Transcript The Curriculum Project: Directions and Issues

The Curriculum Project:
Directions and Issues
Vince Wright
The University of Waikato
Who me?
Outline
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Background to the development
Structure of curriculum
Issues
Sources of enlightenment
Where to?
Curriculum Stocktake
1989
1991
1993
1992-97
1996
1997
1999
Tomorrow’s Schools
Achievement Initiative
Curriculum Framework
Curriculum Statements
Pause for completion of
statements
2 year phase in
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 Curriculum
Key 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
20022003
Year 5
Relative Strengths
Year 5
Number
Year 9

Patterns and
Relationships
Measurement
Geometry
Data
NB: Time allocated
Number
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Patterns and
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Relationships
Measurement
Geometry
Data
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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
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What is mathematics and
statistics?
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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
Two
Level
One
Stage
Advanced
Counting
Percentage
62%
Four
Two
Early Additive
Part-whole
67%
Six
Three
Advanced
Additive
50%
Eight
Four
Advanced
Multiplicative
45%
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 and
Measurement
Number and
Algebra
Statistics
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
In a range of meaningful contexts students will learn to:
Number and Algebra Strand
Number Strategies
Use simple additive strategies to solve
problems involving whole numbers, and
fractions.
Number Knowledge
Know forward and backward counting
sequences with whole numbers to 1000,
doubles, and groupings with tens.
Equations and Expressions
Record and interpret simple additive
strategies represented by words,
diagrams (pictures), and symbols.
Patterns and Relationships
Generalise 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.
Level Two
Geometry and Measurement Strand
Measurement
Create and use measurement units
sensible for a task, including grouping
units to simplify counting.
Time and Rates
Develop ways to measure time intervals
in order to compare the duration of
events.
Shape and Space
Classify 2 and 3 dimensional objects by
visual features noting similarities and
differences. Image and draw shapes.
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.
Transformation
Predict the results of slides, flips, turns,
and enlargements on objects.
Number
and
Algebra
Geometry and
Measurement
Statistics
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 Literacy
Compare the features of category data
displays with statements made about
the data.
Probability
Recognise apparent equal likelihood,
impossibility and certainty from trialing
of simple chance events.
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 inspiration
Assessment 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…
10 (8)
As above, except not
including 4 small flaps
7 (11)
4 sides and 2 ends,
appropriately proportioned
30 (34)
Basic idea correct but
significant distortions
27 (18)
More inspiration
Research since 1992…
For example:
Probability ideas:
• Variability
• Independence
• Distribution
• Sample space (possible outcomes)
What do these students think
about…?
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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.
Progressions
Level One
With simple chance events, systematically record
trialing.
Level Two
Recognise apparent equal likelihood, impossibility
and certainty from trialing of simple chance
events.
Level Three
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.
Level Four
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.
Abstract
Relational
Classifies shapes hierarchically by their properties.
Deduces that one property implies another.
Formal
Deduction
Operates logically on statements about geometric
shapes, solve problems and prove new results from
statements.
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…