Definition Of Problem Solving In Math

Definition Of Problem Solving In Math-34
The mathematics of modern computer science is built almost entirely on discrete math, in particular combinatorics and graph theory.This means that in order to learn the fundamental algorithms used by computer programmers, students will need a solid background in these subjects.You faithfully highlighted the key words, and went to work.

The mathematics of modern computer science is built almost entirely on discrete math, in particular combinatorics and graph theory.

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However, discrete math has become increasingly important in recent years, for a number of reasons: Discrete math—together with calculus and abstract algebra—is one of the core components of mathematics at the undergraduate level.

Students who learn a significant quantity of discrete math before entering college will be at a significant advantage when taking undergraduate-level math courses.

That approach could be characterized as “teaching about problems”, or “teaching how to solve problems”.

The school mathematics we envision is more fulsome, and uses problems as the basis for exploring the mathematical ideas of the curriculum, building skills and understanding, and builds more flexible and capable mathematical thinkers.

We strongly recommend that, before students proceed beyond geometry, they invest some time Introduction to Number Theory textbooks, or by signing up for our introductory Counting and Number Theory classes—with very little algebra background.

Also see our article Don’t Fall into the Calculus Trap, which discusses the pitfalls of rushing into calculus too quickly and/or with inadequate preparation.

By contrast, discrete math, in particular counting and probability, allows students—even at the middle-school level—to very quickly explore non-trivial “real world” problems that are challenging and interesting.

Prominent math competitions such as MATHCOUNTS (at the middle school level) and the American Mathematics Competitions (at the high school level) feature discrete math questions as a significant portion of their contests.

For over 30 years, with NCTM reforms, we have been talking about “teaching through problem-solving”, rather than teaching *about* problem-solving. I am not sure “teaching through problem-solving” is all that well-defined.

We who are, broadly speaking, constructivist teachers need to answer for how kids will do enough math, to be good at math, in problem-solving classrooms, but that’s a topic for another post. Somewhere, on a dusty shelf, you might have an old binder full of problems.


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