Students initially investigate counting, and then grouping in a concept sequence we call ‘Early Counting and Grouping’. Select here for in-depth Early Counting and Grouping Professional Learning. Continue here for a summary and diagram of the Early Counting and Grouping learning.
Students in Kindergarten investigate Number concepts informally – no mathematical symbols are used! This is for 2 reasons:
i. students in Kindergarten learn 10 symbols for numbers, 26 symbols for lower case letters, and 26 symbols for upper case letters – that’s a huge 62 symbols!
ii. students need to be able to understand and explain the concepts behind the symbols +, -, x, ÷, and = before they begin to use the symbols.
Students begin investigating conventions of counting including the forward and backward number sequences, writing numerals and recognising numerals in 2 ways – when their name is spoken and when seeing its numeral (Early Counting and Grouping 1, 2, 3). These are conventions because we all agree on the sequence and the numerals! However knowing these is essential to begin to investigate mathematical counting.
Students begin investigating counting with one-to-one correspondence. explaining that the last number they said is the total, and that the number after is one more and the number before is 1 fewer. They explain that counting forwards is adding one each time, while counting backwards is taking away one each time. Students subitise the number in a small collection (without counting). (Early Counting and Grouping 4, 5, 6, 7, 8, 9).
Students need to be able to explain groups flexibly before they can investigate joining groups (informal adding) and taking a group away from a group (informal subtracting). Flexibly explaining groups means starting with 1 group, then making 2 groups, making 2 groups again, then making 3 groups – all from the same group of counters! Students estimate the number in a group, explain that numbers are inclusive (2 is inclusive of 1, 3 is inclusive of 2 and of 1) (Early Counting and Grouping 10, 11, 12).
Once students can explain groups flexibly, they begin to join 2 or more groups together and to start with 1 group and take a group away. They also investigate finding the difference between 2 groups in 2 ways – by adding to the smaller group to make the larger group, or taking away from the larger group to make the smaller group (Early Counting and Grouping 13, 14, 15)