The language of Mathematics Concepts in Mathematics

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Please  go  to  my  website  http://sites.google.com/site/ctmathelp . The  notes  been  loaded  on  the  teachers  page. B.Ed  notes.Some  have  difficulty  accessing  the  links  from the  power  point  file. If  you  are using  the  power  point  programme  and  you  click on  a  website,  you  may  need  to  come  out  of  power  point and  then  click  on internet  browser at  the  bottom  of  the  screen. 

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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").

Everything! What is different about The Language of Mathematics? 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

LINK Mathematics as Language 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. 13-14 Native 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.pdf Teachers 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 life TM Porter - 1996 - books.google.com

Concepts in Mathematics What is a number? LINK http://www.mathpath.org/concepts.htm http://www.mathpath.org/concepts/number.htm

Concepts in Mathematics LINK 1 LINK 2 LINK 3 LINK 4

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