What is Mathematical Literacy?. MATHEMATICAL LITERACY “The ability to read, listen, think...
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Transcript of What is Mathematical Literacy?. MATHEMATICAL LITERACY “The ability to read, listen, think...
What is Mathematical Literacy?
MATHEMATICAL LITERACYMATHEMATICAL LITERACY
“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)
MATHEMATICAL LITERACYMATHEMATICAL 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)
What is the role of the elements of What is the role of the elements of literacy in developing mathematical literacy in developing mathematical
literacy?literacy?
Thinking ObservingSpeaking ListeningCreating
ReadingWriting
STANDARDS for SCHOOL STANDARDS for SCHOOL MATHEMATICSMATHEMATICS
CONTENT
NumberAlgebraGeometry &
MeasurementProbability &
Statistics
PROCESS
Problem SolvingReasoningCommunicationConnectionsRepresentations
MATHEMATICS as a MATHEMATICS as a LANGUAGELANGUAGE
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 )
What are the necessary ingredients for mathematical
literacy?
MATHEMATICS as MATHEMATICS as COMMUNICATIONCOMMUNICATION
The 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;
MATHEMATICS as MATHEMATICS as COMMUNICATION (cont.)COMMUNICATION (cont.)
Reflect on & clarify their own thinking about mathematical ideas & situations;
Develop common understandings of mathematical ideas, including the role of definitions;
Appreciate the value of mathematical notation & its role in the development of mathematical ideas.
(NCTM Standards, pp 78)
“The Mathematical Communication Standard is closely tied to problem solving and reasoning. Thus as students’ mathematical language develops, so does their ability to reason and solve problems. Additionally, problem-solving situations provide a setting for the development & extension of communication skills & reasoning ability.”
(NCTM Standards, pp 80)
READING MATHEMATICSREADING 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, ….)
READING MATHEMATICSREADING MATHEMATICS
Reading mathematics means decoding and comprehending not only words but mathematical signs and symbols, as well.
Consequently, students need to learn the meaning of each symbol and to connect each symbol, the idea that the symbol represents, and the written or spoken word(s) that correspond to that idea.
READING MATHEMATICSREADING MATHEMATICSMultiple Representations of the same idea and
same translation:
12 4
12/4
4 12
Twelve divided by 4
4 divided into 12
How many groups of 4 are in 12? (Draw a model, act it out…)
You try one…. Use the language of mathematics ( in this case the language of division) to solve the following problem.
How many groups of 1/4 are in 7/8? (Draw a model, act it out, or ……)
7/8 1/4
The Precise Language of The Precise Language of MathematicsMathematics
An illustration of the role of written symbols in representing ideas where students learn to use precise language in conjunction with 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:
Attending to the Language of Attending to the Language of Mathematics is Connected to Mathematics is Connected to
Developing Meaningful Developing Meaningful Mathematical KnowledgeMathematical 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
Observations from the Third Observations from the Third International Mathematics & International Mathematics &
Science Study (TIMSS)Science Study (TIMSS)
America Lessons placed greater
emphasis on definitions of terms and less emphasis on underlying rationale
Definitions were the beginning & the end of the lesson
(The Teaching Gap, J.W.Stigler, pp59)
Japan Lessons used the
definitions as a stepping stone for understanding mathematical concepts
Definitions are used to look for patterns & develop proofs of mathematical relationships
Use of Deductive Reasoning to Support Use of Deductive Reasoning to Support Vocabulary Development, Conceptual Vocabulary Development, Conceptual
Understanding, & RelationshipsUnderstanding, & Relationships
America
Define supplementary angles
Find the supplement of a 70-degree angle.
Japan
Draw an “X” and investigate the relationships of the angles formed
Use the definition of supplementary angles to prove that all vertical angles will be equal
Strategies for Promoting Strategies for Promoting Mathematical Literacy Mathematical 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”