Using the model to find the solution:
There is some overlap among these topics, so I recommend reading the whole page. Ultimately, what are the sources of errors and of misunderstanding? What kinds of biases and erroneous preconceptions do we have? Two of my favorite historic discoveries are Einstein's discovery of relativity and Cantor's discoveries of some of the most basic rules of infinities.
These discoveries are remarkable in that neither involved long, involved, complicated computations. Both are fairly simple, in retrospect, to anyone who has studied them.
But both involved "thinking outside the box" par excellence -- i. As philosopher John Culkin said, "We don't know who discovered water, but we are certain it wasn't a fish.
Errors in Communication Some teachers are hostile to questions. That is an error made by teachers. Teachers, you will be more comfortable in your job if you try to do it well, and don't think of your students as the enemy.
This means listening to your students and encouraging their questions. A teacher who only lectures, and does not encourage questions, might as well be replaced by a book or a movie. To teach effectively, you have to know when your students have understood something and when they haven't; the most efficient way to discover that is to listen to them and to watch their faces.
Perhaps you identify with your brightest students, because they are most able to appreciate the beauty of the ideas you are teaching -- but the other students have greater need of your help, and they have a right to it.
A variant of teacher hostility is teacher arrogance. Actually, most of the errors listed below can be made by teachers, not just by students.
However, most teachers are right far more often than their students, so students should exercise great caution when considering whether their teachers could be in error.
If you're a student with a hostile teacher, then I'm afraid I don't know what advice to give you; transfer to a different section or drop the course altogether if that is feasible. The remarks on communication in the next few paragraphs are for students whose teachers are receptive to questions.
For such students, a common error is that of not asking questions. When your teacher says something that you don't understand, don't be shy about asking; that's why you're in class! If you've been listening but not understanding, then your question is not a "stupid question. Think of yourself as their spokesperson; you'll be doing them all a favor if you ask your question.
You'll also be doing your teacher a favor -- your teacher doesn't always know which points have been explained clearly enough and which points have not; your questions provide the feedback that your teacher needs.
If you think your teacher may have made a mistake on the chalkboard, you'd be doing the whole class a favor by asking about it. To save face, just in case the error is your own, formulate it as a question rather than a statement. For instance, instead of saying "that 5 should be a 7", you can ask "should that 5 be a 7?
Don't wait until the very end of the example, or until the end of class. As a teacher, I hate it when class has ended and students are leaving the room and some student comes up to me and says "shouldn't that 5 have been a 7? Now all your classmates have an error in the notes that they took in class, and they may have trouble deciphering their notes later.
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In the early s, I managed a computer retail store. Several of my employees were college students. One bright your man was having difficulty with his Freshman college algebra class.
I tutored him and he did very well, but invariably, he would say, "the professor worked through this problem on the board, and it was nothing like this.
I sure hope we got the correct answer. The professor was from the music department, and didn't normally teach college algebra he had been pressed into duty when over enrollment forced the class to be split.I am trying to find both the parametric and symmetric equations of a line passing through two points.
This is for a study exam, so exact answers are not as helpful as detailed solutions. Para mis visitantes del mundo de habla hispana, este sitio se encuentra disponible en español en: América Latina España. This Web site is a course in statistics appreciation; i.e., acquiring a feeling for the statistical way of thinking.
Here is the gist of a question that I replied to in another forum. Q: Can someone advise a conversion method for phone number formats? I have (many!) phone numbers in multiple formats and I would like to convert them all to numbers for comparison.
General Equation of a Line: ax + by = c. Explore the graph of the general linear equation in two variables that has the form ax + by = c using an applet. Recall that the slope (m) is the "steepness" of the line and b is the intercept - the point where the line crosses the y-axis.
In the figure above, adjust both m and b . For question 1 convert and for question 2 write a polynomial function Write an equation in standard form of the line that passes through the point (-3,2) and has the slope What is the standard form of What is the standard form of ×10 over four.