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# Inckuding mathematical

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• Teachers must have a set of strategies they use to help students understand the content they are encountering. With the use of appropriate strategies that support learning, they can expect student to engage meaningfully with challenging and rigorous text. ((Ruth Schoenbach, March 2002). From Education Digest 1991: Content literacy does not require teachers to teach reading and writing. Content literacy has the potential to help students learn content more deeply and efficiently. Content literacy relies on the context of content and cannot be isolated from it. Reading and writing are complementary tasks in content classrooms. Content literacy is different than content knowledge. Teaching content is not the same as teaching content literacy.
• Use a concept map to display participant responses. Necessary Ingredients include an understanding of the following: Multiple symbol system – both numbers and symbols ( %, \$, !, ±, ¼, &gt;, =, Ø…..) Content (Number Theory, Geometry &amp; Measurement, Algebraic Ideas, Probability &amp; Statistics – Data Analysis); Process &amp; Skills; Relationships/connections Vocabulary or Language of Mathematics Representations of Mathematics (Models, charts, graphs, symbols…) Problem Solving Reasoning Communicating Let’s look at the Communication Standard more closely…..
• The issue is – you can’t have one without the other – the ability to communicate mathematically provides one with the tools to solve problems and reason. And then- to be able to solve problems and reason – I must have the language of the science. Thus I must know the vocabulary and symbols; must be able to read the problem and write about my understanding of the solution. An understanding of the symbols we associate with mathematics come from within a long process of exploring, questioning, challenging, and of doing mathematics. How do you create an environment that is safe and encourages students to investigate, make &amp; test conjectures, look for patterns, reflect &amp; rewrite, communicate mathematically,…..?
• Allow participants to represent these series of steps in any symbol system that choose to use. Walk around and hopefully you will be able to have participants present various representations – numeric, pictorial/tiles (model), symbolic (abstract symbols).
• The language of mathematics is very precise. When defining a word in mathematics, you exclude all other mathematical possibilities. We put things in groups a lot – categorizing and then describing that categorization. [Could use the activity from geometry to categorize and justify that categorization – see JCPS.] Importance of translating your thoughts and descriptions in mathematics – even posing/creating your own problems. The challenge is to get teachers to think differently about mathematics. Symbol manipulation vs. seeing what real problems are – where mathematics becomes the tool by which you solve real world problems ( seeing the mathematics that governs the physics of the problem ) and students must have some language by which to communicate these things.
• Use of categorizing Link between writing to learn and writing to demonstrate learning Vocabulary development Reading mathematics strategies – what are the text features, how is reading a mathematics text different from other text, how do you support vocabulary development, what are strategies for reading word problems and/or problem situations Vacca and Vacca – Content Area Reading: Literacy and Learning Across the Curriculum; talk about student’s prior knowledge is “the single most important resource in learning from texts”. Reading and learning are constructive processes: each learner actively draws on prior knowledge and experience to make sense of new information. The more knowledge and skills that students bring to a text, the better they will learn from and remember what they read. Activating prior knowledge prepares students to make logical connections, draw conclusions, and assimilate new ideas.
• ### 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”