
Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted:
Nov 25, 2013 12:07 PM


I got kind of behind on my email including this thread but Pam is right here, Bob. This approach, combined with competent arithmetic through ordinary fractions of course, is the best algebra readiness I've ever seen. As I mentioned, if it's been done well, by the more complicated problems of 6th grade, it's really time to drop it in deference to symbolic algebra but it IS a general approach with everything in place for genuine "algebraic thinking" as opposed to the nonsense that gets advertised as such (mathematically insupportable pattern recognition, for example).
Wayne
At 06:27 AM 11/18/2013, Pam wrote: >Posted: Nov 18, 2013 8:05 AM: > > > > > On Nov 17, 2013, at 7:42 PM, Pam wrote: > > > > > > Why, oh why, would I not use the information > > given?? 3/5 is three fifths! "Magically"? There is > > no magic involved, simply an understanding of > > fractions! > > > > But if you understand fractions, then wouldn't you > > just do the arithmetic at that point? > > > > > > > > >Perhaps because your approach requires "magic" and "reverse >engineering" and my approach does not? > >Think about the difference between the tart problem and the sundae >and cherry/bush and tree problems, within the context of bar >diagrams. In the tart problem, we did not know the total tarts >made, but we did know exactly what portion of that total was sold in >the morning (3/5) and in the afternoon (1/4 of 2/5). Hence, I could >divide the bar with some precision, and that allowed me to relate, >on my diagram, the morning tarts to the afternoon tarts. > >In the sundae problem, we knew the total for a sundae plus cherry, >but not what each cost individually. Hence, we had to divide our >bar arbitrarily. Similarly for the bush and tree >problem. Different unknowns require us to develop our bar diagrams >differently. > > > >> > > >>> See? Simply algebra but without having to know > > how > > >> to do algebraic manipulations with variable > > letters. > > >> > > >> I don't understand what you mean? > > > > > > An algebra mirror then. The solution via bar > > diagrams mirrors the algebraic solution. Although, > > since in both we are manipulating unknowns, simply > > with different representations, I think algebra is > > not such a stretch. > > > > It has some of the same elements as algebra, but > > lacks the transformative elements that promote reuse > > and generalization. But I agree that it is on the > > path. Sans the crayons.:) I still get the hint that > > you think this (even my version) is a replacement for > > algebra. > > > > Bob Hansen > >Gosh, Bob, only and ever in your arrogant and biased >misinterpretation of "what I think". Born not in small part from >your ignorance of how the use of bar diagrams develops throughout >the curriculum, as well as your reactionary response to approaches >different from your own. > >And, again, NOT your version, if you refer to the sundae/bush >problems. Yes, your mistaken version if you refer to the tart >problem with its different unknown requiring a different approach. > >And, please, could you not include my email address in your >reply? It is appearing in your replies for any and all to see. Thanks. > >Pam

