Changes

"Critical Thinking in Math" is an experimental course with four independent purposes in mind:

"Critical Thinking in Maths" is an experimental course with four independent purposes in mind:

*sharpen the analytical skills of students and improve their math [[College Board]] scores

*sharpen the analytical skills of students and improve their maths [[College Board]] scores

*awaken an interest in [[mathematics]] by students who did not realize they had extraordinary aptitude for math, the future [[Bernhard Riemann]]s

*awaken an interest in [[mathematics]] by students who did not realize they had extraordinary aptitude for math, the future [[Bernhard Riemann]]s

*encourage adults to keep their mind sharp through mathematics, and fend off mental decline

*encourage adults to keep their mind sharp through mathematics, and fend off mental decline

*help parents who would like to teach math to their [[homeschooled]] children

*help parents who would like to teach maths to their [[home-schooled]] children

The experiment is to use only fundamental or elementary techniques to accomplish the above results.  No tools beyond about 9th grade math is required, and motivated students younger than 9th grade will not have difficulty with the concepts.

The experiment is to use only fundamental or elementary techniques to accomplish the above results.  No tools beyond about 9th grade maths is required, and motivated students younger than 9th grade will not have difficulty with the concepts.

This course seeks the contributions of both teachers and students to make it is effective as possible.  It will be begin in September.  Possible topics include:

This course seeks the contributions of both teachers and students to make it is effective as possible.  It will be begin in September.  Possible topics include:

*major problems that remain unsolved using elementary techniques

*major problems that remain unsolved using elementary techniques

*a look at the history of the development of math

*a look at the history of the development of maths

*an analysis of what skills [[College Board]] exams test, and how to improve those skills

*an analysis of what skills [[College Board]] exams test, and how to improve those skills

*different methods of proof:  constructive, induction, contradiction, existence

*different methods of proof:  constructive, induction, contradiction, existence

*Goldbach's Conjecture and Fermat's Last Theorem

*Goldbach's Conjecture and Fermat's Last Theorem

*Types of math problems presented in [[College Board]] exams, [[math contests|American math contests]] and UK math contests [http://www.wpr3.co.uk/UKMT/jmc.html][http://www.wpr3.co.uk/UKMT/imc.html][http://www.wpr3.co.uk/UKMT/smc.html]

*Types of maths problems presented in [[College Board]] exams, [[maths contests|American maths contests]] and UK maths contests [http://www.wpr3.co.uk/UKMT/jmc.html][http://www.wpr3.co.uk/UKMT/imc.html][http://www.wpr3.co.uk/UKMT/smc.html]

*Interesting problems in number theory and Euclidean geometry

*Interesting problems in number theory and Euclidean geometry

*greatest mathematicians in history, and why

*greatest mathematicians in history, and why

::: Well I come from Burma, but the colleges and university there are good. Your point about unsolved problems is good, too - have you heard of the folding@home project? It is a different concept, I know, but perhaps relevant - maybe what one brilliant mathematician might struggle at, us many lesser minds might gain insight into! I would also recommend for point 3 the UKMT papers [http://www.wpr3.co.uk/UKMT/jmc.html][http://www.wpr3.co.uk/UKMT/imc.html][http://www.wpr3.co.uk/UKMT/smc.html] - I do not know about how it is in the USA, but they are typical here. [[User:AungSein|AungSein]] 20:06, 5 August 2007 (EDT)

::: Well I come from Burma, but the colleges and university there are good. Your point about unsolved problems is good, too - have you heard of the folding@home project? It is a different concept, I know, but perhaps relevant - maybe what one brilliant mathematician might struggle at, us many lesser minds might gain insight into! I would also recommend for point 3 the UKMT papers [http://www.wpr3.co.uk/UKMT/jmc.html][http://www.wpr3.co.uk/UKMT/imc.html][http://www.wpr3.co.uk/UKMT/smc.html] - I do not know about how it is in the USA, but they are typical here. [[User:AungSein|AungSein]] 20:06, 5 August 2007 (EDT)

:::: Your additions to the above curriculum are superb!  Thanks much, and thanks also for the links to those U.K. tests.  I just printed one out am reviewing it.    Questions look challenging but doable, which is what we want.  Lord knows that students can really improve after practicing on lots of those types of tests.  We also have high school contests in the U.S. here:  [[Math contests]].--[[User:Aschlafly|Aschlafly]] 20:37, 5 August 2007 (EDT)

:::: Your additions to the above curriculum are superb!  Thanks much, and thanks also for the links to those U.K. tests.  I just printed one out am reviewing it.    Questions look challenging but doable, which is what we want.  Lord knows that students can really improve after practising on lots of those types of tests.  We also have high school contests in the U.S. here:  [[Maths contests]].--[[User:Aschlafly|Aschlafly]] 20:37, 5 August 2007 (EDT)

::: AungSein, a second student in this class took the UKMT Junior contest you cited, and she marked 17 correct, 5 wrong, and 3 non-answered.  How did you do on that test?--[[User:Aschlafly|Aschlafly]] 21:54, 6 August 2007 (EDT)

::: AungSein, a second student in this class took the UKMT Junior contest you cited, and she marked 17 correct, 5 wrong, and 3 non-answered.  How did you do on that test?--[[User:Aschlafly|Aschlafly]] 21:54, 6 August 2007 (EDT)

*I'm interested in this math critical thinking class too. --[[User:Luke314|Luke314]] 16:38, 9 August 2007 (EDT)

*I'm interested in this maths critical thinking class too. --[[User:Luke314|Luke314]] 16:38, 9 August 2007 (EDT)

:: Fantastic!  Welcome and Godspeed.  Please click "Watch" on this page so that you can easily see updates as September approaches.  This will be a great learning experience.  Feel free to make suggestions on the curriculum.--[[User:Aschlafly|Aschlafly]] 16:42, 9 August 2007 (EDT)

:: Fantastic!  Welcome and Godspeed.  Please click "Watch" on this page so that you can easily see updates as September approaches.  This will be a great learning experience.  Feel free to make suggestions on the curriculum.--[[User:Aschlafly|Aschlafly]] 16:42, 9 August 2007 (EDT)