Posted on

Abstract Thinking in Problem Solving

Why does the Narwhal have a spiral in its tusk? While many people had wondered about this, the most rational explanation came from D’Arcy Thompson, Scottish biologist and mathematician.

Thompson’s explanation for the spiral was that each stroke of the narwhal’s tail produced not just a forward motion but also a twist that made the narwhal go slowly around it’s own horn. While some of Thompson’s theories were proven wrong, he found many interesting reasons for different shapes and forms in nature. His book, On Growth and Form, laid the foundation for the field of morphogenesis, the process by which body structures are formed.

One of the reasons that Thompson was able to find interesting patterns in nature, was because of his ability to abstract simpler elements from the form of an animal or plant. As Stephen Jay Gould, who was inspired by Thompson’s work, explains “he tried to explain form by reducing its complexity to simpler elements that could be identified as cause.” In other words, his abstraction abilities helped him understand the underlying causes of different forms in nature.

So, what is abstract thinking? There are two aspects of abstract thinking – simplifying by removing details to find salient features, and generalizing to find the core essence. The ability for abstract thinking underlies creative and complex problem solving in many different domains. 

Jeff Kramer, Professor of Computer Science, noticed over his 30 years of teaching that some students were able to handle complexity better than others. They were able to understand distributed algorithms more easily and produced more elegant models and designs. In his words, “What is it that makes the good students so able? What is lacking in the weaker ones? Is it some aspect of intelligence? I believe the key lies in abstraction: The ability to perform abstract thinking and to exhibit abstraction skills.”

The ability to abstract plays a key role in creative problem solving as well. Tina Seelig, Professor at Stanford University and author of InGenius, notes that reframing a problem by asking “why?” can open up a whole new set of solutions. For example, by reframing  “How should we plan a birthday party?” to “How do we make this a special day?” can open up a whole new set of possible ideas.

Reframing a problem typically involves moving to a higher (or more general) level of abstraction. Two ways to reach a higher level of abstraction is to ask ‘why’ or find a category that a given concept belongs to.   

We created our new brainteaser, ‘High and Low‘ to build the ability for abstract thinking and make students comfortable with navigating different levels of abstraction. The brainteasers give a routine activity and the goal is to find one or more ‘High’ and ‘Low’ levels for the activity. The ‘High’ level corresponds to the more general level of abstraction while the ‘Low’ level corresponds to the more specific one.  

Liberman and Trope, describe how the high and low level descriptions can fit into a pattern, “superordinate, high-level descriptions of an activity fit the structure “[description] by [activity]” whereas subordinate low-level descriptions fit the structure “[activity] by [description]”.” For example, if the activity is ‘reading a book’, a high-level description could be ‘learn new things’ (I [learn new things] by [reading a book]) while a low-level description could be ‘by flipping pages’ (I [read a book] by [flipping pages]).

Our goal with these brainteasers is to build this crucial skill of abstract thinking early on through simple exercises. In a recent trial, we were excited to see 8-9 year old students solving these exercises appropriately and being able to apply abstract thinking in reframing problems. We hope that by starting to use abstract thinking in different areas, students will be able to handle complex problem solving more easily later in any domain. 

Posted on

How Neurodiversity Helps in Creativity

As a child, Isaac spoke little and had trouble reacting appropriately in social situations. He found it hard to form friendships and preferred to spend time alone. He lacked the ability to understand the motives of others’ and was prone to having angry outbursts.

If you saw signs of autism in the description, you are probably right. But you might be surprised to know that Isaac grew up to have a successful career. Isaac, as in Isaac Newton, laid the foundations of classical mechanics, made significant contributions to optics and even developed Calculus!

Simon Baron Cohen, psychologist at the University of Cambridge, believes that scientists like Newton and Einstein likely had Asperger’s syndrome (a high functioning variant of Autism Spectrum Disorder).

If Newton was indeed on the spectrum, did his condition help him or hurt him in his intellectual pursuits?

A growing area of research, Neurodiversity, shows that some of the common neurological conditions actually help in certain situations and may have evolutionary advantages.

Recent research has found that disorders like autism, ADHD and Dyslexia can be beneficial when it comes to creative thinking, a skill that is becoming increasingly important. We certainly see some evidence of that in our work with our diverse student population.

Autism Spectrum Disorder (ASD)

Autism is primarily characterized with challenges in social relationships and deficits in the “theory of mind”.

However, Scott Barry Kaufman, author and professor at University of Pennsylvania, explains that people with ASD do care about others and desire connection – they just do it differently. As he writes, “Perhaps instead of viewing people with ASD as “socially awkward” individuals who need to be “fixed,” we should instead conceptualize them as socially creative. They may not do things the “right” way, but they do them their way.”

Outside of social situations, people with ASD have show differences in cognitive creative thinking. For instance, in divergent thinking tasks, people with ASD produce fewer but more original ideas. Contrast this with the conventional guideline of “one needs to generate lots of ideas to get to the more unique ones“. Since the goal of brainstorming is to end up with creative ideas, autism seems to confer some efficiency in this process.

Attention Deficit Hyperactive Disorder (ADHD)

ADHD is characterized by three key groups of symptoms: hyperactivity, impulsivity and distractibility. But these same traits are also helpful in some tasks.

Bonnie Cramond, director at the Torrance Center for Creativity and Talent Development at the University of Georgia, found that the set of traits used to identify ADHD were nearly identical to the set of traits for creative people. 

Recent research has also confirmed the link between ADHD and Creativity. The part of the brain known as the Default Network or the Imagination Network, becomes active during the passive or rest phase and plays a crucial role in creative thinking. In people with ADHD, the brain structure responsible for filtering data from the Imagination Network is “leaky” leading to a more diffused attention style along with more creative thoughts. As Prof. Kaufman explains, “Both creative thinkers and people with ADHD show difficulty suppressing brain activity coming from the “Imagination Network.”” 

Dyslexia

Dyslexia is a reading disorder characterized by difficulty with reading, writing, spelling and grammar, and affects from 5 to 20 percent of all school children.

In dyslexic readers  brain areas (in the left hemisphere) used in recognizing letters and words, and  in sounding out words are under-activated but the parts of the right hemisphere become more active to compensate. That might explain why dyslexics are better at visual spatial skills, out-of-box thinking and holistic perception – skills useful in creative and entrepreneurial work.

In a survey sent to entrepreneurs and corporate managers, Julie Logan, professor of entrepreneurship at Cass Business School in London, found that 35% of entrepreneurs identified themselves as dyslexic compared to only 1% of corporate managers. Richard Branson, one of most famous dyslexic entrepreneur, has often commented that far from being a disability, dyslexia has been his biggest business advantage.

 

To clarify, in highlighting the strengths associated with these disorders we do not intend to trivialize the challenges faced in more severe forms of these disabilities. We hope that by understanding the cognitive strengths that accompany these conditions, we can create better environments for different neurotypes to work together and be productive. As Thomas Armstrong says in his book, Neurodiversity, “diversity among brains is just as wonderfully enriching as biodiversity and the diversity among cultures and races.”

Posted on

How To Think Like A Scientist

Wilson Greatbatch was an American engineer and inventor, who had more than 150 patents to his name over his lifetime. His most famous invention is the implantable Pacemaker, which has saved countless lives since it came out. But it almost didn’t happen!

Greatbatch was working on a device to record heart sounds, when he accidentally installed the wrong resistor and realized that the device was now giving off rhythmic electrical pulses. He realized at that moment, that he had hit on something important. Pacemakers before that time were bulky devices that worked on power mains, but Greatbatch’s discovery showed that they could work with battery and could be made small enough to be implanted.

While this may seem at the surface to have been an accidental discovery, Greatbatch was really thinking like a good scientist. Kevin Dunbar and Nancy Nersessian, have studied scientists and their thought processes for many years, and have distilled the core thinking patterns that underlie creative scientific thinking. Here are a few strategies and techniques that they believe lead to better scientific accomplishments:

Unexpected Results

Accomplished scientists have often mentioned the role of chance in leading to a discovery. But what distinguishes great scientists from average ones is how they pursue the unexpected results. As Dunbar explains, a good heuristic to go by is, “If the finding is unexpected, then set a goal of discovering the causes of the unexpected finding.”

To investigate an unexpected finding, scientists have to pay attention to the finding and recognize that it could lead to some new learning first. It turns out that some scientists have a tendency to make serendipitous discoveries. Sandra Erdelez, a scientist at University of Missouri, has been studying this for many years and found that some people, called the encounterers, have a tendency to stop and “collect” useful or interesting information they bump into. Based on their individual differences in bumping into unexpected information, she classifies people into three types – non-encounterers, occasional encounterers and super-encounterers.

Analogical Thinking

One of the most useful cognitive techniques frequently used in science is analogical thinking. Rutherford-Bohr’s analogy between solar system and atoms or Newton’s analogy between projectiles and moon helped those scientists construct a better model.

Analogies have helped with different aspects of scientific thinking like generating models, designing experiments or formulating hypotheses. As Dunbar explains, “We have found that rather than trying various permutations on a question, the scientists search for a similar problem that has been solved and seek to import its answer to their current problem.” The advantage of analogical thinking, is that it helps the scientists come to a solution quickly by avoiding iterative trials.

Imagistic Reasoning

Imagistic reasoning makes use of images to help in analyzing and understanding a phenomenon. For example, Faraday’s starting point in constructing his field concept was using an image to represent the lines of field like those that form when iron filings are sprinkled around a magnet. By using a more idealized representation through an image, he was able to capture the underlying model.  

Nersessian believes that imagistic reasoning, along with analogical reasoning and thought experiments are part of “abstraction techniques” and help construct a model of a scientific concept.

While most people are familiar with analogical reasoning, As Nersessian explains, “…there are numerous cases that establish the prominence of reasoning from pictorial representations in the constructive practices of scientists who were struggling to articulate new conceptualizations. Such imagistic representations have often been used in conjunction with analogical reasoning in science.”

 

Research in over a decade has demonstrated the significance of these cognitive techniques and strategies in science, and should be included in science education.

We are excited to launch a new middle school science program in partnership with Positive Ally, starting this coming academic year. Our goal is to bring these cognitive techniques to the forefront to build deeper understanding of scientific concepts and help students apply their thinking in solving real world problems.

Posted on

Summer Camp: Applications in Thermochromism

We just wrapped up our summer camps for this year and are excited to share some of the interesting inventions our students came up with! This year we collaborated once again with Archimedes school (who taught 3D printing), and explored a newer STEM area – smart materials.

A smart material changes its physical property in reaction to its environment. The reaction could be a change in volume, color or some other material property and is triggered by a change in the environment (e.g. temperature, stress, electrical current).  In other words, “…this material has built-in or intrinsic sensor(s), actuator(s) and control mechanism(s) by which it is capable of sensing a stimulus, responding to it in a predetermined manner and extent, in a short or appropriate time and reverting to its original state as soon as the stimulus is removed.”

Smart materials are being used in a lot of interesting applications including smart wearables, aerospace and environmental engineering. In our camps, we experimented with one kind of smart material – thermochromic paint, or paint that changes color with temperature. Some common examples of products that use thermochromic paints are mood rings and baby spoons.

Thermochromic paints use liquid crystals or leuco dye technology. After absorbing a certain amount of light or heat, the molecular structure of the pigment changes in such a way that it absorbs and emits light at a different wavelength than before. After the heat source is removed, the molecular structure comes back to its original form.

In our camp, we tried out different ways to change temperature and induce color change in the pigment like body heat, friction, warm light bulbs and electrical current (with high resistance wires). After the students had a chance to play with thermochromic paints, they started the process of coming up with different applications that would benefit from thermochromism.

Students used a variation of mind-mapping, and techniques like associative thinking and challenging assumptions to come up with several different ideas that could use thermochromic paint in a meaningful way. As last year, students found that by using these creative thinking techniques they could come up with 2-3x more ideas. Then they picked a final idea (after evaluating all the ideas on different criteria) to build their prototype. Quite a few of students also 3D printed their prototype (or at least parts of the prototype) by themselves!

As we expected, student ideas were all over the map. Here is a sample of some of the ideas our campers came up with:

  • Electronics: Quite a few ideas were related to overheating of electronic devices so users can take a break from their device. These include cell phone cases, stickers or attachments for laptops and gaming devices.
  • Thermometers: We had a few interesting thermometers for sensing indoor, outdoor and body temperature. For instance, a soft headband to put on babies and little children that can sense when they have fever – very handy to keep track of when to give the next dose of mediation!
  • Baking: One student made a flexible band that goes around baking dishes and can help you keep track when the dish has cooled down and is safe to eat from. A couple students also made multipurpose gloves that could be useful during baking or other activities.
  • Outdoor Activities: Students also created some interesting products like icemakers, tents and even shoes that could warn their users when it’s getting too warm.

We also had a bunch of interesting ideas like an animal shelter/cage (to help the staff easily figure out if its getting too hot for the animal), fun outdoor sunglasses, a cover for steering wheels and cupholders.

What was most heart-warming though, was to see the sense of accomplishment in these students for coming up with their own idea, following it through with prototyping and proudly presenting it on the last day!

Posted on

Stanford Innovation Lab’s Sock Challenge Results

One of the most well-known divergent thinking problem is the Alternate Uses (AU) task where you come up with different ways to use simple, everyday objects. Professor Tina Seelig, who teaches Creativity and Innovation at Stanford University, often uses challenges that build on the AU task for her students. The goal is for students to build both creativity and entrepreneurship by learning to look at an old thing in new ways, and create some kind of value from it.

We recently participated in Stanford Innovation Lab’s (SIL) Sock Challenge, where students had to create value out of mismatched socks. With students from C-Pillars Academy (most of them between 7 and 10 yrs), we used a session to try out the sock challenge one afternoon.

As expected, we got a range of ideas from our students – some common and some original. Five of our student entries were selected and showcased by the SIL team – ideas that we would have picked as well! Here is what we liked about these particular entries.

Mental Transformations

Creativity comes from the mental transformations you make to an existing object or concept to adapt it to a new situation. At one of the spectrum, you could generate ideas that use very few (or no transformations) by simply using a key aspect of the object. An example of this is using the sock as a bag to hold different objects. This doesn’t really require any big mental leaps since a sock resembles an elongated bag and the overall shape of the sock triggers that idea quickly.

On the other extreme, you could do a lot of transformations (typically to get down to the material the object is made of) till there is no longer any resemblance to the original object, and then create something different from the material. An example of this is cutting the sock(s) open and then using it to make a T-shirt or a sweater. In essence, these ideas use the sock as a piece of cloth out of which you can now fashion many different things and it doesn’t really matter that you started out with socks.  

Both of these extremes produce ideas that are not very creative, but the ideas in the middle – the “Goldilocks Ideas” – are where interesting things happen. These are where the transformations preserve some essential properties of the original object, and the changes are applied very thoughtfully to allow the object to be used in a different situation.

The Sock Ball Game created by one of our students is an example. The goal of the game is to toss the colored ball into the matching colored pouch. The bottom part of the sock was cut at the right place to make pouches and the top part of the sock was converted carefully into colored balls to make the game work. The Arm-Warmer is another such example, where another student made holes at exactly the right places (leveraging the heel of the sock for the thumb part) to make the design work.

Remote Associations

Another aspect of Creativity is being able to combine unrelated ideas, or associational thinking. The cloth diaper idea is an example of making a connection with a third world social issue of using simple pieces of cloth as diapers. The idea proposes using old socks to add an additional, absorbent layer on the cloth to make better diapers while reusing socks. The idea stands out since it combines a concept that you don’t normally associate with socks to make something useful.

Elaboration

Elaboration measures the amount of detail and flourishes added to the core idea to make it more complete. Elaboration helps clarify and articulate an idea which results in a better understanding, and often leads to improvements in the core idea. The headband and purse created by two students are great examples of elaboration for this challenge. The headband uses extra parts of the sock to make the flower decoration and the purse uses rolled up pieces of sock to make the handles. And of course, the beautiful designs just make you want to use them!

 

Our students had a lot of fun working on this challenge and we look forward to doing more of these in the future!