What is Mathematical 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 LITERACYThe 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 literacy in developing mathematical literacy?

Thinking ObservingSpeaking ListeningCreating

ReadingWriting

STANDARDS for SCHOOL MATHEMATICS CONTENT

NumberAlgebraGeometry &

MeasurementProbability &

Statistics

PROCESS

Problem SolvingReasoningCommunicationConnectionsRepresentations

MATHEMATICS as a LANGUAGEIncludes Elements, Notation, and SyntaxIs the language (science) of patterns and

changeAccording 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 COMMUNICATIONThe 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;

“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 MATHEMATICSWords 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 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.

Multiple Representations of the same idea and same translation:

12 412/44 12

Twelve divided by 44 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

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 Mathematics is Connected to Developing Meaningful Mathematical 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

Strategies for Promoting 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”