Myth #1: Math is about numbers and computation but I'm not very good at doing calculations in my head.
There are two things wrong with this statement. First, math is not about computation and second, its not about speed or the ability to do things in your head.
So what is math about then? It's about patterns and relationships and about using our skills for language to describe the abstract world around us in ways that make it easier to understand. Computation actually has very little to do with mathematics. In fact, some of the most brilliant mathematicians and scientists are horrible number crunchers. It's much more about recognizing and describing patterns and relationships between objects than it is about being able to do long division or multiply decimals.
Also, who cares how fast you are or how good of a number cruncher you are? My senior year of college I had a take home test with 6 problems that took 10 days to finish. It was definitely not a test of calculating speed. In fact, most of the problems didn't even have numbers in them! The goal of math is not to show who is the fastest, it is to challenge our ability to think creatively, find connections, and communicate our ideas clearly so others can understand.
Sure, timely calculations have their place but they should not be the initial focus when learning math. Start by focusing on the patterns and relationships first then your speed and accuracy will follow as you understand the concepts more deeply.
So what is math about then? It's about patterns and relationships and about using our skills for language to describe the abstract world around us in ways that make it easier to understand. Computation actually has very little to do with mathematics. In fact, some of the most brilliant mathematicians and scientists are horrible number crunchers. It's much more about recognizing and describing patterns and relationships between objects than it is about being able to do long division or multiply decimals.
Also, who cares how fast you are or how good of a number cruncher you are? My senior year of college I had a take home test with 6 problems that took 10 days to finish. It was definitely not a test of calculating speed. In fact, most of the problems didn't even have numbers in them! The goal of math is not to show who is the fastest, it is to challenge our ability to think creatively, find connections, and communicate our ideas clearly so others can understand.
Sure, timely calculations have their place but they should not be the initial focus when learning math. Start by focusing on the patterns and relationships first then your speed and accuracy will follow as you understand the concepts more deeply.
Take a look at this diagram as an example. This picture categorizes many of the major topics in mathematics. It is tough to categorize some topics since there is so much overlap between them all. Other topics (such as Discrete Math or Engineering) are not included since they are applications of a variety of different topics. Whatever the case, it is helpful to get the "big picture" and to notice how certain topics start to relate to each other. The math that is taught in elementary, middle and high school barely scrapes the surface of what is actually out there in the world of mathematics. |
In the bigger picture, math studies the patterns that exist in the universe around us. Some are quantifiable and measurable such as patterns in change, chance, and number. Others are more abstract such as the study of structures and algebra. Whatever the area being studied, it's all about the patterns involved.
Notice also that all of these patterns fall under another topic: "Logic and Reasoning". This is the fundamental item that makes math work. Math follows the rules of logic and once you start to look toward the bigger picture and notice the themes and patterns involved, the connections will come quicker and math as a whole will begin to make a lot more sense.
Notice also that all of these patterns fall under another topic: "Logic and Reasoning". This is the fundamental item that makes math work. Math follows the rules of logic and once you start to look toward the bigger picture and notice the themes and patterns involved, the connections will come quicker and math as a whole will begin to make a lot more sense.
Myth #2: Math ability is a genetic thing. Some people have it and some people don't.
Remember what we just said math is all about? Patterns and relationships. Do you know what our brains are biologically wired to do? Discover and define patterns and relationships. This is how all train of thought happens! When you see an object your brain automatically processes all the experiences it has had and finds similarities and differences that help to define what that object is.
Have you ever used the phrase "Oh, that reminds me..."? Bringing up past experiences, memories, and making connections between ideas is what our brains do best. Math is actually much more natural than we often think it is.
Sure, there are certain people who are obviously very gifted at mathematics just like there are sports, music, or literary prodigies. But what makes these special talents so special? It's just about their brain's ability to find connections. We all have this ability since our brains all function in the same basic way. Some people can just build synapses faster and fire neurons quicker which means they can make more connections and recognize patterns easier. The important thing to realize is that, yes, it is easier for some people but the genetic ability to do math is in all of us. Math is not an on/off switch where some brains are turned on and others are off. Everybody's got the ability, it's just a matter of the degree to which we use it and practice it that make us successful.
Mathematician and author Keith Devlin has two great books on this topic that I highly recommend. He does a great job of explaining how our minds handle mathematics in a writing style that is simple and entertaining.
The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip (Here's a nice book review of The Math Gene)
The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs)
Have you ever used the phrase "Oh, that reminds me..."? Bringing up past experiences, memories, and making connections between ideas is what our brains do best. Math is actually much more natural than we often think it is.
Sure, there are certain people who are obviously very gifted at mathematics just like there are sports, music, or literary prodigies. But what makes these special talents so special? It's just about their brain's ability to find connections. We all have this ability since our brains all function in the same basic way. Some people can just build synapses faster and fire neurons quicker which means they can make more connections and recognize patterns easier. The important thing to realize is that, yes, it is easier for some people but the genetic ability to do math is in all of us. Math is not an on/off switch where some brains are turned on and others are off. Everybody's got the ability, it's just a matter of the degree to which we use it and practice it that make us successful.
Mathematician and author Keith Devlin has two great books on this topic that I highly recommend. He does a great job of explaining how our minds handle mathematics in a writing style that is simple and entertaining.
The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip (Here's a nice book review of The Math Gene)
The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs)
Myth #3: I don't have a logical or sequential way of thinking. I am much more artistic and creative than I am scientific.
Combine this myth with the previous one and you can see why there are so many people that believe that they are physically and mentally unable to handle mathematics. Remember above where we said that all of math falls under the rules of logic and reasoning? Well we should also mention that logic and creativity are not disjoint. You can have both and, in fact, the best mathematicians are both logical and extremely creative.
Sometimes in math there are straightforward rules and laws that have to be followed to get from point A to point B. Other times (more often than not) you are given a number of details or restrictions and you have to use your resources to come to a solution. There is logic involved but there is also a great deal of creative thinking needed to figure out which methods to use. Math is about solving problems. Creative thinkers tend to be better problem solvers.
When presented with a difficult problem or situation, which train of thought do you think is going to lead to more frustration and anxiety?
"This doesn't match up with my skills and abilities so I can't do it."
or
"I know what my strengths and skills are.....how can I use them to my advantage??"
A simple change in perspective can go a long way.
Sometimes in math there are straightforward rules and laws that have to be followed to get from point A to point B. Other times (more often than not) you are given a number of details or restrictions and you have to use your resources to come to a solution. There is logic involved but there is also a great deal of creative thinking needed to figure out which methods to use. Math is about solving problems. Creative thinkers tend to be better problem solvers.
When presented with a difficult problem or situation, which train of thought do you think is going to lead to more frustration and anxiety?
"This doesn't match up with my skills and abilities so I can't do it."
or
"I know what my strengths and skills are.....how can I use them to my advantage??"
A simple change in perspective can go a long way.
Myth #4: Only really smart people are good at math.
To that I pose the question, what do you mean by the word "smart"? What do you picture when you hear the word "smart"? Do you think of some uncoordinated geeky looking guy or girl who wears glasses and is really good at math, science, and computer technology?
Did you picture a talented artist? Or a famous actress? An accomplished author or poet? Probably not.
Why do you think that is? Why do we associate intelligence and "smartness" with science and technology skills? There is something to be said about the abstract thinking involved that makes it more challenging than other subjects, but when it comes down to it, does being good at math make you more intelligent than someone who is equally talented in a different area?
There is a psychologist from Harvard named Howard Gardner who aimed to answer this question. He came up with a new way to define intelligence that takes into consideration the wide range of skills and abilities that we all have. He split our personalities and abilities into 8 categories:
- Bodily/Kinesthetic
- Interpersonal (social relationships and communication)
- Intrapersonal (self-reflection and self-realization)
- Verbal/Linguistic
- Logical/Sequential
- Visual/Spatial
- Musical/Rhythmic
- Naturalistic (awareness of nature and natural surroundings)
His belief is that we have different learning styles and different abilities that allow us all to thrive in different areas. He says that we go back and forth between a number of these areas and eventually grow a preference for one or two learning styles.
These categories represent ways of thinking and perceiving the world around us and we avoid attaching any specific skills to these "intelligences". For example, if you tend to prefer visual/spatial tasks over others, that does not mean that the only thing you will ever be good at is drawing and art. It means that when you are given a math problem, you might need to draw a picture of it or think about it in a different context before you can wrap your mind around it. This is not a bad thing. In fact, by looking at the problem in different and unique ways, you will probably have a deeper and more interesting understanding of it than the logical/sequential students that just memorized the formulas and plugged in numbers.
This philosophy is called the 'Theory of Multiple Intelligences" and is actually a very common tool in education today. Based on your experience in school or at work or with your peers, you have probably seen this in action. You might have a friend who is an amazing guitarist but couldn't catch a football if his life depended on it. Or maybe you know someone who reads like crazy, loves writing, poetry, and is an outstanding public speaker but struggles to draw even the simplest of stick figures.
We all have skills and talents in different areas and being "smart" or "intelligent" is not limited to a certain skill set. Find out what you do best and use it to your advantage. However, your strength in one area is not an excuse to slack off in another. You can learn to develop your other intelligences and broaden your skill set but just keep in mind that there might be specific methods you need to use to help you be successful in these other areas.
Here are a couple videos on this idea of creativity and intelligence that are worth watching to get more insight into this theory.
YouTube: Howard Gardner explains his theory of Multiple Intelligences
TEDTalks: Sir Ken Robinson presents on the importance of creativity in education
There is another great book on math anxiety that touches a great deal on this concept of multiple intelligences. It's a good read to help understand how this idea can be used in the math classroom.
Overcoming Math Anxiety by Shelia Tobias
Did you picture a talented artist? Or a famous actress? An accomplished author or poet? Probably not.
Why do you think that is? Why do we associate intelligence and "smartness" with science and technology skills? There is something to be said about the abstract thinking involved that makes it more challenging than other subjects, but when it comes down to it, does being good at math make you more intelligent than someone who is equally talented in a different area?
There is a psychologist from Harvard named Howard Gardner who aimed to answer this question. He came up with a new way to define intelligence that takes into consideration the wide range of skills and abilities that we all have. He split our personalities and abilities into 8 categories:
- Bodily/Kinesthetic
- Interpersonal (social relationships and communication)
- Intrapersonal (self-reflection and self-realization)
- Verbal/Linguistic
- Logical/Sequential
- Visual/Spatial
- Musical/Rhythmic
- Naturalistic (awareness of nature and natural surroundings)
His belief is that we have different learning styles and different abilities that allow us all to thrive in different areas. He says that we go back and forth between a number of these areas and eventually grow a preference for one or two learning styles.
These categories represent ways of thinking and perceiving the world around us and we avoid attaching any specific skills to these "intelligences". For example, if you tend to prefer visual/spatial tasks over others, that does not mean that the only thing you will ever be good at is drawing and art. It means that when you are given a math problem, you might need to draw a picture of it or think about it in a different context before you can wrap your mind around it. This is not a bad thing. In fact, by looking at the problem in different and unique ways, you will probably have a deeper and more interesting understanding of it than the logical/sequential students that just memorized the formulas and plugged in numbers.
This philosophy is called the 'Theory of Multiple Intelligences" and is actually a very common tool in education today. Based on your experience in school or at work or with your peers, you have probably seen this in action. You might have a friend who is an amazing guitarist but couldn't catch a football if his life depended on it. Or maybe you know someone who reads like crazy, loves writing, poetry, and is an outstanding public speaker but struggles to draw even the simplest of stick figures.
We all have skills and talents in different areas and being "smart" or "intelligent" is not limited to a certain skill set. Find out what you do best and use it to your advantage. However, your strength in one area is not an excuse to slack off in another. You can learn to develop your other intelligences and broaden your skill set but just keep in mind that there might be specific methods you need to use to help you be successful in these other areas.
Here are a couple videos on this idea of creativity and intelligence that are worth watching to get more insight into this theory.
YouTube: Howard Gardner explains his theory of Multiple Intelligences
TEDTalks: Sir Ken Robinson presents on the importance of creativity in education
There is another great book on math anxiety that touches a great deal on this concept of multiple intelligences. It's a good read to help understand how this idea can be used in the math classroom.
Overcoming Math Anxiety by Shelia Tobias
Myth #5: Math is so much more difficult that other subjects.
Actually, this one is not as much of a myth as the previous ones. You are correct here...math is hard. I think it's hard. My students think it's hard. Professional mathematicians think it's really hard. Some topics in math are very simple and straightforward. Others are extremely difficult to understand but eventually you get a grasp of it. Other topics have baffled mathematicians for hundreds of years and still have them scratching their heads to this day.
So what is it about math that makes it so difficult for so many people? First, take in to consideration all the previous psychological barriers that we have mentioned plus all the cultural attitudes towards math then add in the inherent difficulties of the subject itself and you can see why math education has so many issues. Let's set aside all the psycho-social problems for a minute though and look at the subject itself.
In The Math Gene, Keith Devlin poses and interesting explanation of what makes math such a challenging subject. He describes 4 levels of abstract thinking that our minds can handle:
Level 1: You can look at things in your present environment and imagine them rearranged. For example you can imagine what it would look like if you moved that chair over to the corner of the room or if you moved the picture on the wall over a few inches.
Level 2: You can imagine what an item looks, smells, feels like, etc. without it being present in your environment. For example, I can imagine what a rose looks and smells like without actually having one in front of me. You can take past experiences and apply them to an imaginary situation.
Level 3: You can take things that exist in the real world and use their properties and details to create things that don't exist. Picture your favorite mythical beast with the head of a lion, tail of a serpent and wings of an eagle. This creature is not present in your current environment, nor is it something that you have actually experienced in the past. It is an imaginary creation using real-life objects.
Level 4: You can take a concept and represent with tools that are not real or tangible. Take for example language. The concept of a noun is completely abstract. Or take numbers and mathematics as another example. We can use symbols and abstract concepts to describe relationships and objects that we cannot touch, feel, or experience in real life. The expression 3x+4 is totally abstract. We have three abstract objects: 3, 4, and x and we are using abstract relationships (multiplication and addition) to relate them. None of these things exist in real life but they are symbols and concepts used to describe things that we experience.
As you can see, our capacities for language and mathematical reasoning fall in this 4th category. It is very easy for our minds to handle levels one, two, and three, since they all revolve around things that we can experience with our senses. Day to day life requires abstract thinking only in these first three levels most of the time. We have grown to be comfortable with this and it is not difficult for us to do.
The last level of abstract thinking takes away all the comforts of reality and requires us to use our minds and only our minds to describe things and work through problems without the use of our senses and life experiences. This is hard and this is equivalent to your brain running on a treadmill when you are working at this level. Your brain functions a lot like your other muscles and this type of brain workout is very healthy even though it is tough (just like working out really hard can be miserable and painful while you're doing it, but feels so good knowing that you did something healthy and rewarding for your body).
So yes, math is hard. But knowing this can help understand your own situation a little better. You are not the only one that thinks it is hard and it's perfectly normal for you to feel "brain dead" after working on math for a while. It's the same feeling your muscles get after working out. I personally can only focus really hard on a tough math problem for a couple hours before my brain feels exhausted and I need a break. Your brain has an endurance level just like your muscles do. If you never work out your brain, it won't be able to last very long when you work on tough things. The more you practice, the longer you will able to focus and endure difficult levels of abstraction.
This is one of the main reasons that math is a core subject area in school. It is one of the only subjects that can challenge your mind in this way for an extended period of time. It's kind of like a PE class for your brain. Just like in your PE class, some people are in better shape than others and can endure more and tackle more difficult challenges. Just like with any other skill, the more you practice and work at it, the better you become .
So what is it about math that makes it so difficult for so many people? First, take in to consideration all the previous psychological barriers that we have mentioned plus all the cultural attitudes towards math then add in the inherent difficulties of the subject itself and you can see why math education has so many issues. Let's set aside all the psycho-social problems for a minute though and look at the subject itself.
In The Math Gene, Keith Devlin poses and interesting explanation of what makes math such a challenging subject. He describes 4 levels of abstract thinking that our minds can handle:
Level 1: You can look at things in your present environment and imagine them rearranged. For example you can imagine what it would look like if you moved that chair over to the corner of the room or if you moved the picture on the wall over a few inches.
Level 2: You can imagine what an item looks, smells, feels like, etc. without it being present in your environment. For example, I can imagine what a rose looks and smells like without actually having one in front of me. You can take past experiences and apply them to an imaginary situation.
Level 3: You can take things that exist in the real world and use their properties and details to create things that don't exist. Picture your favorite mythical beast with the head of a lion, tail of a serpent and wings of an eagle. This creature is not present in your current environment, nor is it something that you have actually experienced in the past. It is an imaginary creation using real-life objects.
Level 4: You can take a concept and represent with tools that are not real or tangible. Take for example language. The concept of a noun is completely abstract. Or take numbers and mathematics as another example. We can use symbols and abstract concepts to describe relationships and objects that we cannot touch, feel, or experience in real life. The expression 3x+4 is totally abstract. We have three abstract objects: 3, 4, and x and we are using abstract relationships (multiplication and addition) to relate them. None of these things exist in real life but they are symbols and concepts used to describe things that we experience.
As you can see, our capacities for language and mathematical reasoning fall in this 4th category. It is very easy for our minds to handle levels one, two, and three, since they all revolve around things that we can experience with our senses. Day to day life requires abstract thinking only in these first three levels most of the time. We have grown to be comfortable with this and it is not difficult for us to do.
The last level of abstract thinking takes away all the comforts of reality and requires us to use our minds and only our minds to describe things and work through problems without the use of our senses and life experiences. This is hard and this is equivalent to your brain running on a treadmill when you are working at this level. Your brain functions a lot like your other muscles and this type of brain workout is very healthy even though it is tough (just like working out really hard can be miserable and painful while you're doing it, but feels so good knowing that you did something healthy and rewarding for your body).
So yes, math is hard. But knowing this can help understand your own situation a little better. You are not the only one that thinks it is hard and it's perfectly normal for you to feel "brain dead" after working on math for a while. It's the same feeling your muscles get after working out. I personally can only focus really hard on a tough math problem for a couple hours before my brain feels exhausted and I need a break. Your brain has an endurance level just like your muscles do. If you never work out your brain, it won't be able to last very long when you work on tough things. The more you practice, the longer you will able to focus and endure difficult levels of abstraction.
This is one of the main reasons that math is a core subject area in school. It is one of the only subjects that can challenge your mind in this way for an extended period of time. It's kind of like a PE class for your brain. Just like in your PE class, some people are in better shape than others and can endure more and tackle more difficult challenges. Just like with any other skill, the more you practice and work at it, the better you become .
Take-Aways
Let's sum up the big ideas presented here:
- Math is hard because it is a physical workout for your brain. Approach it like you approach exercise. It's tough to get into shape, but so
rewarding when you finally do. It takes work and you need to build up endurance and strength so you don't feel so overwhelmed.
- There is no such thing as a "math person". There is not a genetic switch for math ability. Everybody has it.
- People have preferred learning styles and different "intelligence" strengths. Find what you do best and use it to access your math skills
in ways that make sense to you. Use your strengths as a tool to help, not as an excuse to give up.
- There are thousands and thousands of different topics in math and very few of them deal with number crunching and computation. Just
because you don't excel at a certain topic or enjoy a certain topic in math doesn't mean you should give up on math all together. That's
like reading one book you didn't like and deciding to never read again. There is a lot out there in the world of math, keep your mind open
and give it a chance. You might eventually find something you really enjoy.
- Math is hard because it is a physical workout for your brain. Approach it like you approach exercise. It's tough to get into shape, but so
rewarding when you finally do. It takes work and you need to build up endurance and strength so you don't feel so overwhelmed.
- There is no such thing as a "math person". There is not a genetic switch for math ability. Everybody has it.
- People have preferred learning styles and different "intelligence" strengths. Find what you do best and use it to access your math skills
in ways that make sense to you. Use your strengths as a tool to help, not as an excuse to give up.
- There are thousands and thousands of different topics in math and very few of them deal with number crunching and computation. Just
because you don't excel at a certain topic or enjoy a certain topic in math doesn't mean you should give up on math all together. That's
like reading one book you didn't like and deciding to never read again. There is a lot out there in the world of math, keep your mind open
and give it a chance. You might eventually find something you really enjoy.
For more information and specific ways you can apply these ideas, check out the links below.
Tips for Students Tips for Parents
Tips for Students Tips for Parents