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# The Quality of Teaching in Years 4 and 8: Mathematics (June 2006)

## Teaching and learning resources in mathematics

### Overall effectiveness of the use of resources in mathematics

### Year 4 and Year 8 teachers

### School characteristics

### Resource use in schools

### Appropriateness of teaching and learning resources

### Teachers’ and students’ use of resources

### Integration and use of Information and Communication Technologies

How effectively are resources and technologies used in the teaching of mathematics in the classroom?

This section reports on the appropriateness and use of teaching and learning resources in mathematics. It begins with a description of the resources that are in use or available for schools. ERO evaluated the overall effectiveness of the appropriateness and use of resources and technologies in mathematics in relation to the following indicators:

- appropriate teaching and learning resources are present in classrooms;
- appropriate teaching and learning resources are being used; and
- teachers are confident in the students’ use of resources.

Review officers also considered any additional or supporting information concerning the use of resources and technologies.

Figure 2 shows that twenty two percent of the 121 teachers were ‘highly effective’ at using resources and 46 percent were ‘effective’. A further third of the teachers were not always effectively using teaching and learning resources in mathematics and two percent were ineffective in this area.

Figure 2: Resource use

The effectiveness of teachers of Year 4’s use of resources and technologies in mathematics programmes was compared with that of the teachers of Year 8. Overall, teachers of Year 4 students were more likely to have appropriate resources and to use them more effectively than teachers of Year 8 students. The difference between the groups was statistically significant.

The overall effectiveness of the appropriateness and use of resources in mathematics for the different types of schools, and their locality was compared. There was no statistically significant difference within each of these groupings.

A comparison of schools within the decile groupings revealed statistically significant differences in the appropriateness and use of resources in mathematics. High decile schools were more likely than low decile schools to have appropriate resources and for teachers and students to use them effectively.^{
[20]}

ERO found that Boards of Trustees at high decile schools were more likely to prioritise the resourcing of mathematics, in particular the provision of practical equipment and ICT. Teachers at these schools were more likely to have participated in recent mathematics-related professional development and were more effective in using resources to model concepts to their students. This finding warrants further investigation.

Teachers that use high quality, appropriate resources effectively enhance the mathematics programme for students. *Developing Mathematics Programmes* states that teachers should use a variety of resources and equipment to support classroom teaching, including technology.

These resources should:

- provide for a range of student abilities;
- allow for the application and extension of student skills;
- acknowledge the New Zealand cultural mix;
- be visually attractive;
- have clear instructions;
- facilitate independent and cooperative work; and
- have learning activities and outcomes that are consistent with the achievement objectives.
^{ [21]}

The Ministry of Education provides teaching and learning resources to schools to support the teaching of mathematics. These include materials such as the *Figure It Out *series^{
[22]} and Numeracy Booklets.^{
[23]} Teacher notes are provided for both of these series and the notes are available on the *Te Kete Ipurangi* (TKI) website^{
[24]} and the *NZ Maths* website.^{
[25]} As part of the Numeracy Project, schools are able to purchase, or make, NumP kits of manipulative resources designed to support lessons in the Number strand. These resources include: rulers, counters, dice, abacus, 100s boards, number fans, number lines, traction squares, and animal strips.

Teachers are able to get other resources and information through TKI. *NZ Maths* provides mathematics teaching resources for Years 1 to 13, professional readings, resources and suggested projects for students. Detailed information on assessment practices and assessment tools is also available through TKI.

In 75 percent** **of the classes, teachers were providing students with a good range of appropriate resources for learning programmes in mathematics. Teachers used activities and games from Ministry of Education books and websites. Mathematics equipment and Information Communications Technologies (ICT) resources matched the activities and games and supported the learning outcomes for lessons. In most of these classrooms, resources were widely available for teachers’ and students’ use. In some schools, teachers in the school shared resources with one another; the resources were well organised and teachers were able to access them easily.

In the remaining 25 percent of classes, the resources were limited. These teachers tended to rely on textbooks, worksheets and blackboards.

In** **72 percent of classes, teachers and students were using appropriate resources to create everyday learning settings for student learning in mathematics. In these classes, teachers were using resources to reinforce previous learning, model problem solving, and explain concepts. Students were using resources independently from the teacher to solve problems, demonstrate strategies to other students, and expand their understanding of key concepts.

In the remaining 28 percent of classes, students and teachers used resources less effectively to model problem solving or to explain mathematical concepts. Students often revised their learning through worksheets and textbook examples alone. This was unlikely to help students apply their learning to practical situations, or challenge and engage students. In some classrooms where *Figure It Out* booklets, mathematics games, and other manipulative resources were available, students were either not using them, or using them incorrectly. In some classes, resources were limited or not available in the classroom.

In 42 percent** **of the classes, ICT was integrated into the mathematics programme. Teachers in these classes made effective use of ICT for planning and delivering student activities. Examples of this included: teachers accessing websites for planning and activity ideas; students using software for graphing; students generating statistics; teachers presenting learning outcomes, activities and tasks; and teachers incorporating calculators and digital cameras into mathematics programmes. In these classes, students were using ICT to support their learning in all strands of the mathematics curriculum. ICT was often used in practical ways to develop and strengthen students’ understanding of mathematical concepts. For example, one class was using computers, digital cameras, pedometers and a Global Positioning Satellite to measure the school cross country track.

In 58 percent of the classes, there was limited use of ICT to support the mathematics programme. While many of these students and teachers used calculators and computers, at times this did not further students’ learning. In some classes, ICT was used as a reward rather than as part of the mathematics programme. Many of these teachers were beginning to identify how and when ICT could be integrated into mathematics programmes.

Often integration was limited by teachers’ knowledge of ICT. In other classes, there was no evidence of ICT in the mathematics programme. This was usually for one of two reasons: a lack of equipment in the classroom or school meant access was limited; or teachers did not incorporate ICT into the lessons, as they were not confident in doing so.

[20]

*
*A Kruskal-Wallis H test was used to test for a statistically significant difference in the distributions of the test scores for each of the different decile group samples. A subsequent Mann-Whitney U test was used to test for statistically significant differences in distributions of the test scores for each of the different decile group samples. This showed a statistically significant difference between high and low decile schools, but not high and medium, or medium and low decile.

[21]

*
*Ministry of Education, *Developing Mathematics Programmes* (Wellington: Ministry of Education, 1997).

[22]

The *Figure It Out* series are mathematics curriculum support books designed to supplement classroom mathematics programmes.

[24]

*Te Kete Ipurangi* is a bilingual portal-plus web community that provides quality assured educational material for New Zealand teachers, school managers, and the wider education community. It is an initiative of the Ministry of Education. See
www.tki.org.nz.

[25]

*
NZMaths* provides lessons and activities to support teaching of Levels 1 to 4 of *Mathematics in the New Zealand Curriculum*. It is an initiative of the Ministry of Education. See
www.nzmaths.co.nz.