What do you see in the image?The image can be challenging to interpret,and most people need a clue to see the pattern.It shows a Dalmatian dog.An interesting aspect of this experience is that once you've perceived the pattern,you can't unset the dog.
Whether we like it or not,our brains look for patterns in various contexts.Much of our everyday understanding is linked to the concepts we lean in school and through interaction with others.On top of this,there are learned cultural patterns to interpret works of art,music,poems,etc.Once we know the patterns,they profoundly influence how we perceive cultural products.So we see the world through patterns we have acquired.
These patterns can 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.The key question,therefore,is how a student can discover the relevant patterns and create real understanding.
There are different ways to highlight patterns.Analogies(类比)are powerful tools for creating understanding.An example is the number line(数轴)in elementary mathematics. When children learn addition,it is easy for concrete combinations of objects:three apples plus two apples make five apples.The same is true for subtraction(减法):If you have six apples and remove four,you are left with two.
But this 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?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 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.