4. Why Is It So Hard for Students to Understand Abstract Ideas?

• We understand new things in the context of things we already know, and most of what we know is concrete. When dealing with abstract material, it’s best to expose students to many different versions of the abstraction in familiar ways. This can help to get the right ideas into working memory so they can be rearranged. Analogies are often useful when introducing new abstract material.
• There are three kinds of knowledge. Rote knowledge involves no understanding of the material. Shallow knowledge involves limited understanding and only in the context that it was provided. Deep knowledge is interconnected and the student understands the whole, not just the parts. If you understand an abstract principle you will be able to successfully apply old knowledge to a new problem. This is called transfer. Teachers can test all three types of knowledge, but it is vital to test for deep knowledge at some point. Shallow knowledge is better than no knowledge at all, and it is the natural step on the way to deeper knowledge.

5. Is Drilling Worth It?

• Drilling has a bad name as in drill and kill. What we are really talking about is practice, and unfortunately, it’s necessary if you want to become a better thinker. You want to practice the important building blocks of any subject of study so that they become automatic. This frees up room in working memory where thinking takes place. Practice also makes memories long lasting, and increases the likelihood that learning will transfer to new situations.
• Since it’s easy for practice to be boring, the challenge for teachers is to try to make it interesting. There is sound evidence that practice is more effective if it is spread out overtime. If you ever crammed for a test you know how fast you tend to forget the material that you crammed in just before the test. Ideally, students can get practice in the basics while they are working on more advanced skills. (Doug: Games may be another way to make practice seem less boring and more like fun.)

6. What’s the Secret to Getting Students to Think Like Real Scientists, Mathematicians, and Historians?

• The short answer here is that you can’t get students to think like experts in any field. The typical expert spends ten years or so building a knowledge base and automating vital procedures. If you try to design lessons that expect a great deal of discovery and creation by your students, you are likely to be in for a good deal of disappointment and frustration. Experts are likely to be better at transferring knowledge to similar domains. Expert writers, for example, will do a better job of writing about an unfamiliar topic than non experts with a lot of domain knowledge. Experts think abstractly and see the deep structure in their field.
• The same can be seen when looking at how new teachers and expert teachers handle a discipline problem. The rookie will treat the behavior while the expert deals with the root cause. Since experts make much more efficient use of limited working memory, they have room to talk to themselves at an abstract level about the problem in question. The realistic goal for teachers is to get students to understand key aspects of the material at hand. Look for opportunities for students to be creative, which can be motivating, but be realistic.

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