Targeting Early Numeracy
A quality teaching process
A bit about TEN...
- Originally a targeted intervention program
- Was shaped into a whole class quality teaching process in numeracy
- Grew out of the Best Start Kindergarten Assessment program
- It is not an in-the-box program
- Useful data + regular monitoring = quality teaching and improvement
What have teachers noticed?
- It's what teachers already do - it helps us work as a team to refine and improve
- Teacher understanding has developed
- Assists familiarity with the new Mathematics syllabus
- Links between stages are more obvious
- Students can explain their thinking
- Students have a deeper understanding of mathematical strategies
- Professional dialogue/discussions
- Application in different roles, in different ways
- Transition strategies
- Awareness of progress and goal setting
- Students selecting learning partners/making responsible choices
- Strong willingness to participate
- Manageable with time
- Growing independence
- Influence in other KLAs
- Confidence, pride and success!
Why have we seen improvements?
- Dedicated meeting time (regular)
- Consistent language and expectations
- Team planning
- Ongoing assessment and monitoring
- Flexible grouping
- Professional dialogue
- Working mathematically outcomes
- Strong purpose, learning intentions and success criteria
- Same concept through a variety of resources
What do we teach?
MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
Addition and Subtraction
MAe-5NA combines, separates and compares collections of objects, describes using everyday language, and records using informal methods
· Describe the number before as 'one less than'
· Describe the number after as 'one more than' a given number
· Compare numbers and groups of objects eg. more than, less than, the same as
· Order numbers and groups of objects
· Use the term 'is the same as' to express equality of groups
· Compare two groups of objects to determine 'how many more' or ‘how many less’
· Read and use the ordinal names to at least 'tenth'
· Use 5 as a reference in forming numbers from 6 to 10, eg 'Six is one more than five'
· Use 10 as a reference in forming numbers from 11 to 20, eg 'Thirteen is 1 group of ten and 3 ones'
· Create and recognise combinations for numbers to at least 10, eg 'How many more make 10?'
· Reads and represents numbers in the range 0-20
· Read numbers to at least 20, including zero, and represent these using objects (such as fingers), pictures, words and numerals
· Recognise numbers in a variety of contexts eg. Charts, telephone, computer keyboard
· Subitise small collections of objects displayed in traditional arrangements eg. dot patterns on dice or dominoes
· Subitise small collections of objects displayed in random arrangements instantly recognise (subitise) different arrangements for the same number, eg different representations of five
· Recognise that the way objects are arranged affects how easy it is to subitise
· Estimate the number of objects in a group of up to 20 objects, and count to check
· Count with one-to-one correspondence and
· Recognise that the last number name represents the total number in the collection when counting
· Count forwards to 30 from a given number
· Count backwards from a given number in the range 0 to 20
· Apply counting strategies to solve simple everyday problems and justify answers
OPERATIONS – ADDITION AND SUBTRACTION
· Describe the action of combining, separating and comparing using everyday language
· Use visual representations of numbers to assist with addition and subtraction, eg ten frames
· Record addition and subtraction informally using drawings, words and numerals
· Use concrete materials or fingers to model and solve simple addition and subtraction problems
· Combine two or more groups of objects to model addition
· Count forwards by ones to add
· Model subtraction by separating and taking away part of a group of objects
· Count backwards by ones to subtract
MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
Addition and Subtraction
MA1-5NA uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers
- Number lines and charts
- Commutative properties (4+5=5+4, where = means ‘same as’)
- Addition and subtraction facts/number combinations up to 20
- Inverse operations (4+5=9 so 9-5=4 etc.)
- Near doubles
- Count on and back
- Partition/Split (37+45 = 30+40+7+5 = …)
- Bridge to tens (7+5 so 7+3=10 and 2 more)
- Jump strategy
The quality teaching framework
A student who is an emergent counter may have some knowledge of numbers and counting but cannot correctly match the sequence of counting words with objects where each object is allocated a number in turn, with the final number word corresponding to the total.
A student who is a perceptual counter can count items that he or she can perceive (see, hear or touch). A perceptual counter will demonstrate the one-to-one principle, generating terms in the sequence of number words as needed and matching one number word to one item, without skipping or double-counting items.
The figurative counting stage is characterised by students using a figurative representation of numbers. That is, students reconstruct numbers relying on imagined or figural items. The students match the sequence of counting words to figural items rather than perceptual ones. Counting from the number one appears to be necessary for the student to give meaning to the numbers.
Counting On and Back Counters
The counting-on-and-back stage involves students using the names of numbers as being equivalent to completed counts. That is, to find the total of six and three a student can take six as the result of a count that has already occurred and say: “Six, … seven, eight, nine, … nine!”. The essential feature of this strategy is that the student counts on from “six”. This way of counting on to find the total is sometimes described as counting up from a number. To successfully count up from a number the student needs a way of keeping track of the number of counts to know when to stop.
Facile (or Flexible) Counters
The flexible or facile counting stage is characterised by using number properties combined with number facts. Typically, flexible strategies can be described as using ‘this’ to work out ‘that’. A student may determine that 7 + 6 is 13 because double 6 is 12 (or double 7 is 14) and 7 + 6 is 1 more (or 1 less than double 7). Flexible strategies make use of the properties of numbers and do not employ counting by ones.
A LEARNING PLAN
Let's have a go!
Consider the progression of strategies, the links between groups/concepts and connections between the syllabus and continuum to the task.