The Curriculum Project: Directions and Issues

Vince Wright

The University of Waikato

Who me?

Outline• Background to the development

• Structure of curriculum

• Issues

• Sources of enlightenment

• Where to?

Curriculum Stocktake1989 Tomorrow’s Schools

1991 Achievement Initiative

1993 Curriculum Framework

1992-97Curriculum Statements

1996 Pause for completion of statements

1997 2 year phase in

1999 Stocktake begins

Stocktake Report• Essential skills modified from eight groupings

to five essential skills and attitudes:

creative and innovative thinking

participation and contribution to communities

relating to others

reflecting on learning

developing self-knowledge

making meaning from information

“The broad and flexible nature of the achievement objectives should be maintained, but they should be revised to ensure that they:

• Reflect the purposes of the curricula• Are critical for all students; and• Better reflect the future focused curriculum

themes of social cohesion, citizenship, education for a sustainable future,

multi-cultural and bicultural awareness, enterprise and innovation and critical literacy”

Teacher self-assessment of Content Knowledge

Knowledge rated as good or satisfactory

Rated as needing more content knowledge

90.1% 7.9%

Key Competency Groupings

• Thinking (critically, creatively, logically)• Relating and participating• Belonging and contributing• Managing self• Making meaning (multi-literacies, using

language, movement, symbols, technologies)

Mathematics Curriculum

National CurriculumKey Competencies

Each ELA:Essence statement and

achievement objectives. Teacher resource material

“2nd Tier”

What does curriculum mean?Intended- What national curricula say.Planned- What schools/teachers plan to teach.Delivered- What is taught to students.Learned- What is learned by students

Issue 1: School Based Curriculum Development

At what level do we expect teachers, schools, and their communities to invent or interpret the curriculum?

“The most striking feature of the school experiences of students in most other countries (than USA) whose test performance is very high, is that of a common, coherent, and challenging curriculum through 8th grade.”

- William H. Schmidt

USA research co-ordinator for TIMSS

TIMSS 2002-2003

Year 5

Relative Strengths

Year 5 Year 9

Number Number Patterns and

Relationships Patterns and

Relationships Measurement Measurement Geometry Geometry Data Data NB: Time allocated

Are these items assessing what we think is important?

Who is the audience?

Students?

Parents?

Teachers?

Audience

“Primarily teachers but bearing in mind a much wider audience. The present New Zealand curriculum framework document was recognised as a document that communicated to a wide audience.”

Essence Statement

• What is mathematics and statistics?

• Why does it deserve its place in the curriculum?

Mathematician -Someone who turns coffee into theorems.

Statistician -

Someone with their head in an oven and their feet in a refrigerator who says, “On average I feel just fine.”

Mathematics is the exploration and use of patterns and relationships in quantities, space and time.

• Abstract structures that help us to describe, classify, organise and model our world

•Symbolism that facilitates both communication between people and their thought processes

•Methods of proof that involve making initial assumptions and deriving new results from them

Statistics is the exploration and use of patterns and relationships in data.• Investigates phenomena which seldom can be

interpreted with absolute certainty• Ways of classifying and presenting data that

facilitates the recognition of relationships as well as displaying the relationships

• Has variation and distribution as central ideas in considering similarity and difference

• Used extensively in the media to validate assertions

NB: Brenda and Dave

Why teach Mathematics and Statistics?

• Real world utility

• Informed citizenship

• “Gatekeeper” for future study and occupations

• Ways of thinking that empower individuals to solve problems and model their world

• Creative challenge and enjoyment

Mathematical processes

• To be integrated and not left as a separate strand

• Will be represented as a stem applying to all AO’s at all levels

• Will also be represented through active verbs in the AO’s

• May be different to statistical processes• May contribute to a synthesised list of

processes aligned to the key competencies

Levels- a given!

Where do we set the levels?Year Level Stage PercentageTwo One Advanced 62%

Counting

Four Two Early Additive 67%Part-whole

Six Three Advanced 50%Additive

Eight Four Advanced 45%Multiplicative

Ten Five Advanced Prop ?

Ten Five Advanced Proportional ?????

Level 6: Number

Use strategies based on transforming quantities and units to solve problems involving scaling, approximation, betweeness (continuity), infinity, and lack of closure.

A cricket ball covers 20 metres in 0.6 seconds.

What speed is that in kilometres per hour?

Issue 2:What kind of knowledge do we want our students to learn?

Issue 3: Progressions vs

“Mess-iness”

Learning trajectories Learning as networking

Capturing ideas as “objects”

NB: Brown and Askew

Stages as broad progressions

Strand Structure

Geometry andMeasurement

Statistics

Number and Algebra

Threads (Key ideas)

Number and Algebra

Geometry and Measurement

Statistics

The Key Ideas

Statistics Strand

Potential change: focus on variation and distribution at all levels

• Statistical Thinking (Investigations)

• Statistical Literacy (Interpreting reports)

• Probability (Probability)

Number and Algebra Big Ideas

Potential change: focus on generalisation at all levels ( and all strands)

• Number Knowledge (Exploring)• Number Strategies (Computation and

estimation)• Patterns and Relationships• Equations and expressions

Geometry and Measurement

• Spatial properties (Shapes and solids)

• Transformations (Reflection, rotation, etc.)

• Direction and Movement

• Measurement of physical attributes

• Time and rate

Shape and SpaceClassify 2 and 3 dimensional objects by visual features noting similarities and differences. Image and draw shapes.

MeasurementCreate and use measurement units sensible for a task, including grouping units to simplify counting.

Time and RatesDevelop ways to measure time intervals in order to compare the duration of events.

TransformationPredict the results of slides, flips, turns, and enlargements on objects.

Position and Orientation Create and use simple maps to show position and direction. Describe different views and pathways from a given location on a map.

Number and Algebra Strand

Patterns and RelationshipsGeneralise that counting the number of objects in a set tells how many (cardinality). Use systematic counting strategies to find the number of objects that make up sequential patterns.

Number StrategiesUse simple additive strategies to solve problems involving whole numbers, and fractions.

Equations and Expressions Record and interpret simple additive strategies represented by words, diagrams (pictures), and symbols.

Number KnowledgeKnow forward and backward counting sequences with whole numbers to 1000, doubles, and groupings with tens.

Statistics Strand

Statistical Investigation (thinking)To answer questions, gather appropriate data in categories. Compare categories within datasets, and use data displays to highlight patterns and variations.

Statistical LiteracyCompare the features of category data displays with statements made about the data.

ProbabilityRecognise apparent equal likelihood, impossibility and certainty from trialing of simple chance events.

In a range of meaningful contexts students will learn to:

Level Two

Geometry and Measurement Strand

Statistics

Geometry and Measurement

Number and

Algebra

Issue 4: What if we don’t know the

progressions?Link to the number framework stages:

For example:

What is the area of this rectangle?

Sources of inspirationAssessment research projects, e.g. Exemplars, PAT development, NEMP.

For example:

Year 8 students are given a Jaffa packet and told to draw the net with measurements to the nearest centimetre.

4 sides, 2 ends, 3 gluing flaps, 4 small flaps appropriately proportioned…

As above, except not including 4 small flaps

4 sides and 2 ends, appropriately proportioned

Basic idea correct but significant distortions

10 (8)

7 (11)

30 (34)

27 (18)

More inspiration

Research since 1992…

For example:

Probability ideas:

• Variability

• Independence

• Distribution

• Sample space (possible outcomes)

What do these students think about…? • Variability

• Independence

• Distribution

• Sample space

Issue 4: Can do’s vs can’t do’s

Level One

What we say:

With simple chance events, systematically record trialing.

What we want to say:

Uses subjective criteria to assess likelihood.

Level Two

What we say:

Recognise apparent equal likelihood, impossibility and certainty from trialing of simple chance events.

What we want to include:

Does not recognise variability and places too much faith on small samples.

ProgressionsLevel One

Level Two

Level Three

Level Four

With simple chance events, systematically record trialing.

Recognise apparent equal likelihood, impossibility and certainty from trialing of simple chance events.

Predict trailing results from lists, diagrams, or visual models of all the outcomes. Compare the trial data with predictions, acknowledging that samples vary. Find all the possible outcomes for simple independent and conditional events. Describe the probability of outcomes using simple fractions, and recognise when the variation from a trial sample is reasonable or unreasonable.

What if we don’t know?

Spatial Reasoning- Van Hieles’ Levels:Pre-recognition Unable to identify shapes or image them, and

recognises only a few characteristics when classifying.

Visual Recognises shapes by visual comparison with other similar shapes rather than by identifying properties.

Descriptive/Analytic Classifies shapes by their properties.

Formal Deduction

Operates logically on statements about geometric shapes, solve problems and prove new results from statements.

Abstract Relational

Classifies shapes hierarchically by their properties. Deduces that one property implies another.

Resort to the wisdom of practice…

and hope nobody asks this!

Where to…?

We will be successful with the mathematics curriculum revision when…

• Teachers recognise the good parts of the ‘old’ in the ‘new’.

• The changes transparently signal critical improvements that will better prepare our students for tomorrow’s world.

May the future be better than this…