What is Mathematical Literacy?

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 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 literacy in developing mathematical literacy? Thinking Observing Speaking Listening Creating Reading Writing

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

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 )

What are the necessary ingredients for mathematical literacy?

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;

MATHEMATICS as 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 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 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 MATHEMATICS Multiple Representations of the same idea and same translation: 12  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 Mathematics 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

Observations from the Third International Mathematics & 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 Vocabulary Development, Conceptual Understanding, & 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 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”