It is very important that you learn about traxoline. Traxoline is a new form of zionter. It is montilled in Ceristanna. The Ceristannians gristerlate large amounts of fevon and then brachter it to quasel traxoline. Traxoline may well be one of our most lukized snezlaus in the future because of our zionter lescelidge.Directions: Answer the following questions in complete sentences. Be sure to use your best handwriting.1. What is traxoline?2. Where is traxoline montilled?3. How is traxoline quaselled?4. Why is it important to know about traxoline?
An important part of learning mathematics consists of learning the impressive amount of definitions required to cope with any topic. What seems natural and obvious to us specialists, like "a differentiable function is continuous" might sound a lot like montillation of traxoline to first year students.
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I think that the first problem with definitions is the way they are formulated. Any dictionary is a good example of precisely bad definitions (e.g., "annoyance : a person or thing that annoys"). So, the first thing is to avoid such piffalls and more generally to use as few other concepts/definitions as possible when defining a new objects (which for first year courses is definitely possible).
ReplyDeleteDefinitions being an important part of teaching, how do you think the example you give should influence our way of teaching? (Spend more time (if possible) on definitions and concepts? repeat them again and again?)
And more generally, how could we make our students understand the importance of definitions?
Repetition is my favorite way of stressing the importance of a definition. I recall the definition every time I mention continuity in an example. I (try to) show them that the first step to solving any question is to write down the definitions of all things present. If you can convince them that this first step makes problem-solving easier, then you are well on your way to expressing the importance of definitions.
ReplyDeleteOf course, the definition of continuity is not clear to them, so supplementing this with an intuitive definition can be helpful (provided they know that the formal one is to be used to solve problems).