GS Chandy
Posts:
7,127
From:
Hyderabad, Mumbai/Bangalore, India
Registered:
9/29/05


Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted:
Nov 17, 2013 6:45 AM


MVTutor posted Nov 12, 2013 7:51 AM (http://mathforum.org/kb/message.jspa?messageID=9322712): > > How would you advise students in the example > "1(x+23)"? > Can I tell them to drop the parentheses and reverse > the signs of each term? > Is the explanation that if we change the subtraction > to an addition we can use the associative property of > addition? > Are there alternative methods? > I've seen one book that suggests solving it as > follows: > 1(x+23) => 1+ 1(x+23)=> then solve 1(x+23) >  1(x)+1(2) (1)(3) > but this seems a bit confusing to me. > Any suggestions? > Thanks, John > SUGGESTION:
Each of us would have his/her own preferred way of 'learning things'.
For instance: When I manually multiply two numbers (for myself), here is a (very rough) illustration of how I'd do it (the numbers below aren't accurately aligned 'placewise' as I would do it when I do it manually): My way: ...5635 ....x963   ...50715 .....33810 .......16905 ======== ....5426505 ======== whereas one of my granddaughters would do it differently: My granddaughter's way (numbers below aren't accurately aligned 'placewise' as she would do it when she does it manually):: ...5635 ....x963   .......16905 .....33810 ...50715 ======== ....5426505 ======== [The younger granddaughter uses the method I do].
(I'm certain readers at Mathteach would be able easily to compensate for the deficiencies in alignment in what I've been able to achieve in this editor).
Insofar as 'examinations' (/tests/quizzes) are concerned, the important thing is that we both get the correct 'answer' (solution).
Insofar as 'understanding' is concerned, the important thing is that we both adequately understand the underlying process so that we can each repeat it correctly and get the right 'answer' for any numbers we may come across in real life situations.
Likewise for the algebra problem posed [ "1(x+23)"?]. The teacher would probably show his/her students using whatever protocol he/she is most familiar with  but hopefully would also demonstrate to the students that other (comfortable  and correct) ways may well be possible. The ONLY important issue is that the students adequately understand the underlying process so that they can each repeat it correctly and get the right 'answer' for any numbers they may come across in real life situations.
In one of the responses (dt. Nov 14, 2013 11:51 PM  http://mathforum.org/kb/message.jspa?messageID=9325444 ), Joe Niederberger has rightly suggested (possibly after Lou Talman):
> "What is the thought process that guides the formation > of such an expression? Or, what is an English > translation of that expression that relates naturally > to the word problem as given? Is there any way to do so > without mentioning the implicit "x"?
It is the underlying thought process(es) that is (/are) relevant to the students being 'taught'.
And the teachers should always be adequately aware that 'teaching' is NEVER a 'thinginitself', but only a part of the 'learning+teaching dyad'. AND that  while 'teaching' is an important part of the dyad  the 'learning' is by far the most important part of it. (Many teachers do not adequately understand this simple fact of 'systems life').
The Education Process is something that hopefully takes place in the 'Education System'  and the 'learning process' is, as noted, by far the most important part of education. More information about 'systems' and the processes within systems that could help us all (teachers as well as students) 'get' the underlying processes  and some useful tools to help out  are described in the attachments to my post heading the thread "Democracy: how to achieve it?"  http://mathforum.org/kb/thread.jspa?threadID=2419536 . It would be useful to remember that 'learning' is always something that should be done by 'teachers' as much as it is done by their 'students': in the conventional system, this does not usually happen, except in the cases of 'great teachers'.
[To be upfront fair and open about it, I should acknowledge that Haim (who has unfortunately left us at Mathteach) and Robert Hansen (RH) are both profoundly skeptical about the tools described at the attachments to the post noted above. Also (continuing to be upfront fair and open about it) I should mention that Haim is the prime proponent of the slogan:
["PUT THE EDUCATION MAFIA IN JAIL!"
while RH is the prime proponent of the slogan:
["Children must be PUSHED to learn math (other stuff)!"
[IMHO, each slogan is about as ridiculous you will find in any nook, cranny or crevice of modern civilisation]. GSC

