We changed our privacy policy. Read more.
26

In my experience, students are often predisposed to "learn" by memorizing facts; that's how much of their early education worked, so that's what they're used to. When you give them a definition and then a bunch of consequences of the definition, they don't think "okay, I have a definition and then 87 examples of using the definition", ...


16

First of all, you should test them on remembering the definitions. Second, there are probably a significant number of your students who do not understand the definitions. Suppose you gave them an example of a grammar that was not right-linear and the definition of a right-linear grammar, and asked them why, according to the definition, the example grammar ...


8

You asked: Students trying to learn all kinds of facts [...] by heart rather than recognizing that these are just consequences of the general definitions. [...] Are there any better techniques to get this point across? Or maybe some insight why this seems to be so difficult? The answer is simply that the students are unable to do basic logical reasoning. ...


5

This is something I know very well from the other side, as an amateur student of maths for the last 40 years or so. In my experience, reading a definition and actually understanding it are two very different things. Once you understand the definition at a deeper level, you very often forget how hard it was to get to that point. It simply takes a certain ...


4

I've said in the past that the math discipline has a problem of jumping into the higher-levels of conceptual difficulty with exercises too fast. Let's say we take Bloom's Taxonomy as a model. Non-STEM teachers constantly complain that they spend all their time at Level 1, memorizing facts, and can't move past that. Math teachers, on the other hand, give a ...


4

insight why this seems to be so difficult? I have studied CS with a side-dish of math (some decades ago) and I was surprised by (but very much enjoyed) the actual theoretical aspects of CS. I generally didn't know what to expect from a CS curriculum except that in my case it was abundantly clear that I wanted to study whatever there is to know about ...


3

I try to stress that definitions are just useful shortcuts, ways to put several disparate phenomena under the same roof (like context free grammars and the others in the classification), and show the similarities/usefulness of said definitions. One of the basic "proof techniques" taught in the discrete math course (first one that for our students ...


2

This is a little long for a comment so it will have to be an answer. First, you should talk to your professor; I'm pretty sure that they will be able to definitively clear your issue up with a small amount of back-and-forth discussion. You seem to have trouble starting around your encounter with the word "define". I'm not really sure what we are ...


2

Give them the definitions they should learn. Then, various exercises that can be solved using the definitions. Occationally, an exercise may invoke older definitions for repetition. When we learned the Pythagoras theorem, lots of triangle exercises followed. Also, tell them early on: "Memorizing everything won't get you an A here. Perhaps not even a C. ...


2

Maybe do an in-class exercise with 1 simple (fast) problem, where the students don't have access to the definition. For ease of grading, use a multiple choice answer format. Collect papers and set aside. Then follow up with similar exercise, but with the appropriate definition included the handout. Have students pass the papers and grade them in class, ...


1

I’ve been able to inculcate students with the awareness that definitions are not just legal agreements—which they basically are—or boring fine print, by persistently demonstrating҂ using definitions to successfully deal with problems: for example, in modelling scenarios and translating texts, manipulating expressions, and crafting explanations. Frequently, ...


Only top voted, non community-wiki answers of a minimum length are eligible