Timeline for Teaching undergraduate students to write proofs
Current License: CC BY-SA 2.5
7 events
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| Jan 16, 2011 at 22:17 | comment | added | Qiaochu Yuan | Excellent point about standard textbooks. I have seen exactly one textbook not specifically written for the purpose give advice about how to construct proofs, and it was not a mathematics textbook: it was Sipser's Introduction to the Theory of Computation. | |
| Jan 13, 2011 at 20:15 | comment | added | Santo D'Agostino | Hi Amit, to continue my response, this was a required course for math majors at my (former) school, and it was an "honest math course" as we learned analysis at the same time as learning how to do proofs. This is part of what I liked about the course: the training in doing proofs was in the context of core mathematics. Since all math majors were required to take this course, one can't do the kind of comparison you ask about. However, some of the students who went through the course and are now graduate students say that it was an important preparation for graduate school for them. | |
| Jan 13, 2011 at 20:11 | comment | added | Santo D'Agostino | Hi Amit, Yes, I did notice that students tended to improve their abilities a lot more than in a typical lecture course. They were forced to prepare for each class, and the additional work they did was the main reason. However, there are additional reasons. I find that students were far more engaged ... there was real enthusiasm for learning, particularly on the part of some of the students, not all of whom were math majors. (I recall one student in particular who did not accept Cantor's diagonal argument, and kept at it the whole semester, trying to poke holes in it. | |
| Jan 13, 2011 at 19:49 | comment | added | Amit Kumar Gupta | I'm also curious, were there any math majors who didn't take your course? Do you have any idea how those students fared in comparison to your students in some of their fifth semester math courses? | |
| Jan 13, 2011 at 19:48 | comment | added | Amit Kumar Gupta | Thanks Santo. You mention the students' feedback was positive and they claimed to have learned a lot more than in a regular course, so that's some evidence for the effectiveness of this method. What about what you saw? Did you notice real improvements in their proof-writing abilities from the start of the semester to the end? What about on an absolute scale - by the end of the semester did they seem prepared to take an honest math course in their next semester? | |
| Jan 13, 2011 at 14:58 | history | edited | Santo D'Agostino | CC BY-SA 2.5 |
corrected a spelling error and added a few words
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| Jan 13, 2011 at 14:51 | history | answered | Santo D'Agostino | CC BY-SA 2.5 |