Developing Critical Thinking
1. Overview
Critical Thinking is the ability to analyze a problem or concept. The real philosophical question is “What is a problem?” Once you understand what is a problem, there are steps to solve the problems. Critical Thinking is the ability to define, analyze and ultimately solve a problem.
2. How to define a problem?
The simple definition of a problem is something we don’t understand or something we don’t know how to solve. For example, we have a Number Pyramid Logiticabelow in figure-1. We need to find the missing numbers in the pyramid. Is that the real problem? If we look closely, the real problem is not finding the missing number, because if we try to do that, we could solve only one problem. The real problem here is finding how the numbers in a pyramid are related to each other (if they are)?
2.1 Definition of the problem:
Let us continue to explore the problem. Let us first define what we mean by a Number Pyramid.
♛ Definition — Number pyramid
A Number Pyramid is a collection of cells arranged in a pyramid. Each cell in the pyramid contains a number, which is the sum of two numbers in the cells directly below it. This rule obviously does not apply to the bottom row, as it has no row below it. An example of a Number pyramid is shown above in figure-1.
2.2 Analysis of the problem: This means there is a relation between the numbers in the bottom row and the number in the topmost cell. And, to solve this problem, we need to find that relation. Before we solve a bigger problem, we need to learn how to break the bigger problem to smaller solvable unit. As shown in figure-2 below, once we have a smaller solvable unit, we can always solve bigger problem iteratively. This approach or thinking refers to as Analytical Thinking.
2.2 Smallest solvable unit of a problem: For any complex problem, there exists a smaller unit. If identified correctly, this unit is generally solvable and helps to find the pattern of the problem. Therefore, before we solve a bigger problem, we need to learn to identify the smallest unit the problem. For example, the smallest unit of a pyramid problem is a 2-row pyramid. Once we know how to study a 2-row pyramid, we can analyze a 3-row pyramid problem. This analysis will lead us to the formula used in a 3-row pyramid. You can find this derivation in one of Logitica books. The formula for a 3-row pyramid can be shown below in figure-3. You can easily verify : 48 = 8 + 2x12+16.
2.3 Solve the next higher unit of the problem: Once we solve the smallest unit of the problem, we need to recognize the next higher unit of the problem. For example, once we found the formula for the 3-row pyramid, we should try to find the formula for a 4-row pyramid. The formula for a 4-row pyramid can be shown below in figure-4. You can easily verify : 41 = 1 + 3 x 9 + 3 x 3+ 4.
2.4 Solve the problem: Now that we have found the formula for the 4-row pyramid, we can easily solve the original problem in figure-1. If we assume the missing row in the pyramid as x, we can find the value of x using the formula as described below in figure-5.
Once we find all the missing numbers in the bottom row, we can easily find the remaining missing numbers using simple addition as shown in figure-6.
2.5 Solve a more complicated problem: Now that we have found the answer to the problem, you can analyze 5-row or 6-row or higher-row pyramids. Using this approach will help you in improving problem-solving and Critical Thinking skills. You can refer to LOGITICA books to learn how can we derive these formulas. Also you can explore the book further to learn an interesting relation between Number Pyramid and Pascal’s Triangle.
3. Summary
Critical Thinking helps in developing Problem-Solving skills as it is based on systematically analyzing and solving problems. In this blog, we have taken a concrete example, where we have followed the steps listed below:
(1) Define the problem.
(2) Analyze the problem.
(3) Simplify the problem and solve the simpler problem first.
(4) Then solve the next level of the problem.
(5) Finally, solve the original problem.
(6) Once you learn enough about the concept, try solving a more complex problem.
The above steps are blueprints of improving Critical Thinking. LOGITICA books contain a variety of problems where the above steps can be applied for improving Critical Thinking. Readers are recommended to proactive a variety to LOGITCA problems to improve their understanding of the topic discussed in this article.
4. References
Logitica books: Top Seller in Amazon in the respective category.
(1) Learn Logic & Math Together(9+ Ages) : https://www.amazon.com/dp/1796641383
(2) Number Pyramid (8+ Ages): https://www.amazon.com/dp/1793423830
(3) Improve Your Critical Thinking And Problem-Solving Skills (12+ Ages): https://www.amazon.com/dp/1793423830
Author: Neelabh Kumar is a thinker. Having memorized the first 1500 digits of Pi (π) using sequential recollection, he is ranked among the top 150 on the Pi World Ranking List. He is the creator behind Wisgo Logitica, which stimulates both sides of the brain. One of the Wisgo Logiticas Kumar created has a patent filing in Hong Kong. After earning a Masters Degree from one of the most prestigious universities in India (IIT), Kumar is now employed in Hong Kong at a large financial firm, while also creating and designing a new Logitica, with more to come. His authored books are listed in the reference section.
