The Numeracy Contract and it’s Implications

Presented by

C and B

Educational Change

• “Students today depend on paper too much. They don’t know how to write on slate without dust all over themselves. What will they do when they run out of paper?”Principal’s Association 1815

Educational Change

• “Students today depend on store bought ink. They don’t know how to make their own. When they run out of ink they will be unable to cipher. This is a sad commentary on modern education.”

The Rural American Teacher 1929

Educational Change

• “Students today depend too much on expensive fountain pens. They can no longer write with a straight pen and nib, not to mention sharpening their own quills. We parents must not allow them to wallow in such luxury to the detriment of learning how to cope in the real business world.”

PTA Gazette, 1941

Why change?

• Just as knowledge expands, circumstances alter, and needs change with time, so too is the content and structure of maths programmes adjusted and refined to reflect current needs and future visions for learners.

• Expecting students to get right answers in the shortest possible time with the least amount of thinking is no longer a prime goal of mathematics education.

» NEMP Report 23 Assessment Results 2001

The Big Picture

For most students a major aim is to help them to develop attitudes and abilities to be flexible, creative thinkers who can cope with open ended real world problems. This requires them to become confident in their understanding and application of mathematical ideas, procedures and processes. NEMP 2001

MiNZC

There are 3 major directions in this mathematics curriculum statement

1. Special emphasis to continuity and progression in learning mathematics……

2. Focus on the importance of diagnostic and formative assessment to enhance the learning and teaching process for all students.

3. Mathematics needs to be taught and learned within the context of problems which are meaningful to the students….

» MiNZC page 5 1992

Assessment

• Assessment should as far as possible, be integral to the teaching and learning programme.

• Avoid tests which focus on a narrow range of skills e.g. the correct application of an algorithm. A consequence of a narrow assessment regime which isolates discrete skills or knowledge is the students tend to learn that way. Mathematics becomes for them a set of separate skills and concepts with little obvious connection to other aspects of learning or to their world.

» MiNZC page 15 1992

The Problem Solving Approach

• Open ended problems encourage thinking rather than mere recall.

• Closed problems develop only a limited range of skills. They encourage memorisation of routine methods.

• While fluency with basic techniques is important, such routines only become useful tools when students can apply them to realistic problems.

» MiNZC page 11 1992

Concerns from NEMP 2001

• Students performed poorly on tasks involving estimation, in both number and measurement.

• A similar lack of improvement is evident in work with fractions.

• Most students do not demonstrate ability to use a variety of effective strategies when completing mathematical tasks.

• Students displayed limited ability to explain processes and strategies used in mathematical tasks.

Suggestions for progress

• Use of estimation should be a focus for teaching and learning.

• Addition and subtraction as opposite operations need to be taught together. (Also multiplication and division)

• Students need to be encouraged to explore a range of strategies for solving mathematical tasks, so they can learn to select the most efficient method.

• Students need practice in describing the strategies and processes they use for mathematical tasks.

• Programmes and learning opportunities need to help students become aware of how they can incorporate mathematical thinking into everyday life.

» NEMP Forum Comment July 2002

Where do we start?

What are the challenges along the way?

How do we know if we are succeeding?

Effective change

Bridge of uncertainty

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Learning Zone

Persistence and Practise

Rew

ard

Change takes 3 – 5 years or longer!

The bridge of uncertainty

• Is it worth doing?• I don’t know where I

am going.• I don’t know what I

am doing.• It’s scary.• It will take time.• I need support from

my colleagues.

So what do we do now?

• Be visionary, explore where you want to get to on the other side.

Find out about the New Zealand Number Framework.• Look at ways of putting a handrail on the bridge before

you start to cross.Appoint a lead teacher. Look at operating systems in your

school, maths policy, assessment policy, reporting policy. • Prepare yourselves with all you need to make the crossing

easier. Make adequate budget provision for professional

development time and purchase of resources & equipment.

The New Zealand Number Framework

• Educational research has shown us clear evidence that there are developmental stages in the learning of number operations.

• The stages are not age related, but developmental.

Blueprint for Literacy Success• Using strategies rather

than items of knowledge is important in reading and writing acquisition because it leads to independence. Once children know how to use appropriate strategies in their reading and writing, they are able to learn a little more about reading and writing every time they read and write.

• Using strategies rather than items of knowledge is important in mathematics acquisition because it leads to independence. Once children know how to use appropriate strategies in their mathematics, they are able to learn a little more about mathematics every time they do mathematics.

Strategy is about how children solve number problems, in particular the mental processes they use.

Creates new knowledge through use

Strategy Knowledge

Provides foundation for strategies

Knowledge considers the key items of knowledge that children need to acquire.

Mental Maths

What is it?

• Computation• Estimation• Number Sense

• Not factual recall

What’s the difference?INTENSITY OF FOCUS

PAT’sProgrammed Acts of Teaching

• Teaching based on a set programme

• Teaching a class• Balanced across strands• Wide coverage of objectives• Material focused yr 1 – 3• Written focus Yr 4 +• Aims to get the methods

learned

• DAT”sDeliberate Acts of Teaching

• Teaching based on diagnosed student needs

• Teaching a group• Strong number emphasis• Focus on specific targets• Mental focus all levels

• Aims to develop number sense

The Teaching Model

Maths in the junior school is great but when you get to the seniors you’re not supposed to use equipment so maths is boring and you don’t understand it anymore.

Year 6 child (2000)