Verified by 
Key points
- Patterns help students solve new problems, so use them in education.
- Analogies are strong tools for teaching patterns.
- For example, subtraction from a smaller number is like walking backward on a number line.
Look at the image. What does it show?
The image can be challenging to interpret, and most people need a clue to see the pattern. It shows a Dalmatian dog (with its head to the ground in the middle of the image and the body to the right). Suddenly, the pieces fall into place, and you can understand the image. An intriguing aspect of this experience is that once you've perceived the pattern, you can't unsee the dog.
Whether we like it or not, our brains look for patterns in various contexts. At the core of our understanding are biological mechanisms that strongly influence how we perceive the world around us.
Much of our everyday understanding is linked to the concepts we learn in school and through interaction with others. On top of this, there are learned cultural codes that must be mastered to interpret works of art, music, poems, etc.
However, once we know the codes, they profoundly influence how we perceive cultural products. There is no "naked" eye or ear—therefore, no "objective" description of the world. We see and hear through the patterns we have acquired.
In the early 20th century, Gestalt psychology sought to establish the "laws" governing how our perceptions are organized. This branch of psychology was long suppressed, but related ideas are returning. We now know much more about how the brain functions and can explain how perception works for many of the principles psychologists formulated.
These principles should be applied in all forms of teaching. The great benefit of seeing a pattern in an area of knowledge is that it can be applied to new problems. A student who has understood a pattern can not only answer questions taken directly from the learning material but can use it in other types of tasks.
A central goal of teaching is to make students understand. The key question, therefore, is how a learner can be helped to discover the relevant patterns and thus create real understanding. A student (and a teacher) who has understood something is also much better at explaining an area of knowledge to others. In other words, the one who understands can teach.
There are different ways to highlight patterns. Analogies are powerful tools for creating understanding. An example is the number line in elementary mathematics.
When children learn addition, it is easy to anchor in concrete combinations of objects: three apples plus two apples make five apples. The same is true for subtraction when the result exceeds zero: If you have six apples and remove four, you are left with two.
But this concretization doesn't work when it comes to negative numbers. How do you explain that if you have three apples and remove five, two are missing? It is not possible to remove five from three.
Then, an effective analogy is to see the number line as something you walk along—the line becomes a path. Addition with three is like walking three steps forward, and subtraction with five is like walking five steps backward. No wonder then, that if you walk three steps forward and then five steps back, you are two steps behind where you started.
In this way, the negative numbers acquire a meaning rooted in experience. More patterns of numbers can now be understood.
Another example comes from psychologists Dedre Gentner and Donald Gentner, who have studied two analogies for electricity. Electricity is something you cannot see. You only perceive its effects.
So, how can we understand what electricity is? One way is to construct a mechanical analogy of the phenomenon.
A first analogy says that electricity is like water flowing through a water pipe system. The cables for the electricity are like the pipes for the water. The voltage of the electricity, measured in volts, corresponds to the pressure of the water, and its flow rate, measured in amperes, corresponds to the flow of the water.
The resistance is determined by how narrow the pipe is. The word "current" used to talk about electricity is a metaphor based on this analogy.
A second analogy says that electricity is like people crowding a narrow street. The individuals correspond to the electrons moving in the wires. Now, the amount of electrical flow is linked to the number of persons passing a certain point on the street and the voltage to the pressure on the people in the crowd.
Both analogies are good enough for high school students to reason successfully about what happens to current and voltage when you connect several batteries or insert a resistor into an electrical network. But the two analogies still work differently. For example, it is easier for subjects to reason about multiple batteries when using the water model than the crowd model.
References
P. (2007): “Understanding cultural patterns”, in Learning in the Global Era: International Perspectives on Globalization and Education, ed. by M. M. Suarez-Orozco, University of California Press, pp. 67-84.
Gentner, D. och Gentner, D. (1983): Flowing waters or teeming crowds: Mental models of electricity (pp. 99-129). In D. Gentner & A. L. Stevens (Eds.), Mental models. Hillsdale, NJ: Lawrence Erlbaum Associates.
