Embedded Media
Concepts. Skills. Strategy.
A mathematical Concept is the picture we form in our minds about some objects or word or idea.
The picture we form in our minds surrounding whole numbers will be determined by individual real-world and classroom experiences. This could include, cardinal numbers, 0, 1, 2, 3…, quantity numbers, recognising the amount within a group without counting the object individually, ordinal numbers, 1st, 2nd, 3rd, and nominal numbers, such as phone numbers, or car number plates.
Following Romina Jamieson-Proctor Language Model for Mathematics (2011), students will first use familiar objects to identify whole numbers. In the early years students are most likely to have some form of concept of cardinal and ordinal whole numbers as there are closely related to real world objects or events, such as story books, songs, games and rhymes.
As students’ progress, they will begin to form more complex and broad ideas surrounding whole numbers, and eventually will require no concrete/ visual aids to from a concept of whole numbers and move from the student language stage through to symbolic language stage.
Text Box
Cardinal numbers
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Concept: When students are first introduced to cardinal numbers, they will need to be given the opportunity engage, explore and create objects that represent a whole number (Van De Walle, 2010, p286). By creating an engaging task with familiar/real-world objects, Students will be able to reflect on their learning and identify the link between their real-world and mathematics.
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Skill: Being able to use the skill of one to one correspondence, stable order, cardinal principle, abstraction and order irrelevance (left to right or right to left) is the ability to process the concept of whole numbers. Teacher: "what number is before 6?" Student thinks 1,2,3,4,5,6, Students says "5". |
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Strategy: For teachers to understanding the thinking strategies their students use when working with whole numbers, they need to be able to reflect on their thinking process. By this time students will be at the symbolic language stage and will be practicing their strategies to reinforce and practice whole numbers. Strategies could include reciting a counting song or story to establish a one to one correspondence, or order irrelevance. |
References:
Baek, J, M. (2008). Children’s mathematical understanding of invented strategies for multidiget multiplication. Teaching children mathematics, 12(5),Pp. 242-247.
Van De Well, J. Karp, K. and ay williams, J (2010). Elementary & Middle School Mathematics Teaching Development. (7th Ed.). Pearson Education, Inc.
Evans, J. (2002) education 3-13.Talking about maths. Education: 30 (1), Pp 66-71.
Griswold, N, A (1997). Using Exponential Notation. Retrieved August 25 2011, From http://cerlabs.brookscole.com/experiments/10875404901.pdf
Howden, H. (1989). Teaching Number Sense. Arithmetic Teacher, 36(6), 6-11.
Piaget, J. (1977). The Grasp of Consciousness: Action and concept in the young child. London: Routledge and Kegan Paul
Jamieson-Proctor, R. (2010). EDX1280: wk4 slides. Retrieved August 16 2011, from http://usqstudydesk.usq.edu.au/mod/resource/view.php?id=405688