Actually, even some very good math curricula, like Singapore Math, ask fifth-grade students to solve two equation/two unknown problem using bar diagrams. When I worked through SM with the first child, my sibling and I were simultaneously going through the same level with our respective first children and both had the same reaction--why not just teach them algebra? Having gone through it with a second child (both of us, actually, again at the same time) it has become more clear that it has some value as a means of teaching problem solving, and providing a better conceptual basis (vs the procedural fluency/conceptual ignorance prevalent in North America).

If a teacher is not sufficiently deep in his or her own mathematical understanding to know how to probe students for -their- understanding, he or she will not be able to judge whether a student's use of algebraic language and procedures is an indication that they have already surpassed the level at which they need to develop conceptual grounding, or is just a sign that they have been hot-housed into knowing a few manipulations.

At one point, our first child was in a similar, though much less severe, situation. My approach was to talk about the value of understanding multiple ways of approaching, understanding, and communicating problem solving. Even if it's obvious to you, someday you might want to explain it to someone else, and having a few strategies might be helpful. Conveniently, that's our child who wants to teach.


...pronounced like the long vowel and first letter of the alphabet...