Without pre-typed lecture notes (or a textbook that is being followed reasonably closely), many students often feel pressured to copy down every scrap that the lecturer writes down, in case they are missing out on something that will be vitally important later. This often comes at the cost of the student being able to comprehend what is going on in real-time. A related problem is that without the backup of official notes or textbook, a single typo in lecture can lead to hours of confusion on the student's part when reviewing his or her transcribed notes afterwards. (The problem is mitigated somewhat nowadays by the plethora of online mathematics resources, combined with modern search engines, but the situation is still less than ideal.)

Note also that while the lecturer may know in advance which portions of the lecture are important enough to remember, and which ones are more trifling, many students will not be able to make the distinction in real time, and will thus have to record everything, leading to a sub-optimal allocation of the student's mental resources.

To me, the above dangers are worse than the opposite danger that the students are lulled into complacency by the existence of official lecture notes, and thus cease to pay attention to the class. The latter problem can be fixed by a variety of means (e.g. making the classes more interactive or entertaining, or making the homework challenge the student beyond what is presented in the notes), and in any case is more a matter of the responsibilities of the student than of the lecturer. The former problem is however difficult for the student to address by himself or herself (using third-party lecture notes, for instance, is usually a terrible solution).

Ideally, the existence of lecture notes should free up lecture time to focus on other aspects of the course (e.g. one could do a simple example in class, and refer to the notes for a more detailed example; or a heuristic proof with some details partially filled in, with the more technical details left to the notes; one can also present the more improvisational and free-form side of mathematics effectively in lecture, whereas the text medium is far superior for presenting the polished and structured side). Using class time to mechanically repeat what is written in the notes or textbook is a waste, and reduces one to essentially being a fancy text-to-speech synthesiser; instead, lectures should complement and support, rather than replicate, text, and vice versa.

I discuss these issues more in my teaching statement,

http://www.math.ucla.edu/~tao/teaching.dvi

Without pre-typed lecture notes (or a textbook that is being followed reasonably closely), many students often feel pressured to copy down every scrap that the lecturer writes down, in case they are missing out on something that will be vitally important later. This often comes at the cost of the student being able to comprehend what is going on in real-time. A related problem is that without the backup of official notes or textbook, a single typo in lecture can lead to hours of confusion on the student's part when reviewing his or her transcribed notes afterwards. (The problem is mitigated somewhat nowadays by the plethora of online mathematics resources, combined with modern search engines, but the situation is still less than ideal.)

Note also that while the lecturer may know in advance which portions of the lecture are important enough to remember, and which ones are more trifling, many students will not be able to make the distinction in real time, and will thus have to record everything, leading to a sub-optimal allocation of the student's mental resources.

To me, the above dangers are worse than the opposite danger that the students are lulled into complacency by the existence of official lecture notes, and thus cease to pay attention to the class. The latter problem can be fixed by a variety of means (e.g. making the classes more interactive or entertaining, or making the homework challenge the student beyond what is presented in the notes), and in any case is more a matter of the responsibilities of the student than of the lecturer. The former problem is however difficult for the student to address by himself or herself (using third-party lecture notes, for instance, is usually a terrible solution).

Ideally, the existence of lecture notes should free up lecture time to focus on other aspects of the course (e.g. one could do a simple example in class, and refer to the notes for a more detailed example; or a heuristic proof with some details partially filled in, with the more technical details left to the notes; one can also present the more improvisational and free-form side of mathematics effectively in lecture, whereas the text medium is far superior for presenting the polished and structured side). Using class time to mechanically repeat what is written in the notes or textbook is a waste, and reduces the lecturer to essentially being a fancy text-to-speech synthesiser (this is the dual problem to that of the student being reduced to essentially a fancy speech-to-text synthesiser); instead, lectures should complement and support, rather than replicate, text, and vice versa.

I discuss these issues more in my teaching statement,

http://www.math.ucla.edu/~tao/teaching.dvi

Without pre-typed lecture notes (or a textbook that is being followed reasonably closely), many students often feel pressured to copy down every scrap that the lecturer writes down, in case they are missing out on something that will be vitally important later. This often comes at the cost of the student being able to comprehend what is going on in real-time. A related problem is that without the backup of official notes or textbook, a single typo in lecture can lead to hours of confusion on the student's part when reviewing his or her transcribed notes afterwards. (The problem is mitigated somewhat nowadays by the plethora of online mathematics resources, combined with modern search engines, but the situation is still less than ideal.)

Note also that while the lecturer may know in advance which portions of the lecture are important enough to remember, and which ones are more trifling, many students will not be able to make the distinction in real time, and will thus have to record everything, leading to a sub-optimal allocation of the student's mental resources.

To me, the above dangers are worse than the opposite danger that the students are lulled into complacency by the existence of official lecture notes, and thus cease to pay attention to the class. The latter problem can be fixed by a variety of means (e.g. making the classes more interactive or entertaining, or making the homework challenge the student beyond what is presented in the notes), and in any case is more a matter of the responsibilities of the student than of the lecturer. The former problem is however difficult for the student to address by himself or herself (using third-party lecture notes, for instance, is usually a terrible solution).

Ideally, the existence of lecture notes should free up lecture time to focus on other aspects of the course (e.g. one could do a simple example in class, and refer to the notes for a more detailed example; or a heuristic proof with some details partially filled in, with the more technical details left to the notes). Using class time to mechanically repeat what is written in the notes or textbook is a waste, and reduces one to essentially being a fancy text-to-speech synthesiser; instead, lectures should complement and support, rather than replicate, text, and vice versa.

I discuss these issues more in my teaching statement,

http://www.math.ucla.edu/~tao/teaching.dvi

Without pre-typed lecture notes (or a textbook that is being followed reasonably closely), many students often feel pressured to copy down every scrap that the lecturer writes down, in case they are missing out on something that will be vitally important later. This often comes at the cost of the student being able to comprehend what is going on in real-time. A related problem is that without the backup of official notes or textbook, a single typo in lecture can lead to hours of confusion on the student's part when reviewing his or her transcribed notes afterwards. (The problem is mitigated somewhat nowadays by the plethora of online mathematics resources, combined with modern search engines, but the situation is still less than ideal.)

Note also that while the lecturer may know in advance which portions of the lecture are important enough to remember, and which ones are more trifling, many students will not be able to make the distinction in real time, and will thus have to record everything, leading to a sub-optimal allocation of the student's mental resources.

To me, the above dangers are worse than the opposite danger that the students are lulled into complacency by the existence of official lecture notes, and thus cease to pay attention to the class. The latter problem can be fixed by a variety of means (e.g. making the classes more interactive or entertaining, or making the homework challenge the student beyond what is presented in the notes), and in any case is more a matter of the responsibilities of the student than of the lecturer. The former problem is however difficult for the student to address by himself or herself (using third-party lecture notes, for instance, is usually a terrible solution).

Ideally, the existence of lecture notes should free up lecture time to focus on other aspects of the course (e.g. one could do a simple example in class, and refer to the notes for a more detailed example; or a heuristic proof with some details partially filled in, with the more technical details left to the notes; one can also present the more improvisational and free-form side of mathematics effectively in lecture, whereas the text medium is far superior for presenting the polished and structured side). Using class time to mechanically repeat what is written in the notes or textbook is a waste, and reduces one to essentially being a fancy text-to-speech synthesiser; instead, lectures should complement and support, rather than replicate, text, and vice versa.

I discuss these issues more in my teaching statement,

http://www.math.ucla.edu/~tao/teaching.dvi