These are my notes from the maths PD session I attended at Kohia on 14/3/18.
The presenter was Lucie Cheeseman.
The presenter was Lucie Cheeseman.
Give one - get one strategy. Activating prior knowledge.
What does it mean to be numerate?
To be able to use maths in everyday life.
To problem solve.
To be mathematically literate.
Less emphasis these days on the right answer, more how did you get the answer?
Efficiency - we need to ensure, even with little kids, that they are solving problems efficiently.
Unpack the word ‘efficient’ with little kids - we are looking for the quickest way, the way that
is going to take the smallest number of steps.
Unpack the word ‘efficient’ with little kids - we are looking for the quickest way, the way that
is going to take the smallest number of steps.
Eg. Why would you count from 1 when you could count on from the bigger number.
Pictures and diagrams just as important as mathematical equations.
Knowledge and strategy are interlinked.
Ask questions, rather than give statements, so that children are doing the thinking,
not being dependent. For example, show a number, say 11. “How could you show me this number?”
Children can choose which materials they use, which are most efficient for showing the number.
not being dependent. For example, show a number, say 11. “How could you show me this number?”
Children can choose which materials they use, which are most efficient for showing the number.
If you can answer in 4 seconds, that’s knowledge. Longer than 4 seconds to process
you’re using a strategy.
you’re using a strategy.
Kids learn more from each other than us. This is a good reason for mixed-ability grouping.
To be meeting the standard after the first year at school they need to know the numbers
1-20 securely, to understand the place value not just read the numerals.
1-20 securely, to understand the place value not just read the numerals.
STAGES
Emergent
Stage 1 - 1:1 counting
Stage 2 - Counting from 1 on materials. A lot of kids will move straight from Stage 2 to Stage 4.
Stage 3 - Counting from 1 by imaging (need to be working with relatively small numbers).
Stage 4 - Advanced counting - AFTER 2 YEARS Counting on from the bigger number.
Encourage them to use their fingers to track their counting on. They need to be able to count
on or back from the bigger number using numbers 0-100.
on or back from the bigger number using numbers 0-100.
Stage 5 - Early Additive AFTER 3 YEARS
AT AFTER 4 YEARS.
They would solve a problem like 9+5 by splitting the 5, by knowing that 9+1=10, 10+4=14.
Stage 6 - Advanced Additive - Solving problems like 132-59.
Can show difference between two numbers with sets of counters. Subtraction is not always
taking away or finding what’s left.
taking away or finding what’s left.
Set up examples where the algorithm is inefficient. Like 1007-999 - it’s more efficient to
know that 1 makes 1000 and 7 makes 1007, 7+1=8, rather than using the algorithm.
know that 1 makes 1000 and 7 makes 1007, 7+1=8, rather than using the algorithm.
Book 1 of the Numeracy Project books has all the strategies and the expectations at the
different stages.
different stages.
Components of group teaching
Knowledge check - opportunity to activate prior knowledge- should be quick and pacy.
Can have cards and get kids to read the number. “How many more do I need to make 10?”
/Quik pix - for example subitising images. You don’t necessarily want the kids to count.
They can look at tens frame and get a sense of how many there are. Sketch when image is gone.
About 90 seconds to draw what they see. Site good for occasional maths chat - Maths Eyes.
When they’ve got the hang of that they can add numbers to their drawing to explain it.
Mathematical word problem - NZ Maths is good for word problems Eg. Pete the Cat -
good picture book series for mathematical ideas - link to word problems.
Launch problem, hook children into problem. Example problem - additive strategies -
Pete the Cat and his brother Tom have 10 buttons to share between them.
What are the different ways their buttons could be shared?
The teacher’s role during problem solving is to monitor, to ask deep questions,
but not to rescue children when they are struggling. “Spray and walk away.”
Can physically take children to another table to see another group’s strategy.
Parallel problems - differentiation - same problems, change numbers.
Knowledge check - opportunity to activate prior knowledge- should be quick and pacy.
Can have cards and get kids to read the number. “How many more do I need to make 10?”
/Quik pix - for example subitising images. You don’t necessarily want the kids to count.
They can look at tens frame and get a sense of how many there are. Sketch when image is gone.
About 90 seconds to draw what they see. Site good for occasional maths chat - Maths Eyes.
When they’ve got the hang of that they can add numbers to their drawing to explain it.
Mathematical word problem - NZ Maths is good for word problems Eg. Pete the Cat -
good picture book series for mathematical ideas - link to word problems.
Launch problem, hook children into problem. Example problem - additive strategies -
Pete the Cat and his brother Tom have 10 buttons to share between them.
What are the different ways their buttons could be shared?
The teacher’s role during problem solving is to monitor, to ask deep questions,
but not to rescue children when they are struggling. “Spray and walk away.”
Can physically take children to another table to see another group’s strategy.
Parallel problems - differentiation - same problems, change numbers.
Use cards with job descriptions for people in the group - can put on lanyards to start with.
Use of materials - children choose which materials will be the most efficient for solving
the problem.
Can give them play opportunities first - eg. using toy cars as maths materials.
Thinking groups = collaboration
Modelling books/thinkboards - these should be a record of student learning.
A thinkboard is a piece of paper divided into three sections:
“Clues,” “Mathematical Proof,” “Reflection - where are you in the learning pit?”
Co-constructed WALT or LI - at end “Were we counting from 1 or were we counting
on from the bigger number? Were we skip counting?” Then they leave the teacher with
the idea of what they were learning.
Use of materials - children choose which materials will be the most efficient for solving
the problem.
Can give them play opportunities first - eg. using toy cars as maths materials.
Thinking groups = collaboration
Modelling books/thinkboards - these should be a record of student learning.
A thinkboard is a piece of paper divided into three sections:
“Clues,” “Mathematical Proof,” “Reflection - where are you in the learning pit?”
Co-constructed WALT or LI - at end “Were we counting from 1 or were we counting
on from the bigger number? Were we skip counting?” Then they leave the teacher with
the idea of what they were learning.
‘We’re a whanau,’ not ‘we’re a team.’ Supportive rather than competitive.
$2 shop microphone for child sharing thinking. Teacher needs to make strategic
choices about which groups will share and the sequence in which they will share.
choices about which groups will share and the sequence in which they will share.
Teaching Channel - good youtube channel for PD in different curriculum areas.
Take away: These are some ideas I'd like to use from this PD
Co-constructing WALT at end.
Try Quick pix for maths warmup.
Use cars as a maths context.
‘Thinking thumb’ when you’re ready to share.
Can use ‘what’s the pattern?’ rather than ‘what’s the answer?’
Choral counting - record on board and get children to notice the patterns.
When pairing up kids think about personality rather than maths ability.
Don’t change the pairs all the time, give them some stability.
Don’t change the pairs all the time, give them some stability.
Finger on the arm as a signal ‘I need more thinking time.’
Revoicing - making what they said more succinct. Remember to go back to kids
‘Is that what you meant?’
Class Dojo mindset videos - make links to them when kids are struggling. ‘Is that what you meant?’
Independent activities - purpose to these activities
Construction
Pattern blocks
Jigsaws
Threading
Focus or task card to support it.
Number investigations - eg. have a number and they tell you all they know about that number.
Maths detective activities for a guided reading book - make up a task card for a book.
Maths detective box for little ones - make a box of some books with a magnifying glass
and they can find numbers and other maths in the books.
and they can find numbers and other maths in the books.
Spot the Difference books.
Simon Says/Boppit game
Memory
Memory match - one group per day, promote to parents too.
Board games
Ipad games
