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Loddon Mallee Numeracy and Mathematics Module 3 Mathematical Language Mathematical Literacy
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• Loddon MalleeNumeracy and MathematicsModule 3Mathematical LanguageMathematical Literacy

• Mathematical LanguageWordsSymbolsGraphics

• Mathematical Language

Many problems which students experience in mathematics are language related.

Understanding Knowledge Contextual

eg: consider the context of a teacher who is introducing students to the concept of volume..and the student who thinks, .Isnt that the control on the TV?

Paul Swan, Mathematical Language

• Mathematical LanguageA point to consider:

Many words we use in mathematics have different meanings in the real world

eg: volume, space ..

• Mathematical LanguageA point to consider

many words have more than one meaning

• Mathematical Language

If John had 14 pencils and then was given 12 more. How many pencils does he have now?

Bana, J., Marshall, L., and Swan, P. [2005] Maths terms and tables Perth: Journey Australia and R.I.C Publicationsmore - subtraction

If John has 20 pencils and I have 7 pencils, how many more pencils does John have?

• Mathematical LanguageA point to consider:

the specialised nature of mathematics vocabulary

• Mathematical LanguageSpecialised mathematical vocabulary:

eg: if you do not know that sum means to add and product means to multiply then any word problem that includes these terms will cause difficulties.

The word sum is often used to describe written algorithms

• Mathematical LanguageA point to consider:

many students experience reading problems, miss words or have difficulty comprehending written work

• Mathematical LanguageA point to consider:

mathematics text may [and often does], contain more than one concept per sentence

• Mathematical LanguageA point to consider:

mathematical text may be set out in such a way that the eye must travel in a different pattern than from reading left to right

• Mathematical LanguageGraphics:representations may be confusing because of formatting variations graphics will need to be read differently from text

graphics need to be understood for mathematical text to make sense

• Mathematical LanguageA point to consider:

mathematical text may consist of words as well as numeric and non numeric symbols

• Mathematical LanguageSymbols:can be confusing because they look alike

different representations can be used to describe the same process* x

complex and precise ideas are represented in symbols

• Mathematical LanguageVocabulary:mathematics vocabulary can be confusing because words can mean different things in mathematical and non-mathematical contexts [volume, interest, acute, sign]

two words sound the same [plain/ plane, root/route,..]

more than one word is used to describe the same concept [add, plus, and..]

there is a large volume of related mathematical vocabulary

• Mathematical LanguagePaul SwanStrategies which may help:model correct use of languagemathematics dictionariesexplain the origin of words and or historical context acknowledge anomaliesbrainstormuse Newman Analysis practicesuse concept maps, mind maps and or graphic organisers to demonstrate connectionsspeak in complete sentences- essential for fact memorisation [stimulus and response pairing]

• Mathematical LanguageStrategies which may helpPaul SwanExplain the origin of words:eg: Prefixes- deca- decagon, decadeSuffixes- gon- comes from the Greek gonia or angle, corner

Historical context:eg: Brahmagupta, an Indian mathematician ..in his book AD 628, Brahmasphutasiddhanta [The Opening of the Universe] ..the book is believed to mark the first appearance of negative numbers in the way we know them todayICE-EM Mathematics Secondary 1B

• Mathematical LanguageStrategies which may helpPaul SwanAcknowledge/explain/ historical context.. of anomalies:eg:the distance around a shape [perimeter] / the circumference of a circle

the [approximate] value of pi [3.14.]

bar /column graph

• Mathematical LanguageStrategies which may helpPaul SwanThe Newman Five Point Analysis

This technique was developed by a teacher who wanted to pinpoint where her students were experiencing language problems in mathematics

It was developed to determine where the breakdown in understanding is occurring

Newman Analysis References Bana, J., Marshall, L., and Swan, P. [2005] Maths Terms and Tables. Perth: Journey Australia and RIC publications

• Mathematical LanguageStrategies which may helpPaul SwanNewman Analysis

Please read the question to me. If you dont know a word leave it out.

Reading error If a student could not read a key word or symbol in the written problem to the extent that it prevented him or her proceeding further an appropriate problem solving path.

Newman Analysis References Bana, J., Marshall, L., and Swan, P. [2005] Maths Terms and Tables. Perth: Journey Australia and RIC publications

• Mathematical LanguageStrategies which may helpPaul SwanThe Newman Analysis

2. Comprehension:

Tell me what the question is asking you to do.

Comprehension error The student is able to read all the words in the question, but had not grasped the overall meaning of the words and therefore, was unable to identify the operation.

Newman Analysis References Bana, J., Marshall, L., and Swan, P. [2005] Maths Terms and Tables. Perth: Journey Australia and RIC publications

• Mathematical LanguageStrategies which may helpPaul SwanNewman Analysis

3. Transformation:

Tell me how you are going to find the answer.

Transformation error The student had understood what the question s wanted him/her to find out but was unable to identify the operation, or sequence of operations, needed to solve the problem.

Newman Analysis References Bana, J., Marshall, L., and Swan, P. [2005] Maths Terms and Tables. Perth: Journey Australia and RIC publications

• Mathematical LanguageStrategies which may helpPaul SwanNewman Analysis

4. Process skills:

Show me what to do to get the answer. Tell me what you are doing as you work.

Process skills errorThe child identified an appropriate operation, or sequence of operations, but did not know the procedures necessary to carry out the operations accurately.

Newman Analysis References Bana, J., Marshall, L., and Swan, P. [2005] Maths Terms and Tables. Perth: Journey Australia and RIC publications

• Mathematical LanguageStrategies which may helpPaul SwanNewman Analysis

5. Encoding:

Now write down the answer to the question.

Encoding Error The student correctly worked out the solution to a problem, but could not express the solution in an acceptable written form.

Newman Analysis References Bana, J., Marshall, L., and Swan, P. [2005] Maths Terms and Tables. Perth: Journey Australia and RIC publications

• Mathematical LiteracyDEECDTo be mathematically literate, individuals need competencies to varying degrees around:Mathematical thinking and reasoningMathematical argumentationMathematical communicationModellingProblem solving and posingRepresentationSymbolsTools and technologyNiss 2009, Steen 2001

• Mathematical Language Paul Swan Link

Bana, J., Marshall, L., and Swan, P., 2005 Maths Terms and Tables. Perth: Journey Australia and R.I.C. Publications