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The 5 Elements of Effective Thinking



In this article I interview Dr. Edward Burger the co-author of The 5 Elements of Effective Thinking. Dr. Burger is President of Southwestern University as well as a professor of mathematics and an award-winning educational leader on thinking, innovation, and creativity. 

This is an excellent article to read if you want to improve your thinking.

In this article: The 5 Elements of Effective Thinking

  1. Understand deeply
  2. Make mistakes
  3. Raise questions
  4. Follow the flow of ideas
  5. Change

Let’s begin:

The 5 Elements of Effective Thinking

Michael Frank: What are the 5 Elements of Effective Thinking?

Dr. Edward Burger: The 5 Elements of Effective Thinking are:

  1. Understand deeply
  2. Make mistakes
  3. Raise questions
  4. Follow the flow of ideas
  5. Change

When you first hear these things, they sound so obvious or trivial that you want to move on. But I want to caution listeners that there’s depth in each of these things, which needs to be explored.

Element 1: Understand deeply

Dr. Edward Burger: The first element of effective thinking is deep understanding, and having a rock solid understanding of whatever it is that you’re learning.

If you ask someone on the street if they understand something you’ll get either one of two responses:

  • Yes
  • No

Neither of which is correct.

We need to acknowledge the fact that understanding occurs across a spectrum. It comes in layers. And wherever we are on that spectrum we can go deeper.

Michael Frank: What are some practical activities or exercises that we can do to get a deep understanding when we’re learning something new?

Dr. Edward Burger: Well the goal is not to go from zero knowledge to a very deep knowledge overnight, but just incrementally:

How can I understand something a little bit better?

How can I understand simple things more deeply, and with an unusual depth than I would otherwise do?

How can I look at things from different perspectives, and see them in a different way?

You can also take something that you’re expert at, and just declare that in fact:

“I don’t know this”

Because the moment you declare you don’t know something, it will force you to see that thing in a different light, and thus you will see it more deeply.

Another idea is to take something that you take for granted, something that seems so simple, and force yourself to see something new within it.

Add the adjective

Adding the adjective is another activity I always enjoy, and it says that when you’re faced with a challenge, instead of trying to do it head on, just add descriptors. How many words can you add to describe the issue at hand? The more words you can use to describe the thing, the clearer you will see it, and all of a sudden structure and nuance will unfold.

“Let’s return to a time in which photographs were not in living color. During that period, people referred to pictures as “photographs” rather than “black-and-white photographs” as we do today. The possibility of color did not exist, so it was unnecessary to insert the adjective “black-and-white.” However, suppose we did include the phrase “black-and-white” before the existence of color photography. By highlighting that reality, we become conscious of current limitations and thus open our minds to new possibilities and potential opportunities.” – Edward Burger

Now none of these elements, especially deep understanding, are easy practices. It may sound easy, to understand simple things deeply. What could be easier than that?

Well, you know what?

If you’re a student and you’ve got a lot of work ahead of you, and you’re just trying to keep up with the latest thing that’s going on in that class, the idea of going back in time and studying something that you already know seems like a complete waste of time.

But that is a mistake because if you spend time on that which seems obvious, you will realize that within the simple is the complex. And when you unpack that at the subatomic particle level, then that which originally seemed daunting and complex becomes much more simplified. And that’s what deep understanding means.

Can you get 100% on all of your previous exams?

Michael Frank: I loved the way you spoke in the book about going back and studying what you think you’ve already learned. If you can’t get 100% on your last exam, and all of your previous exams, you’re not ready for the next one.

“In any class, when preparing for your next exam, make sure you can earn a 100% on all the previous exams – if you can’t, then you’re not ready for the test looming in your future.” – Edward Burger

“Students often say, “I got an 80% on this homework; that’s good enough and I’m moving on.” Bad idea. By not exploiting this great opportunity to learn from their mistakes, they’re essentially throwing away – on average – 20% of their grade on their next exam before they’ve even taken it, and they’re building future work on a cracked foundation. Why not learn from your current missteps today and give yourself a 20% bonus in your future?” – Edward Burger

Dr. Edward Burger: That’s exactly right and it might seem like an extreme point of view, and I’m certainly not suggesting that we should focus on perfection, in fact, I would argue the opposite.

When we discuss failure, you’ll hear me say that perfection is often the death of creativity and forward movement. But it’s a reality from a very practical perspective that if I get 80% on an examination and I don’t do anything about it, then that’s an example of ineffective failure, because there is still 20% or one fifth of that material I have yet to master.

So the idea of just ignoring it and going onto the next thing is an example of how we can trip over ourselves by not understanding simple things deeply. I’ve got the exam back, I’ve got some assessments, so let me work on this until I have a rock solid understanding. Even though the class keeps moving forward and other exams loom in my future, by getting that 80% to an intellectual 100%, I become better prepared for the next exam on new or more complex material.

Element 2: Making mistakes, failing to succeed

Dr. Edward Burger: The second element of effective thinking is making mistakes, and failing effectively.

Michael Frank: Yes and most people are afraid to fail, they’re afraid to make mistakes.

How can we adopt a mentality of not being afraid to fail and actually embracing failure, and looking forward to making mistakes?

“I never lose. I either win or I learn.” – Nelson Mandela

Dr. Edward Burger: Well most people today are focused on perfection and that becomes a problem, because the reality is that innovation and learning happens through a process of making mistakes.

However if we can became more process focused, where a mistake becomes a powerful way of learning something new that will get us even further along the way, towards a better inevitable resolution, we’ll be better off.

Here’s what I tell people: Suppose you and I were given a really big difficult challenge. And so we go into our corner and we start to scheme and we try something. But of course it doesn’t work because it’s a really big challenge. But we feel like we’ve failed. Our whole lives are ruined. We’ll get fired. We’ll never go to college. We’ll never do anything. We’re going to live with our parents for the rest of our lives.

Now let’s rewind that scenario. Play it from the beginning again. What if the person that gave us this really big challenge said to us:

“To realize success with this challenge, you will have to fail ten times. It is requisite that you fail ten times in order to succeed.”

Now we go off into our corner. We try the first thing, and of course it doesn’t work, but what’s our mindset now?

Michael Frank: One down, nine to go!

Dr. Edward Burger: We’ve made progress!

And that’s how to look at effective failure.

However, the goal is not just to make a mistake for the sake of making mistake. You want to fail effectively.

A lot of people engage in what I call ineffective failure, where they make a mistake and they keep on trying, and then they try something else. That’s tenacity, which is wonderful and is to be encouraged and applauded, but it’s also ineffective failure because you’re throwing away an opportunity for learning.

A more mindful approach to effective failure that I have, is to hold that failed attempt like a jewel, and to look at it from all of its many facets until you have an epiphany or an aha moment of insight, and then you can leave it and try something else. But just to say, well, that didn’t work let’s try something else, that’s ineffective failure.

The idea is that we need to learn from our mistakes. There is no greater teacher than our own mistakes if we take a moment to learn from them. And that’s what effective failure is.

On my curriculum, on my syllabus, you are graded on your effectiveness of failure.

I teach my students to intentionally fail. If we’re going to learn from every single mistake we make, then shouldn’t we intentionally fail intermediately, so that we can learn something?

So don’t stare at a blank screen. If you’ve got a project to do, a paper to write, a report to author, just write a really bad version of it as quickly as you can. Just write junk instead of waiting for those ideal words to hit your fingertips so you can become like Homer or Shakespeare, which is not how it happens anyway. Instead write junk so that you have something to react to. You know, I often say you might not know how to do it right all the time, but you could always do it wrong.

So there’s a practice: Just do it wrong and then respond to that attempt to learn something.

“The mind-set that mistakes are poisonous often freezes us into inaction. If we have the healthier attitude that failure is a potent teacher and a scheduled stop along the road to success, then we find ourselves liberated to move forward sooner, because mistakes are actions we definitely can take at any time. If you’re stuck, a mistake can be just the thing to unstick you.” – Edward Burger

2 reactions to mistakes

Michael Frank: You also talk about having two reactions to mistakes when you see or make a mistake:

  1. You can either let the mistake lead you to a better attempt
  2. Ask whether the mistake is the correct answer to a different question

Dr. Edward Burger: Yes and I think one of the greatest examples of doing something that doesn’t do what you wanted it to do, but is an amazing thing for something else, is the international company 3M.

In 1970 Scientists at 3M were trying very hard to make a very sticky adhesive for one of their upcoming products of tape. And they came up with this chemical bond but instead of it being strong and sticking to the paper, it was so weak that you could just peel it right off. It was a completely ineffective and a totally failed attempt to create something really powerful and strong.

However one of the scientists at 3M who used to keep little bookmarks in his hymnal when he would go to church, thought to himself, wait a minute, maybe we can do something with that weak adhesive. It wouldn’t fall out or damage the pages, and he could just peel it off when he’s done. And that’s how Post-it notes were invented.

The largest product that 3M now sells, it’s dominant feature in the business world, was created by trying to do something that didn’t work and realizing that false start led to an interesting solution to something they weren’t even thinking about.

“Sometimes when your attempt fails to resolve one issue, you might discover that you have actually found an imaginative answer to a totally different question. That is, your bad solution to one problem might lead to a different project altogether – a project suggested by the accidental virtues of your mostly bad attempt.” – Edward Burger

“Seeing a mistake as possibly a correct answer to a different question puts our thinking on its head. We look at a mistake not as a wrong answer, but instead as an opportunity to ask, “What is the question to which this is a correct answer?” – Edward Burger

Element 3: Raising questions, being your own Socrates

Dr. Edward Burger: The third element of effective thinking is the art of creating questions and being your own Socrates.

Michael Frank: What are some questions you might suggest a student should be asking themselves when learning something new?

Dr. Edward Burger: Well there are so many so I’ll just offer some generic ones.

Whatever I’m learning something new, I’ll ask questions like:

What did I just learn?

And then I’ll try to guess: What will come next? 

And: What came before this? (e.g. algebra before calculus)

What was our understanding before this thing?

Why do people look at the thing, whatever it is, the way they’re looking at it?

Can we look at it in a different way?

What happens if we think of it in a different way?

The other thing is that if someone’s actually talking to us, whether it’s a presentation or a lecture or someone is sharing:

Why are they presenting it that way?

And especially if it’s complicated or unnatural to us:

Why is this unnatural to me?

What am I missing?

And if there’s obviously a gap between where the speaker is and where I am:

Why does that gap exist?

Is it because I don’t know the background as well?

Is it because the person is not describing it in a way that makes sense to me?

What is going on here?

These are the kinds of questions that allow us to provoke thought, and I often tell people that when you’re sitting in the audience, whether it’s in a class or a lecture, it is not the speaker’s job to provoke thought. It is your job to create questions to provoke your own thought.

Michael Frank: I think the elementary questions I would add to those great questions too is:

Why is this important?

Why do I need to know it?

I think a lot of students struggle because they don’t see the connection between what they’re learning and how it’s applicable to their real life.


What are the top 5 most important ideas and lessons presented in this article/book/lecture/podcast/video?

What isn’t clear? What points do I need to clarify?

How am I going to use this information and put it into practice?

Element 4: Follow the flow of ideas

Dr. Edward Burger: The forth element of effective thinking is to look back, look forward, and to follow the flow of ideas.

Following the flow of ideas is a powerful way of seeing the world in a deeper way, and it’s also to acknowledge that every idea came from previous ideas and evolved to today.

Michael Frank: We might know the science and the mechanics of an idea. We might know the facts/figures/formulas around an idea, but why do we need to know the history behind an idea? Why is it important to know where it came from?

Dr. Edward Burger: It depends on what your goals are. If your goal is just to pass the exam on Friday and move on, then maybe not. Although I would argue that you will do better on the exam if you understand the background that’s behind it, and that comes back to the very first element, deep understanding.

The only way to have a deep understanding of anything is to understand where it comes from. You need to appreciate the evolution of those ideas and see where they came from, and much more importantly, see where they’re going next.

Every new idea should be a beginning and never an end. So whenever you come up with a new idea or create something new, or just learn something you didn’t know before, don’t stop there, but ask yourself:

How can I take this and do something else with it beyond its intended purpose or beyond its current utility?

What else can we do with it?

How can we repurpose it?

How can we apply it to something different?

How can we take that idea and connect it with something that seems totally disparate to that?

That is the flow of ideas.

“Knowing the history is certainly helpful, but not if we tend to see current solutions as summits. We must get in the habit of seeing each advance as putting us on the lower slope of a much higher peak that has yet to be scaled.” – Edward Burger

Element 5: Change

Michael Frank: The fifth element of effective thinking is change. How do we go about embracing change and making these practices a part of our life?

Dr. Edward Burger: Well by capturing and practicing all four elements:

  1. Understanding deeply
  2. Making mistakes/failing effectively
  3. Creating questions
  4. Following the flow of ideas

What will happen is that you will just naturally change. You will be a different version of yourself. And I’m not suggesting that we change your DNA and make you into someone you’re not, but rather that we amplify the you in you and make you a better version.

Years ago I used to talk about becoming the “best” version of yourself. Well, that somehow implies that there’s a destination and when you get there, you kind of max out. But we never max out. Ideally, if we’re lifelong learners and truly effective thinkers, we’ll continue to evolve and become better until we’re no longer breathing.

By applying the five elements of effective thinking, we can change and become better versions of ourselves, and we can start to think and analyze in deeper and more creative ways, and in more innovative and imaginative ways.

Michael Frank: I want to ask you some other questions before we wrap up…

How to ace a test

Michael Frank: How do we ace a test? Is it just a matter of anticipating the questions which might be asked and then writing up your own mock test? Is it a case of doing lots of practice tests? All of the above? Something else? What would you recommend?

Dr. Edward Burger: I love all of those suggestions. I always encourage my students to create their own tests, and I’ll often collect them and grade them. And if I use a question that you submitted, then you not only get the advantage of seeing the question in advance because you created it, but I’ll also give you extra credit.

So ask yourself: What’s a good question for an exam?

What’s a hard question and what’s an easy question?

That forces you to think about the material in a deeper way.

If you’re in a math course, open the textbook or go online and do lots of practice questions, even if you’re not going to create them, because there’s countless endless lists of questions that you can do that relate to the material.

“If an exam is looming in your future, prepare by writing the test itself. Well beforehand, compose a list of good exam questions, put it away for a few days, and then later dig it out and take that mock test. Contemplating questions that you think should appear on the test will force you to ask, “What are the central ideas here and do I truly understand them?” And metaphorically write your own exam in other circumstances in which you are sharing information or skills, such as in preparing for an interview or a presentation. This “create-a-test” exercise is an excellent one to employ before you face an audience for a Q&A session. Do you know the material so well that you know what the good questions are? If you don’t, then you do not understand the material well enough, and you need to go deeper. The questions will help you uncover weak points as well as place what you are saying into a larger context. Remember: If you can’t create the questions, you’re not ready for the test.” – Edward Burger

Here’s the thing not to do: Don’t read over your notes again and again and again and look at the examples that were worked through and discussed to the point where you say “Oh, I completely understand it. There’s no problem. I got it”.

That is a fake sense of basic knowledge. You only understand it by doing it. So reading over notes and saying “Oh, that makes sense” does nothing. You’ve got to be active in your learning and do new challenges, whatever the subject is.

Teach it to learn it

Michael Frank: A lot of people say that the best way to learn something is to teach it. Do you agree? And if so, why?

Dr. Edward Burger: I completely agree with that. Teaching something is the best way to learn it. And I will say that when I’m teaching math, I probably learn far more than anyone else in that room. And it’s because when we’re teaching we’re actively involved in thinking about the material that we’re sharing with others, and equally importantly, we’re also thinking about how to make this make meaning.

I’ll let you in on a little secret. When I lecture mathematics these days, I am lecturing to an audience of one: me.

I’ve now come to a point after 30 some odd years of being able to speak from my mouth, whilst simultaneously listening with completely naive ears to what I’m literally saying, rather than to what I think I’m saying, or just having the attitude that I understand it.

“If you are writing an essay, read literally what you have written – not what you intended to communicate. Pretend you don’t know the argument you are making and read your actual words. What’s confusing and what’s missing? If you think you know an idea but can’t express it clearly, then this process has identified a gap or vagueness in your understanding. After you admit and address those weaknesses, your exposition will be clearer and more directed to the actual audience. When delivering an address or making a presentation, apply this same process of deliberately listening to the actual words you are speaking rather than what you imagine you are saying.” – Edward Burger

And when I’m lecturing to a class or to colleagues, if I say in the middle of a lecture, “Let me say that in different way”, that’s actually a top secret cue. That means that whatever I just said I didn’t understand it myself. And so I have to explain it to myself again because it came out all garbled, or in a way that was meaningless. And so therefore I’m going to build a deeper understanding into the content.

And so absolutely, if you can teach someone, if you can tutor, if you’re a young person in school, teach it to a family member, teach it to a friend, find people who are struggling and just tutor them. And by doing so you will understand it far more deeply than you would ever have done on your own.

Think outside of the box

Michael Frank: How can we think outside of the box? What are some exercises the average person can do to improve their creative thinking skills?

Dr. Edward Burger: One idea is to look at extreme cases. So if you’re trying to create something that has a practical essence to it, just think impractically. Free yourself of all constraints, throw away everything so that there’s no budget anymore that’s confining you. There’s no physical confinement of space. You now have all the freedom in the world. What would you do then?

Now whatever you come up with of course is not going to work because it will be impractical. So you’ve intentionally failed. But now you can take a look at that impractical solution and see if he can whittle it down to size. And quite often you will find that your own creativity allows you to see something that you’ve never seen before.

Ask the exact opposite question

Another idea is to think about the opposite. So if you’re trying to accomplish something, ask yourself the exact opposite question.

So if I’m trying to maximize sales of something, and I don’t know how to do that, ask yourself:

How can I minimize sales?

Without just saying I’m going to stop making the product:

How could I discourage consumers from buying this?

And often asking questions like that will lead you to some clever or quirky or interesting ideas, or give you an insight into some essential element, or allow you to see something in a different way, which then allows you to create something and move forward.

So thinking about the opposite question, or putting the issue on its head, is a great way to see it in different light and therefore perceive it in a more creative way.

Learning mistake – not acknowledging biases

Michael Frank: In addition to everything we’ve discussed, what do you feel are the biggest mistakes that most people make when learning something new?

Dr. Edward Burger: I think sometimes we don’t acknowledge our own biases and preconceived notions, and therefore if something seems very foreign or threatening to us, we have a knee-jerk initial reaction and we let that carry the day.

Whereas I think being much more mindful and saying:

How can I understand this – even if I disagree with it?

Even if I find it awful or disgusting or disgraceful – how can I empathize?

Today in our world, we have conflated the notion of empathy and sympathy, and in fact, they’re very different things. Sympathy means I agree with you. We’re on the same page. Empathy means I might agree or I might disagree, but at least I understand what it is that you’re saying, and maybe even why you might say it, and how your life history could have led you to that thought, even if it’s offensive to me.

Being open to our biases is a very difficult to do, but it’s often a mistake if we don’t do it.

This interview has been edited and condensed for clarity.

An excellent 23 minute overview of the 5 Elements of Effective Thinking with Dr. Edward Burger

Dr. Edward Burger is President of Southwestern University as well as a professor of mathematics and an educational leader on thinking, innovation, and creativity. Previously he was the Francis Christopher Oakley Third Century Professor of Mathematics at Williams College. He has delivered over 700 addresses worldwide at venues including Berkeley, Harvard, Princeton, and Johns Hopkins as well as at the Smithsonian Institution, Microsoft Corporation, the World Bank, the International Monetary Fund, the U.S. Department of the Interior, the U.S. Department of the Treasury, the New York Public Library, and the National Academy of Sciences. He is the author of over 70 research articles, books, and video series (starring in over 4,000 on-line videos), including the book The 5 Elements of Effective Thinking which has been translated into over a dozen languages worldwide. His latest book, Making Up Your Mind: Thinking Effectively Through Creative Puzzle-Solving was on several of Amazon’s Hot New Releases lists.

In 2006, Reader’s Digest listed Burger in their annual “100 Best of America” as America’s Best Math Teacher. In 2010 he was named the winner of the Robert Foster Cherry Award for Great Teaching—the largest prize in higher education teaching across all disciplines in the English speaking world. Also in 2010, he starred in a mathematics segment for NBC-TV on the Today Show; that appearance earned him a 2010 Telly Award. The Huffington Post named him one of their 2010 Game Changers: “HuffPost’s Game Changers salutes 100 innovators, visionaries, mavericks, and leaders who are reshaping their fields and changing the world.” In 2012, Microsoft Worldwide Education selected him as one of their “Global Heroes in Education.” In 2013, Burger was inducted as an inaugural Fellow of the American Mathematical Society. In 2014, Burger was elected to The Philosophical Society of Texas. He is now in his fourth season of his weekly program on thinking and higher education produced by NPR’s Austin affiliate KUT. The series, Higher ED, is available at and on iTunes.



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