How Can Teachers Foster Real Mathematical Thinking in Primary Students?

[electronic engineer]

I'm now teaching mathematics for primary stage and i need good guidance for the purpose of raising my students to real mathematic thinking, maybe the guidance will contain some general advices for teachers...i don't know!

anyway thanks for any reply posted!

 

[mathwonk]

what does primary stage mean? 6-10 year olds?

at that age I recommend just getting them to master the basic skills. And to practice reading problems and translating them into mathematical computations.

real mathematical thinking for high school or junior high students should involve thinking about how we measure various quantities, i.e. what do we mean by length, area, volume.

some logical principels should be learned, such as the difference between "if A then B", and "if B then A". This seems obvious, but it is not. most high schoolers think that solving x -y = 4, and x+y = 2 is done by adding the equations, and concluding that 2x = 6, so x = 3.

they do not realize that this reasoning shows only that 3 is the only possible solution, not that it actually is one. I.e. they do not distinguish between "if there is a solution, then it equals 3", and "if x = 3, then this is a solution".

this becomes more important in exampels like sqrt(x-2) = -3, so x-2 = 9, so x = 11. i.e., assuming sqrt(u) means the non negative one as usual, then x = 11 is actually not a solution of the problem.

 

[electronic engineer]

thanks for these comments. I'm teaching 11-13 olds students so if you have more comments, tell me please but concerning my title topic "mathematical techer's notebook " does anyone here have such notebook , may be in PDF form?!

regards!

 

[jtbell]

I'm now teaching mathematics for primary stage

It would really really help if you gave us some clue as to where in the world you are located, and what mathematics your students have already studied. At least now you've told us how old your students are.

Educational systems differ tremendously from one country to another, and in some cases between different kinds of schools in the same country. In the USA, the term "primary stage" suggests "primary school" or "elementary school" which usually serves 6-12 year-olds.

 

[electronic engineer]

I live in Syrian arab republic , if you really want to know more things , please ask me certain questions.

thanks a lot!

 

[mathwonk]

Try reading "how to solve it" by george polya.

 

[kb3lja]

An excellent Resource

Greetings,
I appreciate your interest in getting your students minds a real thinking power. When I got my HAM radio license, I came across this wonderful collection of documents about maths and physics (electronics in particular)

http://www.earth2.net/parts/?basics/math.php
It has very vital collection in mathematics all in PDF.
It is from US Navy's course series and after looking into it, I found the distribution is unlimited meaning anyone can use it.
Feel free to download, if you like it and know someone who may need it, just spread the word.

Together, we can make our next generation a pleasant one.

Thanks
Murali (kb3lja)