Supporting Literacy and Numeracy 14 th November, 2011 How to Teach Children good numeracy skills

Aims Look at importance of learning to count Consider the process of learning to coutn Look at different strategies Look at different games.

Number Sense Number sense has been described as a: “ good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms ” (Howden, 1989). It refers to a persons general understanding of number and operations along with the ability to use this understanding in flexible ways to make mathematical judgments and to develop useful strategies for solving complex problems (Burton, 1993; Reys, 1991).

Numeracy To be numerate, children (and adults) need good number sense – this means understanding numbers, ways of representing numbers, relationships among numbers and number systems.

Early Start… Early introduction to number influences how well children do with numeracy in school. Early skills are related to skills in reciting conventional counting sequences (rote counting). It is really important the schools are aware of existing knowledge and build on it. Initial praise of the ability to rote count helps build self esteem.

Prenumber Concepts Patterning Sorting Classifying

Counting The correct way to count something is a very important element of life. It is always preferable that children learn to count before they go to school. Best way to start is by teaching numbers in order. Ways to do this: Sing along counting rhymes, using cards, connecting blocks, role-play shopping.

Counting Early number concepts begin with counting, which even thought is sounds simple is, in reality, the culmination of a lengthy developmental process. The development of this process is fostered by every day social interaction. Children come to school with a basic understanding of what counting is all about, that is, that there is a set of fixed number names, said in a specific order, which are matched one-to-one with things, and that the last word in the sequence tells "how many." Although children who have been fortunate enough to live in a complex, supportive environment possess these basic understandings, their ability to carry out the process free of errors generally is not fully developed and formal teaching is needed to complete their development.

Counting Principles Each object to be counted must be assigned one and only one number name. The number-name list must be used in a fixed order every time a group of objects is counted. The order in which the objects are counted doesn’t matter. The child can start with any object and count them in any order. The last number name used gives the number of objects. The cardinality rule connects counting with how many. Regardless of which block is counted first or the order in which they are counted, the last block named always tells the number. These principles help teachers recognize the levels of children’s counting skills. Careful observation of children, coupled, with a good understanding of these principles, will pinpoint counting errors. Once the trouble is diagnosed, instruction can focus on the specific problem.

Rote Counting Rote counting involves only the ability to recite the number names in sequence. Potential problems with rote counting to look out for A child using rote counting may know some number names, but not necessarily the proper sequence. Consequently, the child provides number names, but they may not be in the correct order. Rote counters may know the proper counting sequence, but may not always be able to maintain a correct correspondence between the objects being counted and the number names.

Counting Stages Rote Counting

Rational Counting Rational counting uses the ability to rote count, but goes one step farther. Rational counting by ones requires the child to make a one- to- one correspondence between each number name and one object. In addition, the child must realize that the last number said is the total number of objects in the set. Children must also be taught to use partitioning strategies, that is, to systematically separate those objects counted from those that still need to be counted. Rational counting is an important skill for every primary aged child.

Counting Stages Rational Counting

Counting Strategies Counting On - the child gives correct number names as counting proceeds and can start at any number and begin counting. For example, the child can begin with 7 pennies and count eight, nine, ten“or begin with 78 pennies and count“79, 80, 81). Counting on is an essential strategy for developing addition. Counting Back - children give correct number names as they count backward from a particular point. It later becomes helpful in developing subtraction. Skip Counting - the child gives correct names, but instead of counting by ones, counts by twos, fives, tens, or other values. In addition to providing work with patterns, skip counting provides readiness for multiplication and division

Relationships Among Numbers Spatial Relationships – learn to recognise sets of objects in patterned arrangements and tell how many without counting. One and Two More, One and Two Less Number Benchmarks Part-part-whole Relationships

Writing Numerals Start with very clear, very strong models. Focus on one number at a time. Provide maximum guidance at first. Be accepting of initial efforts. Gently reduce the amount of guidance. Reward correct performance. Review previously-learned material at regular intervals.

Conclusions There is a well-established sequence of development from counting into mental methods for addition and subtraction up to 20 To make progress children need to learn to compress counting procedures. In the process of adding numbers up to twenty, children progress through a sequence: count all, count on from the first number, count on from the larger number, use known facts and derive number facts. (Gray 1991) Evidence that children can be taught through sequence – using number counting skills – to learn further number skills.