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Haylock, D. and Thangata, F. (2007) Key concepts in teaching primary…
Haylock, D. and Thangata, F. (2007) Key concepts in teaching primary mathematics London: Sage
Language difficulties in Mathematics, page 100
“We understand mathematical ideas by making connections between language, symbols, pictures and real-life situations (Haylock and Cockburn, 2003: 1–19)”
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Definition: “The particular language difficulties inherent in mathematics that are discussed in this entry relate to vocabulary, syntax, abstract and natural language, miscues in word problems, and the predominance of structure over content.”
Examples of the difficulties of syntax that occur
frequently for pupils trying to make sense of mathematical statements:
Teachers need to be aware of ambiguities associated with prepositions in some mathematical statements, such as 'what is 10 divided into 5?' (2 or 0.5?); and 'how much is 5 more than 3?' (2 or 8?)
Teachers should recognise the syntactical complexity of statements they make and questions they pose in maths. For example, asking ' which number between 25 and 30 cannot be divided equally by either 2 or 3?' involves holding detailed information in their mind as well as relating them together in the precise way implied by the complex syntax of the sentence.
Modelling process (representing), page 129
Definition: "Mathematical modelling is the process whereby abstract mathematical symbols are used to represent a problem in the real world and then manipulated to find a mathematical solution, which is then used to determine an appropriate solution to the original problem back in the real world."
"The application of mathematics to real-life problems is one of the key purposes for learning the subject... a representation of the real-life situation in mathematical symbols"
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Children in primary schools can begin to experience something the process of modelling. English and Watters (2005: 59) suggest that research in this field supports the view that 'the primary school is the educational environment where all children should begin a meaningful development of mathematical modelling'.
'When young children correctly record tally marks to count, draw block graphs to find most frequent outcomes or use number sentences to represent some practical problem, they are beginning their journey down the road as mathematical modellers'.
The modelling process
Step 2: perform the necessary calculations or other processing of the mathematical information to obtain a mathematical solution
step 3: recontextualise this, to interpret the mathematical solution back in the context of the original problem
Step 1: represent a problem in the real world in mathematical symbols, to formulate the mathematical problem.
Step 4: check that the solution is appropriate and that it satisfies the constraints of the original problem.
I chose to read this chapter so that I can understand how language in math can be harder for others to understand. Also, being familiar with mathematical language can help in clarifying the points and ideas that are put across when teaching and learning.
I chose to read this chapter because I wanted to understand the importance and impact of modelling mathematical problems.
