From one of my favorite blogs, which has a focus on looking at brain functioning to understand all sorts of issues in education, learning, and life, there is a wonderful post about mathematical minds.
Gifted math minds really do 'light up' differently than average math minds when looking at math-related problems. And because of the way the brain is organized and behaves for different mental tasks, gifted math students can be difficult to identify from commonly used assessments and classroom behaviors. For instance, many truly advanced math students are not strong verbally, which can make them difficult to pick out of a crowd, and many like to 'do their own thing' when it comes to math and not at all be interested in the rote math memorization so often done in school. And likely the single most common trait is the love of solving problems of any type. This shows up not just in the 'numbers people,' but also tinkerers. Can you relate to any of these traits?
Showing posts with label education. Show all posts
Showing posts with label education. Show all posts
Thursday, July 21, 2011
Wednesday, December 22, 2010
Where do New Ideas come from?
Two terms we hear quite frequently in education are innovation and creativity. CEOs and other private sector leaders largely agree that these two 'skills' are essential for the present generation of children who are moving through the education system, as manufacturing jobs are largely gone and the economy is fast becoming one built around services and the flow of information, i.e. technical jobs that will be the thrust of job growth over the next couple decades.
But what exactly are innovation and creativity? The dictionary definition of innovation is 'the introduction of new things or methods,' while creativity is 'the ability to create meaningful new ideas, forms or methods' that are original and imaginative. So the key notion is the development of new ideas in whatever field one is working. A question naturally develops, which is where do new ideas come from? How do we begin preparing children now to be creative and innovative in the future? In the past, many would have first thought about the arts as being the training ground for creativity. Now, we realize that the development of the abilities and mindsets and skills necessary to be creative in every field of study is necessary.
Steven Johnson's new book, Where Good Ideas Come From: The Natural History of Innovation, provides the argument that there are seven common themes that have led to the vast majority of great ideas throughout history. He gives numerous examples of such ideas, ranging from Darwin's development of the theory of evolution to the of the GPS system, from Google to the creation of the first mechanical computing devices centuries ago, and so on. It is an interesting read.
Here is a summary of the seven themes that lead to good ideas. Keep in mind there is certainly some degree of overlap and relationships between the themes, but overall they can be thought of as distinct concepts.
1. The Adjacent Possible: Even if you have an interest in some topic or problem, if there is not a good environment conducive to presenting the necessary pieces to solve the problem, good ideas will almost certainly not develop. You may be brilliant with some of the information (i.e. pieces of a puzzle) in your mind that is necessary to solve a problem, but if your surroundings are not able to provide the remaining pieces of information or experiences, you will endlessly search for them to no avail. If you are isolated from others who know something about your problem or issue, or if there is no means of gathering further information (which is becoming less of a problem with the advent of the Internet), or if your environment does not provide the physical infrastructure or supplies to finish building a new physical device, you will be unable to develop the Idea or solution to your problem.
2. Liquid Networks: Great ideas can develop when information is allowed to flow through a larger network. One possible network is a social network, or often and more specifically, a professional network. The focus of this is the ability to collaborate to solve problems. It turns out that there are almost no great ideas throughout history that have been developed in isolation or by an individual who did not need any help in the development of that great idea. One may think Newton or Einstein did their work in isolation, but this is not entirely true. Those two individuals come about as close as you can get to not needing a network to develop the laws of motion or relativity, but they relied on some level of feedback, reading others' work, and ultimately talking and discussing issues with close colleagues and friends.
An interesting study was done that looked at how research groups reach the coveted 'Eureka!' moment, where a new discovery is made. It turns out that these rare moments of discovery or problem solving almost never happen in the lab! Instead, the 'Aha!' are yelled out at the conference table, where members of the group are throwing ideas around and sharing results of their latest work over the past week. The person who figures it out needs to have input they have not thought about from the larger group or network, before the grand idea is formed.
3. Slow Hunch: This is the notion of wanting to solve a complex problem or answer a difficult, involved question, but needing long periods of time to find 'the idea' that allows you to solve it. This could be over a period of years. Darwin, for example, had all sorts of data and observations he mulled over for nearly twenty years; same for Johannes Kepler, and countless others. It takes percolation of ideas in one's mind before the right mix is found. Especially in the past, individuals would keep 'commonplace books' where they would write down all thoughts and experiments and notes from literature. They would review it frequently see where their thoughts have been and where they are presently. Now many people do similar things electronically, but the idea is the same. For inventors and experimentalists, the slow hunch is an analogue of tinkering. Whatever you call it, people have hunches they follow, some of which work and others that do not, but over time the right connections of ideas are made in the brain and 'the idea' forms. While it may seem like more of an 'Eureka!' moment, it was likely a slow hunch that evolved into the great idea.
4. Serendipity: This is the accidental connection. This theme stems from the many examples of artists and scientists and businesspeople who get the great idea in dreams. Thoughts and information are processed subconsciously, and the idea seems to come from 'out of the blue.' But it is something that has been thought about consciously and then develops during the stormy brain activity during REM sleep. Every so often the right synapses fire that connect the appropriate thoughts in the mind. In fact, brain studies in 2007 by Robert Thatcher show how busier, noisier brains do better on IQ tests, since the increased neural activity allow for more interactions of more synapses between neurons. If one gets lucky, the right combination of thoughts are processed during the chaos and the idea is hatched.
This notion of the accidental discovery can be accelerated and encouraged during brainstorming sessions, where ideas are being thrown around, some chaos is present, and someone puts out just the right example or bit of information that clicks, and the idea is born. There is an argument that the Internet and web surfing can encourage serendipity because it is so easy to go off on tangents during research that a new piece of data from a site you never would have guessed would be useful actually turns out to be the key to forming a solution or great idea. Taking walks and showers are other ways to encourage this, and the prime Eureka moment of Archimedes took place in the tub!
5. Error: I think of this as learning from trial and error us a powerful way to modify initial, likely incorrect, ideas or solutions, to form the correct idea or solution. As an experimentalist, I have experience with this. On paper, you think you have the perfect design to test something. You put it together, and it is a complete flop! You need to play with it, learn from any mistakes, and modify. Perhaps you need to scrap the design altogether. But that is OK, since you learned from the errors. Theorists of all disciplines must learn from errors in their predictions when in conflict with experimental data, and this is a way to develop new ideas to replace those which are flawed in the initial theoretical model.
Errors are helpful because they help eliminate some number of incorrect ideas, and allows us to explore other ideas outside of the set of those that are incorrect.
6. Exaptation: This is borrowing a mature technology or idea from, typically, a different field and putting it to use to solve a seemingly unrelated problem. Some have called Gutenberg's printing press the most significant invention of the past millennium. But he borrowed a technology from the wine producing industry of the day, which was a screw system for pressing the grapes. It turned out this inspired him to develop the model for the press, using the same screw system. In economics, mathematical modeling and functional solutions in physics inspired new economic modeling and mathematical solutions to statistical problems, to the point of there being a new subfield of econophysics. We are using natural designs in plants and animals to develop new ideas for manmade products, ranging from structures for robotics to membrane systems to aerodynamic designs.
A big part of this, in my mind, includes analogies. The use of analogies is powerful in teaching and learning, cognition, and in just about any field of study one can imagine. It is making something more familiar by using ideas or concepts from entirely different fields or contexts. I certainly agree that this theme is completely relevant to the formation of new ideas, as well as for learning about new topics.
7. Platforms: The last theme for forming good ideas is to have a foundational set of principles, concepts, ideas, thoughts, or rules and build off that foundation, or platform. Physics is one of the great examples. Classically, there is Newton's laws and Maxwell's equations. For centuries, those provided a platform to build from, and science and technology prospered. Ideas continuously develop as 'what ifs' of known problems and solutions. This led all the way to taking people to the moon. For the GPS system, it all began with Sputnik, when two engineers used the Doopler effect to pinpoint the orbital trajectory of the satellite. This one development got the military to ask them if it is possible to invert the system, and if one could use the technique for a satellite to pinpioint the location of a signal on the ground. Turned out it is, and our ballistic missile system was born. Years of playing with this technology platform developed into a 30-satellite GPS system (as well as weather satellite and radar systems).
Looking over this list, it seems fairly complete. Some are more obvious than others, but the production of good ideas is something one cannot predict. However, identifying circumstances and environments that increase the likelihood of good idea production is useful. Many of these ideas are already employed in industry, such as Google's 20% rule (all engineers must take 20% of their time and devote it to their own interests and research, where the slow hunch is encouraged), as well as in university research, where the development of multi- and inter-disciplinary research collaborations and research institutes are being formed (perhaps most famous is the Santa Fe Institute, which has a focus on complex systems analysis) and utilize several of the above themes. We can certainly implement some of these ideas into the classroom, to provide exposure and training to students about the skill sets they need when they move into college and beyond.
What is also clear is that regardless of the pattern(s) of innovation being used, these work best in open environments where ideas and information can freely flow in unregulated channels. This certainly means having an open Internet will be vital to the continuation of progress and the production of ideas that will, hopefully, benefit humankind.
But what exactly are innovation and creativity? The dictionary definition of innovation is 'the introduction of new things or methods,' while creativity is 'the ability to create meaningful new ideas, forms or methods' that are original and imaginative. So the key notion is the development of new ideas in whatever field one is working. A question naturally develops, which is where do new ideas come from? How do we begin preparing children now to be creative and innovative in the future? In the past, many would have first thought about the arts as being the training ground for creativity. Now, we realize that the development of the abilities and mindsets and skills necessary to be creative in every field of study is necessary.
Steven Johnson's new book, Where Good Ideas Come From: The Natural History of Innovation, provides the argument that there are seven common themes that have led to the vast majority of great ideas throughout history. He gives numerous examples of such ideas, ranging from Darwin's development of the theory of evolution to the of the GPS system, from Google to the creation of the first mechanical computing devices centuries ago, and so on. It is an interesting read.
Here is a summary of the seven themes that lead to good ideas. Keep in mind there is certainly some degree of overlap and relationships between the themes, but overall they can be thought of as distinct concepts.
1. The Adjacent Possible: Even if you have an interest in some topic or problem, if there is not a good environment conducive to presenting the necessary pieces to solve the problem, good ideas will almost certainly not develop. You may be brilliant with some of the information (i.e. pieces of a puzzle) in your mind that is necessary to solve a problem, but if your surroundings are not able to provide the remaining pieces of information or experiences, you will endlessly search for them to no avail. If you are isolated from others who know something about your problem or issue, or if there is no means of gathering further information (which is becoming less of a problem with the advent of the Internet), or if your environment does not provide the physical infrastructure or supplies to finish building a new physical device, you will be unable to develop the Idea or solution to your problem.
2. Liquid Networks: Great ideas can develop when information is allowed to flow through a larger network. One possible network is a social network, or often and more specifically, a professional network. The focus of this is the ability to collaborate to solve problems. It turns out that there are almost no great ideas throughout history that have been developed in isolation or by an individual who did not need any help in the development of that great idea. One may think Newton or Einstein did their work in isolation, but this is not entirely true. Those two individuals come about as close as you can get to not needing a network to develop the laws of motion or relativity, but they relied on some level of feedback, reading others' work, and ultimately talking and discussing issues with close colleagues and friends.
An interesting study was done that looked at how research groups reach the coveted 'Eureka!' moment, where a new discovery is made. It turns out that these rare moments of discovery or problem solving almost never happen in the lab! Instead, the 'Aha!' are yelled out at the conference table, where members of the group are throwing ideas around and sharing results of their latest work over the past week. The person who figures it out needs to have input they have not thought about from the larger group or network, before the grand idea is formed.
3. Slow Hunch: This is the notion of wanting to solve a complex problem or answer a difficult, involved question, but needing long periods of time to find 'the idea' that allows you to solve it. This could be over a period of years. Darwin, for example, had all sorts of data and observations he mulled over for nearly twenty years; same for Johannes Kepler, and countless others. It takes percolation of ideas in one's mind before the right mix is found. Especially in the past, individuals would keep 'commonplace books' where they would write down all thoughts and experiments and notes from literature. They would review it frequently see where their thoughts have been and where they are presently. Now many people do similar things electronically, but the idea is the same. For inventors and experimentalists, the slow hunch is an analogue of tinkering. Whatever you call it, people have hunches they follow, some of which work and others that do not, but over time the right connections of ideas are made in the brain and 'the idea' forms. While it may seem like more of an 'Eureka!' moment, it was likely a slow hunch that evolved into the great idea.
4. Serendipity: This is the accidental connection. This theme stems from the many examples of artists and scientists and businesspeople who get the great idea in dreams. Thoughts and information are processed subconsciously, and the idea seems to come from 'out of the blue.' But it is something that has been thought about consciously and then develops during the stormy brain activity during REM sleep. Every so often the right synapses fire that connect the appropriate thoughts in the mind. In fact, brain studies in 2007 by Robert Thatcher show how busier, noisier brains do better on IQ tests, since the increased neural activity allow for more interactions of more synapses between neurons. If one gets lucky, the right combination of thoughts are processed during the chaos and the idea is hatched.
This notion of the accidental discovery can be accelerated and encouraged during brainstorming sessions, where ideas are being thrown around, some chaos is present, and someone puts out just the right example or bit of information that clicks, and the idea is born. There is an argument that the Internet and web surfing can encourage serendipity because it is so easy to go off on tangents during research that a new piece of data from a site you never would have guessed would be useful actually turns out to be the key to forming a solution or great idea. Taking walks and showers are other ways to encourage this, and the prime Eureka moment of Archimedes took place in the tub!
5. Error: I think of this as learning from trial and error us a powerful way to modify initial, likely incorrect, ideas or solutions, to form the correct idea or solution. As an experimentalist, I have experience with this. On paper, you think you have the perfect design to test something. You put it together, and it is a complete flop! You need to play with it, learn from any mistakes, and modify. Perhaps you need to scrap the design altogether. But that is OK, since you learned from the errors. Theorists of all disciplines must learn from errors in their predictions when in conflict with experimental data, and this is a way to develop new ideas to replace those which are flawed in the initial theoretical model.
Errors are helpful because they help eliminate some number of incorrect ideas, and allows us to explore other ideas outside of the set of those that are incorrect.
6. Exaptation: This is borrowing a mature technology or idea from, typically, a different field and putting it to use to solve a seemingly unrelated problem. Some have called Gutenberg's printing press the most significant invention of the past millennium. But he borrowed a technology from the wine producing industry of the day, which was a screw system for pressing the grapes. It turned out this inspired him to develop the model for the press, using the same screw system. In economics, mathematical modeling and functional solutions in physics inspired new economic modeling and mathematical solutions to statistical problems, to the point of there being a new subfield of econophysics. We are using natural designs in plants and animals to develop new ideas for manmade products, ranging from structures for robotics to membrane systems to aerodynamic designs.
A big part of this, in my mind, includes analogies. The use of analogies is powerful in teaching and learning, cognition, and in just about any field of study one can imagine. It is making something more familiar by using ideas or concepts from entirely different fields or contexts. I certainly agree that this theme is completely relevant to the formation of new ideas, as well as for learning about new topics.
7. Platforms: The last theme for forming good ideas is to have a foundational set of principles, concepts, ideas, thoughts, or rules and build off that foundation, or platform. Physics is one of the great examples. Classically, there is Newton's laws and Maxwell's equations. For centuries, those provided a platform to build from, and science and technology prospered. Ideas continuously develop as 'what ifs' of known problems and solutions. This led all the way to taking people to the moon. For the GPS system, it all began with Sputnik, when two engineers used the Doopler effect to pinpoint the orbital trajectory of the satellite. This one development got the military to ask them if it is possible to invert the system, and if one could use the technique for a satellite to pinpioint the location of a signal on the ground. Turned out it is, and our ballistic missile system was born. Years of playing with this technology platform developed into a 30-satellite GPS system (as well as weather satellite and radar systems).
Looking over this list, it seems fairly complete. Some are more obvious than others, but the production of good ideas is something one cannot predict. However, identifying circumstances and environments that increase the likelihood of good idea production is useful. Many of these ideas are already employed in industry, such as Google's 20% rule (all engineers must take 20% of their time and devote it to their own interests and research, where the slow hunch is encouraged), as well as in university research, where the development of multi- and inter-disciplinary research collaborations and research institutes are being formed (perhaps most famous is the Santa Fe Institute, which has a focus on complex systems analysis) and utilize several of the above themes. We can certainly implement some of these ideas into the classroom, to provide exposure and training to students about the skill sets they need when they move into college and beyond.
What is also clear is that regardless of the pattern(s) of innovation being used, these work best in open environments where ideas and information can freely flow in unregulated channels. This certainly means having an open Internet will be vital to the continuation of progress and the production of ideas that will, hopefully, benefit humankind.
Saturday, April 10, 2010
Rest Before Mental Work a Plus
The Drs. Eide had a brief post about the positive effects of taking a nap prior to doing mental gymnastics that relate to memory and learning. A UC-Berkley study showed a significant gain in learning for those who nap/rested prior to doing the mental activity compared to those who did not nap.
I like the example they use where, at Google, employees have access to what are effectively napping modules (nap pods) that block light and sound. By resting for, say, 30 minutes or so, worker productivity, innovation and creativity should be enhanced by being able to take that quick rest period, particularly if it is just prior to a working group meeting or research period. The brain literally has a chance to reset and blood flow to the hippocampus increases, which is good preparation for the parts of the brain where learning and memory physically take place.
This has implications for education. If there is a more intense period of learning planned towards the end of a class period, where students have already been working for some period of time, a brief few minutes to rest may in fact enhance the learning immediately prior to the more intense learning period. Many teachers, myself included, know that using something like a 20-5 strategy works with students (meaning 20 minutes of activity followed by 5 minutes of practice/rest) seems to be effective for many students. This type of research helps explain why such strategies work, and suggests we should do more of work-rest periods in the classroom help our students maximize what they get from a lesson or activity. A detailed article about what is happening with the brain can be found here.
I like the example they use where, at Google, employees have access to what are effectively napping modules (nap pods) that block light and sound. By resting for, say, 30 minutes or so, worker productivity, innovation and creativity should be enhanced by being able to take that quick rest period, particularly if it is just prior to a working group meeting or research period. The brain literally has a chance to reset and blood flow to the hippocampus increases, which is good preparation for the parts of the brain where learning and memory physically take place.
This has implications for education. If there is a more intense period of learning planned towards the end of a class period, where students have already been working for some period of time, a brief few minutes to rest may in fact enhance the learning immediately prior to the more intense learning period. Many teachers, myself included, know that using something like a 20-5 strategy works with students (meaning 20 minutes of activity followed by 5 minutes of practice/rest) seems to be effective for many students. This type of research helps explain why such strategies work, and suggests we should do more of work-rest periods in the classroom help our students maximize what they get from a lesson or activity. A detailed article about what is happening with the brain can be found here.
Saturday, October 17, 2009
My Class Blog
At the start of the school year, I started a separate blog specifically for my physics classes. It will be a work in progress, of course, with one aspect being a variety of 'how to' videos for numerous physics problems and topics. The latest, for example, is 'how to do multi-body systems with tension,' which can be confusing to students who are first exposed to such problems. The videos are actually screencasts with voice, made with ScreenToaster, which I recommend to all teachers. This online tool, along with a tablet computer, is truly a powerful combination for producing useful presentations that can be embedded online. I have already used such screencasts for students who miss a couple days due to illness or college visits, where examples done in class and then put online have allowed them to catch up immediately. I plan on making an online library with all sorts of examples, notes, and demonstrations so students can review at their leisure, whether it is just to remind themselves of what went on during class, or reviewing for a quizzam, or catching up when absent. It is also a good tool for parents to check out if they are interested in what happens in their child's class.
Tuesday, July 15, 2008
More Differences between how boys and girls process same information
Another thank you to the Drs. Eide at Eide Neurolearning Blog. A recent post shows how smart girls and smart boys, as defined by matched scores on IQ and performance on a verbal comprehension task, process the same verbal information differently. They show some nice functional MRI (fMRI) images from a girl and a boy, where girls use connections between their left superior temporal gyrus connection to left hemispheric language areas, whereas boys relied more on the connections between the right superior temporal gyrus and left inferior frontal gyrus to connect to left hemispheric language areas.
Without knowing much at all about the neurobiology of all this, I suspect this fits with other data and studies I have read, which all seem to suggest a common conclusion: boys take longer than girls to process and learn the same material. Some have suggested that one factor of boys performing more poorly in classes (in terms of grades) when compared to girls is that, because they take longer to process and learn material, boys are more likely to not complete homework. If they miss an assignment, or turn one in incomplete, most teachers are likely to either not accept it or give it a lower grade. What would happen if boys had a longer time to complete homework? Or take tests and other assessments? Would the gender achievement gap seen in some areas of studies and age groups begin to diminish? This would be an interesting question to answer. It is time more educators at all levels look long and hard at cognitive science and research, so we can best work the brains of individual students to maximize learning for everyone.
Without knowing much at all about the neurobiology of all this, I suspect this fits with other data and studies I have read, which all seem to suggest a common conclusion: boys take longer than girls to process and learn the same material. Some have suggested that one factor of boys performing more poorly in classes (in terms of grades) when compared to girls is that, because they take longer to process and learn material, boys are more likely to not complete homework. If they miss an assignment, or turn one in incomplete, most teachers are likely to either not accept it or give it a lower grade. What would happen if boys had a longer time to complete homework? Or take tests and other assessments? Would the gender achievement gap seen in some areas of studies and age groups begin to diminish? This would be an interesting question to answer. It is time more educators at all levels look long and hard at cognitive science and research, so we can best work the brains of individual students to maximize learning for everyone.
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