loddon mallee numeracy and mathematics module 3 mathematical language mathematical literacy
TRANSCRIPT
Loddon MalleeNumeracy and Mathematics
Module 3
Mathematical Language
Mathematical Literacy
Mathematical Language
Words
Symbols
Graphics
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, ….‘Isn’t that the control on the TV?’
Paul Swan, Mathematical Language
Mathematical Language
A point to consider:
Many words we use in mathematics have different meanings in the ‘real world’
eg: volume, space ……..
Mathematical Language
A point to consider
many words have more than one meaning
Mathematical Language
• ‘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?
Mathematical Language
A point to consider:
the specialised nature of mathematics vocabulary
Mathematical Language
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
Mathematical Language
A point to consider:
many students experience reading problems, miss words or have difficulty comprehending written work
Mathematical Language
A point to consider:
mathematics text may [and often does], contain more
than one concept per sentence
Mathematical Language
A 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 Language
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 Language
A point to consider:
mathematical text may consist of words as well as numeric and non numeric symbols
Mathematical Language
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
Mathematical Language
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
Mathematical LanguageStrategies which may help
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
Mathematical LanguageStrategies which may help
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
Mathematical LanguageStrategies which may help
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
Mathematical LanguageStrategies which may help
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.
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 help
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.
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 help
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.
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 help
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.
Newman Analysis References Bana, J., Marshall, L., and Swan, P. [2005] Maths Terms and Tables. Perth: Journey Australia and RIC publications
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