What if you don’t need any math tutor or expert to solve problems for you or give you a detailed explanation for your better comprehension? Well, you may be thinking that this would be amazing. The good news is that it is now possible with online math problem solvers and smartphone applications. Whether you are a teacher or a student, now you can avail online math problem-solving websites and smartphone applications to determine the step-by-step answer to a complex problem. Teachers can even use these tools to develop math quizzes.

In this article, we have compiled a list of these websites that will help you to figure out the solution to any math problem.

It is a smart math problem solver which gives you a step-by-step solution to any math problem. Just type your question and press enter to reveal a detailed answer to your math problem.

It is a smartphone application which is also known as a camera calculator. All you have to do is take a picture of a math problem and upload it. This math app will scan the problem, solve it, and will display a detailed solution on your screen.

From algebra and trigonometry to statistics and calculus, Microsoft math solver provides you a free platform where you can not only get detailed solutions to your questions, but also other supporting materials such as interactive graphs, relevant practice problems, and online videos.

Cymath is a free application that gives a step-by-step solution to any math problem. This app does not give you the final answer only, rather the whole solution is broken down into steps for your understanding.

This math application that allows you to take a picture of a math problem, solves it intuitively, and displays answer on the screen. This app provides solutions to many math problems ranging from algebra to calculus. The best thing about this app is that it can recognize handwritten math problems too. Isn’t that cool?

Quick math provides quick solutions to students for all types of math problems, whether they are related to algebra, calculus, or matrices.

Symbolab is another amazing online website that gives you detailed solutions for any math problem related to algebra, trigonometry, and calculus.

It gives you full-time access to an online calculator or math solver where you can type any math question and get a detailed explanation along with the final answer.

]]>Critical thinking is a 21st-century skill that enables a person to think rationally and logically in order to reach a plausible conclusion. A critical thinker assesses facts and figures and data objectively and determines what to believe and what not to believe. Critical thinking skills empower a person to decipher complex problems and make impartial and better decisions based on effective information.

Critical thinking skills cultivate habits of mind such as strategic thinking, skepticism, discerning fallacy from the facts, asking good questions and probing deep into the issues to find the truth.

Acquiring critical thinking skills was never as valuable as it is today because of the prevalence of the modern knowledge economy. Today, information and technology are the driving forces behind the global economy. To keep pace with ever-changing technology and new inventions, one has to be flexible enough to embrace changes swiftly.

Today critical thinking skills are one of the most sought-after skills by the companies. In fact, critical thinking skills are paramount not only for active learning and academic achievement but also for the professional career of the students. The lack of critical thinking skills catalyzes memorization of the topics without a deeper insight, egocentrism, closed-mindedness, reduced student interest in the classroom and not being able to make timely and better decisions.

Certain strategies are more eloquent than others in teaching students how to think critically. Encouraging critical thinking in the class is indispensable for the learning and growth of the students. In this way, we can raise a generation of innovators and thinkers rather than followers. Some of the benefits offered by thinking critically in the classroom are given below:

- It allows a student to decipher problems and think through the situations in a disciplined and systematic manner
- Through a critical thinking ability, a student can comprehend the logical correlation between distinct ideas
- The student is able to rethink and re-justify his beliefs and ideas based on facts and figures
- Critical thinking skills make the students curious about things around them
- A student who is a critical thinker is creative and always strives to come up with out of the box solutions to intricate problems
- Critical thinking skills assist in the enhanced student learning experience in the classroom and prepares the students for lifelong learning and success
- The critical thinking process is the foundation of new discoveries and inventions in the world of science and technology
- The ability to think critically allows the students to think intellectually and enhances their presentation skills, hence they can convey their ideas and thoughts in a logical and convincing manner
- Critical thinking skills make students a terrific communicator because they have logical reasons behind their ideas

We have compiled a list of 11 activities that will facilitate you to promote critical thinking abilities in the students.

Divide students into teams and introduce each team with a hypothetical challenging scenario. Allocate minimum resources and time to each team and ask them to reach a viable conclusion using those resources. The scenarios can include situations like stranded on an island or stuck in a forest. Students will come up with creative solutions to come out from the imaginary problematic situation they are encountering. Besides encouraging students to think critically, this activity will enhance teamwork, communication and problem-solving skills of the students

It is a very flexible game that allows students to think creatively. To start this activity, divide students into groups. Give each group a limited amount of resources such as pipe cleaners, blocks, and marshmallows etc. Every group is supposed to use these resources and construct a certain item such as building, tower or a bridge in a limited time. You can use a variety of materials in the classroom to challenge the students. This activity is helpful in promoting teamwork and creative skills among the students.

It is also one of the classics which can be used in the classroom to encourage critical thinking. Print pictures of objects, animals or concepts and start by telling a unique story about the printed picture. The next student is supposed to continue the story and pass the picture to the other student and so on.

In this activity, you can ask students to identify a real-world problem in their schools, community or city. After the problem is recognized, students should work in teams to come up with the best possible outcome of that problem.

Make groups of three or four in the class. Ask them to drop an egg from a certain height and think of creative ideas to save the egg from breaking. Students can come up with diverse ideas to conserve the egg like a soft-landing material or any other device. Remember that this activity can get chaotic, so select the area in the school that can be cleaned easily afterward and where there are no chances of damaging the school property.

In this activity, the teacher can act as a facilitator and spark an interesting conversation in the class on any given topic. Give a small introductory speech on an open-ended topic. The topic can be related to current affairs, technological development or a new discovery in the field of science. Encourage students to participate in the debate by expressing their views and ideas on the topic. Conclude the debate with a viable solution or fresh ideas generated during the activity through brainstorming.

This project-based learning activity is best for teaching in the engineering class. Divide students into groups. Present a problem to the students and ask them to build a model or simulate a product using computer animations or graphics that will solve the problem. After students are done with building models, each group is supposed to explain their proposed product to the rest of the class. The primary objective of this activity is to promote creative thinking and problem-solving skills among the students.

This activity can be used in computer science, engineering or any of the STEM (Science, Technology, Engineering, Mathematics) classes. Introduce a variety of alternatives such as different formulas for solving the same problem, different computer codes, product designs or distinct explanations of the same topic.

Form groups in the class and ask them to select the best alternative. Each group will then explain its chosen alternative to the rest of the class with reasonable justification of its preference. During the process, the rest of the class can participate by asking questions from the group. This activity is very helpful in nurturing logical thinking and analytical skills among the students.

Present an article from a journal related to any topic that you are teaching. Ask the students to read the article critically and evaluate strengths and weaknesses in the article. Students can write about what they think about the article, any misleading statement or biases of the author and critique it by using their own judgments.

In this way, students can challenge the fallacies and rationality of judgments in the article. Hence, they can use their own thinking to come up with novel ideas pertaining to the topic.

In this activity, students will come up with their own questions. Make pairs or groups in the class and ask the students to discuss the questions together. The activity will be useful if the teacher gives students a topic on which the question should be based.

For example, if the teacher is teaching biology, the questions of the students can be based on reverse osmosis, human heart, respiratory system and so on. This activity drives student engagement and supports higher-order thinking skills among students.

Silence is a great way to slow down thinking and promote deep reflection on any subject. Present a driving question to the students and divide them into groups. The students will discuss the question with their teammates and brainstorm their ideas on a big paper. After reflection and discussion, students can write their findings in silence. This is a great learning activity for students who are introverts and love to ruminate silently rather than thinking aloud.

]]>**Neuroplasticity** also known as brain plasticity is a field in neuroscience that is closely associated with the growth mindset. Neuroplasticity is a process by which our brain can alter its synaptic networks as a result of learning, the experience of an injury. According to neuroscientists, neuroplasticity is a lifelong process and our brain can grow new neurons at any age through stem cells.

What does it mean in our life? It means that if you are not good at something, you can train your brain to become the best at that thing through effort. Isn’t that amazing?

A **growth mindset** basically encourages us that nothing is impossible in this world and success comes through hard work, persistence and determination instead of gifted and inborn talents of an individual.

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Contrary to the growth mindset, the fixed mindset is of the view that a person’s talents are fixed and set in stone. They cannot be enhanced through learning and experiences. A fixed mindset denies the importance of a person’s effort to improve himself.

For educators, the growth mindset is an asset as it can lead to higher academic achievement and test scores of students. We know that every student has distinctive mental abilities and innate talents, however with effort students can acquire a higher mental ability in any subject. A teacher plays a fundamental role in transforming the fixed mindset of the student. Teachers can adopt different strategies in the class to motivate students and instill a growth mindset among them.

Studies show that growth mindset offers the following benefits to the students:

- Students with a growth mindset respond positively to feedback and constructive criticism.
- A growth mindset changes their attitude towards learning and effort because for them failure is just a step towards a greater success.
- They continuously improve and regulate themselves and they are not apprehensive of the change. We know that change is inevitable for success. Hence, students with a growth mindset are likely to be more successful in their fields than students with a fixed mindset.
- The dropout rate of students with a growth mindset is lower than the students having a fixed mindset.
- Students with a growth mindset face new challenges head on and are more innovative.
- A growth mindset reduces stress and anxiety and helps in emotional well-being of the students.
- It enhances self-esteem among the students and makes them more confident.

The people who inspired the world by their outstanding work in their fields have some great things to say about the growth mindset. Let’s explore some inspirational quotes on a growth mindset that will inspire you to try, learn, evolve and succeed.

*Love challenges, be intrigued by mistakes, enjoy the effort and keep on learning. Carol Dweck*

*Don’t worry about failure. Worry about the chances you miss when you don’t even try. – Sherman Finesilver*

*Great works are performed, not by strength, but by perseverance. Samuel Johnson*

*Whether you think you can or you think you can’t, you‘re right. Henry Ford*

*A person who never made a mistake never tried anything new. Albert Einstein*

*Nothing is impossible, the word itself says ‘I’m possible’. Audrey Hepburn*

*I hated every minute of training, but I said, ‘Don’t quit. Suffer now and live the rest of your life as a champion.’ Muhammad Ali*

*Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. Thomas Edison*

*Don’t worry about failure. Worry about the chances you miss when you don’t even try. Sherman Finesilver*

*Effort is grossly underrated. Gary Vaynerchuk*

*Education is not the learning of facts, but the training of the mind to think. Albert Einstein *

*Just because you haven’t found your talent doesn’t mean you don’t have one. Kermit the Frog*

*There is no failure. Only feedback. Robert Allen*

*It’s not that I’m so smart, it’s just that I stay with problems longer. Albert Einstein*

*It is impossible to live without failing at something unless you live so cautiously that you might as well not have lived at all. In which case, you fail by default. J.K Rowling*

*Stop being afraid of what could go wrong and start being excited about what could go right. Anonymous*

*In a growth mindset, challenges are exciting rather than threatening. So, rather than thinking, ‘Oh, I am going to reveal my weakness, you say, wow here’s a chance to grow. Carol Dweck*

*All things are difficult before they are easy. Thomas Fuller*

*The very best thing you can do for the whole world is to make the most of yourself. Wallace Wattles*

*Genius is one percent inspiration and ninety-nine percent perspiration. Thomas Edison*

*I haven’t failed. I have just found ten thousand ways that don’t work. Thomas Edison*

*Success comes from knowing that you did your best to become the best that you are capable of being. John Wooden*

*Most of the important things in the world have been accomplished by people who have kept on trying when there seemed no hope at all. Dale Carnegie*

*If you are facing a new challenge or being asked to do something that you have never done before don’t be afraid to step out. You have more capability than you think you do but you will never see it unless you place a demand on yourself for more. Joyce Meyer*

*Always do what you are afraid of doing. Ralph Waldo Emerson*

*Most of the important things in the world have been accomplished by people who have kept on trying when there seemed no hope at all. Dale Carnegie*

*If parents want to give their children a gift, the best thing they can do is to teach their children to love challenges, be intrigued by mistakes, enjoy effort, and keep on learning. That way, their children don’t have to be slaves of praise. They will have a lifelong way to build and repair their own confidence. Carol Dweck*

*If you find a path with no obstacles. It probably doesn’t lead anywhere. Frank A Clark*

*If you quit once, it becomes a habbit. Don’t quit. Michael Jordon*

*It does not matter how slowly you go so long as you do not stop. Confucius*

*Patience, persistence and perspiration make an unbeatable combination for success. Napoleon Hill*

*It takes courage to grow up and become who you really are. E.E Cummings*

*It’s hard to beat a person that never gives up. Babe Ruth*

*A challenge only becomes obstacle when you bow to it. Ray Davis*

*The only thing that overcomes hard luck is hard work. Harry Golden*

*Effort is one of those things that gives meaning to life. Effort means you care about something, that something is important to you and you are willing to work for it. Carol Dweck*

*If people knew how hard I had to work to gain my mastery, it would not seem so wonderful at all. Michelangelo*

*Twenty years from now you will be more disappointed by the things you did not do than by the ones you did. Mark Twain*

*There is no failure. Only feedback. Robert Allen*

*Believe you can…. and you are halfway there. Theodore Roosevelt*

*Progress is impossible without change and those who cannot change their minds cannot change anything. George Bernard Shaw*

*There are better starters than me, but I am a strong finisher. Usain Bolt*

*Failure is so important. It is the ability to resist failure or use failure than often leads top greater success. J.K. Rowling*

*Becoming is better than being. Carol Dweck*

*Would you like me to give you a formula for success? It’s quite simple, really. Double your rate of failure. Thomas Watson*

*The expert at anything was once a beginner. Helen Hayes*

*Growth in painful. Change is painful. But nothing is as painful as staying somewhere you don’t belong. Mandy Hale*

*No problem can withstand the assault of sustained thinking. Voltaire*

*You can achieve anything you want in life if you have the courage to dream it, the intelligence to make a realistic plan, and the will to see that plan through to the end. Sidney A. Friedman*

Here, a, b and c are constants and x is a variable. The leading coefficient of quadratics should be non zero. If we set the above quadratic equation equal to 0, we will get a quadratic formula.

Unlike linear equations, graphing quadratic equations in a graphing calculator will yield a parabola.

Some examples of quadratic functions are given below:

If the leading coefficient in a quadratic equation is not given like in this equation below, then we assume that its coefficient is 1.

There are multiple methods for solving quadratic functions. It is important to choose the correct method based on the question.

- First, we try to solve the equation by factoring because it is the simplest method to get the values of x.
- If we can’t solve by factoring, then we see if the equation is a perfect square or not. If so, we find the value of x by taking the square root on both sides of the equation. Be careful with plus-minus signs after taking the square roots.
- If the leading coefficient is 1 and the middle term of the quadratic function is even, we can solve the equation by completing the square method.
- If you are unable to solve the equation through any of the above methods, then try using the quadratic formula.

In this article, we will only discuss how to factor quadratic equations and find the zeros and roots through factorization.

Before proceeding to examples, let us see how to solve quadratic equations by factoring.

**Step 1** – Multiply the constant with the leading coefficient.

**Step 2** – Expand the middle term bx into two terms in such a way that the addition or subtraction of two terms is equal to the midterm and the multiplication of expanded terms is equal to the product obtained in step 1.

**Step 3 **– You will have four terms now. Factor the terms by grouping and write the final answer as a product of two binomial terms. Binomials are polynomial functions constituted of two terms only.

Solve the following quadratic equation through factorization.

**Solution**

**Step 1** – Multiply first term with the constant to get -42 x ^ {2}.

**Step 2** – Expand the midterm -x into two terms in such a way that adding or subtracting two terms will be equal to -x and their product is equal to -42 x ^2.

**Step 3 **– Group the first and second, and third and fourth terms together and find the greatest common factor between them in pairs.

Hence, the factors of the quadratic equation are (x – 7) (x + 6). Let us use these factors to find zeroes or roots of the function. Set these factors equal to zero:

(x – 7) (x + 6) = 0

According to zero product property, either x – 7 = 0 or x + 6 = 0. Solve for x by taking -7 and 6 to the right hand side of the equations. Hence, x = 7 or x = - 6. The numbers 7 and -6 are the roots of the above quadratic polynomial equation.

Solve the following quadratic equation by factoring.

**Solution**

Follow the following steps for solving the equation by factoring.

**Step 1** – Multiply the constant term -3 by the leading term of the equation to obtain the product -6 x ^2.

**Step 2** – Expand the midterm +5x into two terms in such a way that adding or subtracting two terms will be equal to +5x and their product is equal to -6 x ^ {2}.

Step 3 – Group the first and second, and third and fourth terms together and find the greatest common factor between them in pairs.

=2x (x +3) -1 ( x + 3)

=(x -1) (x + 3)

Now, we have the factors of the polynomial, let us find the roots of the polynomial by applying the zero product property.

(2x – 1)(x + 3) = 0

Set individual factors equal to zero and solve for x by taking constants to the right-hand side of the equation.

2x – 1 = 0, x =1/2

x + 3 = 0 , x = -3

Hence, 1/2 and -3 are the roots of the quadratic equation.

Follow the steps below to solve it by factoring.

**Step 1 **– Multiply -2 by the first term 5x ^ 2 to obtain the product -10 x ^2.

**Step 2** – Expand the second term -9x into two terms in such a way that when we add or subtract two terms, the result will be equal to -9x and the product will be -10 x ^2.

Step 3 – Group the first and second, and third and fourth terms together and find the greatest common factor between them in pairs.

= 5x (x - 2) + 1 ( x - 2)

= (5x + 1) (x - 2)

Now, we have the factors of the polynomial, let us find the roots of the polynomial by applying the zero product property.

(5x + 1) (x – 2) = 0

5x + 1 = 0, x = -1/5

x – 2 =0, x = 2

Hence, the roots of the polynomial are -1/5 and 2.

**Solution**

**Step 1** – To factorize the quadratic expression, multiply -18 by the first term x ^ 2 to obtain the product -18 x ^2.

**Step 2** – Expand the midterm -3x into two terms in such a way that adding or subtracting two terms will be equal to -3x and their product is equal to -18 x ^2.

**Step 3** – Group the first and second, and third and fourth terms together and find the greatest common factor between them in pairs.

=x (x - 6) +3 ( x - 6)

= (x - 6) (x + 3)

Now, we have the factors of the polynomial, let us find the roots of the polynomial by applying the zero product property.

(x - 6) (x + 3) = 0

x - 6 = 0, x = 6

x + 3 =0, x = -3

Hence, the roots of the polynomial are -3 and 6.

**Solution**

Step 1 – Multiplying -40 by the first term x ^ 2 will give us -40 x ^2.

**Step 2** – Expand the midterm +3x into two terms in such a way that adding or subtracting two terms will be equal to +3x and their product is equal to -40 x ^2.

**Step 3** – Group the first and second, and third and fourth terms together and find the greatest common factor between them in pairs.

=x (x + 8) - 5 ( x + 8)

=(x + 8) (x - 5)

(x + 8) (x - 5) = 0

x + 8 = 0, x = -8

x - 5 =0, x = 5

Hence, the roots of the polynomial are -8 and 5.

**Solution**

**Step 1** – To factorize the given equation, -1 will be multiplied by the first term 3x ^ 2 will give us -3 x ^2.

**Step 2 **– Expand the midterm -2x into two terms in such a way that adding or subtracting two terms will be equal to -2x and their product is equal to -3 x ^2.

Step 3 – Group the first and second, and third and fourth terms together and find the greatest common factor between them in pairs.

=3x (x - 1) + 1 ( x - 1)

=(x - 1) (3x + 1)

(3x+1) (x - 1) = 0

3x + 1 = 0, x = -1/3

x - 1 =0, x = 1

Hence, the roots of the polynomial are -1/3 and 1.

**Solution**

**Step 1** – To solve this equation, -12 will be multiplied by the first term to get -24 x ^2.

**Step 2** – Expand the midterm -2x into two terms in such a way that adding or subtracting two terms will be equal to -2x and their product is equal to -24 x ^2.

**Step 3 **– Group the first and second, and third and fourth terms together and find the greatest common factor between them in pairs.

=2x (x - 3) + 4 ( x - 3)

=(x - 3) (2x + 4)

(2x + 4) (x - 3) = 0

2x + 4 = 0, x = -4/2 = -2

x - 3 =0, x = 3

Hence, the 3 and -2 are the roots of a quadratic equation. It means that when these roots are substituted in the original equation, the result will be zero.

**Solution**

**Step 1** – To solve the equation by factoring, the first term and the constant -30 will be multiplied together to get 30 x ^ 2

**Step 2** – Expand the midterm 11x into two terms in such a way that adding or subtracting two terms will be equal to 11x and their product is equal to 30 x ^2.

**Step 3** – Group the first and second, and third and fourth terms together and find the common factors between them in pairs.

=x (x + 5) + 6 ( x + 5)

=(x + 5) (x + 6)

(x + 5) (x + 6) = 0

x + 5 = 0, x = -5

x + 6 =0, x = -6

Hence, the -5 and -6 are the roots of a quadratic equation. It means that by substituting these roots in the original polynomial function we will get the result zero.

**Solution**

**Step 1** – By multiplying the first term and the constant -2 we will get -30 x ^ 2

**Step 2** – Expand the midterm +x into two terms in such a way that adding or subtracting two terms will be equal to +x and their product is equal to -30 x ^2.

**Step 3** – Group the first and second, and third and fourth terms together and find the common factors between them in pairs.

=3x (5x + 2) - 1 (5 x + 2)

=(5x + 2) (3x - 1)

(5x + 2) (3x - 1) = 0

5x + 2 = 0

Solve the terms algebraically by taking 2 on the right hand side of the equation and then dividing it by 5

x = -2/5

3x - 1 =0

Take -1 on the right-hand side and divide it by 3 to isolate x on the left-hand side of the equation:

x = 1/3

Hence, the 1/3 and -2/5 are the roots of a quadratic equation. It means that substituting these roots in the original polynomial function will yield zero.

**Solution**

**Step 1** – To solve equation, the first term and the constant +2 will be multiplied together to get 8 x ^ 2

**Step 2** – Expand the second term +6x into two terms in such a way that adding or subtracting two terms will be equal to +6x and their product is equal to 8 x ^2.

**Step 3** – Group the first and second, and third and fourth terms together and find the common factors between them in pairs.

=4x (x + 1) + 2 ( x + 1)

=(x + 1) (4x + 2)

Now, we have the equation in factored form, let us find the roots of the polynomial by applying the zero product property.

(4x + 2) (x + 1) = 0

4x + 2 = 0, x = -1/2

x + 1 =0, x = -1

Hence, - 1 and -1/2 are roots of a quadratic equation. It means that substituting these roots in the original polynomial function will yield zero.

Hope you liked the article. We at Educationise are passionate about education and you can contact us if you want us to develop educational materials especially customized according to your needs. Quality, communication and deadlines are the cornerstone of our business. We have wide range of experience of working on educational projects and we aim to deliver the highest quality output.

]]>Project-based learning is a student-centered pedagogy used in the classrooms in which students acquire in-depth knowledge and skills by solving real-world challenges.

This pedagogical approach can be called as **inquiry-based learning** or **learning by doing **because it supports deep learning by engaging students in hands-on learning activities. For educators, it is one of the most effective teaching methods and for students, no method of learning offers more benefits in terms of active learning than the PBL approach.

PBL does not engage students in a project for an hour or a day, but it entails active participation for a longer period to build meaningful products or find an answer to a complex question. However, it doesn’t imply that no schedule is followed in PBL, because it may stretch from a week to a whole semester.

Project-based learning helps students to learn how to work in teams and encourages them to use their creative, problem solving and critical thinking skills to come up with innovative solutions and products for real life audience.

You might be wondering how to implement the PBL approach in the classroom. Well, we have you all figured out in the next section of this article.

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The six steps of project-based learning are shown in the following flow chart and explained below in this section of the article.

This is the leading step in project-based learning. Teachers or students identify a problem or an opportunity from their surroundings that requires meticulous work and demands a resolution. This problem can be related to the curriculum and may be affecting the school, community, city or a country.

This is an inquiry-based step that requires great attention to detail and group work because the learning goals of students will be based on the precise mapping of the driving problem statement. Brainstorming and bloom’s taxonomy will assist you in this step to formulate the driving question.

The next step is to design a learning plan for the project which means that the teachers assess how the problem or opportunity connects with the standards he/she is intending to teach. The best approach is to involve the students in this process so that they can feel included.

Select the project path which corresponds to the syllabus or curriculum. It is better to integrate multiple subjects for enhanced student engagement and dynamic learning. Make sure that the learning resources and content are at the students’ disposal while they are working on the project. A teacher should be prepared to provide deep content knowledge to the students because the project can move in any direction and students may require a deeper understanding of the concepts to reach a viable conclusion.

This is the third step of the PBL which involves setting a timeline and schedule for the project activities. Students should be given a set date or time frame in which they had to present their final project work. However, to realize the benefits of the whole process, be prepared to be flexible in your schedule. Set the schedule by working collaboratively with students.

In PBL, a teacher is engaged in the process right from the beginning to the end. Teachers should incessantly monitor student work and progress. The role of the teacher in PBL is that of a facilitator who strives to make the learning experiences worthwhile for the students.

This is the fifth step of the PBL, and it involves assessing the learning outcomes and participation of students. Teachers can use a rubric to record students’ progress and their learning outcomes.

Rubrics allow teachers to grade student learning against certain standards and give effective feedback to the individual student at the end of the project. The assessment helps students in enhancing their skills and thus increases their confidence. Besides teachers, experts and the audience can also be consulted to give feedback.

This is the last step in PBL which involves reflecting what worked and what didn’t during the whole process. Reflection helps teachers to improve their instructional strategies in the future. Teachers are also able to incorporate changes in their teaching strategies.

We all have done projects during our academic life in colleges and universities. So, you might be thinking that PBL is like doing a project. But it’s not the case as both are fundamentally different. Some differences between the projects and PBL are explained below:

1. The main difference between the project and project-based learning is that projects are components of the course and they are not intended to teach students the content of the course. Rather students are expected to use their content knowledge that they acquired during the course to do a project. On the other hand, in project-based learning, the main intention is to transfer content knowledge through projects.

2. The audience of the project is the class fellows of students or their school, while PBL is intended for the real-world audience.

3. Projects are submitted to the teacher for grades, whereas projects done under PBL are published for real-world audiences.

4. Projects can be done at home or in school, whereas PBL emphasizes collaborative learning, teamwork and communication.

5. The teacher is involved in projects after the project has ended. In PBL, the teacher is involved right from the beginning to the end.

6. The project follows the teacher’s guidelines, whereas PBL is based on real-world challenges and questions.

7. While doing projects, the student’s mindset is of a student who is completing his/her coursework. On the other hand, during project-based learning student assumes a greater responsibility which is beyond the school setting because he/she is solving the real-world challenges.

8. The projects are closed-ended, i.e. they have the same outcome. On the other hand, the PBL is open-ended which means its outcome is not pre-determined, and students can adopt any research path to come up with a conclusion. They may even surprise their teacher by inventing or discovering a new path, model or product.

Project-based learning is gaining momentum worldwide as more and more educators are taking interest to incorporate this approach in their classroom because of the numerous benefits it offers to the students. We have narrowed down the following 8 benefits of project-based learning.

- PBL emphasizes teamwork and effective collaboration between the team members working on the projects. When students work cohesively as a unit to solve a real-world problem, their interpersonal and communication skills are enhanced.
- PBL supports problem-based learning and helps students to think critically. Consequently, it unleashes and polishes the problem-solving skills of the students. Since students are working on problems that affect the real-world audience, their 21st-century skills like critical thinking and problem-solving are significantly enhanced.
- PBL is an activity-based approach that supplements higher order thinking skills among students.
- Project based learning facilitates deep learning of the students. Learning through textbooks and other resources in a traditional classroom is a trivial concept now.
- PBL instills self-confidence in the students. Students engage in the learning process and voice their opinions during the phases of PBL. When the student voice and choice are valued, his/her self-confidence is enhanced.
- PBL leads to enhanced student engagement. When students are gaining knowledge practically, their natural curiosity and interest in the subject matter increase. As a result, we see a greater student achievement in academic which can be measured through variables such as higher attendance in the classroom, increased interest and improvement in grades
- Students gain a deeper understanding of the technological tools which help them to achieve their intended learning objectives.
- PBL enhances the decision-making skills of the students because they had to take critical decisions during the course of projects regarding the research path and tools which should be used to reach an effective outcome.
- We know that every individual is unique and has his/her own strengths and weaknesses. PBL helps teachers to judge the students’ abilities, strengths, and weaknesses which are often overlooked in the other assessment methodologies.
- Students learn valuable lessons in PBL for a lifetime. In other words, PBL supplements the lifelong learning of the students.

*'Learning is the only thing the mind never exhausts, never fears, and never regrets.' –Leonardo Di Vinci*

*'Once you stop learning, you start dying' – Albert Einstein*

*'The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires.' – William Arthur Ward*

*'The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn.’ – Alvin Toffler*

*'In times of change, learners inherit the earth; while the learned find themselves beautifully equipped to deal with a world that no longer exists.' – Eric Hoffer
*

*'Tell me and I forget, teach me and I may remember, involve me and I learn.' – Benjamin Franklin*

*‘You don’t learn to walk by following rules. You learn by doing, and by falling over.’ – Richard Branson*

*'In an effective classroom, students should not only know what they are doing. They should also know why and how.' – Harry Wong*

*'You can teach a student a lesson for a day; but if you can teach him to learn by creating curiosity, he will continue the learning process as long as he lives.' – Clay P. Bedford*

*'Any fool can know. The point is to understand.' – Albert Einstein*

*'I am still learning' – Michelangelo*

*'Study while others are sleeping, work while others are loafing, prepare while others are playing and dream while others are wishing.' – William Arthur Ward*

*'Curiosity is the wick in the candle of learning.' – William Arthur Ward*

*'Education breeds confidence. Confidence breeds hope. Hope breeds peace.' – Confucius*

*'Anyone who stops learning is old, whether at twenty or eighty. Anyone who keeps learning stays young.' – Henry Ford*

*'Learning is a treasure that will follow its owner everywhere.' –Chinese Proverb*

*'Formal education will make you a living. Self-education will make you a fortune.' – Jim Rohn*

*'Continuous learning is the minimum requirement for success in any field.' – Brian Tracy*

*'We now accept the fact that learning is a lifelong process of keeping abreast of change. And the most pressing task is to teach people how to learn.' – Peter Drucker
*

*‘Being ignorant is not so much a shame, as being unwilling to learn.’ – Benjamin Franklin*

*'It’s what you learn after you know it all that counts.' – John Wooden*

*'Learn as if you were not reaching your goal and as though you were scared of missing it'*

*– Confucius*

*'Making mistakes simply means you are learning faster.' –Anonymous*

*'The purpose of learning is growth, and our minds, unlike our bodies, can continue growing as we continue to live.' – Mortimer Adler*

*'Change if the end result of all true learning' – Leo Buscaglia*

*'If learning is an act of exploration, then technology equips the explorer for the journey of a lifetime.' Anonymous*

*'Shall I tell you a secret of **a true scholar**? It is this: Every man I meet is my master in some point, and in that, I learn from him.' – Ralph Waldo Emerson*

*'Intellectual growth should commence at birth and cease only at death' – Albert Einstein*

*'Learning is not compulsory….neither is survival '– W Edward Deming*

*'The beautiful thing about learning is that nobody can take it away from you.'*

*– B.B. King*

*'Your most unhappy customers are your greatest source of learning' – Bill Gates*

*'The wisest mind has something yet to learn' – George Santayana*

*'An organization’s ability to learn, and translate that learning into action rapidly, is the ultimate competitive advantage' – Jack Welch*

*'Education is not the learning of facts, but the training of the mind to think' – Albert Einstein*

*'I never learned from a man who agreed with me.' – Robert A. Heinlein*

*'Leadership and learning are indispensable to each other.' – John f. Kennedy*

*'Personally, I am always ready to learn, although I do not always like being taught' – Winston Churchill*

*'There is divine beauty in learning…. To learn means to accept the postulate that life did not begin at my birth. **Others have been here before me**, and I walk in their footsteps.' – Elie Wiesel*

*'The only real mistake is the one from which we learn nothing '– Henry Ford*

*'Learning and innovation go hand in hand. The arrogance of success is to think that what you did yesterday will be sufficient for tomorrow.' – William Pollard*

*'Play is the highest form of research' – Albert Einstein*

*'A man who asks is a fool for five minutes. A man who never asks is a fool for life.' – *

*Chinese Proverb *

*'If a person will spend one hour a day on the same subject for five years, that person will be an expert on that subject.' – Earl Nightingale*

*'Learning is not attained by chance. It must be sought for with ardor and attended to with diligence.' – Abigail Adams*

*'Don't let your learning lead to knowledge. Let your learning lead to action.' – Jim Rohn*

*'The world is a university and everyone in it is a teacher. Make sure when you wake up in the morning, you go to school.' –T. D. Jakes*

*'Learning is experience. Everything else is just information' – Albert Einstein*

*‘Ideas without action aren’t ideas. They’re regrets.' – Steve Jobs*

*'It is what we know already that often prevents us from learning' – Claude Bernard*

*'What are learners supposed to do after learning the course? Figure that out and build the appropriate interactive element.' – Tom Kuhlmann*

*'Knowledge isn’t power until it is applied '– Dale Carnegie*

*'You learn more from failure than from success. Don’t let it stop you. Failure builds character'– Anonymous*

*'Love challenges, be intrigued by mistakes, enjoy the effort and keep on learning' – Carol Dweck*

*'Leaning without thought is labour lost' – Confucius*

*'I never lose. I either win or learn.' – Nelson Mandela*

*'There is no end to education. It is not that you read a book, pass an examination, and finish with education. The whole of life, from the moment you are born to the moment you die, is a process of learning.' – Jiddu Krishnamurti*

*'Educating the mind without educating the heart is no education at all '– Aristotle*

*'The only things worth learning are the things you learn after you know it all.' – Harry S Truman
*

*'The goal of early childhood education should be to activate the child’s own natural desire to learn' – Maria Montessori*

*'The noblest pleasure is the joy of understanding' – Leonardo da Vinci*

*'He who learns but does not think is lost! He who thinks but does not learn is in great danger' – Confucius*

*'A man only learns in two ways, one by reading, and the other by association with smarter people.' – Will Rogers
*

*'Prepare for the unknown by studying how others in the past have coped with the unforeseeable and the unpredictable.' – George S. Patton
*

*'I never learn anything talking. I only learn things when I ask questions.' – Lou Holtz*

*'It is only when we forget all our learning that we begin to know.' – Henry David Thoreau*

*'Aim for success, not perfection. Never give up your right to be wrong, because then you will lose the ability to learn new things and move forward with your life. Remember that fear always lurks behind perfectionism.'– David M. Burns
*

*'The first problem for all of us, men and women, is not to learn, but to unlearn.' – Gloria Steinem*

*'You teach best what you most need to learn.' – Richard Bach
*

*'The things that have been most valuable to me I did not learn in school.' – Will Smith
*

*'It has been said that 80% of what people learn is visual.' – Allen Klein
*

*'Learning is the beginning of wealth. Learning is the beginning of health. Learning is the beginning of spirituality. Searching and learning is where the miracle process all begins.' – Jim Rohn*

*'The only real progress lies in learning to be wrong all alone.' – Albert Camus
'There are no secrets to success. It is the result of preparation, hard work, and learning from failure.' – Colin Powell*

*'Each life is made up of mistakes and learning, waiting and growing, practicing patience and being persistent.' – Billy Graham*

*'Teaching is only demonstrating that it is possible. Learning is making it possible for yourself '– Paulo Coelho*

*'In those parts of the world where learning and science have prevailed, miracles have ceased; but in those parts of it, as are barbarous and ignorant, miracles are still in vogue.' –Ethan Allen
*

*'We do not learn, and what we call learning is only a process of recollection.' – Plato
*

*'I'm learning all the time. I'm evolving all the time as a human being. I'm getting better, I hope, in all of the important ways.' – Neil Peart
*

*'The only person who is educated is the one who has learned how to learn …and change.' –
Carl Rogers*

Bloom’s taxonomy is a hierarchical order of learning objectives that educators set for their students

It is widely used in education and is also branded as the Taxonomy of Educational Objectives. It facilitates the teachers to achieve their teaching objectives by setting goals for the student learning and then creating assessments to observe the learning outcomes. The use of bloom’s taxonomy is widespread among educators as it helps them in:

- Creating lesson plans, learning activities and instructional strategies based on the complexity of the subject matter
- Curriculum mapping and designing courses
- Creating assessments to measure the learning outcomes of the students

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Bloom’s taxonomy is named after Benjamin Bloom - an educational psychologist at the University of Chicago who chaired the committee which proposed bloom’s taxonomy in 1956. The committee proposed the following three domains of learning.

**Cognitive:**It corresponds to the mental abilities of a person. It is divided into six learning objectives which are explained below in this article in detail.**Affective:**It involves emotional areas and growth in feelings. Like cognitive domain, this level comprises of five categories. These five categories are receiving, responding, valuing, organization and characterization.**Psychomotor:**Psychomotor domain encompasses physical or manual skills which require practice. These skills are measured against factors such as speed, precision, distance, procedures, or techniques in execution.

Bloom’s committee originally proposed five learning levels of the cognitive process which were ranked in the order of their complexity. However, in 2001 it was revised to incorporate the 6th level. These 6 levels are used by the teachers all over the world to formulate curriculum, lesson plans, learning standards or objectives and assessments for courses.

Originally it was proposed to devise a common teaching language for educators so that they can communicate learning and assessment methods with each other. The primary goal of bloom’s taxonomy is to create a higher-level thinking and skills among students starting from the most basic level.

The six levels of learning proposed by Bloom’s taxonomy are explained below along with the 30 examples of learning goals and objectives for teachers.

It is the lowest level of bloom’s taxonomy hierarchical model which encompasses the ability to recall the learned information. Before a student can understand a concept, he must be able to recall the information. Common teaching or learning methods used at this knowledge level are lectures, book reading, online resources, memorization and watching videos.

**Examples Of Learning Objectives**

- By the end of this lesson, students will be able to
**define**acceleration. - By the end of this lesson, students will be able to
**outline**various stages of design thinking. - By the end of this lesson, students will be able to
**label**different parts of the human brain. - By the end of this lesson, students will be able to
**list**various kinds of loops in javascript. - By the end of this lesson, students will be able to
**name**different parts of nervous system

The next level is comprehension. At this stage, students are able to understand, interpret and summarize the concepts learned in the knowledge phase in their own words. The most common methods for teaching and learning at this stage are charts, graphs, discussion, reading material, and presentations.

**Examples Of Learning Objectives**

- By the end of this lesson, students will be able to
**explain**how sensory receptors in our brain detect stimuli. - By the end of this lesson, students will be able to
**recognize**different types of number sequences. - By the end of this lesson, students will be able to
**explain**how the heart pumps blood throughout our body. - By the end of this lesson, students will be able to
**distinguish**between mass and weight. - By the end of this lesson, students will be able to
**discuss**the factors that affect the solubility of a liquid.

**3. Apply**

At this stage, students are able to apply facts, ideas, and concepts into another context.

**Examples Of Learning Objectives**

- By the end of this lesson, students will be able to
**compute**their annual pocket money using this mathematical formula. - By the end of this lesson, students will be able to
**use**this accounting software for their annual family budget. - By the end of this lesson, students will be able to
**forecast**the annual revenue of any company using its past data. - By the end of this lesson, students will be able to
**demonstrate**how work in a diverse culture. - By the end of this lesson, students will be able to
**show**how to demonstrate emotional intelligence during an interview.

At this stage, students are finally able to break down the concepts into individual parts, think critically to draw a connection between the broken parts, analyze, draw inferences and make attributions.

**Examples Of Learning Objectives**

- By the end of this lesson, students will be able to
**differentiate**between differential and inferential statistics. - By the end of this lesson, students will be able to
**compare and contrast**prokaryotic and eukaryotic cells. - By the end of this lesson, students will be able to
**illustrate**how DNA code translates into RNA code. - By the end of this lesson, students will be able to
**analyze**information in the marketing research. - By the end of this lesson, students will be able to
**analyze**how leaves change colors during the fall season.

At this stage, students make judgments about the concepts, defend or criticize them based on certain criteria and standards.

**Examples Of Learning Objectives**

- By the end of this lesson, students will be able to
**explain**which kind of medicine is better for leukemia and why? - By the end of this lesson, students will be able to
**defend**their proposed hypotheses. - By the end of this lesson, students will be able to
**assess**the environmental impact of coal mining. - By the end of this lesson, students will be able to
**measure**the effectiveness of project-based learning. - By the end of this lesson, students will be able to
**appraise**the practice of social media advertising in business.

This is the last level of learning in Bloom’s taxonomy. At this stage, students can demonstrate their knowledge by applying the learned concepts to create something meaningful. It could involve developing an application or part of a machine, designing a website, creating a report or a video.

**Examples Of Learning Objectives**

- By the end of this lesson, students will be able to
**develop**an application for the Google play store. - By the end of this lesson, students will be able to
**create**financial statements in MS Excel. - By the end of this lesson, students will be able to
**compose**the scientific name of an organism. - By the end of this lesson, students will be able to
**come up**with the innovative ideas to tackle climate change. - By the end of this lesson, students will be able to
**make**their own battery charger.

Below are 180 plus examples of the bloom’s taxonomy action verbs which the educators can use while formulating the learning objectives for their courses.

**Knowledge:** order, mention, outline, illustrate, define, select, explain, match, recognize, locate, quote, list, describe, duplicate, recite, describe, tell, copy, identify, label, arrange, recollect, name, relate, recall, reproduce, state, read, state, memorize, repeat

**Comprehension (Understand):** review, illustrate rewrite, identify, estimate, distinguish, paraphrase, explain, explore, inquire, give examples of, discuss, summarize, restate, cite, associate, select, extend, classify, convert, express, extend, indicate, infer, contrast, defend, locate, paraphrase, predict, translate, interpret, describe

**Application:** change, perform, manipulate, produce, report, administer, paint, dramatize, actuate, use, demonstrate, calculate, solve, relate, complete, modify, compute, sketch, articulate, present, transfer, show, act, involve, model, prepare, teach, discover, respond, experiment, act

**Analysis: ** differentiate, conclude, divide, inspect, distinguish, analyze, contrast, connect, relate, criticize, devise, correlate, illustrate, distill, problem-solve, break down, diagram, scrutinize, categorize, discriminate, take apart, calculate, simplify, deduce, subdivide, order, adapt, separate, explain, infer

**Evaluate:** revise, support, assess, argue, judge, decide, refine, re-design, pivot, evaluate defend, tabulate, select, convince, score, gauge, reframe, measure, value, estimate, prioritize, rank, appraise, plan, sort, grade, explain, criticize, test, designate, choose, evolve, analyze

**Create:** come up with, build, develop, design, rewrite, re-frame, summarize, frame, form, modify, imagine, generate, role-Play, make, manufacture, compose, contrive, assemble. derive, conceive, create, pivot, modify, collaborate, write, formulate, invent, set up

]]>

Well, today in this article we will discuss why you should focus on developing mental math skills and what are some of the mind-blowing tricks to do so? First, let us define what mental math or mental calculation is.

Mental math refers to solving basic arithmetic questions using the human brain only, without the aid of external devices such as calculators.

The following math tricks are quite useful in mental math calculations. You can surprise everyone around you by coming up with instant answers without a calculator and gain a reputation of a math genius in your circle.

Do you know that you can switch the percentages? It means that if you are given a % of b, then you can write it as b% of a. In both cases, the answer will be the same.

**Example**

Suppose you have to find 2% of 50. Instead of grabbing the calculator, you can write it as 50% of 2 which is equal to 1.

This is a very common and popular mental math technique. To see either a large number is divisible by 3 or not, add the digits of the number. If the sum of digits is divisible by 3, then the number will also be divisible by 3.

**Example**

To check whether 13467 is divisible by 3 or not add the digits like this:

=1 + 3 + 4 + 6 + 7

= 21

Is 21 divisible by 3? Certainly, yes because 3 into 7 is equal to 21. So, the number 13467 is also divisible by 3.

The complement of a single-digit number is any other number which will make the sum of the number and its complement equal to **10**. It means that the complement of 1 is 9, 2 is 8, 3 is 7, 4 is 6 and so on.

When you are presented a list of numbers, the fastest way to add them in your head is to find the complements in the list.

**Example**

Consider the following list of numbers:

2 + 3 + 5 + 7 + 4 + 1 + 8 + 9 + 5 + 7 + 6 + 5 + 3

Well, this is a long list of addition. To solve it faster, rearrange the digits by writing the numbers and their complements together. The numbers which are left can be written in the end.

2 + 8 + 3 + 7 + 3 + 7 + 5 + 5 + 4 + 6 + 1 + 9 + 5

The complements have their sum equal to 10:

=10 + 10 + 10 + 10 + 10 + 10 + 5

=65

Teach this trick by presenting problems using addition worksheets. Set the time, so that students are compelled to apply these tricks and come up with the answers instantly.

When you are adding the large numbers round them off to the nearest ten, hundred or thousand. If the rounded number is greater than the original number, then subtract the additional number from the answer and vice versa.

**Example**

Add number 387 and 415. To add it quickly in your head, round off the number 387 to 400 and 415 to 400. Adding these two numbers will give us 800. Now, subtract 13 from 800 to get 787 and add 15 to get 802.

When you are dealing with a problem in which you must subtract a large number from 1000, then use the following strategy:

- Subtract first and the second digit from 9 separately
- Subtract the last digit from 10.

**Example**

Subtract 786 from 1000. To answer this without the use of the calculator and even pencil or paper, use the steps explained above. Subtracting 7 from 9 gives us 2. The subtraction of 8 from 9 will yield 1. Finally, subtracting the last digit 6 from 10 will give us 4. Hence, the final answer will be 214.

To determine whether a number is divisible by 5 or not, see its last digit. If it contains 0 or 5, then we can say that the number is divisible by 5.

**Example**

The numbers 234675 and 9865430 are both divisible by 5 because their last digits are 5 and 0 respectively.

If you are asked to multiply a two-digit number by 11, you can do it faster in your head and come up with the answer instantly. Surprised? Well, consider examples below to learn about this mind-blowing trick.

**Examples**

**Multiply 72 by 11.**

The first and last digit of the resulting number will be the same, i.e. 7 and 2. To calculate the mid digit add 7 and 2 together.

7+ 2 = 9

The resulting answer will be 792.

Be careful if the sum of the number has a 2 digits and includes 1 because it will be done differently. Consider another example below.

** 2. Multiply 68 by 11**

Add 6 and 8 together to get the following:

6 + 8 = 14

Now, add the 1 of 14 to 6 and place 4 in the middle. The last digit will be the same, i.e. 8. The answer will be 748. It is surely one of the coolest division facts that you will ever come across.

If you need to multiply a large number by 5, then do it instantly by taking half of the number and multiplying it by 10.

**Examples**

**Multiply 48 by 5**

Half of 48 is 24 and when it is multiplied by 10 we get 240. Hence, the answer is 240.

**Multiply 75 by 5**

Half of 75 is 37.5. Multiplying it by 10 will give us 375 which is the correct answer.
**9. Square Root **

Do you know that you can calculate the square root of a number by following simple steps?

Consider an example below to know how to do it.

**Example**

Find the square root of 41. Most people will say that it is impossible to find the answer without a calculator, but the truth is this can be done in few seconds following these steps.

- Take the next lower perfect square. In the case of 41, the next lower perfect square is 36.
- Add it to the number. By adding 36 and 41, we get 77.
- Now, divide it by the square root of 36. In the case of 77, we will divide it by 6 to get 12.8.
- Now divide the answer by 2 to get the square root of the number. When 12.8 is divided by 2, we get 6.4 which is the square root of 41.

If you are given a large number and you want to check whether it is divisible 8 or not, then see its last 3 digits. If the last 3 digits are divisible by 8, then the whole number is divisible by 8. Isn’t this a cool division math skill?

**Example**

For example, consider the number 456789064

The last three digits 064 are divisible by 8, so the whole number is divisible by 8.

To check whether a number is divisible by 4 or not, look at its last two digits. If they are divisible by 4, then the whole number is also divisible by 4.

**Example**

The number 1654380 is divisible by 4 because the last two digits are 80 which are divisible by 4.

The arithmetic operations should be executed in order to reach the answer to a complex question which involves multiple operations. The order of operations is PEMDAS which is the acronym for:

*P: Parentheses*

*E: Exponents*

*M D: Multiplication or division*

*A S: Addition or subtraction*

**Example**

Consider an expression below:

This order is very helpful in solving algebraic expressions. Consider an example below:

Solve (2 + 7) – 7 x 6 ÷ 3

To solve the above expression first solve the term inside the parenthesis.

2 + 7 is equal to 9, so the resultant expression will be written as:

9 – 7 x 6 ÷ 3

Now, apply the division operation by solving 6 ÷ 3 which is equal to 2.

9 – 7 x 2

The next step is to multiply 7 and 2 to get 14. The final step involves subtracting 14 from 9 to get the answer -5.

Teachers can use math flashcards and worksheets to teach these simple yet powerful math tricks to the students. It will improve the basic math skills of the students and make math education fun and exciting in the class. The best thing about these math facts is that they can be memorized easily. Teaching math concepts through interactive math lessons and hands-on math activities is the best way to drive greater student engagement.

Mental math enhances your cognitive and problem-solving skills. Without knowing mental math strategies, it would be very difficult for you to understand complex concepts and perform daily life activities. These cool math tricks will train your brain to improve its concentration skills. Help your child to practice math facts by presenting math puzzles and fun math games. It will also increase their number sense.

According to a study published in the journal Clinical Psychological Science, stimulating a certain part of the brain while solving mental math problems may be beneficial for the emotional health of the person. We use the dorsolateral prefrontal cortex to solve memory-based math problems. This part of the brain is also linked with depression and anxiety. Higher math activity can stimulate this part of the brain and may help in combating these mental disorders.

Memory-based math games and activities also help children in boosting their self-confidence. When math teaching is coupled with math riddles, worksheets, workbooks, puzzles and games, it sparks off student’s interest in mathematics and gives them more confidence in his math skills. If you are a math teacher, you can avail number of printable math worksheets templates and other math resources available online to teach these math concepts.

Hope you liked this article. If you have any queries and suggestions, then please comment in the section below. We at Educationise are passionate about education and you can contact us if you want us to develop educational materials especially customized according to your needs. We have wide range of experience of working on educational projects and we aim to deliver the highest quality output.

Hope you liked the article. We at Educationise are passionate about education and you can contact us if you want us to develop educational materials especially customized according to your needs. We have wide range of experience of working on educational projects and we aim to deliver the highest quality output.

]]>**Geometric sequence** is a series of numbers in which each subsequent term is found by **multiplying** the previous term by a constant. This constant can be positive or negative, but it can never be zero. This constant is known as **common ratio**.

A geometric sequence is also known as **geometric progression**. In general form, we write geometric sequences like this:

**a**is the**scale factor**which means that it is the starting value of the sequence. We can also call it as the common factor of the series.**r**is the**common ratio**of the sequence

Remember in **arithmetic sequences** the numbers are arranged in such a way that the **common difference** between any two consecutive terms is the same. As the name implies, the common difference is found by subtracting the preceding term from the subsequent term. Arithmetic sequence is also known as arithmetic progression.

The primary difference between arithmetic and geometric sequences lies in the way they are arranged or their subsequent terms are found. These two progressions are quite common in college algebra. Once students are familiar with these two progressions, they can better understand complex Fibonacci numbers and harmonic series.

**Example 1**

What is the common ratio of the geometric sequence { 4, 8, 16, 32, …..}.

**Solution**

To find the common ratio, any term in the series is divided by the preceding term.

If we take the second term 8 and divide it by the first number 4, we get the answer 2.

Similarly, when the third term 16 is divided by the second number 8 or the fourth term 32 is divided by 16, we get the same answer 2.

Hence, **2** is the common ratio.

Use the following general notation to write the series as the product of exponent and common ratio:

** = {4 , 8 , 16 , 32 , .....}**

Let us evaluate another geometric sequence below:

**Example 2**

**{3 , -9 , 27 , -81 , .....}**

**Solution**

The above sequence is geometric because when we divide a term by the last term in the sequence, we get the constant -3. This constant -3 is the common ratio, r of this geometric series.

Note that when a common ratio is a negative number in a geometric sequence, we get an **alternating sequence** like above. It is also known as alternating series because the signs of the terms are alternating.

Now, that we know what geometric sequences are and how to recognize them using a common ratio “r”. Next, we will learn how to find the nth term in the geometric progression.

The explicit formula to find the nth term of a geometric sequence is:

Here, a = initial term of the sequence

r = common ratio of the progression

The above rule of geometric sequence follows a recursive relation and can be written recursively as:

Here, n is an integer which is greater than or equal to 1.

**Example 1**

Find 13th term of the given sequence {5 , 15 , 45 , ....}.

**Solution**

First, determine whether this sequence is geometric or arithmetic. Since the common ratio between the consecutive numbers in the series is constant, i.e. 3, so the above numbers are arranged in a geometric sequence.

In the above question, **a = 5**, **r = 3 **and **n = 8.** Use the formula for finding the nth term to get the 8th term of the sequence:

The geometric sequence can also decrease and have smaller values as it progresses. Consider another example below:

**Example 2**

Find the 10th term of the following geometric sequence:

**{9, 3.6 ,1.44 , .....}**

**Solution**

If we divide 3.6 by 9 or 1.44 by 3.6, we get the common ratio, r = 0.4. Substituting the values of **a = 9** , **r = 0.4 **and** n = 10** in the formula, we will get the 10th term of the sequence:

Hence, the sequence gets smaller and smaller as it proceeds.

The sum formula for finite geometric sequence is denoted below in summation notation:

The symbol used in the above formula is known as **sigma**. Hence, the summation notation is also known as **sigma notation**.

Remember that the sum of the finite and infinite geometric series are calculated using different formulae. You may be wondering how do I find whether the question is about finite or infinite sequence. Well, here's the clue. When number of terms in a sequence for sum are specified in the question, then we will use formula of finite sequence. When they are not specified, then we assume that we need to find the sum of the series to infinity. For example,

"Find sum of first 100 natural numbers" is an example of finite sequence. On the other hand, "Find sum of natural numbers" is an example of infinite sequence.

**Example 1**

Find the sum of the first four terms of the following sequence:

**{58 , 116 , 232 , ....}**

**Solution**

In the question, we are asked to find the sum of the first four terms of a sequence. We don’t need to find the fourth term to find the sum of the above sequence.

In this sequence, **a** is the first term, **r** is the common ratio found by dividing the subsequent term with preceding term, for example 116/58 = 232/116 = 2. Finally, **n** is the number of terms for which we have to find the sum.

Put the following values in the summation formula:

**Example 2**

Find the sum of first 10 terms of the following geometric series:

**Solution**

To get the sum, first, we need to find the common ratio, r of the above geometric progression.

When we divide any term by the previous term in the series, we get a constant number 1/3. Hence, this is the common ratio of the number sequence.

Plugging the values of a = 3 and r = 1/3 in the formula of sum, we will get the sum of the first 10 numbers of the above geometric sequence.

0.999 is approximately equal to 1, so the sum is equal to 9/2.

An infinite series that has the common ratio is called an infinite geometric series. Use the following formula if you are asked to find the sum of an infinite geometric series:

The above formula has a limitation, i.e. this formula can be applied if and only if the absolute value of the common ratio |r| is less than 1.

**Example 1**

Find the sum of all the terms of the following geometric series:

** Solution**

In the above sequence:

Substitute these values in the following formula:

**Example 2**

Find the sum of all the terms in the following geometric sequence:

**Solution**

In the above series:

Now, you can plug these values in the following summation formula:

Take a short quiz below to test your skills in geometric sequence.

Hope you liked the article. We at Educationise are passionate about education and you can contact us if you want us to develop educational materials especially customized according to your needs. We have wide range of experience of working on educational projects and we aim to deliver the highest quality output.

]]>Design thinking is a pedagogy that helps solving multifaceted problems in a human-centered way. It is fundamentally a solution-based methodology to determine the unknown by going through five iterative steps. It begins with realizing the problem, re-defining it in a user-centered manner, brainstorming the possible solutions, creating innovative prototypes and testing the prototypes for an ultimate solution. These five phases are summarized as empathizing, defining, ideation, prototyping, and testing.

This methodology is attracting attention worldwide because the entire five-step process allows us to come up with unconventional solutions to problems that are often complex through critical thinking and creative skills. The design process is followed to discover the solution of the problem keeping in mind the end-user. This popular approach gives us a new perspective on the problems. In this way, we are successful in unraveling those paths that we thought never existed.

The business environment was never as volatile as it is today. Innovation is the key to business success. Therefore, businesses need to generate innovative solutions to conventional problems they face by following the design thinking creative process.

Formulating business strategy using design thinking is becoming increasingly popular in a business environment because it offers deeper consumer insights and out of the box solutions to the problems. It is also helpful in stages of product design and packaging which helps in maximizing the market opportunity, while giving a competitive edge to the businesses.

Global business giants like Google, IBM, Apple, and Uber are already torchbearers in this regard. If you want to know how design thinking has led to the invention of some of the great consumer goods as well as educational, financial and healthcare services, then visit the page __THE ACCIDENTAL DESIGN THINKER____.__

**Design Thinking – a Solution-based Approach**

Design thinking facilitates in developing the skills that are critical for the success of an individual. Keep in mind that design thinking is a solution-based approach rather than a problem-based approach. You may be wondering what’s the difference between these two approaches? Well, the answer lies in their names.

As the name suggests, the problem-based approach focuses on the problems, hindrances and obstacles. On the other hand, the solution-based approach focuses optimistically on the possible solutions to the problems. Hence, we can conclude that the solution-based approach is more successful in solving the problems than the problem-based approach.

Now, let’s discuss the five steps of the design thinking methodology. Keep in mind that these steps are non-linear, i.e. they are not sequential. It is not mandatory to follow these steps in sequential order rather can also go through these steps in a parallel fashion.

This is the first step of the design thinking iterative innovation process which emphasizes on empathizing with your target audience by immersing yourself in their physical environment. The purpose of this stage is to conduct some user research to gain deeper insights into the user needs, feelings, and behavior towards the problem they are facing. In other words, the design thinker puts himself in users shoes for solving problems that are affecting them.

Accumulate as much information as possible by employing qualitative and mixed research methods to analyze user needs. Depending upon the available resources, design thinkers can consult with the experts besides users.

Using the information amassed during the empathy phase, define the problem creatively in a user-centric way. The observations made in the first stage are synthesized for defining the problem meaningfully. Your own assumptions and company's wishes should not overshadow your problem statement.

This phase is critical for the success of the other phases because when you have effectively formulated a problem statement, only then you can transpire creative solutions. If the problem statement is ambiguous, it can lead to misleading solutions or you can end up nowhere. A proper definition will give you and your team a sense of clarity and hence you can spark off in the right direction.

**The Good and Bad Problem Statement**

Besides being a user-centered approach, the problem statement should be broad enough and not single out a precise method that should be used to find the solution. In other words, it should focus on the user rather than the resources which should be used to solve the problem.

For example, the problem statement “To improve the health conditions by training doctors” makes no sense in the design thinking approach because the solution is already narrowed down in the problem statement.

But keep in mind that the problem statement should not be too broad either, which means that by reading it a person should get a fair idea of the problem. For example, the problem statement “To improve health conditions” is too broad and an example of a bad problem statement.

Besides, brainstorming you can employ other techniques like brain write, worst possible idea, challenge assumptions, analogies and scamper to evaluate alternatives. However, brainstorming is the most popular method to generate ideas.

Creativity and critical thinking skills come in full swing in this phase of the design thinking process. This is the phase where designers use divergent thinking to unearth solutions that were never imagined before by anyone else. This phase demands patience, team interactivity, and concentration to generate fruitful results.

In this experimental phase, design thinkers develop prototypes of the solutions related to the problem statement generated in the ideation phase. Rapid prototyping is an iterative process of experimentation. These prototypes are inexpensive versions of the product which are re-evaluated again and again based on the requirement.

In other words, in this phase, we are able to discover what works and what doesn’t. The purpose of rapid prototyping is to specify the best possible solution to the given problem. The prototypes or inexpensive versions of the products are tested repeatedly and the phase ends with the selection of the best prototype.

This is the last stage of the design thinking process map. After you have selected the best possible solution in the prototyping phase, you need to test that prototype rigorously. If during the testing phase, you find that the solution needs to be more refined, you can move to the previous steps because design thinking is a repeatable process.

In this phase, you should be empathetic towards the users and demonstrate how a specific solution is the best among all the alternatives. Soliciting user feedback is critical for the refinement of the solution or a product. In other words, we can say that this phase demands the practical demonstration of the solution rather than relying on storytelling.

Schools worldwide are adopting design methods and processes by integrating this pedagogical approach in their curricula and syllabus for innovation. D school at Sandford University is a pioneer in this regard. In the educational industry, primary, middle and high school teachers are employing hands-on activities in the class guided by design principles and processes which help students to solve problems affecting millions of population worldwide. Teaching early childhood education through design thinking prepares students for future success.

The schools conduct design thinking workshops, fieldwork, education week and summer learning programs to encourage creativity among the students. In these workshops and summer programs, authentic problems related to socioeconomic and human development subjects are presented to the students to encourage them to use their good design and logical reasoning skills to reach a viable solution.

Consequently, these workshops can promote student learning through hands-on experiences and experimentation. During the design thinking activity in the class, the teacher serves as a facilitator who guides the students through the whole process, while encouraging students to collaborate and think critically.

Top universities across the world are teaching design thinking courses because they know that in the 21st century; creative and critical thinking are the most sought-after skills by employers. Design thinking is especially critical in entrepreneurship education programs because they lead to positive youth development and cultivate entrepreneurial mindset among them.

Educators think that the integration of design thinking methodology at the school level will prepare the students for the coming challenges. As a result, we will be able to see more inventors and entrepreneurs in the future than ever before.

Some of the benefits of incorporating design thinking in education are given below:

- The process is supporting the students to learn actively and enhance their analytical thinking and reasoning skills.
- Design thinking supports in tackling the deep-rooted fear of failure among the students and encourages them to accept the criticism with an open heart.
- During the entire iterative design cycle, students can learn many valuable lessons from learning to empathize with human needs and desires to the importance of working as a team by solving complex problems.
- Going through the stages of design thinking, students can rediscover themselves. It gives them a sense of achievement and confidence which is a valuable asset in their lives.

Number of online resources are available for educators that leverage the creative problem-solving skills of the students and enable them to emerge as thinkers and innovators. Some of these design thinking activities for students which give them immersive learning experiences through engaging in hands-on class projects are given below:

**1.** __Design thinking for educators__

Refine the design thinking skills in the classroom using an instructional design toolkit on this website. It also contains examples of human-centered designs used by the schools to tackle real-world problems.

**2. **__Nureva__

This website has 6 design thinking project ideas that assist students to enhance their problem solving and creative thinking skills. Students will dive into the design process to evaluate the best solutions to problems.

**3. **__LiveTiles__

This website has 3 design thinking projects which you can implement in your classroom following principles of design thinking in a fun way. Teachers can examine the prototype development process and guide the students to analyze the design solutions.

**4. **__Edutopia__

Navigate through this website to access 10 project ideas. These projects will help students to brainstorm innovative ideas to tackle some of the piercing issues. At the end of the activity, teachers should solicit student feedback on these activities to know how the problems can be defined more creatively.

This website has some of the amazing design-driven ideas for elementary teachers. It will help the students in idea generation and will guide them through problem-solving process.

Hope you enjoyed the article. If you like the article, please comment on the section below.

]]>This term was first coined in 2005 by Make magazine and the first Maker Faire in 2006. However, this mindset is as old as the life of humans on this planet. We as humans are extremely curious creatures. We work hard to discover the unknown and invent for our better lives since we started to populate this planet billions of years ago. Every invention that has a significant influence in our lives today like planes, 3d printers, rockets, machinery, and computers etc. is attributed to the Maker mindset.

The Maker movement believes in the incorporation of inclusive culture. Therefore, this movement emphasizes on shared spaces where makers can interact to share their ideas. The place where the makers harmonize to create prototypes of their impactful innovations is known as makerspace.

The primary objective of makerspace is to permit the free flow of creative ideas and information, while working cohesively as a community to invent something meaningful. Fortunately, because of technological advancements sharing and comparing project ideas and information has become easier.

Maker movement has taken the educational industry by storm. Maker education is a term coined by educators keeping in mind a famous and trending "Maker movement". Educators are eager to instill a maker mindset among students especially those studying the STEM (Science, technology, engineering, and mathematics) or STEAM (incorporates Arts in STEM) subjects.

Kids are already inclined towards project-based learning, i.e. they have a basic instinct to learn by doing and playing with materials. The maker education basically exploits this deep-rooted curiosity of children to make them innovators. The development of makerspaces in and out of the schools helps to enhance learning opportunities for students at an unprecedented pace.

When students work in harmony to accomplish a shared purpose, they become more empathetic. Incorporating the maker mindset in the school setting has the potential to nurture creative and learning skills of the students while encouraging them to think out of the box solutions for complex problems. Project based learning activities are critical to strengthen their content knowledge in STEM fields. Focusing on this pedagogy of teaching also supports active learning and drives greater student engagement.

Maker movement harnesses the power of natural curiosity and creativity of kids. In other words, we can say that the focal point of Maker education is project-based learning or learning by doing. Learning through textbooks in a traditional classroom setting is a 20th-century thing. Traditional curriculum which is designed to prepare students for better grades and standardized tests has failed to give individualized learning experiences to students that are essential to build 21st century skills like critical thinking and problem solving.

21st century skills are built when educators emphasize on teaching STEM or STEAM concepts through inquiry based activities. These hands on activities allow the students to learn by prototyping their ideas in design studios or makerspaces.

Fortunately, we are living in the era of the internet which has made sharing of information and tools online much easier and affordable than ever before. Before the maker education, students were expected to get enrolled in the specific courses and keep studying up to a certain age.

After the completion of education, they were actually able to realize their ideas and start practical work in their fields. But maker education is revolutionizing the educational sphere by empowering the students to pursue their interests while studying. In other words, maker education engages students and prepares them to solve the complex real world problems.

The maker community practically implements the saying “Sharing is caring”. Makers work in collaboration because they believe that it's about “Us” as opposed to “me”. Their outlook towards creation is not limited to projecting themselves, but they care about the people around them. They share their codes, designs, tools and ideas with other makers and embrace criticism with an open heart. In educational setting, this openness let the students think beyond instructor led classroom learning for grades and value the importance of practical inquiry based learning.

Makers employ state of the art and modern technology to design their prototypes. The design of material-based prototypes or designs is an outdated concept now. Nevertheless, many schools are still using it. Now, the computers can be used to simulate impeccable designs that can be painlessly distributed, analyzed and enhanced.

Makers believe that “Practice makes a man perfect”, hence they are continuously looking for ways to improve their designs. Unfortunately, there is a little space for anomalies in material-based designs and the mistakes can be expansive. On the other hand, computer-based designs offer cheap revisions to the prototypes while enabling the students to take risks.

Makers are not only interested in how the technological tools work, but they are also eager to use them for problem based learning. Take an example of a 3d printer. Makers not only decipher how it works to get 3d printed designs, but also utilize it for printing the design of the next AI-powered robot that will revolutionize the manufacturing industry.

Similarly, take another example of a computer algorithm. Makers are not only interested in how this algorithm works, but they are also determined to learn how this algorithm will be helpful in problem solving. Consequently, this mindset serves a dual purpose - helping to work on new inventions and improving the existing ones.

The Maker movement does not discriminate individuals based on their age, ethnicity, nationality, and country. It embraces people of all ages and nationalities, given they are passionate about deeper learning and sharing their expertise. This aspect of the Maker movement is very helpful for schools that want to embrace the Maker education because they can benefit from the mentorship of senior makers, scientists, designers and engineers.

Teachers may have limited content knowledge or experience in practical applications of the concepts. Therefore, it is a wise decision to take the gold standard expertise of senior designers, artists, engineers and scientists rather than just an instructor or teacher to make the professional learning experience more worthwhile for students. Alternatively, teachers can play the role of the facilitator to conduct the maker workshops and host the maker events. A teacher is responsible to create a learning environment that is critical for student interest development in STEM subjects. Consequently, students will be a part of multicultural learning community that promotes their success and retention in STEM courses.

Now, that you are aware of what maker education is, you might be wondering where to start and fetch ideas to incorporate the Maker education in the class setting? Well, we understand that the Maker education emphasizes on sharing the knowledge, ideas, and designs. Keeping this attribute of the Maker education in mind, the number of schools and educators have shared their valuable resources online which will support you in your teaching journey. Some of these online resources are given below:

This website shares many inexpensive and creative makerspace or STEM project design ideas and inspirations which you can incorporate in your class effortlessly. Interestingly, the majority of these project based instructions involve the use of recycled goods as raw materials that are easier to get and are pocket-friendly. You can also get the free Ebook on the website which has 250 + makerspace resources. In addition to this, the website offers many other E-books related to the makerspace ideas that can be purchased.

If you are teaching a course related to technology or engineering, then this website is a great resource for educators as they can find many useful project ideas. These projects are a brainchild of the group of four students belonging to the Queensland University of Australia who share a common passion of sharing technology-based educational resources with others.

This website has a collection of fun and exciting STEM projects that will help the students in utilizing their creativity to learn and invent new things. When you will click on each project on the left side of the web page, you will be exposed to tons of resources available on other sites. Students can also work on the projects by watching videos that are given at the bottom of each project resource.

The place where makers collaborate to invent is known as makerspace. The design and aesthetics of makerspaces in schools are essential to foster creativity among students. Schools around the world are investing capital in designing professional makerspaces for their students. Maker Ed contains an extensive list of innovative makerspace ideas and inspirations which you may find helpful.

This website contains an extensive list of makerspace projects which are tried and tested by professional teachers. The web page shares the resources which have been implemented in the schools already. The professional teachers have shared these resources because they consider them as a powerful tool for engaging students in STEM subjects.

From science and technology to digital design, this website offers many makerspace project ideas. Follow this link to access the amazing list of makerspace project ideas.

This website has curated some of the great Maker education articles, useful advice and project ideas.

I hope you enjoyed the article. If you are an educator, then join the movement by integrating maker culture in your curriculum. It will be the best decision that you will ever take for enhanced student learning experience. The project based lesson plans in the above resources are intelligently curated and are easy to implement in the class. The resources will facilitate self directed learning and promote critical thinking among the students.

Don’t forget to share your creative ideas with the rest of the world online, if you have any. After all, you are part of the maker's community and it’s all about sharing . If you like the article, then comment in the below section. You can also give suggestions for new topics.

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You may have heard a term discrete mathematics. By its name, you may be thinking that it is probably a branch of mathematics, but it’s not the case. Rather, it is a common name given to the branches of mathematics which have a single common characteristic – i.e. they are discrete instead of continuous. While it may be difficult to define discrete mathematics, but we can say that:

*It is a study of mathematical structures that are distinct and unconnected*

The following mathematical concepts or theories can be put under the banner of discrete mathematics because of their common discrete characteristic:

- Graph theory
- Logic and Boolean algebra
- Number theory
- Group theory
- Matrix theory
- Set theory
- Permutations and combinations
- Induction and recursion
- Partial Order and Lattice
- Probability theory
- Theory of computation
- Algorithmic analysis

Discrete and continuous sets are opposite to each other.

**Discrete set** in mathematics is defined as a set having unique and distinct elements. Discrete sets can be finite or infinite. For example, consider a set of natural numbers N = {1,2,3,…}. It is discrete because the elements in the set are distinct and there is a strident shift between the elements. In other words, we can say that discrete data take specific values and there are no values in between. The discrete examples from our daily lives involve countable variables such as our age, number of holidays and the number of voters who voted during the elections.

On the other hand, a set of real numbers which includes both rational and irrational numbers is **continuous** because we cannot count the elements in this type of set. For example, all real numbers between 1 and 2 will be written as 1. …, 1.00001… , 1.100001, …..It shows there are infinite real numbers between these two numbers which can neither be counted nor they are discrete. The examples of continuous variables from our daily lives include weight, height, mass, and temperature.

A probability can be discrete or continuous depending on its nature. The most common discrete probability distributions are binomial, Poisson and geometric distribution. On the other hand, normal and continuous probability distributions are examples of continuous probability.

*Interesting fact: Do you know that a digital clock is characterized as having a discrete nature because of the smooth transition of time. On the other hand, an analog clock is termed as continuous because of the separate hour, minute and second hands. There can be infinite different times between let say 1: 10: 20 A.M and 1: 11 A.M.*

The comprehension of discrete structures not only assists in a mathematics major, but is also quite worthwhile if you are determined to go for a computer science major. Colleges and universities extend many subjects under a computer science course. These subjects encompass compiler design, databases, operating systems, combinatorics, automata theory, and different programming languages. Discrete mathematics is a foundation of all these computer science courses. The uses of discrete mathematics are widespread, but some of them are listed below:

- It helps in the analysis of algorithms
- It is helpful in software design specifications and other practical applications
- It enhances our problem-solving skills
- It encourages analytical thinking and improves mathematical reasoning skills

Students often ask how mathematics is applicable in real life. If you are a mathematics teacher, then you might have a hard time answering this question in every class because mathematics courses include abstract concepts like algebra, geometry, and trigonometry. However, while teaching discrete mathematics, you can easily answer this question because the discrete mathematics is helpful in solving problems that students may encounter in their real lives. Some of these problems are listed below:

- What is the shortest path from your home to the supermarket?
- What is the probability of the occurrence of an event?
- Are two computers in the same network connected to each other?
- How can you encrypt a message and send it to the person in such a way that no one is able to read the message except the intended person?
- How many password combinations are possible given a fixed number of alphanumeric digits?

STEM is an acronym for science, technology, engineering, and mathematics. The main goal of STEM education is to integrate all these four disciplines and teach them cohesively through project-based learning so that the students can apply the concepts learned in classroom to solve real-world problems.

Remember that STEM education is inherently different from traditional science and math education because under STEM curricula, school teachers use a blended approach to teach these four disciplines in the classroom which drives student engagement.

**Best Articles from Educationise**

**11 Activities that promote critical thinking in the class****6 steps to implement project based learning in the class****What is design thinking and why it is critical for success in business and education****?****30 examples of Bloom's taxonomy learning objectives for teachers****,**__What is Growth mindset? 50+ motivational quotes on growth mindset.__

** 1. Tackling Real World Challenges Through Innovation**

Technology is defining every aspect of our lives including education. The modern economy needs a workforce that is capable of tackling challenges which are affecting millions of people worldwide. Developing problem solving and creative skills among students is the cornerstone of STEM education. Through STEM education students can take an initiative and come up with out of the box solutions to solve complex problems.

For example, you will need STEM skills to find a cure for the common and deadly diseases like Cancer. Similarly, we need mathematicians and engineers to develop robots that are capable of doing the tasks and take decisions like humans. To develop the seeds for the crop that will help combat malnutrition and hunger globally will require the combination of agricultural sciences and technical education.

** 2. STEM Careers**

STEM education is important because the job industry needs employees who have a sound foundation of STEM skills. In this competitive world, industries are investing a hefty capital in research and development to stay relevant. Therefore, there are ample research opportunities for students and professionals in this field. Employees who have an academic background in STEM fields are a valuable asset for the company and help it to achieve a competitive edge.

However, the employers are complaining the workforce is not skilled enough to fill the job positions which are in high demand. The number of jobs that require a STEM degree is growing and is expected to grow at an unprecedented pace in the next decade. However, the number of students majoring in the STEM fields is decreasing which shows our flawed education system and is a matter of concern for our colleges and universities.

If students are adequately supported by the colleges and universities in their journey of learning science and mathematics, then they are more likely to choose or stay in the STEM field. This support can be provided in terms of finances, professional career counselling services or individualized learning experiences that are essential for growth and development of students. Consequently, STEM graduates will emerge as innovators who will be proficient and skilled in problem solving and critical thinking skills.

Technology especially artificial intelligence is replacing many manual jobs and will continue to do so in the future. In these circumstances, STEM graduates will be more likely to find suitable jobs in the future than graduates of other fields. STEM education prepares students for future occupations in fields of robotics and artificial intelligence.

** 3. Develops Leadership Skills**

Integrating STEM education in the school curricula will help students to discover their interests and aptitude and hence they can make the right decisions regarding the career pathways which they want to pursue in the future. Decision making and leadership skills are nurtured among the students studying the STEM subjects. Consequently, the student emerges as an innovator rather than a follower.

** 1. Plan STEM Curricula for your Class**

Fortunately, the nonprofit organization like Project Lead The Way (PLTW) is working to provide support services to the elementary, middle and high school teachers to promote STEM education in the United States. STEM students can benefit from hands-on-learning activities and engaging classroom environment through the implementation of the PLTW curriculum. Teacher professional development is the focal point of PLTW. The organization trains science teachers and provides professional development resources which helps them to teach the STEM subjects in class in an engaging manner. This training provided to teachers positively impact student achievement in the STEM fields.

PLTW has customized its curriculum for the elementary, middle and high school students. It offers a Launch curriculum for the elementary teachers and Gateway curriculum for middle school teachers. It offers three-course pathways – computer science education, engineering and biomedical science for high school students and allows the students to earn college credit in high school in these disciplines.

** 2. Use Project-Based Learning Approach to Teach STEM Subjects**

Teachers need to be innovative and employ the latest teaching strategies to teach science, technology, engineering and math subjects. One such innovative teaching strategy for educators is the project-based learning approach which prepares the student for the afterschool life. This approach works by presenting a real-life problem to the student and encourage critical thinking to reach a viable solution.

**3. Teach the STEM Subjects in a Fun Way**

Teach mathematics and science courses in a fun and engaging way. Students usually are of the view that math is a boring subject and if they are not naturally good at it, they will never be able to ace it. Similarly, science teaching should be coupled with good educational research to know which teaching method is favored by students.

Teach important concepts by implementing fun science and math activities in the class. These activities will help broaden their knowledge and expertise in these subjects. Afterschool STEM program for talented and dynamic group of students is yet another way to enhance the students interest in math and science subjects.

** 4. Incorporate Art to Make it STEAM**

The “A” in STEAM represents the arts. STEAM fields also include humanities, language, drama, music, and visual arts etc. besides the regular STEM subjects. STEAM allows the students to learn scientific principles creatively while enhancing the 21st-century skills like problem-solving, decision making and leadership skills.

Teaching STEM subjects through artistic expressions is the best way to promote STEM interest among students. Nothing drives more engagement than teaching the STEM subjects through art. The examples of using art to teach STEAM subjects include:

- changing classroom architecture as it is critical in promoting interest
- taking inspiration from social and behavioral science while designing a classroom art for students
- promoting interest in scientific, mathematical and technological topics through movies, conducting science fairs, dramas and other expression of arts

**5. Summer Programs and Field Trips**

Summer programs and field trips are the best ways to promote educational research among students. An occasional field trip to a local museum, park or beach is an ultimate way to foster interest in the concepts learned in the classroom. These beyond school activities have a regenerative effect on student’s learning and creativity.

**6. Organizing STEM Competitions in Schools**

Another way to teach STEM education is to organize annual competitions in schools, colleges and universities. Students can form groups or participate independently in these contests. Give real-world challenges to the students and ask them to come up with innovative solutions.

**7. Design Thinking in Schools**

The five steps of design thinking or human-centric approach are empathize, define, ideate, prototype, and test. It is basically an inquiry based approach that starts with empathizing for those who are facing a particular problem. This approach enables the students to work collaboratively and value the opinion of others before reaching the final conclusion.

Hope you liked the article. If you want article on any educational topic, then please comment in the section below.

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