PaCT Mathematics
Connections to good pedagogy
Post national standards
Developmental progression of learning less clear.
Detracting from teacher broad content knowledge.
Focus on incremental progress.
0
1
2
3
After
1Y
4
After
2Y
6
Adv. +
Early x
5 Early
Add
After
3Y
End
Y4
End
Y5
End
Y6
7
Adv. x
Props.
End
Y7
End
Y8
8
Post national standards
Reporting against a universal
expectation for time at school
eg. Well Below, Below, At, Above
(instead of reporting level of achievement)
Narrows the teacher focus around the
expectation for time at school of the year
level they teach.
Post national standards
High stakes
Post national standards
High stakes
+ limited assessment tools
PAT
Maths
easTTle
Maths
Diagnostic
Interview
GloSS
Post national standards
High stakes
+ limited assessment tools
Narrowed focus for teaching
Tendency to teach to the ‘useable’ assessment measures
When using PaCT...
Judge all aspects at a point in time.
Need relatively current knowledge of where a
student is at across all aspects.
When using PaCT...
Judge all aspects at a point in time.
Need relatively current knowledge of where a
student is at across all aspects.
Need shorter cycles of revisiting ‘strands’
Integrating ‘Strands’ within ‘maths time’
Making sure numeracy strategies are well
integrated into other strands and vice versa.
eg. teaching fractions & probability, or
addition and algebra at the same time
1, 1, 2, 3, 5, 8, 13, … Next five? Rule?
Maths across the Curriculum
Looking for teachable moments and monitoring
the maths aspects as part of teaching in other
learning areas.
eg. building a model animal
enclosure to meet its needs.
Hot Spots/enrichments
that revisit prior learning
International rugby field:
Playing field length - Min 94m, Max 100m
Playing field Width - Min 68m, Max 70m
In-goal length - Min 6m, Max 22m
In-goal Width - Min 68m, Max 70m
Biggest and smallest area?
When using PaCT...
Some important aspects in PaCT haven’t been a
big focus of other assessment tools.
Need to include these in teaching.
Symbols and Expressions
Not really taught explicitly
- knowing
5+6 =? but not 5+?=11
- Common errors eg.
To solve 3+9 writing
3+7=10+2=12
So...
Emphasis on recording thinking
❏ using number lines, arrays, set diagrams etc.
❏ correct use of = sign
❏ understanding number properties eg. associative,
commutative etc.
❏ setting problems that involve a variety of unknowns
When using PaCT...
The illustrations
emphasise how the
students demonstrate
their thinking and
understanding.
Lack of Understanding
Children were taught to manipulate numbers
using strategies almost as algorithms without
any real depth of understanding. This was
evident when students were challenged when
problem solving in other contexts or when
several steps were involved.
Performance of Understanding
Using a variety of contexts within instructional
groups, or rich tasks/problem solving to
demonstrate understanding of concepts
eg. fraction of a number - what’s 2/3 of 24?
- using time, money, measurement, shape,
sets of objects etc.
When problem solving
Importance of teacher
observation/questioning/monitoring - rove, rove rove!
Importance of developing students skills in problemsolving and describing mathematical thinking.
http://nzmaths.co.nz/mathematics-inquiry-communities
http://www.nzmaths.co.nz/bracken/pd/Introduction_to_MIC/index.html
set problems/investigations that involve several steps
2 step problem example
You heard that NZ beat England 15-12. (Yay!)
The points could have been scored in a number
of different ways.
What is the chance that
NZ scored more tries?
(assuming each way is just
as likely as another)
Still wondering...
how useful information within PaCT is to
inform teaching
what assessment information is important to
record and how to best keep track of it (and
what other assessments give us important
information)
Good pedagogy
Regular practice activities that connect to prior learning - with rigour.
Cross-curricula learning to keep cycling through mathematical aspects, connect to other contexts, see maths
as real life
Blend knowledge and strategy teaching (not assessed separately in PaCT) - flow in learning
Problem-solving - observe and question students articulating, manipulating, recording
show understanding through authentic application
require complexity of reasoning or judgement
students recording it!
Teacher roving - observing, questioning, challenging, alternatives, discussing
Problem solving groups, trained in expectation of contribution, allow maths discussion (set expectation),
learning from each other. teach what to do if stuck. teach questions to ask. Mark your work! Reward
persistent behaviour.
Symbols and expressions - understanding and using (like the surface features of writing, phonics and
grammar of reading)
Guided maths - use problems not ‘routines’
Knowing what to look for at the developmental level- critical content knowledge of the teacher