the language of mathematics concepts in mathematics
TRANSCRIPT
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The language of MathematicsConcepts in Mathematics
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Student concerns:
Late arrival, attendance, difficulty with math content, fears, questions.
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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 browserat the bottom of the screen.
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Please go to my website http://sites.google.com/site/ctmathelp .
The word files are done in word 2007. I have saved in word 2003 to allow access to those who do not have word 2007. You also need adobe 9.
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Please send an e-mail to the facilitator with the names of the students who comprise the groups for the practical teaching.
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What is mathematics?
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Mathematics is the science of number and number relationships.
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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
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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?
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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.
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The Language of Mathematics
Vernacular languages are available for communication. What is special about the
language of quantity?
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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.
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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").
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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...")
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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
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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
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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
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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
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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
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Concepts in MathematicsWhat is a number? LINK
http://www.mathpath.org/concepts.htmhttp://www.mathpath.org/concepts/number.htm
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Concepts in MathematicsLINK 1
LINK 2
LINK 3
LINK 4
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Teaching Concepts in Mathematics
Examples
Non Examples
Criterial Attributes
Informal Definition
Formal Definition
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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