Understanding Problem Solving in Mathematics Education

Problem solving in the context of mathematics education is a critical skill that encompasses strategic competence within the framework of the Five Strands model. Strategic competence is defined as ldquo;the ability to formulate mathematical problems, represent them, and solve themrdquo; (National Research Council, 2001, p. 124).

Strategic Competence: The Core of Problem Solving

Strategic competence is a fundamental aspect of mathematical proficiency, essential for students to properly address the challenges posed by real-world problems. Unlike the structured procedures often taught in schools, real-world problem solving frequently demands the ability to understand the problem and select appropriate mathematical methods. Developing strategic competence requires extensive practice with unfamiliar problem situations, enabling students to devise and apply diverse problem-solving strategies.

Often, this process is known as mathematical modelinga technique that involves using mathematics to represent, analyze, make predictions, or provide insights into real-world phenomena (COMAP SIAM, 2016, p. 8).

The Five-Step Problem-Solving Process

At the primary education level through high school, a commonly followed five-step problem-solving process, known as the DEWSI process, is often employed.

D - Define Variables: Identify and define key variables, especially those representing the desired solution to the problem. E - Express Other Quantities: Express other relevant quantities in terms of the defined variables. W - Write Equations: Derive one or more equations or inequalities that represent the relationships between the given quantities. S - Solve Equations: Solve the derived equations or inequalities. I - Interpret the Solution: Interpret the solution in its original context and assess its validity.

While the DEWSI process is a useful guide, effective problem-solving involves a deeper understanding and application of all five strands of mathematical proficiency. Strategic competence primarily refers to the initial planning and conceptualization of the solution, including anticipating the overall steps and maintaining a broader perspective throughout the problem-solving process.

The Role of a Skilled Teacher

Observing a skilled teacher solve a problem on the board can illustrate the seamless execution of the DEWSI process. A knowledgeable instructor seems to intuitively know the next steps, effortlessly navigating through the problem-solving journey. This skill is a result of a well-developed strategic competence.

While some teachers may rely on detailed notes, experienced educators often do not need such assistance, as their strategic competence allows them to reconstruct and discuss the problem-solving process on the fly. This proficiency enables them to guide students through the intricate details while maintaining an overarching understanding of the problem.

In conclusion, the concept of strategic competence in problem solving is integral to developing a robust mathematical education. It requires students to think critically, understand the problem, and devise an effective strategy for solution. By fostering this skill, educators can better prepare students to tackle real-world challenges and advance their mathematical proficiency.