Concept: the metaphor or picture onecreates in their head Number understanding 0 – 9 Creating a picture in a student‟s mind about a number.For example, the number three (3).
According to Jamieson-Proctor (2011), Van de Walle (2010) & Booker et al (2004), mathematics instruction, including the concept of number, should follow a model of learning from concrete to abstract. Thelanguage model moves through 4 stages: (Jamieson-Proctor, 2011) Children‟s Language Materials Language Mathematical Language Symbolic Language
Booker, et al (2004) add at this early stage of concept development the focus of instruction needs to be with materials and patterns that allow insight into the number; rather than concentrating on the recognition and writing of the symbol „3‟ itself. This reinforces the idea of the language model. Children start off learning about the number three with language and objects that are familiar to them, counting to recognise what three toys are. They then move to use their notion of three to group objects into three, firstly with toys and than more mathematical materials. Finally students move to more mathematical language of sorting and matching to manipulate the objects.
Using the Language model, the table below gives a brief overviewof the teaching sequence to develop the concept of a number 0-9, for example 3. Language Materials Language Record stageChildrens Language Familiar items to the „find me three of the child – toys e.g. dolls, same thing‟ or “find me cars, fruit e.g. bananas, three dolls” apples etcMaterials Language Counters, paddlepop “Can you give me a sticks, unifix blocks group of three Pictorial only counters” or “sort those paddle pop sticks into groups of three”Mathematics Language Counters, paddle pop Sort, match or set of sticks, unifix blocks, MAB three blocks,Symbolic Language none needed As above
To provide full meaning of the number e.g „three‟, students need to understand what is meant when we say „three‟. This includes giving children opportunities to encounter three in different situations - three people, three sticks, three pencils, three balls, etc. Using the same material again and again when teaching about numbers restricts childrens experience and prevents them from generalising that three refers to collection of any three objects (Indira Gandhi National Open University [IGNOU], 2012). The next slide shows an example of a child who has had restrictive experiences with the concept of three.
Four year old Sally was reciting number names, some of them in orderand others randomly. The childs aunt sitting nearby asked her "Canyou write three ?"Sally said "yes" and wrote the following:When the aunt asked what had she drawn alongside, the childreplied flowers. On asking her why she had drawn them, she repliedthat: "This is the way three is written in the book". When her aunt said:"If I draw three ducks here, will they be „three?" Sally replied: "No theywill not. "
The previous slide demonstrates that Sally‟s concept of the number three is about „three flowers‟ rather than the notion that three is a collection of a set number of objects. To move Sally beyond this understanding a teacher needs to begin to demonstrate a generalisation of three so Sally can change her concept of three. This can be achieved through singing songs using 3, reading stories that contain 3, allowing children to make groups of 3 either with themselves or objects.
To reinforce the number concept being learned for the day or week the teacher could use the number 3 throughout the day. Choosing 3 stories to read, asking for 3 volunteers to help out, use physical exercise to practice 3, e.g. 3 star jumps.