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# Inckuding mathematical

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### Inckuding mathematical

1. 1. What is Mathematical Literacy?
2. 2. “The ability to read, listen, think creatively, and communicate about problem situations,mathematical representations, and the validation of solutions will help students to develop and deepen their understanding of mathematics.” ( NCTM Standards, pp 80)
3. 3. MATHEMATICAL LITERACYThe ability to translate between a mathematical representation (which may include words and symbols) and the actual situation which that model representsThe ability to create and interpret mathematical models(Galef Institute – Different Ways of Knowing)
4. 4. What is the role of the elements of literacyin developing mathematical literacy?Thinking ReadingObserving WritingSpeakingListeningCreating
5. 5. STANDARDS for SCHOOLMATHEMATICS CONTENT PROCESSNumber Problem SolvingAlgebra ReasoningGeometry & Communication MeasurementProbability & Connections Statistics Representations
6. 6. MATHEMATICS as a LANGUAGEIncludes Elements, Notation, and SyntaxIs the language (science) of patterns and changeAccording to Galileo, “mathematics is the pen God used to write the universe.”Is a necessary ingredient for developing & demonstrating understanding – both oral & written language(Sensible, Sense-Making Mathematics, by Steve Leinwand )
7. 7. What are the necessaryingredients for mathematical literacy?
8. 8. MATHEMATICS asCOMMUNICATIONThe study of mathematics should include opportunities to communicate so that students can:Model situations using oral, written, concrete, pictorial, graphical, and algebraic methods;Use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas;Discuss mathematical ideas and make conjectures and convincing arguments;
9. 9. “The Mathematical CommunicationStandard is closely tied to problem solvingand reasoning. Thus as students’mathematical language develops, so doestheir ability to reason and solve problems.Additionally, problem-solving situationsprovide a setting for the development &extension of communication skills &reasoning ability.”(NCTM Standards, pp 80)
10. 10. READING MATHEMATICSWords that have the same meaning in mathematical English & ordinary English(dollars, cents, because, balloons, distance…)Words that have the same meaning in only mathematics – ‘technical vernacular’- (hypotenuse, square root, numerator..)Words that have different meanings in mathematical English & ordinary English ( difference, similar, ….)
11. 11. Reading mathematics means decoding andcomprehending not only words but mathematical signsand symbols, as well.Consequently, students need to learn the meaning ofeach symbol and to connect each symbol, the idea thatthe symbol represents, and the written or spoken word(s)that correspond to that idea.
12. 12. Multiple Representations of the same idea and same translation: 12 ÷ 4 12/4 4 12 Twelve divided by 4 4 divided into 12How many groups of 4 are in 12? (Draw a model, act it out…)
13. 13. You try one…. Use the language ofmathematics( in this case the language of division) tosolve the following problem. How many groups of 1/4 are in 7/8? (Draw a model, act it out, or ……) 7/8 ÷ 1/4
14. 14. An illustration of the role of written symbols in representingideas where students learn to use precise language in conjunctionwith the symbol systems of mathematics is as follows.The number thought of:Add five:Multiply by two:Subtract four:Divide by two:Subtract the number thought of:
15. 15. Attending to the Language ofMathematics is Connected toDeveloping MeaningfulMathematical Knowledge Why are there right angles and not left or wrong angles? Can you image ‘imaginary’ numbers? What are they – can you describe them? How do degrees change in mathematics? Precision of use of prepositions - of, by, per, into to indicate specific operations
16. 16. Strategies for PromotingMathematical Literacy Developing Vocabulary through Frayer Model (making use of nonlinguistic representation), semantic feature analysis, concept definition mapping, word walls, word sorts Making sense of text features through the organization and presentation of content, SQRQCQ, graphic organizers, think-aloud strategy Activating prior knowledge through questioning, webbing, creating an anticipation guide [Educational Leadership,Nov 2002,”Teaching Reading in Mathematics & Science”