What Is Involved In Critical Thinking In Mathematics

Students nowadays are experiencing an education system which rapidly changes from time to time through implementation of many educational technologies. Learning strategies, teaching processes and roles of teachers, students, parents and administrators

have been upgrading continually in accordance with the demands of 21st century education.

21st century education doesn’t just require good grades, it helps students to become independent learners. It also has a set of skills which we can call as, “21st century skills”.

Let’s have a glance at the list of 21st century skills:

  • Creativity
  • Critical thinking
  • Cultural Awareness
  • Problem solving
  • Innovation
  • Civic engagement
  • Communication
  • Productivity
  • Collaboration
  • Accountability
  • Exploration
  • Initiative
  • Responsibility
  • Leadership

In addition to the above mentioned skills, there are many more skills that 21st century students are required to have. It’s difficult to cover the information about all the 21st century skills in one guide so I’m writing this guide with focus more on two important 21st century skills, Critical thinking and Problem solving. As we know 21st century students will have the jobs that don’t even exist yet, students must have problem solving and critical thinking skills. Let’s learn about them.

Critical thinking:

Critical thinking is a way of deciding whether a claim is true, partially true, or false. 21st century education’s main objective is to help students think critically and not just take in things like a parrot. Critical thinking leads to skills that can be learned, mastered and used. It is the rational examination of ideas, inferences, assumptions, principles, arguments, conclusions, issues, statements, beliefs & actions.

Problem solving:

Problem solving, the term itself indicates that it’s an approach of solving problems or finding solutions to problems. From students to professionals, everyone experiences problems from time to time. Some problems are complicated while many others are easily solved. For every task or work we perform, there are many challenges and issues that make it difficult to complete. 21st century education involves teaching approaches that help students become capable to solve problems that arise in their job, education or life.

Similarity between Critical thinking & Problem solving:

Critical thinking is defined as meaningful, unbiased decisions or judgments based on the use of interpretation, analysis, evaluation, inferences, and explanations of information as it relates to the evidence applied to a specific discipline. Critical thinking differs from student to student as they have different interpretations.  

Problem solving is the ability to find solutions to problems, overcome challenges, completing difficult tasks through techniques, etc.

Both critical thinking and problem solving are similar as their design is to approach and tackle different challenges. Both critical thinking and problem solving (creative problem solving) involves the following procedure:

  • Identify an objective
  • Conduct research
  • Generate ideas
  • Develop solutions
  • Check whether or not the solutions are appropriate.

(Educators’ point of view) Why 21st century students need Critical thinking and Problem solving skills and how educators can improve these skills:

Critical thinking:

Many students have access to technology as well as technological devices and most of them know how to blog, micro blog, connect and collaborate with others through social media, explore and exchange knowledge about any concept, etc. Despite having many educational technologies, students still find it difficult to reach higher learning standards. This is because they’re not being selective in thetechnologies they use. Students nowadays still lack the ability to critically decipher through the “hits” they find on a Google search, and many do not understand the concept of a digital foot-print. Jules, an English teacher, has shared a practice that is being implemented in her school to improve creative thinking of students. Let’s learn about it.

“Many students do not think critically about the sources they select from online sites. We designed and implemented a four year research strategy at my high school that includes Boolean logic, searching for sources, determining the sources credibility, how to differentiate primary and secondary sources, checking how often the material is updated (if ever), etc. I teach mostly seniors and find that most do question the validity of blogs versus articles citing expert opinion, but that does not translate necessarily to them choosing better sources or seeking to find answers that aren’t already provided for them in some way. Thanks for posting. The need and ability of youth to critically think about the media in which they daily engage is increasingly necessary.” says Jules.

“Why” can make students think critically:

According to me, the word or the question “Why” is a great sign of “Critical thinking”. Most of the students just follow what they’ve learnt from teachers, books, or any digital sources. But few students try to learn about what it is and ask why it is being followed. This enthusiastic nature makes them special from the rest of the world.

“In Math, critical thinking usually comes when students ask why, rather than taking what we learn at face value”, says Graham Johnson, Math Department Head -Okanagan Mission Secondary & Instructional Designer - Thinkable Institute

“Learning stops at an answer - thinking happens during questioning. ““Why” is always a great question” - Gary Strickland ‏, HS physics and IPC teacher.

#MysterySkype improves Critical thinking & Collaboration skills among students:

Many educators find MysterySkype as a great tool to promote collaboration among students and improve critical thinking skills.

Mystery Skype is an educational game, invented by teachers, played by two classrooms on Skype. The aim of the game is to guess the location of the other classroom by asking each other questions. It's suitable for all age groups and can be used to teach subjects like geography, history, languages, mathematics and science.

I’d like to provide you with a link on which Paul Solarz has shared his experience of using #MysterySkype.

Solarz has written the whole procedure of the Mystery Skype, his ways of finding partners to play the game, the questioning model, and etc. Read this blog post to know more about it. 

In addition, there are many more important things to know about Critical thinking and also numerous teaching practices to implement it. We’d like to have your views on this. Please share with us in the comment box.

Problem solving:

Einstein's problem-solving formula:

Jeffrey Phillips, an author and an innovation consultant, once shared “When asked how he would spend his time if he was given an hour to solve a thorny problem, (Einstein) said he'd spend 55 minutes defining the problem and alternatives and 5 minutes solving it. Which is exactly opposite of what the vast majority of executives today would do.”

Educational institutions must realize the fact that thinking of different alternatives helps student improves his problem solving skills rather than teaching him a unique procedure to tackle a problem.

‘Asking “Why” 5 times’ can find the root of any problem:

When students learn at higher pace, they’ll experience many challenges and they need to tackle different situations. Let me explain the basic model of this approach:


For example, if you failed to answer a Math problem, ask these questions.

  1. Why didn’t I answer the question? ( Because I didn’t get sufficient time )
  2. Why it took longer time? (Because the concept was very difficult for me)
  3. Why it was difficult only for me? (Because I got stuck at a certain step)
  4. Why I got stuck particularly at that step? (Because I didn’t practice it)
  5. Why didn’t I practice it? ( Because I thought I could do it easily without practice)

Teaching them “How to Code” improves problem solving skills:

Bill Gates once said, “Everybody in this country should learn how to program a computer, because it teaches how to think.” The main reason why young students should be encouraged to learn coding is because it’s a basic computer literacy which helps them understand the logic and challenges behind this digital world.

LeighMarburyNichols, a Math educator, suggests other educators to encourage students to ask questions, answer each and every query of them clearly with patience. Students should get all their questions clarified; this is the best way to improve their problem solving and critical thinking skills.

The above mentioned are the few teaching methodologies to improve problem solving and critical thinking skills. We’d like to have more practices that improve students’ problem solving and critical thinking skills. Please feel free add your views in the comment box. 

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Devotee of Dr. Abdul Kalam. Following his path of Creating Creative Education in India. Contributing my works in "India Vision 2020". Former EdTech Blogger/Researcher at ETR India
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