- Snipped from Karen Dee Michalowicz - >According to Rex Boggs: >> >> No, according to H.S. Hall, in his preface to A School Algebra. I quote, >> >> "Graphs have now been on their trial for several years, and opinions are >> still divided as to what part they should play in a first course in Algebra. >> BTW, this book was published in 1910! > I collect old math texts. Algebras of the l9th and early >20 century didn't even mention graphing. > >If H.S. Hall had a graphing calculator as a tool in Algebra 1, >I doubt that he would have said what he did.
- Snipped from Eileen Abrahamson - Algebraic Thinking in Elem. >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.
Using this technique - graphing the relationships would be quite simple and make lots of sense to fourth grade students:-)