in five–year cycles. The first cycle ran from 2012 to 2016.
In 2018, NMSSA assessed achievement in the mathematics and statistics learning area using a nationally representative sample of about 2,000 students at each of Year 4 and Year 8. A two-stage sampling design was used to construct each sample. In the first stage, a stratified random sampling approach that took into account school decile, geographical region and school size was used to select 100 schools at each year level. In the second stage, a maximum of 25 students were randomly selected from each school to take part in the study1.
Results were reported on a measurement scale called the Mathematics and Statistics (MS) scale. The scale was designed so that the combined average for Year 4 and Year 8 was 100 MS scale score units and the average standard deviation for the two year levels was 20 MS scale score units. Questionnaires were also used to gather contextual information from students, teachers and principals.
The mathematics and statistics learning area was last assessed by NMSSA in 2013. The measurement scales used in 2013 and 2018 were linked based on assessment tasks that were administered at both points of time. This allowed results from the separate studies to be compared. The linking process involved reconstructing the 2013 achievement distributions using the plausible values approach employed in 2018.
This means that achievement statistics presented in this report vary from the statistics presented in the original 2013 report. This report is designed to provide a succinct overview of key findings from the 2018 mathematics study. It is supplemented by a report focused on curriculum insights for teachers, a technical report and an online interactive statistical application. All reports and the interactive application can be found on the NMSSA website (www.nmssa.org.nz)2.
Throughout the 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.
Change in achievement between 2013 and 2018.
Average achievement in mathematics and statistics for all students at Year 8 increased between 2013 and 2018 by 3 MS units. The increase was statistically significant. At Year 4, the average increased a nonsignificant 1 unit over the same period. Statistically significant increases in average achievement scores
between 2013 and 2018 were noted for several population subgroups, including: Year 4 boys, Year 8 boys, Year 8 girls, Year 8 Pacific students and Year 8 students in low decile schools. These increases ranged from 2 (Year 8 boys) to 6 MS units (Year 8 Pacific students).
Achievement in mathematics and statistics in 2018
Most students (81 percent) in Year 4 achieved at or above curriculum expectations (curriculum level 2), while in Year 8, 45 percent achieved at or above curriculum expectations (curriculum level 4).
The difference in average scores between Year 4 and Year 8 indicates that, on average, student achievement increased by 8 MS units per year between Year 4 and Year 8. As indicated above, this rate of ‘progress’ was not enough to maintain the same level of achievement against the curriculum at Year 8 as recorded at Year 4.
There were high and low achievers in all population subgroups. There were also some statistically significant differences between the average scores recorded for different groups.
Boys scored higher, on average, than girls by 3 MS scale score units at Year 4 and 2 units at Year 8.
At both year levels, students from high decile schools scored higher, on average, than those from mid decile schools, who, in turn, scored higher than those from low decile schools. The difference between the average scores for students in the high and low decile bands was 20 MS units at Year 4 and 18 MS units at Year 8.
Scores for Māori students were lower, on average, than non-Māori by 11 MS units at both year levels. Pacific students scored lower, on average, than non-Pacific by 15 MS units at Year 4 and 13 MS units at Year 8. Asian students scored higher, on average, than non-Asian students (by 9 MS units at Year 4 and 11 MS units at Year 8).
Contextual findings in 2018
Most students were ‘positive’ or ‘very positive’ about learning mathematics at school and expressed confidence as mathematics learners. Students in Year 8 tended to be less positive about mathematics and, overall, expressed lower levels of confidence in mathematics than students in Year 4. On average, boys indicated a higher level of confidence in mathematics than girls.
Students’ scores on measures of their attitude to mathematics and confidence in mathematics were positively associated with their achievement scores. Overall, the relationship between confidence and achievement was stronger than the relationship between attitude and achievement. The relationship between confidence and achievement was stronger for Year 8 students than for Year 4 students.
Students indicated frequent involvement in a range of learning opportunities associated with mathematics. One exception to this was the opportunity to use a calculator to solve problems. Over half the Year 4 students and about a quarter of Year 8 students reported they ‘never or almost never’ used a calculator to solve problems.
Most students rated the difficulty of their mathematics learning as ‘about right for me’.
About a quarter of the teachers who responded to the teacher questionnaire indicated that they had syndicate, school, or Community of Learning/Kāhui Ako leadership responsibilities for mathematics. Year 8 teachers were more likely to indicate that they had a specialist focus in their initial teacher education or had an undergraduate or graduate qualification related to mathematics (23 percent compared with 8 percent, respectively).
All teachers agreed that teaching mathematics is important and most indicated that they enjoy teaching mathematics. Most teachers reported that they were confident about teaching it. At both year levels, teachers indicated they were most confident teaching number and least confident teaching algebra. Year 8 teachers expressed greater confidence than Year 4 teachers in teaching all sub-strands of the mathematics and statistics learning area.
All teachers agreed they know at which level of the NZC each of their students is achieving in mathematics. The majority of teachers indicated their students spent 3 to 5 hours per week, on average, learning mathematics.
Ability group-based activities were used regularly as an organisational strategy for teaching mathematics.
Overall, the majority of teachers indicated that they had adequate access to a range of resources for teaching mathematics.
Around two thirds of teachers at Year 4 and Year 8 reported that they had participated in professional learning and development (PLD) associated with mathematics in the last two years.
In general, teachers reported regular opportunities to take part in a range of professional interactions with colleagues related to teaching mathematics. Around a third of teachers indicated they ‘never’ or ‘almost never’ observe a colleague teaching mathematics.
Over 80 percent of principals rated the provision for learning mathematics in their school as ‘good’ or ‘very good’. Most principals were positive about their school’s curriculum planning, assessment and sharing of information related to mathematics. They were also positive about the capabilities of teachers in the mathematics and statistics learning area.
Principals indicated that nearly all mathematics programmes were delivered entirely or primarily by the classroom teacher.
About two thirds of principals reported that their school was part of a Kāhui Ako/Community of Learning.
Half of the principals who identified their school was part of a Kāhui Ako indicated that the Kāhui Ako had achievement challenges for mathematics that involved Year 4 and/or Year 8 students.
Most principals indicated that teachers had moderate to extensive access to external PLD in mathematics.
Around 90 percent of principals reported that the mathematics and statistics learning area had been a focus for development in the last five years.
Changes in contextual findings between 2013 to 2018
Broadly speaking, students, teachers and principals in 2013 and 2018 responded similarly to contextual questions that were used at both year levels. In some cases, changes to wording or response formats made direct comparison difficult. One difference related to involvement in professional learning and development stood out. In 2013, about 80 percent of all teachers reported that they had participated in PLD in mathematics teaching less than 2 years ago. This compared with about two thirds of teachers in 2018.
- Detailed information about the sampling process and the achieved sample can be found in NMSSA Report 21: Technical Information 2018.
- The curriculum insights and technical reports should be available early in 2020.
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