Loddon Mallee Numeracy and Mathematics Module 3 Mathematical Language Mathematical Literacy

Loddon MalleeNumeracy and Mathematics

Module 3

Mathematical Language

Mathematical Literacy


Words

Symbols

Graphics


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, ….‘Isn’t that the control on the TV?’

Paul Swan, Mathematical Language


A point to consider:

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

eg: volume, space ……..


A point to consider

many words have more than one meaning


• ‘more’ - addition

• 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 Publications

• ‘more’ - subtraction

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



the specialised nature of mathematics vocabulary


Specialised 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



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



mathematics text may [and often does], contain more

than one concept per sentence



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


Graphics:• 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 text may consist of words as well as numeric and non numeric symbols


Symbols:• 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


Vocabulary:• 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 Swan

Strategies which may help:• model correct use of language• mathematics dictionaries• explain the origin of words and or historical context • acknowledge anomalies• brainstorm• use Newman Analysis practices• use concept maps, mind maps and or graphic

organisers to demonstrate connections• speak in complete sentences- essential for fact

memorisation [stimulus and response pairing]

Mathematical LanguageStrategies which may help

Paul Swan

Explain the origin of words:• eg: • Prefixes- deca- decagon, decade• Suffixes- 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 today

ICE-EM Mathematics Secondary 1B


Paul Swan

Acknowledge/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


Paul 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


Paul Swan

Newman Analysis

1. Reading:

‘Please read the question to me. If you don’t 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


Paul Swan

The 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.



Paul Swan

Newman 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.



Paul Swan

Newman Analysis

4. Process skills:

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

Process skills error

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



Paul Swan

Newman 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.


Mathematical LiteracyDEECD

To be mathematically literate, individuals need competencies to varying degrees around:– Mathematical thinking and reasoning– Mathematical argumentation– Mathematical communication– Modelling– Problem solving and posing– Representation– Symbols– Tools and technology– Niss 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

http://www.otrnet.com.au/Paul_Swan/Articles/Mathematical_Language.pdf

Documents

Loddon Mallee Numeracy and Mathematics Module 3 Mathematical Language Mathematical Literacy