End of Term 2 Maths Inquiry
Most of the children have developed an understanding of, and can discriminate between, the properties of number - ordinality, nominal aspects as well as cardinality.
They can use this "information" about ordering things to find solutions. They have an understanding that the number line is a pictorial representation of ordering numbers. To do an addition it means increasing the number so they move to the right to increase the magnitude of the number. To answer the number sentence 3 + 2 = they can find the third number on the number line and make two jumps to the right to find the answer is 5.
Similarly to do subtraction or to make something less by taking away means to move to the left or make numbers smaller. Subtraction has been the more difficult concept to teach as the children didn't see straight off that it was the reverse of addition. It was something I needed to teach them. They also find it more difficult to find a number before or to "count down".
Some children are able to solve simple addition and subtraction without symbols. They can orally state what they are doing or they can use manipulatives. With practise they are beginning to rely less and less on manipulatives or fingers.
They also have an understanding that a number can also be a label to distinguish an item. The bus is number 625 or a phone number is 579 3654.
Counting a variety of objects into different sized sets has helped the children develop an understanding of cardinality. Counting the same sets several times starting from different objects has developed their understanding that the number in the set stays the same unless you add or take away some objects.
A small number of children are still struggling with these three aspects. The number line being a visual representation and the corresponding mental representation to work out the magnitude of number remain a mystery. Difficulties with sequencing or ordering is not only with Maths.
We continue to use a variety of examples with songs and chants to learn numbers, to use opportunities through out the day to count items and answer the question "How many?", use guided as well as independent opportunities to practise of counting, use dice and dominos to look at groups, get students to verbalise their strategies and use visual representations. Monitoring their learning is still an important part of helping those with weaker skills.
This does raise the question would some students benefit from intensive one on one help - a "Maths Recovery" series of lessons like the Reading Recovery programme?