The language of MathematicsConcepts in Mathematics

Student concerns:

Late arrival, attendance, difficulty with math content, fears, questions.

Please  go  to  my  website  http://sites.google.com/site/ctmathelp .

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What is mathematics?

Mathematics is the science of number and number relationships.

Set Induction:

Solve a problem requiring the use of algebra and which embodies the use of the language of mathematics.

http://www.esubjects.com/curric/general/algebra/unit_one/pdf/language_of_math_lesson13.pdf

Link

Did the solution involve the use of symbols?

Did we operate on the symbols with the use of specified rules?

Can someone in another culture of setting appreciate and understand our answer?

In this case is the answer unique?

Is there a different way of writing the answer?

The Language of Mathematics

Algebra is written in a symbolic language that is designed to express mathematical thoughts.

Mathematical language skills include the abilities to read with comprehension, to express

mathematical thoughts clearly, to reason logically, and to recognize and employ common

patterns of mathematical thought. 

The Language of Mathematics

Vernacular languages are available for communication. What is special about the

language of quantity?

The Language of Mathematics

The language of mathematics is highly structured and rule bound.

It exacts a severe discipline from its users, a discipline that is very nearly uniform over

most of the globe.

Mathematics has long been synonymous with rigor and universality .

There exists the exclusion of judgment and a struggle against subjectivity.

That language, like other languages, has its own grammar, syntax, vocabulary, word order, synonyms, negations, conventions, abbreviations, sentence structure, and paragraph structure.

It has certain language features unparalleled in other languages (for example, theorems expressed using the letter "x" also apply to "b" and "2x-5").

What is different about The Language of Mathematics?

• Everything!

• Constant emphasis of patterns of thought and expression which recur throughout mathematics

• Thorough explanation of what makes mathematics "algebra"  and how to think "in algebra."

• Emphasis on bringing the students up to a mathematical, abstract, level of expression and understanding

• Emphasis on mathematical examples of sentences and reasoning (logic of this sort: "If it's raining, then I will get wet...")

What is different about The Language of Mathematics? • Everything!

• Emphasis on alternative ways to express the same information until students are comfortable with all the ways mathematical thoughts are expressed

• logical equivalences • letter-switching • theorems which use "iff" • definitions • English v. mathematical expression • abbreviations, notation • Making implicit usages explicit

What is different about The Language of Mathematics? • Everything!

• Little equation-solving until they have the ability to read the theorems which justify the steps (learning to read in order to learn is a major thrust).

• Algebraic methods are justified (and students understand the justifications)

• Proofs are introduced near the end, after students have all the background they need.

LINK Mathematics as Language

Reference

http://augustusmath.hypermart.net/index.html

http://www.cimt.plymouth.ac.uk/journal/ftlangm.pdf

http://www.cut-the-knot.org/language/

http://www.abstractmath.org/MM/MMLangMath.htm

http://press.princeton.edu/chapters/gowers/gowers_I_2.pdf

http://www.dpmms.cam.ac.uk/~wtg10/grammar.pdf

Ministry of education SEA guidelines [mathematics]http://www.moe.gov.tt/parent_guides/SEA-GUIDELINES.pdf

Van de Walle, J.A. (2004). Elementary and Middle School Mathematics: Teaching

Developmentally. Boston: Pearson Education Inc.Of doing mathematics pp. 13-14Native language, in teaching English Language

learners pp. 101

http://alexandria.tue.nl/repository/freearticles/610209.pdf

http://www.esubjects.com/curric/general/algebra/unit_one/pdf/language_of_math_lesson13.pdfTeachers College Record Volume 66

Number 1, 1964, p. 80-80

Krussel, Libby (May 1998), Teaching the Language of Mathematics. Mathematics Teacher, 91 (5) p436-41

Trust in numbers: The pursuit of objectivity in science and public lifeTM Porter - 1996 - books.google.com

Concepts in MathematicsWhat is a number? LINK

http://www.mathpath.org/concepts.htmhttp://www.mathpath.org/concepts/number.htm

Concepts in MathematicsLINK 1

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Teaching Concepts in Mathematics

Examples

Non Examples

Criterial Attributes

Informal Definition

Formal Definition

Concepts in mathematics

Pg 153 Classroom teaching Skills by Cooper.

Tips to help children understand math conceptshttp://www.helium.com/knowledge/24060-tips-to-help-children-understand-math-concepts