I’m not sure how to comment on this one. The most efficient algorithm for me to *solve* the math problems she steps through is to use tools that are immediately accessible to me: by pressing the calculator button on my keyboard, using the calculator function in my cell phone, or use a standalone calculator. The most efficient method for me to *understand* what’s going on in the math problems is somewhat different. While the “standard” algorithms McDermott promotes are very effective in solving problems, they require very little understanding of the math involved.

The bottom line is that we have the tools to solve complex math problems easily. While the new methods try to emphasize on *understanding* the mechanics of the problems, I doubt the abilities of parents and most teachers to have enough of a full grasp of these mechanics to teach the underlying principles of mathematics effectively.

We need to decide if we want students to become better calculators or become better applied problem solvers. I prefer the latter. In that case, we should aggressively adopt the most efficient method for solving math problems by embracing calculators and other tools to solve these problems … even on tests. With the tedium of solving problems put aside, we can focus on building the capacities of learners to understand the underlying mathematics, and apply their creativities toward finding ways to solving new and complex problems that have meaningful applications for each learner.Картини