Garth Ritchie

The question at the heart of this probe study sought to determine if there were groups (clusters) of Year 8 students who shared similar performance profiles across the 2001 NEMP mathematics tasks.

Cluster analysis methods were used to investigate this question. The analyses aimed to determine the following:

• If there were groups of learners (clusters) showing similar structural characteristics in their responses to (and errors on) the NEMP tasks.
• If these groups of learners could be seen as having ‘different competency styles’.
• If variables such as social location, school, and school experiences predicted what cluster a student would be in.
• If there were differentiating cluster group profiles on the tasks associated with particular strands of mathematics.

• There were well-defined cluster groups, with some presenting excellence in mathematics (i.e., succeeding in the mathematics taught in the New Zealand Curriculum), and some having difficulties (not able to do the majority of the NEMP mathematics tasks).

• Most of the students in poorly performing cluster groups showed a good level of performance on number facts and a moderate level of performance on algorithms (subtraction being an exception). However, in problem-solving tasks involving more than procedural knowledge these students performed very poorly.


• For particular types of tasks, students were often located in well-defined cluster groups characterised by particular mathematical misunderstandings and difficulties. For example, there were three separate groups of students identifiable by their particular difficulties with placement of fractions, decimals or percentages.

• Amongst students in poorly performing clusters there was an impoverished ‘drill and practice’ understanding of what mathematics education entails. These students ‘asked a teacher first’, and they placed a higher emphasis on the knowing of mathematical facts and on doing teacher-set worksheets or working in their books.

• Ethnicity and school decile influenced the development of competence in school mathematics. Mäori students and/or students in low-decile schools were very over-represented in poorly performing cluster groups.

• The scope of mathematics education for students experiencing difficulties needs to be expanded—beyond algorithms and the recall of mathematical facts (‘the basics’) to being able to develop their own ‘mathematical intelligence’.

• The NEMP tasks along with the emergent cluster groups highlight the need for teachers to develop strategies for dealing with the learning needs of students located in the developmental bands between achievement levels. Knowledge of the cluster groups likely to be represented in the classroom is an important first step in planning learning experiences.
  • Poorly performing students appear to regard mathematics as drill-and-practice, ‘ask the teacher first’, pencil-and-paper tasks. There are many good open-ended, open-middle, even open-beginning mathematical experiences available to mathematics educators that can help change that view and foster metacognitive mathematics skills.

• More effective interventions must be found for mathematics education in low-decile schools. Directing funding towards Mäori and Pacific Island family mathematics programmes might be more effective than targeted school funding.

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The full report of this probe study will be available on this website by Jan 2004 or can be obtained from USEE.