Why Solving Fewer Math Problems May Actually Benefit Some Kids

While children who are numerate (having the ability to understand and work with numbers) can apply the math and problem solving skills they have to problems that are similar to the ones they have already solved, mathematical mastery prepares youngsters to combine the tools they already have to solve problems unlike ones they have seen before, said Richard Rusczyk, founder and CEO of the Art of Problem Solving (AoPS).

Sam Vandervelde agrees. He's the head of school for Proof School, a San Francisco based private liberal arts secondary school that caters to "students are internally driven to spend more than two hours on math in school every day," according to its website. The school has a need-blind admissions process.

Since solving unfamiliar problems requires contemplation, less is more when it comes to the number of problems kids tackle at once. For instance, kids might spend several hours -- or even days -- attempting to solve five problems.

"My contribution to this discussion would be to underscore that tackling a hard problem is a big deal, and that the process of solving it should not be foreshortened," Vandervelde said.

Coaching Kids Through Mathematical Challenges

Rather than showing high-scoring kids more problems that are similar to the ones their teacher already covered in class, it's beneficial for teachers or guardians to find more difficult problems that may involve five to eight steps before a solution is reached, said Rusczyk. "The point where you're stuck is the point where you learn the most," he said.

Teachers and guardians can help kids develop mathematical mastery by adopting a coaching approach, Rusczyk and Vandervelde noted.

"To illustrate, consider the classic question of which numbers can be expressed as the sum of two or more consecutive positive integers. (For instance, 14 is one such number, since we can write 14 = 2  + 3 + 4 + 5.) For most, this qualifies as a hard problem, in that we’ve never encountered a question like this before, so can’t base our approach on any known method, and consequently may have no idea where to even begin. In this situation, the teacher adopts the role of a coach, providing problem-solving strategies (try specific cases, collect data, look for patterns), supplying encouragement not to give up, celebrating partial results, pushing for a thorough explanation of conjectures, and guiding the student to make an effective presentation of their findings," Vandervelde explained, adding "I would rather a student occasionally spend several days wrestling with a single problem in this manner than forever plowing through more routine exercises."

If more than one student is ready for an extra challenge? Vandervelde has a classroom tip: "Assign each student, or pair of students, unrelated problems so that they can own their progress and not compete with or be scooped by classmates."

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https://www.forbes.com/sites/rachelcrowell/2019/01/30/why-solving-fewer-math-problems-may-actually-benefit-some-kids/#6438011fc174