To the Editor:
In looking at the K-6 algebra-related standards in the draft document released recently by the Common Core State Standards Initiative (“Proposed Standards Go Public,” March 17, 2010), one can’t help but wonder if these standards aren’t overly formalistic. Although such an approach may have some value for future mathematicians, the standards could discourage the average and below-average student.
For example, in the 6th grade standards, students are expected to see the need for and to understand that through the use of the multiplicative identity, the distributive law, and the commutative law they can get from y + y + y to 3y as follows: y + y + y = y(1 + 1 + 1) = y(3) = 3y. This is only one of many instances in which a formalistic approach is used for an obvious result.
Indeed, in the standards for grade 3, students have been informed that multiplication by a whole number can be considered as repeated addition. Hence, adding the same item three times, namely y, is the same thing as having three of those items, that is 3y.
In contrast, standards that would recommend giving students an early and solid foundation for algebra through concrete and pictorial means are lacking. There are in fact such methods through which 4th and 5th graders, including inner-city minority students, can solve equations such as 4x + 2 = 3x + 10, with unknowns on both sides of the equation. Such whole-brain instructional approaches would help students demystify algebraic notation and could serve as a foundation for later algebraic studies.
Formal or semiformal proofs in the elementary grades will do little to encourage the learning of mathematics, and are far more likely to turn students off to the study of the subject.
Henry Borenson
Allentown, Pa.
