GROWTH MINDSET : Visual Thinking vs. Algorithms in Problem Solving

Visual Thinking vs. Algorithms in Problem Solving

Thinking visually about problems can be very beneficial. When we draw out a problem, we often gain a clearer understanding of the relationships and components involved. Visual representations can help us see patterns, make connections, and better comprehend the problem at hand. For instance, drawing the ratios and quantities in the problem involving Charmaine, Tesha, and Holly's cards allowed us to better grasp the relationships and solve the problem accurately.

On the other hand, algorithms are powerful tools that can provide quick and accurate solutions, especially when we are familiar with them. However, relying solely on algorithms without understanding the underlying concepts can lead to mistakes and a lack of flexibility in problem-solving.

Personally, I find drawing problems to be very helpful. It forces me to slow down and think about what is happening, often leading to better insights and solutions. Visual thinking makes abstract concepts more concrete, making it easier to explain my reasoning and understand the solutions of others.

In conclusion, while algorithms are essential, incorporating visual thinking into problem-solving can enhance understanding and lead to more effective and meaningful learning.

Designing a Thinking Process for Students

To help students become aware of and start using a thinking process in math, I propose the following steps that can be implemented in the classroom:

1. Introduce the Thinking Process: Begin by explaining to the students the importance of a structured thinking process in solving math problems. Use simple language and relatable examples to illustrate each step of the process. For instance, describe how an artist plans their painting or how a detective solves a mystery, relating it to the steps in math problem-solving.

2. Visual Posters and Handouts: Create visual posters and handouts that outline the steps of the thinking process. These can be displayed in the classroom and given to students to keep in their notebooks. The steps can include:

   - Stop and Think

   - Estimate

   - Draw or Use Manipulatives

   - Discuss with Peers

   - Mathematize

   - Reflect and Make Sense

3. Model the Process: Regularly model the thinking process during math lessons. Solve problems in front of the class, explicitly narrating each step. For example, when solving a ratio problem, say out loud, "First, I stop and think about the problem. Next, I'll estimate what the answer might be. Now, I'll draw a picture to help me understand the relationships..."

4. Guided Practice: Provide students with problems and guide them through the thinking process step-by-step. Initially, work on problems together as a class, then gradually let students work in pairs or small groups, and finally encourage them to apply the process independently.

5. Reflective Journals: Encourage students to keep reflective journals where they document their thinking process for each problem they solve. They can write about what steps they took, what challenges they faced, and how they overcame them. This practice will reinforce the process and help them internalize it.

6. Peer Discussions and Feedback: Facilitate regular opportunities for students to discuss their problem-solving approaches with peers. Encourage them to explain their thinking process to each other and provide constructive feedback. This will help students learn different strategies and reinforce their understanding.

7. Incorporate Technology: Use educational technology tools, such as interactive whiteboards or math apps, that allow students to visualize problems and manipulate objects. These tools can make the thinking process more engaging and accessible.

8. Celebrate Mistakes: Foster a classroom culture where mistakes are seen as opportunities for learning. Highlight how the thinking process involves trying, refining, and revising solutions. Share stories of famous mathematicians who made mistakes and how they learned from them.

By consistently incorporating these strategies into math instruction, students will become more aware of the thinking process and develop a deeper, more conceptual understanding of mathematics. This approach not only improves their problem-solving skills but also builds their confidence and resilience in tackling challenging math problems.