Rethinking Math Education: From Computation to Problem Formulation

Are you tired of math classes that feel like paint-by-numbers exercises? Do you wish students were taught to think critically and solve real-world problems, rather than just memorizing formulas? It's time for a math class makeover.

The Problem with Traditional Math Education

Traditional math education often focuses on computation and rote memorization, neglecting the crucial skill of problem formulation. This approach leads to several negative consequences:

• Lack of Initiative: Students become dependent on instructors to explain every step, hindering their ability to self-start and explore problems independently.
• Poor Retention: Concepts are quickly forgotten, requiring constant re-explanation.
• Aversion to Word Problems: Students struggle to apply mathematical concepts to real-world scenarios, often seeking formulas rather than understanding the underlying principles.
• Impatience with Complexity: Students expect quick and easy solutions, struggling with problems that require sustained effort and critical thinking.

This "sitcom-sized problem" mentality, where everything wraps up neatly in 22 minutes, doesn't prepare students for the complexities of the real world. We need to shift our focus from simple computation to reasoning and critical thinking.

The Importance of Problem Formulation

As Albert Einstein famously said, "The formulation of a problem is often more essential than its solution." Yet, traditional math education often neglects this crucial aspect. Instead of simply giving students problems to solve, we need to involve them in the formulation of the problem itself.

How to Foster Problem Formulation

Here's a breakdown of how to rebuild math problems in a way that supports math reasoning and patient problem-solving:

1. Start with a Compelling Visual: Instead of presenting all the information at once, begin with a visual that sparks curiosity and encourages discussion. For example, show a picture of a water tank and ask, "How long will it take to fill it up?"
2. Eliminate Sub-Steps: Allow students to develop their own sub-steps and formulate their own approaches to the problem.
3. Remove Distractions: Present only the essential information, forcing students to identify what matters and what doesn't.
4. Embrace the Real World: Use real-world examples, videos, and multimedia to connect math to students' experiences.
5. Encourage Intuition: Create a level playing field where all students can participate, regardless of their mathematical background. Start with intuitive questions that everyone can relate to.
6. Focus on the Process, Not Just the Answer: Emphasize the importance of critical thinking, problem-solving strategies, and collaboration.
7. Verify with Reality: Instead of relying solely on answer keys, use real-world observations or experiments to validate solutions.

Example: The Ski Slope Problem

Instead of presenting students with a fully defined ski slope problem, start with a visual and ask: "Which section is the steepest?" This sparks conversation and encourages students to defend their answers. Only then introduce measurements, mathematical structures, and sub-steps to refine their understanding.

The Power of Multimedia

Multimedia brings the real world into the classroom in high resolution and full color. It encourages student intuition, promotes conversation, and allows students to build the problem themselves. By being less helpful and allowing students to struggle and explore, we empower them to become patient problem solvers and critical thinkers.

A Call for Better Math Curriculum

Math is more than just computation; it's a way to make sense of the world. It's the vocabulary for your own intuition. Whether you're a student, parent, teacher, or policymaker, insist on better math curriculum that prioritizes problem formulation, critical thinking, and real-world application. We need more patient problem solvers to shape a better future.

This is an amazing time to be a math teacher. We have the tools to create high-quality curriculum in our front pocket. The tools to distribute it freely under open licenses has also never been cheaper or more ubiquitous.