OPERATIONS: Theoretical Background Conceptual understanding of operations is developed by students via problem posing, exploration using concrete materials, real world examples, story books etc. (O’Connell, & SanGiovanni, 2011, p.5) supporting Van de Walle’s big idea that concrete resources can be used to solve contextual problems for all operations problems. (2004, p. 138-139). Conceptual Understanding Teachers need to understand the big ideas of mathematics, and be able to represent mathematics as a coherent and connected enterprise. (NCTM, 2000, p.17)

A Big Idea is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole. (Charles, 2005, p.10)

John Van de Walle (2004, p.135) notes the Operations Big Ideas:

Addition and subtraction are connected. Addition is responsible for naming the whole in terms of parts and subtraction is responsible for the missing parts.

•The concept of Multiplication, which includes the counting of equal size groups and working out how many altogether.

Multiplication and division are interconnected. Division involving finding a missing factor in related to a known factor and product. Multiplication taught first, but division introduced soon after to ensure students correlate the two.

•Models can be used in solving all mathematical problems, regardless of the size of the numbers involved. Models can be used to predict the operation required within a mathematical problem. The BIG Ideas! Basic Operations encompasses addition, subtraction, multiplication and division. (Hotmaths, n.d.) Operations are taught in order to firmly connect number concepts, and provide correlations to strategies. A good understanding of operations can firmly connect + and –, so – facts naturally follows on from +. Operations in the Curriculum The Australian Curriculum introduces Operations in Yr 1 & 2. These are the Content Decriptors Year 1:

•Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015)

Year 2:

•Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)

•Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)

•Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) Language & the numeracy connection An integral part of developing student's numeracy and understanding of operations is using the correct Mathematical Language. This language is evolving as the student progresses through 4 stages:

1. Children's Language 2. Materials Language 3. Mathematical Language 4. Symbolic Language

The Australian Curriculum advises this requires that teachers:

identify the specific numeracy demands of their learning area

provide learning experiences and opportunities that support the application of students’ mathematical knowledge and skills

Use the language of numeracy in their teaching as appropriate.

Understanding mathematical terminology and the specific uses of language in mathematics is essential for numeracy. Therefore, teachers should be aware of the correct use of mathematical language in their own learning areas.

(ACARA, n.d) (Van de Walle, 2004; Proctor, 2012) Mapping out Operations The table below maps out the learning and teaching sequence for Operations

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# Operations: Theoretical Background

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