Counting On - More About

Moving from counting all to counting on is a significant stage for three reasons.

Firstly, it is an important step on the way to efficient calculation.

Secondly, it signifies strengthening of knowledge of the number name sequence. It is a more advanced skill to know that 7 comes after 6 than to start at 1 and count past 6 to 7. Counting on requires this skill. The same phenomenon is observed with the alphabet: to say the letter after G younger students need to start at A to get to H - they do not immediately know it.

Thirdly, when counting on is tested using hidden objects, students must demonstrate the ability to 'double count' – keep track of counting two sets at once. For example, if students can see 6 objects and have to add 3 more which are hidden, they have to carry out two simultaneous counts: they have to keep track (eg on their fingers) of how many more they have counted as well as the running total, so they know when to stop. Many students initially use their fingers for the second count.

Example of the double count when counting on
Running total (say this)	(6)	7	8	9
Tally of how many counted (think this)	(0)	1	2	3

Being able to double count is partly reliant on intellectual development, but it is also reliant on increasing familiarity with the number sequence and the counting process. Watch for the transition to double counting in many everyday activities, such as when children become able to keep track of two scores simultaneously when playing games etc.

One of the reasons why children can do more when they are given concrete materials than mentally is because they do not need to double count. For example, when there are counters on the table, to add three more, I touch each one instead of keeping track by double counting. This means that the use of concrete materials is extremely helpful for students to concentrate on new concepts without cognitive overload, but it also means that teachers should plan for their withdrawal.