Index

The Numeracy Story
The Mathematics and Science Taskforce
The focus for professional development
Exploratory Study - Years 4-6
The Number Mountain - Te Maunga Tau
Students' knowledge important
The Count Me In Too pilot-Years 1-3
Impact
The Numeracy Development Projects 2001
Problem solving
Supporting teachers with quality resources

The Numeracy Story

From the Secretary for Education
The world-wide focus on numeracy has highlighted the importance of high-quality mathematics programmes, which emphasise both numerical knowledge and advanced mental strategies. It has also highlighted the importance of integrating mathematical skills into other curriculum areas.

This Curriculum Update provides information about the development work undertaken since the recommendations of the Mathematics and Science Taskforce in 1997 and outlines current and new initiatives to support teaching and learning in mathematics. These initiatives, which are part of the Government's Literacy and Numeracy Strategy, begin from early childhood and build towards the world of adult numeracy. The various groups associated with the Numeracy Strategy have developed a working definition of a numerate person that reflects this breadth of vision: "to be numerate is to have the ability and inclination to use mathematics effectively in our lives - at home, at work, and in the community".

We all have a role in nurturing the development of the numerate person, but I would like to emphasise the special role of the teacher. Numeracy arises out of effective mathematics teaching. Teachers are integral to changing the way mathematics is taught and learned in our schools - they are the key to enhancing numeracy outcomes.

I hope you will be as enthusiastic as I am about the exciting initiatives outlined in this Curriculum Update - initiatives that will help our teachers to be confident and effective in the teaching of mathematics, that will support all students in their learning, and that will involve parents and the community. Through these initiatives, we will ensure that our children become numerate as an integral part of growing up and taking their place in the world.

Howard Fancy
Secretary for Education

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The children have responded by taking risks, exploring, trying, verbalising, and excitedly celebrating their success. This is infectious. The classrooms hum with activity, co-operation, collaboration, and fun during a subject that has, historically, been stilted and, at times, ineffective. Junior teachers love teaching maths, children love learning maths, and their parents are often astounded when observing this phenomenon. Lorraine Smith (project co-ordinator) and Hoana Pearson (principal), from Newton Central School, commenting on the Count Me In Too pilot.

 The Numeracy Story 1992 - 2001

1992
Mathematics in the New Zealand Curriculum published (1992).

1996
Third International Mathematics and Science Study (TIMSS) identifies New Zealand students' achievement in mathematics as below international averages (1996).

1997
Mathematics and Science Taskforce (1997) is established and recommends providing help for teachers of five- to nine-year olds, focusing firstly on number concepts (including place value) and then on algebra and measurement. It also recommends that support material be accompanied by school-based professional development.

Ministry commences publicity programme and website development.

1998
Research seminar on mathematics education (1998) identifies key issues: developing teachers' pedagogical content knowledge, improving teaching quality and confidence, providing resources to support teaching and learning, making research more accessible, and emphasising importance of mathematics education prior to school entry.

Ministry commences the development of a comprehensive numeracy policy and strategy.

1999
Reading, Writing and Mathematics Proposals Pool established 1999. Feed the Mind/ Whāngaihia te Hinengaro, campaign (1999).

Junior Mathematics Review Group (1999) recommends number as the focus at levels 1 and 2 of the curriculum, the development of an early number-learning framework, and the development of diagnostic tools for early number assessment.

2000
Policy development initiatives focus on stages of early number development. Count Me In Too is piloted nationally as an action-research method of informing numeracy policy. Numeracy Think Tank begins work on national number framework for years 1-6.

NAGs modified to emphasise numeracy.

Numeracy Development Project Working Group provides a definition of a numerate person.

Reference group established to widen participation from education sector and to critique and advise on proposed numeracy initiatives.

Numeracy Projects focus on the improvement of teachers' professional knowledge, skills, and confidence.

The number framework becomes basis for initiatives associated with resource development, professional development, and assessment.

Exemplar development project for mathematics commences, with an initial focus on measurement and geometry.

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This taskforce was set up in 1997 to advise on the nature of support required by classroom teachers. The taskforce recommended:

• improving teachers' professional skills, knowledge, and confidence;
• providing teacher support material, accompanied by some form of professional development;
• support for the teaching of Māori and Pacific students;
• greater emphasis on pre-service training;
• greater involvement of parents and the community;
• raising teachers' and parents' expectations of children's mathematics achievement.

Teachers' understanding of subject matter and of pedagogy are critical factors in mathematics teaching. The effective teacher has a thorough understanding of the subject matter to be taught, comprehends how students are likely to learn, and knows the difficulties and misunderstandings they are likely to encounter. Professional development is therefore a key component of the numeracy policy and strategy.

The core of the professional development programme is the Learning Framework for Number (the New Zealand number framework), which provides teachers with:

• an effective means to assess students' current levels of thinking in number;
• guidance for instruction;
• knowledge of how children acquire number concepts and an increased understanding of how they can assist children to progress.

The number framework is a powerful tool for change in terms of pedagogical practice.

This professional development exploratory study provided the context and impetus for the development of the Learning Framework for Number. The framework is based on current numeracy research and will be refined during 2001. It has two interdependent parts: strategy and knowledge. "Strategy" is about how students use various mental strategies to solve number problems. "Knowledge" represents the key items of knowledge that students need to acquire. Strategy and knowledge have a dynamic relationship.

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The number framework relates to most of the achievement aims and objectives at levels 1-4 of the Number strand of the mathematics curriculum.

A sequence of global strategy stages, representing increasingly sophisticated concepts about numbers and how they can be used, underpins the number framework. These global strategy stages are shown below in the diagram of the Number Mountain - Te Maunga Tau. Each stage contains the operational domains of addition, subtraction, place value, multiplication, and fractions.

Students develop variably and will often be between stages. For example, they may display characteristics of one stage, given a certain problem to solve, but they may use more or less advanced strategies with other problems.

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At any of the global strategy stages, what students know is critical to their applying their available strategies successfully across all numbers and problem types. The knowledge aspect of the number framework is broken down into five content areas:

• numeral identification
• number sequence and order
• grouping/place value
• basic facts
• written recording.

Specific items of knowledge can be taught to students across a range of strategy stages. For example, students can read and write decimals long before they develop strategies for using decimals in operational problems.

Recent numeracy research in New Zealand and overseas has produced cutting-edge insights, some of which are outlined below:

• Students can use written recording to "think through" a calculation. Teachers should delay exposing students to standard vertical algorithms until their mental strategies are sufficiently advanced to handle these.
• Counting needs to be developed with all primary students. Counting should extend beyond counting by ones, twos, and other simple multiples to counting in powers of ten, in decimals, and in fractions, and even to backwards-counting sequences, particularly in early primary.
• Teachers can capitalise on students' natural inclination to use groupings of fives - first using finger patterns and then using multiples of five in later work, for example: 35 + 35 = 70, 500 + 500 = 1000.
• The most significant model of fractions is the partitioning of sets. Continuous models such as regions and lengths are useful spatial contexts for fractions, but the sets model is the most effective route to understanding the decimal system.
• Knowledge of basic facts is critical, and the process of coming to know and derive number facts is as important as coming to know the facts themselves. Students need to know a broader range of facts than previously thought, including groupings of "benchmark" numbers and decimal and fraction conversions. Automated recall of key number facts is vital to developing fluency and flexibility in numeracy.
  

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The Count Me In Too professional development programme was piloted nationally during 2000 to inform the development of the numeracy policy. It involved 510 teachers and approximately 10 000 children.

Count Me In Too reflects the principles behind the mathematics curriculum statement. This programme encourages teachers to analyse the mental strategies that students use to solve number problems, as opposed to simply checking that students have the correct solutions. The instruction is then targeted to the specific learning needs of each student.

At the outset of the programme, a diagnostic interview is used to identify each student's number knowledge and strategies. The aspects for assessment are: stage of early arithmetic learning, numeral identification, forward number word sequence, backward number word sequence, and knowledge of base 10. At the end of the fifteen-week phase of targeted classroom instruction, each student is then reassessed using the diagnostic interview.

The results of the Count Me In Too pilot are impressive, with clear and positive growth in each of the five aspects assessed. A full report will be published in March.

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Both the Exploratory Study - Years 4-6 and the Count Me In Too national pilot have had a significant impact on mathematics teaching and learning in the classes concerned.

The gains for teachers have been in:

• pedagogical knowledge;
• mathematics content knowledge;
• an increased confidence in and enthusiasm for teaching mathematics;
• raised expectations of what children can do;
• a recognition of the way that development of number knowledge interacts with the development of mental strategies.

Most children in the studies have made greater gains than expected in number knowledge and strategies, regardless of gender, ethnicity, or the school's decile rating. There is greater enthusiasm for mathematics learning. In fact, children are having fun!
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Numeracy Development consists of three projects, one for early numeracy years 1-3, one for advanced numeracy years 4-6, and an exploratory study in years 7-10. These projects build on evaluation, findings, and developments from the Count Me In Too pilot and the Exploratory Study professional development programmes. A dynamic, evolutionary approach to implementation will provide maximum flexibility and ensure that the projects incorporate developing understandings about numeracy.

The focus for implementation is on:

• improving the performance of all students who are underachieving in mathematics;
• the schools that participated in the Count Me In Too pilot (years 1-3) in 2000 and are participating in the advanced numeracy component (years 4-6);
• an exploratory study of numeracy in years 7-10;
• providing ongoing support for teachers who have previously been involved in the project.

The projects will involve approximately 3055 teachers and 60 000 children.

• refining the number framework further for early number learning, based on recent international and New Zealand research;
• locating the framework in a definition of numeracy and stating what it means to be numerate;
• providing a national professional development programme in which the framework is the core component for all primary school teachers during the next three to five years;
• aligning assessment tools and resources with the framework;
• providing ongoing evaluation and review of the project, complemented by a research programme focused on classroom practice and student achievement;
• establishing links with pre-service education providers;
• ensuring continuity between early childhood education and schools and at various transition points during schooling.

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• briefings for principals and boards of trustees;
• workshops on the framework for number learning, diagnostic assessment, classroom organisation, and resource development;
• in-class modelling, observations, and evaluation.

A small working group of experts will focus on key tasks, such as refining the number framework and the definition of numeracy. The Numeracy Development Projects 2001 Reference Group will critique and advise on proposed initiatives.

 Problem solving

How many muffins?

There are 24 muffins in each basket. How many muffins are there altogether?

How many cars?

At the car factory, they need five wheels to make each car: four wheels for the road and one for the boot.

How many cars could they make with 80 wheels?

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 Supporting teachers with quality resources

The Ministry is developing resources to support the number framework and for use in the 2001 professional development programmes in numeracy. Existing mathematics resources, such as Beginning School Mathematics (BSM), will be aligned to the number framework.

For additional information, see page 3 of the October 2000 Resource Link (the most recent set of Figure It Out is described) or search the Ministry's online catalogue at www.learningmedia.co.nz .
Please direct any enquiries to Learning Media Customer Services - 0800 800 565.

Figure it out

The second set of booklets in the Figure It Out series was distributed in August 2000 to all primary schools, along with an Answers and Teachers' Notes for each booklet. Corresponding booklets for levels 3-4 are due for distribution in 2001, and a set for level 4 is planned for 2002-2003. Additional theme booklets for levels 2-3 and level 3 are being developed. Figure It Out replaces the School Mathematics series.

He Rauemi Pangarau

Connected/Tūhono 1, 2, and 3 (for levels 1-2, 1-3, and 2-4) are parallel series in English and Māori designed to show mathematics, science, and technology in the context of students' everyday lives. The stories and articles provide starting points for further investigations by individuals, groups, or a whole class. The activities make science, mathematics, and technology fun.

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Connected/TŪhono

Connected/Tūhono 1, 2, and 3 (for levels 1-2, 1-3, and 2-4) are parallel series in English and Mˆori designed to show mathematics, science, and technology in the context of students' everyday lives. The stories and articles provide starting points for further investigations by individuals, groups, or a whole class. The activities make science, mathematics, and technology fun.

Key Websites

Visit the mathematics community page on the Ministry's online learning centre, Te Kete Ipurangi (TKI), for a variety of news and help materials: www.tki.org.nz/e/maths/

Visit the New Zealand Maths website at www.nzmaths.co.nz or, if you are already on the TKI maths community page, click on the New Zealand Maths website icon. This website offers quality teaching materials for statistics, algebra, measurement, geometry, and problem solving at levels 1-4, as well as a help-desk service. A monthly online newsletter will enable further discussion of current numeracy issues.

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What's happening in assessment?

Development of the number framework is aligned closely with other Ministry initiatives, such as those in assessment. Current assessment initiatives are developing exemplars and developing new literacy and numeracy tools. Both initiatives support teachers in gathering information about how their students are progressing in relation to national expectations of performance and in using that information to improve teaching and learning.

Feed the Mind/Whāngaihia te Hinengaro

This public information campaign was launched in May 1999 and will run for another two years. The campaign involves television and radio advertisements and a variety of printed materials. A novelty "swatch" in English and Māori, which suggests simple ideas for reinforcing maths and literacy skills, was targeted at households around decile 1 and 2 schools and is available to all schools. Pacific language versions of the swatch are also available. There are also two sets of parent pamphlets, one set for the early years of schooling and one for early childhood. Each set includes a pamphlet on maths ideas and strategies for parents to use with their children. Pacific versions of the early school pamphlets are also available. Please contact Learning Media Customer Services to access any of these items - 0800 800 565.

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Early Childhood

While much of the work on numeracy is directed at the first years of schooling, the foundations for numeracy are laid in early childhood.

The early childhood curriculum, Te Whāriki, highlights the importance of encouraging children to notice, describe, and create patterns; to predict and estimate; and to develop the ability to use symbols, make comparisons, recall, anticipate, and shift focus. Children need opportunities to familiarise themselves with mathematical tools such as rulers, tape measures, scales, and measuring cups. Infants and toddlers need opportunities to participate in everyday activities that highlight number, patterns, and concepts. Toddlers and young children are encouraged to develop the language of position, for example, "above" and "below", and the language of probability, for example, "might" and "can't".

Increasingly, early childhood services and schools are working together to understand the pedagogy of each setting to ensure a smooth transition to school for children. The use of child profiles in early childhood education services enables staff to support and promote children's learning more effectively.

Published 2001 for the Ministry of Education by
Learning Media Limited, Box 3293, Wellington.
Website: www.learningmedia.co.nz

Count Me In Too copyright © Department of Education and Training,
NSW Copyright © Crown 2001 All rights reserved. Enquiries
should be made to the publisher.

Additional copies of Curriculum Update 45 are available free on request from
Learning Media Customer Services. Freefax: 0800 800 570 Email:
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