1. The language of Mathematics Concepts in Mathematics

2. Student concerns:
Late arrival,
attendance,
difficulty with math content,
fears,
questions.

3. 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. 

4. Please  go  to  my  website 
The  word  files  are  done  in  word  I  have  saved  in  word  2003 to  allow  access   to  those  who  do  not   have 
word  You  also  need  adobe  9.

5. Please send an to the facilitator with the names of the students who comprise the groups for the practical teaching.

6. What is mathematics?

7. Mathematics is the science of number and number relationships.

8. Set Induction:
Solve a problem requiring the use of algebra and which embodies the use of the language of mathematics.
Link

9. 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?

10. 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. 

11. The Language of Mathematics
Vernacular languages are available for communication. What is special about the language of quantity?

12. 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.

13. 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").

14. 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...")

15. 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

16. 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

17. Reference

18. Ministry of education SEA guidelines [mathematics]
Van de Walle, J.A. (2004). Elementary and Middle School Mathematics: Teaching
Developmentally. Boston: Pearson Education Inc.
Of doing mathematics pp
Native language, in teaching English Language learners pp. 101

19.
Teachers College Record Volume 66 Number 1, 1964, p
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 books.google.com

20. Concepts in Mathematics
What is a number? LINK

21. Concepts in Mathematics
LINK 1
LINK 2
LINK 3
LINK 4

22. Teaching Concepts in Mathematics
Examples
Non Examples
Criterial Attributes
Informal Definition
Formal Definition

23. Concepts in mathematics
Pg Classroom teaching Skills by Cooper.
Tips to help children understand math concepts