Hi all - I am back and ready to stir up this discussion:-)
I am so-o-o glad to be back on the list!! I just get back on and next thing I know a great discussion about algebraic thinking in elementary is beginning. Thanks, for the intellectual stimulation, and here are my thoughts to add to the discussion :-)
When developing the concept of fractions I use some of Marilyn Burns fraction activities along with many other authors, and materials I have personally made. However, the following activity began with the Marilyn Burns activity called Rod Relationships.
Students use Cuisenaire Rods to develop relationship statements such as; 1/2 O(range) = Y(ellow), 1/3 (Blu)e = L(ight green)
After these relationships have been found I discuss with the students how they have created generalizations about all the Orange and Yellow rods. They have generalized that "if" 1/2 O = Y relationship exists in one instance with the rods "then" that same relationship must exist with all of the yellow and orange rods in the set of Cuisenaire Rods.
We check to see if in fact this "generalization" is true by randomly choosing yellow and orange rods and checking. Once we have determined that this relationship is in fact "true for all rods in the set of Cuisenairre Rods", then we can use this statement to predict other relationships that exist.
For example if 1/2 O=Y and (I don't have the rods here with me, so I am just going to pick some colors for the sake of the example) 1/2 Y= P(ink) then what equation would you write to describe the relationship between O and P? Using what you know about the relationships between O and P if you had 6 P's how many O's would that be? Etc.
(As a side line here I am aware that there is no rod that is 1/2Y, because Y=5, however I cannot remember the color of the eight , the four, and the two rods right at this moment, so I am just using colors randomly for the example. If you don't understand it with the wrong colors, I can rewrite this when I get to school and see the rods.)
This is an example of "constructing" algebraic expressions. It is the way that I believe algebraic concepts should be addressed, because it provides students with the knowledge and the power to utilize algebra in the way that it was intended - to describe relationships that are generalizable.
Looking at algebra in this way makes it crystal clear that algebra is not a subject unto itself, and the continued teaching of it as though it is, appears to be quite ridiculous:-) (Intentionally controversial statement here;-) Maybe, I am missing something - if so I would appreciate your comments.
Cindy Chapman wrote: (snipped) >Anyway, he said that they were thinking that maybe algebra shouldn't>really be >>a subject, rather a strand throughout math education K-12. >There is a great deal of algebraic thinking that goes on at early >levels that could be nurtured with some good training of teachers.I'm >ready! Cindy