college

2. What is Mathematical
Literacy?

3. “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)

4. 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)

5. What is the role of the elements of literacy
in developing mathematical literacy?
Thinking Reading
Observing Writing
Speaking
Listening
Creating

6. STANDARDS for SCHOOL
MATHEMATICS
CONTENT PROCESS
Number Problem Solving
Algebra
Reasoning
Geometry &
Communication
Measurement
Probability & Connections
Statistics Representations

7. 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 )

8. What are the necessary
ingredients for mathematical
literacy?

9. MATHEMATICS as
COMMUNICATION
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;

10. “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)

11. 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, ….)

12. 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.

13. Multiple 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…)

14. 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

15. 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:

16. 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

17. 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”