## Critical Thinking In Mathematics Education

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 21^{st} century education.

21^{st} 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, “21^{st} century skills”.

Let’s have a glance at the list of 21^{st} 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 21^{st} century students are required to have. It’s difficult to cover the information about all the 21^{st} century skills in one guide so I’m writing this guide with focus more on two important 21^{st} century skills, Critical thinking and Problem solving. As we know 21^{st} 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. 21^{st} 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. 21^{st} 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 21 ^{st} 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:

**Students:**

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

- Why didn’t I answer the question? ( Because I didn’t get sufficient time )
- Why it took longer time? (Because the concept was very difficult for me)
- Why it was difficult only for me? (Because I got stuck at a certain step)
- Why I got stuck particularly at that step? (Because I didn’t practice it)
- 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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*What** is critical and creative thinking, and why is it so important in mathematics and numeracy education? *

Numeracy is often defined as the ability to apply mathematics in the context of day to day life. However, the term ‘critical numeracy’ implies much more. One of the most basic reasons for learning mathematics is to be able to apply mathematical skills and knowledge to solve both simple and complex problems, and, more than just allowing us to navigate our lives through a mathematical lens, being numerate allows us to make our world a better place.

The mathematics curriculum in Australia provides teachers with the perfect opportunity to teach mathematics through critical and creative thinking. In fact, it’s mandated. Consider the core processes of the curriculum. The Australian Curriculum (ACARA, 2017), requires teachers to address four proficiencies: Problem Solving, Reasoning, Fluency, and Understanding. Problem solving and reasoning require critical and creative thinking (). This requirement is emphasised more heavily in New South wales, through the graphical representation of the mathematics syllabus content , which strategically places Working Mathematically (the proficiencies in NSW) and problem solving, at its core. Alongside the mathematics curriculum, we also have the General Capabilities, one of which is Critical and Creative Thinking – there’s no excuse!

**Critical and creative thinking need to be embedded in every mathematics lesson**. **Why?** When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.

*How** and when do we embed critical and creative thinking? *

There are many tools and many methods of promoting thinking. Using a range of problem solving activities is a good place to start, but you might want to also use some shorter activities and some extended activities. Open-ended tasks are easy to implement, allow *all* learners the opportunity to achieve success, and allow for critical thinking and creativity. Tools such as Bloom’s Taxonomy and Thinkers Keys are also very worthwhile tasks. For good mathematical problems go to the nrich website. For more extended mathematical investigations and a wonderful array of rich tasks, my favourite resource is Maths300 (this is subscription based, but well worth the money). All of the above activities can be used in class and/or for homework, as lesson starters or within the body of a lesson.

*Will critical and creative thinking take time away from teaching basic concepts?*

No, we need to teach mathematics in a way that has meaning and relevance, rather than through isolated topics. Therefore, teaching *through* problem-solving rather than *for* problem-solving. A classroom that promotes and critical and creative thinking provides opportunities for:

- higher-level thinking within authentic and meaningful contexts;
- complex problem solving;
- open-ended responses; and
- substantive dialogue and interaction.

*Who** should be engaging in critical and creative thinking? *

Is it just for students? No! There are lots of reasons that teachers should be engaged with critical and creative thinking. First, it’s important that we model this type of thinking for our students. Often students see mathematics as black or white, right or wrong. They need to learn to question, to be critical, and to be creative. They need to feel they have permission to engage in exploration and investigation. They need to move from consumers to producers of mathematics.

Secondly, teachers need to think critically and creatively about their practice as teachers of mathematics. We need to be reflective practitioners who constantly evaluate our work, questioning curriculum and practice, including assessment, student grouping, the use of technology, and our beliefs of how children best learn mathematics.

Critical and creative thinking is something we cannot ignore if we want our students to be prepared for a workforce and world that is constantly changing. Not only does it equip then for the future, it promotes higher levels of student engagement, and makes mathematics more relevant and meaningful.

*How will you and your students engage in critical and creative thinking?*

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