Exploring The Similarities Between Problem Solving And Mathematical Investigation

## Routine And Non-Routine Problem || Problem Solving, Mathematical Investigation And Modelling

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## What Are The Differences And Similarities Between Problem Solving And Mathematical Investigation?

Exploring the distinctions and commonalities between problem solving and mathematical investigation sheds light on these two approaches. Problem solving is a focused and convergent process driven by the aim of reaching a specific solution to a given problem. It involves identifying a problem and working towards a definite goal, which is finding the solution. In contrast, mathematical investigation takes a more divergent path. During mathematical investigations, students engage in initial exploration of a mathematical scenario. However, what sets this approach apart is the expectation for students to actively create and formulate their own problems based on their exploration. This distinction encourages a more open-ended and creative exploration of mathematical concepts, fostering a deeper understanding of the subject matter.

## What Is The Relationship Between Math And Problem Solving?

The connection between mathematics and problem-solving is fundamental and centers on the idea that mathematics primarily involves reasoning rather than rote memorization. Problem-solving serves as a vital avenue for students to cultivate a deep comprehension of mathematical concepts and articulate the methodologies employed to reach solutions. This approach contrasts with the mere memorization and application of predefined procedures, emphasizing the dynamic and cognitive aspects of mathematics. In essence, problem-solving acts as a bridge that facilitates the acquisition of mathematical knowledge through active engagement, critical thinking, and the development of analytical skills, thereby enriching the overall learning experience in mathematics.

## What Is The Difference Of Mathematical Investigation And Problem Solving?

What distinguishes mathematical investigation from problem solving? Problem solving involves the application of generic or ad-hoc methods in an organized manner to find solutions to specific problems. On the other hand, mathematical investigation refers to the sustained exploration of a mathematical situation, setting itself apart from problem solving due to its open-ended nature. In mathematical investigation, individuals delve deeply into mathematical concepts, often without a predetermined solution in mind. This exploration allows for a broader and more comprehensive understanding of mathematical principles and their applications. (Date: October 10, 2020)

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