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Critical thinking is a term that we hear a lot, but many people don't really stop to think about what it means or how to use it. This lesson will tell you exactly what it means and make you realize that the average person largely ignores critical thinking.

 

Critical Thinking Defined

Critical thinking means making reasoned judgments that are logical and well-thought out. It is a way of thinking in which you don't simply accept all arguments and conclusions you are exposed to but rather have an attitude involving questioning such arguments and conclusions. It requires wanting to see what evidence is involved in supporting a particular argument or conclusion. People who use critical thinking are the ones who say things such as, 'How do you know that? Is this conclusion based on evidence or gut feelings?' and 'Are there alternative possibilities when given new pieces of information?'

 

Additionally, critical thinking can be divided into the following three core skills:

  1. Curiosity is the desire to learn more information and seek evidence as well as being open to new ideas.

  2. Skepticism involves having a healthy questioning attitude about new information that you are exposed to and not blindly believing everything everyone tells you.

  3. Finally, humility is the ability to admit that your opinions and ideas are wrong when faced with new convincing evidence that states otherwise.

 

Using Critical Thinking Skills

Many people decide to make changes in their daily lives based on anecdotes, or stories from one person's experience. For example, let's say that your aunt told you that she takes a vitamin C supplement every day. Additionally, she told you that one morning she was running late for work and forgot to take her vitamin C supplement. That afternoon, she developed a cold. She now insists that you take vitamin C every day or you will get sick, just like she did in her story. Many people hearing this story would just accept this and think, 'To avoid getting sick I should take vitamin C.'

Although this type of logic is very common, it lacks critical-thinking skills. If we examine this anecdote a little more carefully, you should be able to understand why. For starters, we don't know where the idea for vitamin C stopping illness even came from. Why did your aunt decide to take vitamin C rather than vitamin D, or any other vitamin?

Also, there was never any indication given that there exists a direct link between not taking vitamin C and developing a cold. At first glance, it may seem that way. However, there could be many other variables involved that have nothing to do with vitamin C. Maybe she was already developing a cold and that particular day it just happened to manifest itself. Maybe a sick person sneezed on her in the elevator that morning. Any number of possibilities could have happened, and from just this story, we simply do not have enough information. All of this speculation as to the validity of this particular observation is considered skepticism.

Let's say that these thoughts of skepticism inspired your curiosity. After all, it wouldn't be fair to simply dismiss all new ideas, either. As a result, you looked up articles on the relationship between vitamin C and cold prevention. After reading several reports, you've found that scientific studies on whether vitamin C prevents the common cold have been conducted, and the results have been inconsistent. The overall conclusion found from these studies is that vitamin C is necessary for maintaining overall body function, but cannot be held responsible for preventing people from getting any colds or treating a cold once someone already has one.

Critical Thinking Skills

Critical thinking can be as much a part of a math class as learning concepts, computations, formulas, and theorems. Activities that stimulate critical thinking will also encourage students to think and speak in mathematical terms.

 

Critical Thinking in Math

Critical thinking is a key factor in separating those students who can 'do' math from those who truly understand what they're doing. When students do the math, they can perform computations and explain concepts because they've learned formulas and definitions through practice and rote memorization. They don't necessarily know why the formula works, but they can use it. Likewise, they may not know how some ancient mathematician defined the concept, but they know the definition.

On the other hand, students who've been taught to think critically in math can explain why a formula works, and they can trace the steps used to define a concept. Not only can they solve a problem, they can explain the logic behind the process they used to reach a solution.

Think of it this way: sooner or later, most math students learn the Pythagorean theorem and its related formula. Students can become adept at using the formula A squared + B squared equals C squared to find the length of the hypotenuse or one of the sides. They can solve problems involving right triangles using the formula, provided they are given enough information. Students who have been taught to think critically can explain why the Pythagorean theorem works. More importantly, they know when and how to apply the Pythagorean theorem to solve a problem even if right triangles aren't an obvious part of the solution.

 

Real World Problem Solving

Math textbooks only go so far when it comes to presenting real world problems that require mathematical solutions. Texts are organized around concepts, making it easy for students to see what strategies they need to use to solve a problem. If the chapter is of the quadratic formula, students automatically know they will use that formula at some point to answer every question, even a complex word problem. Critical thinking kicks in when students have a variety of options for solving a problem. Students apply critical thinking to find the best strategy out of many possible methods to reach a solution.

Here's a problem that requires mathematical critical thinking:

Based on current trends in rising or falling temperatures, predict the average high and low temperatures for five different places on Earth five years from now.

To solve the problem, students will need to analyze data, determine the trends in each place, and select a method for predicting the future temperatures. They may need to use a variety of formulas and statistical tools to form their predictions. Teachers can take this a step further by asking students to explain and defend the methods they used.

 

Asking Questions

To think critically is to follow a clear line of logical steps and reasoning. To solve critical thinking problems, math teachers should model the way they think when solving a problem. Students can internalize a set of questions to ask that will help them think their way to a solution. These questions could include:

  • What is the problem? What am I trying to figure out?

  • What do I know? What is the given information?

  • What do I need to know to solve the problem?

  • What problems like this have I solved before?

  • What solutions could work? What strategies will work best in this situation?

 

After students attempt a solution, they can further ask: Why did my solution work? Or they might try to understand why their solution didn't work. Critical thinking activities present the perfect opportunity for students to collaborate and have meaningful conversations using mathematical vocabulary, which is a good sign they have developed a deep understanding of concepts.

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