Loddon Mallee Numeracy and Mathematics Module 3

1. Loddon MalleeNumeracy and MathematicsModule 3 Mathematical Language Mathematical Literacy

2. Mathematical Language Words Symbols Graphics

3. 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

4. Mathematical Language A point to consider: Many words we use in mathematics have different meanings in the ‘real world’ eg: volume, space ……..

5. Mathematical Language A point to consider many words have more than one meaning

6. ‘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

7. Mathematical Language A point to consider: the specialised nature of mathematics vocabulary

8. 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

9. Mathematical Language A point to consider: many students experience reading problems, miss words or have difficulty comprehending written work

10. Mathematical Language A point to consider: mathematics text may [and often does], contain more than one concept per sentence

11. 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

12. 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

13. Mathematical Language A point to consider: mathematical text may consist of words as well as numeric and non numeric symbols

14. 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

15. 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

16. 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]

17. Mathematical LanguageStrategies which may helpPaul 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

18. Mathematical LanguageStrategies which may helpPaul 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

19. Mathematical LanguageStrategies which may helpPaul Swan The 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

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

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

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

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

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

25. 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

26. 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