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Analogical Reasoning

In the early 1860s, when Leo Tolstoy was teaching writing to children of Russian peasants, he hit upon an interesting way to bring more creativity into the exercise. He asked his students to write a story on the proverb, “He eats with your spoon and then puts your eyes out with the handle.” The result of his exercise surprised even him.

After some initial hesitation, his students approached the challenge with an unexpected enthusiasm and produced a much better composition than the one Tolstoy had himself written. Tolstoy commented on the quality of his students’ work in an article with, “Every unprejudiced man with any feeling for art and nationality, on reading this first page written by me, and the following pages of the story written by the scholars themselves, will distinguish this page from all the others, like a fly in milk, it is so artificial, so false, and written in such a wretched style.”

While Tolstoy was simply trying to motivate his students to write with more vigor and authenticity, he accidently introduced his students to a key creative thinking skill – analogical reasoning.

Analogical reasoning is the ability to find relational similarity between two situations or phenomena. Robert and Michele Root-Bernstein in their book, Sparks of Genius, consider analogical reasoning to lie at “the heart of what it means to think creatively” and a skill that many scientists rate as the most important one to possess.

In fact, several discoveries in science can be traced back to finding the right analogy. For instance, early geneticists likened genes to beads on a string to help them understand how traits are passed along. While this simple analogy couldn’t explain everything, it did suggest possible mechanisms for inherited traits. Making analogies is a fundamental way of thinking applicable not just in science, but in almost every field like mathematics, religion and literature. Robert Frost’s metaphor of life to a journey in “The Road Not Taken” is especially powerful because of the unique associations it invokes each time.

While it’s clear that analogical thinking plays an important role in creative thinking, what exactly does it involve? Underlying analogical thinking are three mental processes – Retrieval (with a current topic in working memory, a person may be reminded of an analogous situation in long-term memory), Mapping (aligning the two situations on the relational structure and projecting inferences), and Evaluation (judging the analogy and inferences).  

The MindAntix brainteaser, Proverbial Tales, inspired by Tolstoy’s challenge to his students, aims to strengthen the mental processes used in analogical reasoning. Using proverbs from different cultures, users have to construct an original story that reflects the meaning of the proverb, forcing them to go through the different stages of retrieval, mapping and evaluation.

As Robert and Michele Root-Bernstein point out, “There is so much to be learned by analogizing that we must not neglect to learn how. Like every other tool for thinking, the capacity within ourselves and our children ought to be nurtured, exercised, trained.”

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Our First Summer Camp And Lessons Learned

We just wrapped up our first summer camp to teach children (8-12yr olds) how to think in more innovative ways. For this camp, we wanted to go beyond simply teaching creativity techniques, to having children actually design objects they use regularly. And since this is the back to school season, we picked “Redesigning School Supplies” as the theme of our camp.

We organized camp activities around a few principles and learned what works well and what doesn’t:

Don’t dumb it down

The neat thing about Creativity is that it is relatively age-agnostic – it’s easy to teach kids core creativity concepts. So, we didn’t skimp on the content. The children learned and experienced creativity techniques and design thinking processes that are typically encountered in graduate level courses.

But we did package the material to be more kid-friendly. For instance, we made a “Minion Game” for the Alternate Uses Task, where a group of minions “discover” an object and the minions take turns in interpreting how that object might be used by humans (all while speaking minion-ese, of course).

Lesson Learned: The campers grasped the concept that we were teaching quickly through play and games, although not everything went perfect. For example, we used the Minion-Game as an opening game, and realized that it wasn’t the best decision. While the kids loved the concept (they asked to play it again the next day), they hadn’t sufficiently warmed up to each other to act silly. In hindsight, this game would have probably worked much better had we scheduled for the second day or later. Our other games fared a lot better, and the children had a great time making their own Twist-a-Story skits, and Crime Scene Investigation movie trailers!

Both group and individual thinking are important

Research has shown that when people brainstorm individually and then bring their ideas to the table for group discussion, the outcome is superior compared to group brainstorming. So, our activities alternated between individual thinking and group brainstorming giving everyone a chance to think on their own.

Lesson Learned: This strategy worked out really well and we ended up with a lot of unique, interesting ideas that children were able to use in their final designs! We will definitely keep this approach going forward.

Make it Relatable

Everyday, we also studied an inventor and their creation to illustrate the concept of the day (like using empathy, making associations, or storyboarding). We also wanted to remove the the psychological barrier that children typically have –  that inventing is for adults. So our profiles included young inventors like the 11 yr old girl who invented the crayon holder, to help use up little pieces of crayon.

Lesson Learned: We are not really sure how much (or if) this inspired our campers, but the children did seem to enjoy learning about other inventors. We’ll continue using  this because it also served as a good transition activity between games and project work.

We organized the campers into four teams and each team picked a school supply to redesign. By the time camp ended we  had some interesting new products – a lunch bag that helps you plan healthy portions, a multi-functional scissors, a universal notebook that minimizes paper cuts, and a better organized and safer backpack. Not bad for the one week we had!

But most importantly, the campers had a great time figuring out their own, unique problems with the objects they picked and applying design thinking to solve them!

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3 Simple Ways To Be Creative in Science

Bernard Baruch, the American financier and political consultant, once commented that “Millions saw the apple fall, but Newton was the one who asked why.” While it’s hard to imagine that no one else asked why, it is still worth pondering on how Newton managed to solve the puzzle.

Newton did not arrive at the solution in a sudden flash of insight. Instead, the groundwork for reaching his conclusion had been laid over several years before that. Newton had been mulling over what force prevents the moon from shooting off in a straight line at a tangent to its orbit. His breakthrough came when he connected the dots between the force that holds the moon in it’s orbit and the force that causes an apple to fall to the ground. In other words, by using an analogy, Newton was able to create the right hypothesis that eventually led to his theory of universal gravity.

Contrast that kind of thinking with how science fair projects in most schools are approached today. Most teachers (helpfully) give out a list of ideas to base science projects on and the focus is almost entirely on following the scientific process to construct good experiments. However, just like Newton’s discovery, most scientific breakthroughs are the result of generating new and novel hypotheses – a skill that unfortunately, doesn’t get as much focus.  Prof. William McGuire, who proposed different techniques to help generate hypotheses, laments that “our methods courses and textbooks concentrate heavily on procedures for testing hypotheses (e.g. measurement, experimental design, manipulating and controlling variables, statistical analysis, etc) and they largely ignore procedures for generating them.“

So how can you start to generate your own hypotheses? Let’s take an example. Suppose you wanted to do a science experiment that involves plants, but instead of the typical “how well do plants grown in different kinds of liquids?”, you wanted to use your own hypothesis. Here are three techniques that you could use to generate some interesting, fresh hypotheses.

  • Use Analogies: Say you start with an analogy that plants are like humans. We know that humans grow faster when they are babies and then start slowing down. We can apply this fact to plants to build a hypothesis of  “Do plants grow faster when they are small?”
  • Stretch or Shrink a Variable: We know that leaves have chlorophyll that help in photosynthesis (converting light energy into chemical energy). So one hypothesis could be that If we were to shrink the chlorophyll (maybe by removing all the leaves) would the plant be able to survive?
  • Use Reversals: You can get additional insights by reversing the causality or taking the opposite of a hypothesis. For instance, if your hypothesis is that “nature lovers make better gardeners”, by reversing the causality, you get the hypothesis that “learning gardening can make you into a nature lover”. By examining and experimenting with the new hypothesis, you can potentially uncover some new insights.

As a side note, it’s worth noting that these different techniques fit well with the broader framework of creative problem solving. Using reversals or shrinking a variable are both different kinds of manipulations, while analogies use the associative process.

Every scientific advancement started with asking the right “why?” followed by the right “how?”. We can get a lot more from our science education if in addition to understanding the scientific process, we also start focusing on generating original hypotheses. As Sir Isaac Newton himself said, “No great discovery was ever made without a bold guess.”

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Historical What Ifs

What if Adolf Hitler had died during World War 1? Would there have been a second World War? Or, what if the Boston Tea Party never happened? “What if” questions like these, or in other words, counterfactual questions, have lately become a genre of historical research. But are such questions useful? Is there any benefit to speculating on events that never took place?

While some people dismiss such hypothetical questions as merely entertaining, Professor Richard Lebow believes that Counterfactuals are “essential teaching tools and critical to establishing claims of causation.” He showed that counterfactuals help in a few different ways:

  • Better understanding of different underlying factors: We have a natural bias to ascribe an outcome as inevitable by highlighting some factors more that others. In addition, once the outcome is known, we find it harder to appreciate additional forces in play (“certainty of hindsight bias”). As Lebow puts it, “By tracing the path that appears to have led to a known outcome, we diminish our sensitivity to alternative paths and outcomes.”
  • Evaluating theories and interpretations: By examining the counterfactual associated with a causal theory, we can make explicit the assumptions in the theory. In Lebow’s words, “Counterfactual experiments can tease out the assumptions—often unarticulated—on which theories and historical interpretations rest.”
  • Assessing outcomes of real world policies or events: Counterfactual thinking helps in evaluating how a particular policy might play out in the real world.

Historical counterfactual questions like the ones in the “Virtual History” category at MindAntix, don’t just help understand history better, they also tickle your creative nerve. For counterfactuals to be useful, they need to be plausible – which means that both divergent (coming up with different turning points) and critical thinking (integrating with historical facts) gets exercised. Creativity isn’t just about being imaginative – a solution to has to be both original and appropriate for it to be truly creative.

So, what’s the best way to solve these historical “What Ifs”? There is really no right answer as long as relevant facts have been used to construct a plausible scenario. However, there are some biases to be cautious of:

  • Neglecting general causal forces: A common mistake is to assume that if an event X had not occurred, things would have gone on as they did before X. For example, if the Romans had not been defeated at the Teutoburger Wald, the Roman Empire would have expanded into current day Germany. The fallacy with this theory is that it ignores the underlying forces that caused the event in the first place. In this case, the strain of geopolitical overextension faced by the Romans that would have eventually led to a defeat sooner or later.
  • Making individuals larger than life: Another prevalent  bias is to assume that a particular individual made all the difference in an outcome. For example, believing  that if Hitler had been killed in World War 1, there would not have been a Nazi movement.  This theory assumes that a leader’s charisma mobilizes groups into action. In reality it’s the other way around – charisma arises in times of social unrest and creates leaders. Charismatic leaders are replaceable – when one is eliminated, a new one can easily take it’s place.

Counterfactual reasoning, or the ability to reflect on alternate possibilities is a developmental milestone that occurs around the age of 5-6 in children. Such reasoning, even for day to day events, helps in learning from mistakes and improving outcomes in the future. Historical counterfactuals are a great way to develop such reasoning while building a deeper understanding of that historical period. What ifs can show that “small accidents or split-second decisions are as likely to have major repercussions as large ones.“

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3 Simple Ways to Add Creativity in Math

In a study by the US Department of Education, 81% of 4th graders reported having a positive attitude towards mathematics but that number drops significantly to 35% for 8th graders. Somehow, in the span of four years, children lose their interest in the subject, and as a result their performance declines. Professor Eric Mann, believes that “keeping students interested and engaged in mathematics by recognizing and valuing their mathematical creativity may reverse this tendency.”

In fact, research has shown that creativity can actually help students acquire content knowledge. But, how can we encourage creativity in mathematics, a subject usually considered linear and inflexible? A few people have come up with ways to twist math problems to make them more creative and fun. So, here are three simple ways to add more creativity in mathematics.

Problem Finding

Problem finding, or problem posing, in any domain is considered to be an important and integral aspect of creativity. For this activity, students are asked to come up with as many different problems as they can with a given situation. One example that Harpen and colleagues used to evaluate creativity is:

In the picture above (Fig. a), there is a triangle and its inscribed circle. Make up as many problems as you can that are related to this picture.

Most students were able to come up with problems involving Lengths (“If the triangle is a right triangle, the hypotenuse is 2, another angle is 60o, find the radius of the circle”) or Areas (“Given the radius of the circle r, find out the minimum are of the triangle”). Creative students were able to pose questions from different fields of mathematics including less obvious ones like probability (“If you are to drop something to the circle, what is the probability of it falling into the triangle?”).

Divergent Thinking

Mathematical problems with many possible solutions can help build divergent thinking skills. Exploring multiple solutions forces students to look beyond the obvious and . One such problem posed by Haylock is:

Given a nine-dot centimeter-square draw as many shapes as possible with an area of 2cm2, by joining up the dots with straight lines.

Most children come up with the easiest solution of drawing a rectangle 2cm x 1cm, but finding other kinds of shapes gets harder.  One highly creative solution shown in the picture above (Fig. b) uses two new ideas –  connecting non-adjacent dots and using an internal angle of 315o.

Overcoming Fixation

A key aspect of creativity is to break free from routine patterns of thinking (flexible thinking). By forcing students to drop their established mindsets helps them in examining a problem from different perspectives and arriving at better solutions. In the same study, Haylock gave students a series of questions in which the students are asked to find two numbers given their sum and difference. The first few example use only positive integers which sets the student’s mindset to expect solutions that use only positive whole numbers. Then the students are asked:

Find two numbers where the sum is 9 and the difference is 2.

A surprisingly large number of students assert that this is not possible. The more creative students were able to remove the self-imposed constraint of using only whole numbers and get to the right solution (5.5 and 3.5).