Announcements
Certificates of Completion now available
Well, the course is officially over. You can obtain your Certificate of Completion here.
Sample solutions for the final exam are available on the “Course assignments” page. In calculating the cutoff points for the course, we followed the guidelines described on the “Grading & Certificates of Completion” page. Unfortunately, with over 64,000 students registered, it’s not possible to respond to requests for re-grading. But everyone is welcome to take the course again the next time I offer it. (See below.)
I hope you feel you benefited from the experience. There were many problems on the way, as we all negotiated what for Paul, Molly, and me was very new territory. We set out to do the best we could to provide a valuable learning experience available to anyone in the world (at least, anyone with good Internet access) for free, while recognizing that this would be a massive learning experience for us too.
My particular thanks to the Community TAs (and other knowledgeable forum contributors) who spent many hours helping others as they struggled to master some very difficult concepts. Going into this, I suspected that MOOCs are at heart about community building, and this experience has turned that suspicion into a belief. (If the next iteration of the course turns out similarly, I’ll upgrade it to a conclusion.)
I plan on offering this course again next year, perhaps in two versions, one with the seven week timescale like this one, the other a stretched version to better meet the needs of folks with life commitments that prevent them from keeping pace with a regular university course schedule. Both versions will hopefully benefit from lessons we’ve learned from this first attempt.
We’ll leave the site open for the next four weeks, but won’t be monitoring the forums very often. Then we’ll take it offline to start work on the next iteration.
As we reflect on the course, and start to examine the data that has amassed on the Coursera site, I’ll post thoughts, findings, and statistics on my blog MOOCtalk.org.
Finally, I want to thank Paul and Molly for their help in taking on this crazy endeavor, the folks at Coursera for answering all my questions and responding at all hours to my cries for assistance, and Stanford University, for providing not only the budget to cover the various development and production expenses, but also one of the world’s best environments within which to embark on bold and uncertain enterprises such as this one.
Though I look forward to getting some serious sleep, I’ll miss the daily interactions with you all on the forums, and the frequent adrenalin rushes of trying to fix yet another typo, glitch, or platform bug in the 24/7 world of global MOOCs.
Thank you all for taking this educational journey with me. Please consider coming back again next time, either to improve your performance or to help others.
Keith
Sample solutions for the final exam are available on the “Course assignments” page. In calculating the cutoff points for the course, we followed the guidelines described on the “Grading & Certificates of Completion” page. Unfortunately, with over 64,000 students registered, it’s not possible to respond to requests for re-grading. But everyone is welcome to take the course again the next time I offer it. (See below.)
I hope you feel you benefited from the experience. There were many problems on the way, as we all negotiated what for Paul, Molly, and me was very new territory. We set out to do the best we could to provide a valuable learning experience available to anyone in the world (at least, anyone with good Internet access) for free, while recognizing that this would be a massive learning experience for us too.
My particular thanks to the Community TAs (and other knowledgeable forum contributors) who spent many hours helping others as they struggled to master some very difficult concepts. Going into this, I suspected that MOOCs are at heart about community building, and this experience has turned that suspicion into a belief. (If the next iteration of the course turns out similarly, I’ll upgrade it to a conclusion.)
I plan on offering this course again next year, perhaps in two versions, one with the seven week timescale like this one, the other a stretched version to better meet the needs of folks with life commitments that prevent them from keeping pace with a regular university course schedule. Both versions will hopefully benefit from lessons we’ve learned from this first attempt.
We’ll leave the site open for the next four weeks, but won’t be monitoring the forums very often. Then we’ll take it offline to start work on the next iteration.
As we reflect on the course, and start to examine the data that has amassed on the Coursera site, I’ll post thoughts, findings, and statistics on my blog MOOCtalk.org.
Finally, I want to thank Paul and Molly for their help in taking on this crazy endeavor, the folks at Coursera for answering all my questions and responding at all hours to my cries for assistance, and Stanford University, for providing not only the budget to cover the various development and production expenses, but also one of the world’s best environments within which to embark on bold and uncertain enterprises such as this one.
Though I look forward to getting some serious sleep, I’ll miss the daily interactions with you all on the forums, and the frequent adrenalin rushes of trying to fix yet another typo, glitch, or platform bug in the 24/7 world of global MOOCs.
Thank you all for taking this educational journey with me. Please consider coming back again next time, either to improve your performance or to help others.
Keith
Sat 3 Nov 2012 7:14:00 PM PDT
Re. Distinction
When the grades came in, we noticed some students who had done well on the Problem Sets did much worse on the Final Exam, where there were a lot of problems with what is a very experimental process. (Possibly a few students who were doing well even dropped the exam altogether.) So we allowed high scores in the problem sets to compensate for lower scores on the exam. (As many instructors do.)
From the start, the intention was to determine the distinction category based on an assessment of the entire class. With a class in the many thousands, the data should provide a really sound base for reaching a good decision. A lot of the initial delay in computing the grades resulted from doing a fair amount of CPU-hogging data analysis to minimize any negative effects on students' scores of the beta performance level of CPR. I'd call this applying Mathematical Thinking to determining fair, meaningful grades! It comes in useful, doesn't it?
-- KD :-)
From the start, the intention was to determine the distinction category based on an assessment of the entire class. With a class in the many thousands, the data should provide a really sound base for reaching a good decision. A lot of the initial delay in computing the grades resulted from doing a fair amount of CPU-hogging data analysis to minimize any negative effects on students' scores of the beta performance level of CPR. I'd call this applying Mathematical Thinking to determining fair, meaningful grades! It comes in useful, doesn't it?
-- KD :-)
Sat 3 Nov 2012 7:00:00 PM PDT
Delay in issuing certificates
I was finally able to get the grades calculated. A total of 6,549 students will get Certificate of Completion, and of them, 1,382 will be with Distinction. Unfortunately, a permissions issue on the Coursera site is preventing me from accessing the module to create and make available the certificates. I sent in a request to Coursera Support to have this rectified, but won't be able to do anything until they have fixed it. Since we are now into the weekend, it's possible this won't occur until next week. Sorry about that. I'll post an Announcement, with e-mail duplicate, as soon as the certificates are available.
-- KD
-- KD
Sat 3 Nov 2012 9:56:00 AM PDT
Calculation of Final Grade delayed
The Coursera servers have been crunching the numbers continuously since 12:08 PM PDT, but very slowly. (I understand it should take about 30 minutes!) I suspect this is a consequence of Hurricane Sandy. It may be late tonight before I can complete the process. Sorry for that.
Meanwhile, model solutions to the Final Exam are available on the Course assignments page.
-- KD
Meanwhile, model solutions to the Final Exam are available on the Course assignments page.
-- KD
Fri 2 Nov 2012 3:50:00 PM PDT
Certificates of Completion
Thanks for your patience to all of you who struggled through the peer grading process. [I also fully understand lapses in patience! :-) ] CPR is the current weakest link in all the MOOCs that have tried it. I think we learned enough with this first beta to make a better job next time, though I suspect it will require a number of iterates to get something that works reasonably well. (I discussed some of the problems in the course-related blog, and also said why I think we have to make this work to provide advanced mathematics education at scale.)
I’ve put back the release time for final results to 6:00 PM PDT on Friday November 2. This gives us six hours to adjust and test the grading formula to match our stated goal of around 80% of those who stay the course getting a Certificate of Completion and around 20% of those to be awarded Completion with Distinction. (It takes several minutes to cycle through one trial, and we might need several to get an acceptable result.) I think that will be enough, but as with everything else in this first run of the course, I cannot be sure.
I’ll post an announcement (with duplicate class email) when the results are available, and explain how to obtain your certificate.
-- KD
I’ve put back the release time for final results to 6:00 PM PDT on Friday November 2. This gives us six hours to adjust and test the grading formula to match our stated goal of around 80% of those who stay the course getting a Certificate of Completion and around 20% of those to be awarded Completion with Distinction. (It takes several minutes to cycle through one trial, and we might need several to get an acceptable result.) I think that will be enough, but as with everything else in this first run of the course, I cannot be sure.
I’ll post an announcement (with duplicate class email) when the results are available, and explain how to obtain your certificate.
-- KD
Thu 1 Nov 2012 7:38:00 AM PDT
Cheating & reflections on CPR v.1.0
Several students have contacted me about cases of cheating on the Final Exam. Frankly, why anyone who do this in a course that focuses on learning and offers no credentials, beats me. Students who cheat are really cheating themselves. If you are sure an answer is plagiarized from somewhere else (often easy to determine with a quick web search), you could simply award 1's everywhere, which amounts to a score of 0. Whether you do that for one question or the whole exam is up to you. If there is any doubt that the student has broken the honor code, you have to give the student the benefit of that doubt. 0 on the whole exam is more significant than 0 on one question. Though again, the stakes here are essentially zero; it's mostly about self esteem, surely. For truly egregious cases, send me the details (your login id and the Student number (1, 2, or 3) and I can take it from there. Violation of the honor code is cause for expulsion from the class. Expulsion has occurred, in this class and others, I'm sad to say.
Meanwhile, if you want to know how evaluation training and peer grading looked from our side (the instruction team and the folks at Coursera who were making sure the ship stayed afloat), check out my latest post at MOOCtalk.org to see what was going on behind the scenes.
-- KD
Meanwhile, if you want to know how evaluation training and peer grading looked from our side (the instruction team and the folks at Coursera who were making sure the ship stayed afloat), check out my latest post at MOOCtalk.org to see what was going on behind the scenes.
-- KD
Tue 30 Oct 2012 8:32:00 PM PDT
Evaluation training
Several students reported that they were only offered four training exercises, not five as stated in the course description. I checked and there were five exercises in the system. I also checked the underlying code, and found it was set to display just four, so I re-set it to 5. It should work fine now. Clearly, there are lots of bugs to iron out in the CPR system (as we expected with something so new on this scale), but so far almost 1,000 of the 1521 students who completed the Final Exam have started to grade papers. Thanks for your patience with this. It's always tough being the first ones to try something new.
-- KD
-- KD
Tue 30 Oct 2012 5:41:00 AM PDT
Who can grade exams?
It turns out that Coursera were not able to implement in time the requirement that you have to pass training to grade other students. As many of you have discovered, you are asked if you want to do so right after you complete the final training exercise, however you did. Since all aspects of this process are experimental (we are collecting the first data right now!), I'd suggest that if you feel comfortable grading, go ahead and do so. Most people who have done this find it really helps them understand the material and the nature of proof.
-- KD
-- KD
Mon 29 Oct 2012 9:55:00 PM PDT
Exam self grading
A glitch over at Coursera prevented the next stage in the peer grading from launching yesterday, namely the step where you grade your own exam using the same rubric. This has now been fixed. If you already completed peer grading, please go back to the "Peer assessments" module, where you can now grade your own paper. You have to complete that step in order for your own grade to be registered by the system. Sorry about that.
-- KD
-- KD
Mon 29 Oct 2012 5:10:00 AM PDT
Evaluation training
Some folks seem to be sweating a bit too much on the training system.
First, note there is no such thing as perfect grading of advanced mathematics. No two professionals with years of experience will agree on specifics, though they usually will agree on pass/fail, very good, etc.
Second what we are trying to develop here is a *statistical* method that will result in overall *acceptable* performance. To pass training and qualify as a grader, you need to pass *one* of five testing papers. For each of those, you need to get within 20% of the suggested grade on 80% of the questions.
Are those cutoffs optimal? We don't know. We're hoping this first time out will tell us the answer. We think this will provide enough graders, but we won't know until the data are in.
When we get the various parameters right, there is good reason to believe that CPR will work for this kind of material just as it has elsewhere.
For many questions, it's hard to apply the rubric in a strict fashion, and different people will get different scores on the same item. The purpose of the rubric is to encourage you to view the submission from different angles -- in particular, to look for things that can encourage the student and reward them for what they did manage to do, even in a sea of confusion. It's not a set of rules to assign grade points.
We're also hoping you will learn a lot about mathematical thinking and about the nature of proof by the very act of trying to assess others' attempts.
-- KD
First, note there is no such thing as perfect grading of advanced mathematics. No two professionals with years of experience will agree on specifics, though they usually will agree on pass/fail, very good, etc.
Second what we are trying to develop here is a *statistical* method that will result in overall *acceptable* performance. To pass training and qualify as a grader, you need to pass *one* of five testing papers. For each of those, you need to get within 20% of the suggested grade on 80% of the questions.
Are those cutoffs optimal? We don't know. We're hoping this first time out will tell us the answer. We think this will provide enough graders, but we won't know until the data are in.
When we get the various parameters right, there is good reason to believe that CPR will work for this kind of material just as it has elsewhere.
For many questions, it's hard to apply the rubric in a strict fashion, and different people will get different scores on the same item. The purpose of the rubric is to encourage you to view the submission from different angles -- in particular, to look for things that can encourage the student and reward them for what they did manage to do, even in a sea of confusion. It's not a set of rules to assign grade points.
We're also hoping you will learn a lot about mathematical thinking and about the nature of proof by the very act of trying to assess others' attempts.
-- KD
Sun 28 Oct 2012 3:58:00 PM PDT
Exam question 9
There is a typo in question 9. It should say "any fixed number M > 0". The result is actually true for any M, but to make the question more accessible to beginners, and focus on the main point about limits, I restricted to the case M > 0. That restriction made it to the model solutions document, and hence to the sample solution in the training exercise, but not to the exam question itself. When grading other students, please assume their answer is for M > 0. The other cases are just variations of no real relevance to the issue of limits. Thanks.
I said this part of the course would be live beta! :-)
-- KD
I said this part of the course would be live beta! :-)
-- KD
Sun 28 Oct 2012 2:55:00 PM PDT
Using the grading rubric in evaluating the Final Exam
Please view the grading rubric as a guideline, not a rulebook.
In particular, note that it is geared towards assessing proofs. Though all the exam questions involve proofs (this is, after all, mathematics), in some cases answers can be so short that it’s not feasible to apply the rubric in a strict algorithmic fashion. (My oft-repeated observation that this course is about thinking, not applying rules, applies to evaluating the work of others just as much as producing your own!)
The optimal way to approach the evaluation task is to rely on common sense, using the rubric as a guideline, but nothing more. Being a good proof is a holistic thing, and the final mark you award for an answer should be a measure of how far removed it is from a correct and communicatively effective proof. This consideration should override the scores that a slavish adherence to the rubric might dictate.
For example, if someone gives a solution that is logically sound but they make an arithmetical slip that technically invalidates the argument, you deduct a few points for the slip, but otherwise grade the solution as if the slip had not been made.
On the other hand, given a proof that makes no sense or is obviously way off the target, you might feel that the minimum score of 5 is all you can award. (According to the rubric, a score of 5 is effectively zero; it’s an issue to do with how the evaluation module is set up.)
You should definitely ask if the final grade on a question is fair. For instance, it makes no sense to assign 3 points for a statement or step that would have been appropriate in a correct proof, but plays no real role in a proof that is clearly wrong.
In other words, we are not regarding you as cheap (actually, unpaid) graders whose job is to simply assign grades to students’ work; rather this part of the course is designed to be beneficial to both graders and gradees. You’ll find you get a lot of insight into things we have done when you try to assign grade points to someone else’s work in a meaningful way. In fact, you may find this last two weeks is the most valuable part of the course in terms of mastering mathematical thinking. The grading rubric is there to help you ask the different questions about a piece of mathematical work that an experienced instructor does instinctively.
The very fact that you are still active in the course and taking the exam suggests you are definitely up to the task – probably more so than you think!
[A LITTLE BACKGROUND: One of my goals in this first iteration of the course is to develop a better rubric that more closely contributes to the development of good mathematical thinking. One of the constraints is making it fit the functionality of the platform. I’m working on the rubric at the same time Coursera is building the peer review module, and we are collaborating on trying to develop a good system.]
KD
In particular, note that it is geared towards assessing proofs. Though all the exam questions involve proofs (this is, after all, mathematics), in some cases answers can be so short that it’s not feasible to apply the rubric in a strict algorithmic fashion. (My oft-repeated observation that this course is about thinking, not applying rules, applies to evaluating the work of others just as much as producing your own!)
The optimal way to approach the evaluation task is to rely on common sense, using the rubric as a guideline, but nothing more. Being a good proof is a holistic thing, and the final mark you award for an answer should be a measure of how far removed it is from a correct and communicatively effective proof. This consideration should override the scores that a slavish adherence to the rubric might dictate.
For example, if someone gives a solution that is logically sound but they make an arithmetical slip that technically invalidates the argument, you deduct a few points for the slip, but otherwise grade the solution as if the slip had not been made.
On the other hand, given a proof that makes no sense or is obviously way off the target, you might feel that the minimum score of 5 is all you can award. (According to the rubric, a score of 5 is effectively zero; it’s an issue to do with how the evaluation module is set up.)
You should definitely ask if the final grade on a question is fair. For instance, it makes no sense to assign 3 points for a statement or step that would have been appropriate in a correct proof, but plays no real role in a proof that is clearly wrong.
In other words, we are not regarding you as cheap (actually, unpaid) graders whose job is to simply assign grades to students’ work; rather this part of the course is designed to be beneficial to both graders and gradees. You’ll find you get a lot of insight into things we have done when you try to assign grade points to someone else’s work in a meaningful way. In fact, you may find this last two weeks is the most valuable part of the course in terms of mastering mathematical thinking. The grading rubric is there to help you ask the different questions about a piece of mathematical work that an experienced instructor does instinctively.
The very fact that you are still active in the course and taking the exam suggests you are definitely up to the task – probably more so than you think!
[A LITTLE BACKGROUND: One of my goals in this first iteration of the course is to develop a better rubric that more closely contributes to the development of good mathematical thinking. One of the constraints is making it fit the functionality of the platform. I’m working on the rubric at the same time Coursera is building the peer review module, and we are collaborating on trying to develop a good system.]
KD
Fri 26 Oct 2012 10:00:00 PM PDT
Post-Course Survey is Online
Hi everyone. In addition to the final exam, the post-course survey is now available for you to complete. I, and everyone involved on the research side of this project, would appreciate it very much if you would take the time to do this survey. We're repeating some of the questions from the pre-survey, as well as asking for open-ended feedback on the course. As with the pre-survey, your answers are confidential and will be used to improve future versions of the course.
You can find the survey here. Make sure to click on "week five" to pull up the post survey.
Thank you!
- Paul
You can find the survey here. Make sure to click on "week five" to pull up the post survey.
Thank you!
- Paul
Fri 26 Oct 2012 9:00:00 PM PDT
Final tutorial videos
The tutorial videos for Assignment 10 and Problem Set 5 will go live at 10:00 AM PDT today as usual.
Wed 24 Oct 2012 7:30:00 AM PDT
Assignment 9 solutions
The sample solutions to Assignment 9 are now available on the "Course assignments" page.
Tue 23 Oct 2012 12:01:00 PM PDT
Typo fixed in Exam Q10
There was a small but significant typo in Question 10 in the Final Exam. I just fixed it both in the online version and on the PDF. (I also added clarification in Q4.) If you already completed the online version, please look again at the last question and, if necessary, re-submit your solution. If you downloaded the PDF already, please download the newer version. Sorry about that. -- KD
Tue 23 Oct 2012 8:05:00 AM PDT
Exam open
The Final Exam is now open. You will find it on the “Peer assessments” page. A PDF version of the Final Exam is also now live on the “Course assignments” page. Since there are regular problems displaying mathematical expressions (you frequently get the LaTeX source text), you might find it easier to work from the PDF, which you can print off, and then enter your submission on the site when you are satisfied with your solutions.
I spent several (well, a lot actually) hours last night going through the exam submission process and the grading exercises. (If you were on the site, you may have noticed the exam opening and closing a number of times.) There was the occasional glitch, but all in all it went smoothly.
IMT is only the second Coursera course to use Calibrated Peer Review, and some elements were developed specifically to meet our needs. So it could have gone less well. By the time I logged off, I had successfully submitted and evaluated five different solution sets to the exam.
So, things are looking good. My earlier caution that you should maybe avoid the exam module for the first day or so were probably unduly pessimistic. Nevertheless, when you submit your work on the site, do please keep a complete copy on your machine. I’d also recommend not waiting to the last minute to submit your solution. There could always be a server failure or lost connectivity. One good thing about the exam module is you can keep resubmitting your work until the deadline (overwriting any earlier version).
-- KD
I spent several (well, a lot actually) hours last night going through the exam submission process and the grading exercises. (If you were on the site, you may have noticed the exam opening and closing a number of times.) There was the occasional glitch, but all in all it went smoothly.
IMT is only the second Coursera course to use Calibrated Peer Review, and some elements were developed specifically to meet our needs. So it could have gone less well. By the time I logged off, I had successfully submitted and evaluated five different solution sets to the exam.
So, things are looking good. My earlier caution that you should maybe avoid the exam module for the first day or so were probably unduly pessimistic. Nevertheless, when you submit your work on the site, do please keep a complete copy on your machine. I’d also recommend not waiting to the last minute to submit your solution. There could always be a server failure or lost connectivity. One good thing about the exam module is you can keep resubmitting your work until the deadline (overwriting any earlier version).
-- KD
Mon 22 Oct 2012 10:00:00 AM PDT
Final Exam & Peer Review Training
Up until now, we’ve been adding material to the website on a shadow site and testing it before uploading it to the live site you see. But some aspects of the peer evaluation process can’t be tested in advance that way. We have to launch them on the live site, and we will know they function as intended only when they go live. So please, work offline, keep a copy of your work, and don't start to upload it to the site for the first few days, while we iron out any kinks! [I think you’ll find it takes several days to complete the exam anyway! :-) ]
We have made some (minor) changes to the peer review process. The description in the "Peer review process" section of the website is current as of 06:00 AM PDT on Sunday October 21. It’s possible we will have to make further adjustments, in which case I’ll post announcements, accompanied by a class email. (I'll also update the website description.)
-- KD
We have made some (minor) changes to the peer review process. The description in the "Peer review process" section of the website is current as of 06:00 AM PDT on Sunday October 21. It’s possible we will have to make further adjustments, in which case I’ll post announcements, accompanied by a class email. (I'll also update the website description.)
-- KD
Sun 21 Oct 2012 6:00:00 AM PDT
Final Exam
The end is in sight!
The Final Exam opens on Monday October 22 at 10:00 AM PDT. You will find it on the “Peer assessments” page, where you found the online version of Assignment 9.
As you discovered when you did Assignment 9 online, the PR module is still a bit clunky and buggy. In particular, the raw LaTeX used to encode mathematical formulas does not always render. In general if you wait a few seconds, it will transform to give readable mathematics, but sometimes you need to refresh the page in your browser. Some students have reported success by switching to a different browser.
Just to be safe, however, after the online exam goes live, I’ll release a PDF version of the entire exam on the “Course assignments” page. I suspect you may prefer to print that off and work on the questions the good, old fashioned way, using paper and pencil.
In any event, I strongly urge you to allow yourself lots of time to complete the exam. Note that you can enter and save your answers and continue to edit them until you finally submit them. But do remember to carry out that last step. If your submission is not in the system at the deadline, there is no way you can receive credit for your work.
Paul and I will monitor the forums throughout the week to see if there are any problems, and will try to fix them promptly. (Given the complexity of the system, it will likely require intervention by a Coursera engineer.)
As with the weekly Problem Sets, the Honor Code requires that you work alone on your exam submission. This does not prevent you discussing the relevant issues -- indeed, I urge you to do so! The thing to avoid is simply giving someone else the solution, or posting it on the forum. That simply reduces the learning experience for others. The standard response many experienced teachers give to a request for help is to reply with another question, designed to nudge the questioner to the answer.
The various deadlines are:
Monday October 22, 10:00 AM PDT, Exam opens
Sunday October 28, 12:00 noon PDT, Deadline for submission of answers
Sunday October 28, 1:00 PM PDT, Peer evaluation process commences
Friday November 2, 12:00 noon PDT, Deadline for submission of all grades
Friday November 2, 1:00 PM PDT, Results released and certificate emailed out.
Good luck!
-- KD
The Final Exam opens on Monday October 22 at 10:00 AM PDT. You will find it on the “Peer assessments” page, where you found the online version of Assignment 9.
As you discovered when you did Assignment 9 online, the PR module is still a bit clunky and buggy. In particular, the raw LaTeX used to encode mathematical formulas does not always render. In general if you wait a few seconds, it will transform to give readable mathematics, but sometimes you need to refresh the page in your browser. Some students have reported success by switching to a different browser.
Just to be safe, however, after the online exam goes live, I’ll release a PDF version of the entire exam on the “Course assignments” page. I suspect you may prefer to print that off and work on the questions the good, old fashioned way, using paper and pencil.
In any event, I strongly urge you to allow yourself lots of time to complete the exam. Note that you can enter and save your answers and continue to edit them until you finally submit them. But do remember to carry out that last step. If your submission is not in the system at the deadline, there is no way you can receive credit for your work.
Paul and I will monitor the forums throughout the week to see if there are any problems, and will try to fix them promptly. (Given the complexity of the system, it will likely require intervention by a Coursera engineer.)
As with the weekly Problem Sets, the Honor Code requires that you work alone on your exam submission. This does not prevent you discussing the relevant issues -- indeed, I urge you to do so! The thing to avoid is simply giving someone else the solution, or posting it on the forum. That simply reduces the learning experience for others. The standard response many experienced teachers give to a request for help is to reply with another question, designed to nudge the questioner to the answer.
The various deadlines are:
Monday October 22, 10:00 AM PDT, Exam opens
Sunday October 28, 12:00 noon PDT, Deadline for submission of answers
Sunday October 28, 1:00 PM PDT, Peer evaluation process commences
Friday November 2, 12:00 noon PDT, Deadline for submission of all grades
Friday November 2, 1:00 PM PDT, Results released and certificate emailed out.
Good luck!
-- KD
Sat 20 Oct 2012 12:00:00 PM PDT
Problem Set 5
There was a typo in the LaTeX for question 2. I just corrected it. Sorry about that. -- KD
Fri 19 Oct 2012 5:09:00 PM PDT
Assignment 10
Assignment 10 is now available for access/downloading. It comes in two parts, corresponding to the two parts of Lecture 10.
Fri 19 Oct 2012 1:33:00 PM PDT
Assignment 9 deadline
Note that the deadline for submitting your work on Assignment 9 (online version) is Friday October 19 at noon PDT. The deadline for completing the (restricted) trial peer review process for this assignment is Tuesday October 23 at noon PDT. A solution sheet will be released on this website soon after that second deadline.
-- KD
-- KD
Thu 18 Oct 2012 7:35:00 PM PDT
Peer review
If you find that the questions in the online peer review version of Assignment 9 display as raw LaTeX (lots of $$ signs), refreshing your browser usually resolves the issue. (But make sure you save, or Submit, your work before you refresh. Note that you can revise your submission right up to the final deadline.)
-- KD
-- KD
Wed 17 Oct 2012 4:19:00 AM PDT
Post-Course Logistics and the Final Exam
There have been two prominent questions lately in the forums that I want to address in an announcement on the front page.
1) A number of students have asked what will happen to the course after the end of the final exam. The answer is, we'll keep the course site live for at least several weeks (we haven't decided on an exact number yet). For that time, you'll still be able to view all the lectures and do any of the Problem Sets. You obviously will not be able to get a certificate of completion, but the materials will be available.
Eventually we will close the site, however. Not because we want to keep the resources secret, but because we're planning on running the course again and we don't want to leave this site live while the new version runs. Again, we haven't set an exact date for another run, but a year from now is the absolute latest that would happen. It's possible we'll run the course again as soon as this Spring.
If you do want continued access to the course resources ad inifinitum, therefore, I'd recommend downloading the videos once the course is over, or else simply wait until the next - and likely much improved - iteration of the course.
2) A number of students have expressed concern about the final exam. These concerns take various forms, but they largely concern the peer grading. I'd distill the concerns to these two perspectives: First, how can we be sure that exams will be graded accurately and fairly? Second, if I am not confident in my skill as a grader, why am I required to grade others? These two concerns are different sides of the same coin, really, and they both concern students who have taken the course seriously, but maybe don't have full mastery of all of the concepts and ways of thinking we've covered.
To the first I would say, we are going to be doing some calibration and checking of the peer grades you get against each other. This is not a perfect system, but it's better than just naively assigning the grade you get. We'll also be asking your peer graders to assess their own confidence in their answer to the question they are answering, which will also serve as a way to weight their input.
Which addresses the second concern as well. Even if you really don't get the final, you're free to grade other students because you can let us know that you are not confident in your grading at the front end of the peer review. That said, you should still do your best, because grading each other's work is a huge part of the learning experience in a course like this.
This goes back to the philosophy behind the course that Keith and I are trying to create and implement. If you look at the final exam just as an evaluation of your work, I think you're missing the point. The final is meant to be a learning experience, and the peer review process may very well be the most interesting and engaging formal learning experience of the entire five weeks. So if you're still involved in the course, I highly recommend you engage seriously in the peer review process, because you stand to learn a lot from each other's answers to the questions on the final, as well as the difficult process of trying to assess the proofs of others. I, for one, am really excited about the conversations the peer review process will spark, and the learning it can support.
- Paul
1) A number of students have asked what will happen to the course after the end of the final exam. The answer is, we'll keep the course site live for at least several weeks (we haven't decided on an exact number yet). For that time, you'll still be able to view all the lectures and do any of the Problem Sets. You obviously will not be able to get a certificate of completion, but the materials will be available.
Eventually we will close the site, however. Not because we want to keep the resources secret, but because we're planning on running the course again and we don't want to leave this site live while the new version runs. Again, we haven't set an exact date for another run, but a year from now is the absolute latest that would happen. It's possible we'll run the course again as soon as this Spring.
If you do want continued access to the course resources ad inifinitum, therefore, I'd recommend downloading the videos once the course is over, or else simply wait until the next - and likely much improved - iteration of the course.
2) A number of students have expressed concern about the final exam. These concerns take various forms, but they largely concern the peer grading. I'd distill the concerns to these two perspectives: First, how can we be sure that exams will be graded accurately and fairly? Second, if I am not confident in my skill as a grader, why am I required to grade others? These two concerns are different sides of the same coin, really, and they both concern students who have taken the course seriously, but maybe don't have full mastery of all of the concepts and ways of thinking we've covered.
To the first I would say, we are going to be doing some calibration and checking of the peer grades you get against each other. This is not a perfect system, but it's better than just naively assigning the grade you get. We'll also be asking your peer graders to assess their own confidence in their answer to the question they are answering, which will also serve as a way to weight their input.
Which addresses the second concern as well. Even if you really don't get the final, you're free to grade other students because you can let us know that you are not confident in your grading at the front end of the peer review. That said, you should still do your best, because grading each other's work is a huge part of the learning experience in a course like this.
This goes back to the philosophy behind the course that Keith and I are trying to create and implement. If you look at the final exam just as an evaluation of your work, I think you're missing the point. The final is meant to be a learning experience, and the peer review process may very well be the most interesting and engaging formal learning experience of the entire five weeks. So if you're still involved in the course, I highly recommend you engage seriously in the peer review process, because you stand to learn a lot from each other's answers to the questions on the final, as well as the difficult process of trying to assess the proofs of others. I, for one, am really excited about the conversations the peer review process will spark, and the learning it can support.
- Paul
Tue 16 Oct 2012 2:00:00 PM PDT
Problem Set 4, Question 4
Just saw a forum discussion thread about an ambiguity in the question. I have now edited the question to say "nonempty set". That should have been explicit in the original formulation of the theorem. This provides an excellent illustration of the need for precision! Nothing makes one of the main points of this entire course more compelling than to see the instructor fail to be totally precise!
The theorem is in fact true if we allow the set to be empty, but the induction proof would then have to start with the case n=0. In this course, I have restricted induction to induction over the natural numbers.
BTW, I never give "trick questions" about real mathematical content. There is no need; mathematics is already tricky. :-)
-- KD
The theorem is in fact true if we allow the set to be empty, but the induction proof would then have to start with the case n=0. In this course, I have restricted induction to induction over the natural numbers.
BTW, I never give "trick questions" about real mathematical content. There is no need; mathematics is already tricky. :-)
-- KD
Mon 15 Oct 2012 12:08:00 PM PDT
Assignment 9
Assignment 9 just went up. There are two versions: the familiar PDF file and an interactive online form that you can access by navigating to the "Peer assessments" page on the course website. Anyone who intends to take the Final Exam, which involves the Peer Review process, should use the online version of Assignment 9 to become familiar with the peer review module. For this assignment, it does not involve sending or receiving grades to/from other students. (That part is reserved for the Final Exam itself.) Distinction in the course requires completion of the Final Exam. As I've stressed before, using the Calibrated Peer Review System for a course like this is, I believe, new. (It's certainly new to me and my assistants!) So this is all very much experimental. Please approach it in that spirit!
-- KD
-- KD
Mon 15 Oct 2012 11:45:00 AM PDT
Welcome to Week 5
If you are reading this, congratulations on getting this far. Mathematics transition courses are notorious for losing students -- even full-time students in a regular university course, with a live professor or TA to give them personal attention.
This week you get a test run of the peer review process that will be used to grade the final exam. Assignment 9 will come in two formats: the regular PDF plus a live, interactive version online. If you look at the left-hand navigation bar, you will see a new entry in the "Course materials" section: "Peer assessments". That is where you will access the interactive version of Assignment 9 (and of the final exam when it is released at the start of Week 6).
Use of the peer review system for Assignment 9 does not involve the grading training, nor will you be able to submit grades for submissions of fellow students or of yourself. Rather, its use in this assignment is purely to provide you with an opportunity to familiarize yourself with the basic peer review mechanism and to practice grading work of other students, using the grading rubric.
Note that grading proofs of other students can contribute significantly to understanding what a proof is and how to construct one. (I suspect most professors came to truly understand what constitutes a good proof only when they started grading proofs as TAs, when in graduate school. That is certainly true for me!) So you should approach it as a part of your learning process, not a chore to be gotten through as quickly as possible in order to complete the course.
I believe participation in a peer review process will form a significant -- and essential -- component of advanced mathematics courses in MOOCs. For sure it won't be perfect this first time out. But there has to be a first step, and this is it!
Submission of the final exam and completion of the peer review process is required in order to be eligible for Distinction in the course.
I intend to offer this course again next year (possibly in two formats, running at different paces), so if you find you have fallen too far behind to stay on top of the material in Week 5 (which has far more mathematical content than the first three weeks did), you might want to consider simply auditing the remainder of the course and enrolling again next year.
-- KD
This week you get a test run of the peer review process that will be used to grade the final exam. Assignment 9 will come in two formats: the regular PDF plus a live, interactive version online. If you look at the left-hand navigation bar, you will see a new entry in the "Course materials" section: "Peer assessments". That is where you will access the interactive version of Assignment 9 (and of the final exam when it is released at the start of Week 6).
Use of the peer review system for Assignment 9 does not involve the grading training, nor will you be able to submit grades for submissions of fellow students or of yourself. Rather, its use in this assignment is purely to provide you with an opportunity to familiarize yourself with the basic peer review mechanism and to practice grading work of other students, using the grading rubric.
Note that grading proofs of other students can contribute significantly to understanding what a proof is and how to construct one. (I suspect most professors came to truly understand what constitutes a good proof only when they started grading proofs as TAs, when in graduate school. That is certainly true for me!) So you should approach it as a part of your learning process, not a chore to be gotten through as quickly as possible in order to complete the course.
I believe participation in a peer review process will form a significant -- and essential -- component of advanced mathematics courses in MOOCs. For sure it won't be perfect this first time out. But there has to be a first step, and this is it!
Submission of the final exam and completion of the peer review process is required in order to be eligible for Distinction in the course.
I intend to offer this course again next year (possibly in two formats, running at different paces), so if you find you have fallen too far behind to stay on top of the material in Week 5 (which has far more mathematical content than the first three weeks did), you might want to consider simply auditing the remainder of the course and enrolling again next year.
-- KD
Sun 14 Oct 2012 8:00:00 AM PDT
Tutorial Sessions
The next set of Tutorial Session videos will be released at 10:00AM PDT on Wednesday October10. Note that the tutorial sessions are more than mere presentations of solutions to the previous week's assignments and problem session. They are really lectures based on problems that you have (I hope) already attempted. You can expect to expand your knowledge of the course material beyond the Monday and Friday lectures. Not all questions on the assignments sheets and problem set are considered in the tutorial session. Whereas the lectures were all recorded before the course started, I record the tutorials the day before they are posted, so they can reflect issues raised in the forums.
-- KD
-- KD
Tue 9 Oct 2012 9:00:00 PM PDT
Problem Set 3
I added an explanatory clause to Question 5. If you already submitted your solution, you might want to go back and check what you did before the deadline. See this forum thread for details.
Sun 7 Oct 2012 10:23:00 AM PDT
Kindle edition of textbook re-released
The initial problem with Kindle edition of the course companion book has now been resolved, and the book has been re-released by Amazon. I just viewed it online on Amazon's Kindle Fire emulator, and it looks great, as does a copy I have running on my Mac Kindle app. Anyone who already purchased a copy of the mangled file that was available for a few hours at the end of last week should find their copy automatically replaced by the correct file within a few days. (I have a direct contact at Kindle to approach if there are further problems; they are taking steps to resolve this.)
-- KD
-- KD
Sat 6 Oct 2012 6:00:00 PM PDT
Lecture 6 - first in-lecture quiz
I just noticed that in my explanation of the last part of the first in-lecture quiz, at one point I say "true" when I meant "false". By now you may be sufficiently comfortable with this material that you did not even notice. (I did not spot it when I went through the video during editing! I heard what I was expecting to hear, not what I actually heard.) I actually repeat the point, and the second time I use the right word. But when I get chance, I'll fix that video.
-- KD
-- KD
Fri 5 Oct 2012 11:24:00 AM PDT
Kindle edition of textbook - System glitch at Amazon
If you are thinking of buying the Kindle version of the companion book but have not done so, please hold off for a while. The version of the Kindle edition I have (which was manually created by Kindle engineers) looks as good as any e-book I've seen. But apparently something got screwed up in the Kindle system when the file was uploaded for sale. The folks at Kindle are working on correcting it as a matter of urgency. If you already bought a copy, I am sure you will be able to get the new version at no extra charge when they have resolved the issue. Sorry about that.
-- KD
-- KD
Fri 5 Oct 2012 9:38:00 AM PDT
Kindle edition of the textbook
The engineers at Kindle have just competed the digital version of the companion book. I have a copy and it looks great! It is now officially available, though it may take a few hours to appear on the various Amazon websites around the world. Sorry this was not available sooner.
Thu 4 Oct 2012 12:37:00 PM PDT
Looper
Clearly, Looper would have benefitted from taking this course!
Thu 4 Oct 2012 11:30:00 AM PDT
Course philosophy
From some of the forum discussions, it’s clear that some of you are putting way too much emphasis on the lectures. They are not lessons in the traditional sense of an instructional session that has been lesson-planned. They simply provide an example of a professional engaged in mathematical thinking. Other than editing out pauses while I think, and speeding up some of the handwriting, what you see is what happened when I sat down at my desk. There are errors and slips. Some I noticed during video editing, others are being discovered by some of you. That’s how mathematics gets done. It's a messy, error-prone, human endeavor. (Admittedly, since I’ve given this course many times before, and wrote the companion book just a few months ago, it might look like I’m just reading from the book, but that’s not the case.)
So please don’t pore over the videos repeatedly looking for rules or for answers. They are to set the agenda, provide some key ideas, give an example of one individual thinking mathematically (in real time), and (arguably more importantly) to provoke reflection and discussion.
In other words, the onus is on the student to figure things out. In putting together this course, I set out to try to create over the Internet the kind of experience you’d get if you were sitting next to me in my office at Stanford, or next to any other professional mathematician. (To be sure, not everyone likes this approach, but it’s pretty common in university education.)
The core learning mechanisms in the course are working on the assignments and the associated discussions, both on the forums and in the various groups people have created.
There’s pedagogic research to support this “be less helpful” approach, even at high school level, let alone university. If you are curious about the course philosophy, check out my recent MOOCtalk blog, where I reference some of that research.
Maybe it helps to know this, maybe not. Either way, I hope you stick with the course.
-- KD
So please don’t pore over the videos repeatedly looking for rules or for answers. They are to set the agenda, provide some key ideas, give an example of one individual thinking mathematically (in real time), and (arguably more importantly) to provoke reflection and discussion.
In other words, the onus is on the student to figure things out. In putting together this course, I set out to try to create over the Internet the kind of experience you’d get if you were sitting next to me in my office at Stanford, or next to any other professional mathematician. (To be sure, not everyone likes this approach, but it’s pretty common in university education.)
The core learning mechanisms in the course are working on the assignments and the associated discussions, both on the forums and in the various groups people have created.
There’s pedagogic research to support this “be less helpful” approach, even at high school level, let alone university. If you are curious about the course philosophy, check out my recent MOOCtalk blog, where I reference some of that research.
Maybe it helps to know this, maybe not. Either way, I hope you stick with the course.
-- KD
Mon 1 Oct 2012 5:30:00 PM PDT
Welcome to Week Three
We are now a 60K MOOC. Some late registrations last week pushed the total enrollment to 61,086. While many students simply watch the videos (in many cases because busy schedules don't leave them enough time to really get involved), to date there have been 260,466 completions of the live, in-lecture quizzes. That's a lot of learning!
This week we complete our analysis of language. To get a sense of how far we've come, the last question in Assignment 6 (Friday) deals with one of the most significant applications of linguistic precision in the entire history of mathematics. It took mathematicians over two thousand years to make that journey the first time.
-- KD
This week we complete our analysis of language. To get a sense of how far we've come, the last question in Assignment 6 (Friday) deals with one of the most significant applications of linguistic precision in the entire history of mathematics. It took mathematicians over two thousand years to make that journey the first time.
-- KD
Mon 1 Oct 2012 6:00:00 AM PDT
Grading Update
Hi Everyone,
The grading problems for late assignments have been fixed! Let us know if you still have problems with your Problem Set 1 grades, but I believe there should not be any more issues.
Problem Set 2 has now been up for a couple of days, and many of you have already completed it. Do not be alarmed if you do not get a score right away. A Coursera-wide update caused Problem Set 1 answers and scores to be available right away, but that was not how we set things up originally. Making the scores and answers available right away certainly can lead to good forum conversations (as our many discussions of Alice demonstrate), but it also means that students have a very high chance of coming across "spoilers" before they do the Problem Set. Thus for Problem Set 2, and all future Problem Sets, you won't get your score or the answers until after the deadline.
Hope you're having a good weekend, and keep up the good work!
- Paul
The grading problems for late assignments have been fixed! Let us know if you still have problems with your Problem Set 1 grades, but I believe there should not be any more issues.
Problem Set 2 has now been up for a couple of days, and many of you have already completed it. Do not be alarmed if you do not get a score right away. A Coursera-wide update caused Problem Set 1 answers and scores to be available right away, but that was not how we set things up originally. Making the scores and answers available right away certainly can lead to good forum conversations (as our many discussions of Alice demonstrate), but it also means that students have a very high chance of coming across "spoilers" before they do the Problem Set. Thus for Problem Set 2, and all future Problem Sets, you won't get your score or the answers until after the deadline.
Hope you're having a good weekend, and keep up the good work!
- Paul
Sat 29 Sep 2012 8:11:00 PM PDT
Puzzled about Alice?
If you had trouble with the two questions about Alice in Problem Set 1, make sure to "attend" the tutorial session just released, where I explain some of the problems in Assignments 1 and 2 and in Problem Set 1.
If you are not following the forums closely, do make sure to check out this thread, which is a superb example of how MOOC learning should occur.
-- KD
If you are not following the forums closely, do make sure to check out this thread, which is a superb example of how MOOC learning should occur.
-- KD
Wed 26 Sep 2012 10:01:00 AM PDT
Late Submission Bug
Currently the system is deducting 20% for late submissions instead of 10%. We're working on fixing that, and once we do we'll regrade the quizzes so that everyone gets their appropriate grade.
UPDATE: It seems that the bug has been resolved. Let us know in the forums if you have any further late submission issues.
UPDATE: It seems that the bug has been resolved. Let us know in the forums if you have any further late submission issues.
Wed 26 Sep 2012 8:47:00 AM PDT
Assignment 3
Assignment 3 is now available.
Mon 24 Sep 2012 1:05:00 PM PDT
First Problem Set released
Look top right. This is the first graded assignment. At the end of Lecture 2, I say that Problem Sets are due in by noon the following Wednesday. After I recorded that, we had to change the schedule to require submission by the Tuesday at noon. Sorry about that.
-- KD
-- KD
Fri 21 Sep 2012 1:48:00 PM PDT
Assignments: #2 just released
Assignment 2 (from Lecture 2) can now be found on the "Course assignments" page. (See the left-hand navigation column.) Every lecture has an associated assignment, released at noon that day. Please look at the "Course assignments" page after each lecture, to find its assignment.
Remember, although the assignments are not graded, working on them (coupled with the forum discussions they generate) forms the central part of this course. The lectures play a minor role. No one ever learned to think mathematically by sitting in a lecture, even less by watching one on a screen. The lectures merely set the agenda, give a bit of context and motivation, and provide some examples of mathematical thinking. Recognizing this fact is a key to success (or even survival) at university-level mathematics.
-- KD
Remember, although the assignments are not graded, working on them (coupled with the forum discussions they generate) forms the central part of this course. The lectures play a minor role. No one ever learned to think mathematically by sitting in a lecture, even less by watching one on a screen. The lectures merely set the agenda, give a bit of context and motivation, and provide some examples of mathematical thinking. Recognizing this fact is a key to success (or even survival) at university-level mathematics.
-- KD
Fri 21 Sep 2012 12:00:00 PM PDT
Community TAs total tops 900
Thanks to over 900 of you who have signed up as Community TAs. That's far more than I hoped for, and should go a long way to ensure the course is a success for many of you. Back in early May when I began planning this MOOC, I realized that I had to find a way to ensure that a student with a problem could get it speedily -- and correctly -- answered. In a campus class of 25 students, they can come to me. But with over 56,000 students (the latest count), that's not possible! So I put out a plea for help on the blogosphere. My hope was that we could build up a Wikipedia-like online community of volunteers. With over 900 volunteering already, it looks like there will be one TA for every 50 students. As a result, if you post a question on the forum, the chances are good that you'll get a knowledgable response. Learning math is hard. Thank you all of you who have volunteered to help others turn that into "hard-but-possible".
-- KD
-- KD
Thu 20 Sep 2012 6:17:00 AM PDT
Kindle edition of the textbook
The good folks at Kindle have confirmed that they can take the manuscript of the (optional) textbook and produce a genuine Kindle edition that will play on all Kindle platforms. (The version generated by their automatic conversion algorithm, which I tried originally, could not handle the embedded mathematics.) This will require some technical expertise, and will take some time, so the Kindle edition likely won't be available in time to be of help for this iteration of the course, unfortunately. However, I think it helped persuade them to offer to do this that many of you had asked for a Kindle edition. We are all of us pioneers in this new medium, and we clearly need one another. Thanks for making your views known.
-- KD
-- KD
Wed 19 Sep 2012 6:21:00 PM PDT
First course assignment
The assignment from Lecture 1 can be found on the "Course assignments" page. (See the left-hand navigation column.) Unfortunately, the Coursera platform cannot currently display the assignments in the Upcoming Items box on the Home Page, so you should look at the "Course assignments" page after each lecture, to find the associated assignment.
-- KD
-- KD
Wed 19 Sep 2012 10:15:00 AM PDT
Set Theory supplement
In response to comments on the forum, I've updated the Set Theory supplement to correct a couple of typos and to add a longer preamble clarifying when you need this material and how you might best use the supplement. As several students commented, the supplement assumes familiarity with material that is covered in the first part of the course, and hence can appear daunting if you have not previously seen this stuff (or have long forgotten it). We won't really use much set theory until the final week of lectures, so there is plenty of time to become familiar with it. Thanks for all those students who helped others with the exercises. Collaborative group work is what this course is all about, and it was great for me, as instructor, to observe it in action!
-- KD
-- KD
Tue 18 Sep 2012 6:21:00 AM PDT
Community TA identification
Thanks to all who volunteered to be Community Teaching Assistants. Having Community TAs is a new feature that Coursera is implementing for the first time for our course. At this stage, there is some manual work required to take the volunteers' enrollment names from the Course Survey and tag them so that their status as Community TAs is indicated when they post to the forum discussions. It will thus be some days before those identifications will appear. In the meantime, if you have not yet completed the survey, please do so. It is not a course requirement, but the more feedback we get, the better our chances of making improvements to the course in future years, and, more generally, increasing our understanding of how people learn math.
Mon 17 Sep 2012 9:30:00 PM PDT
Course survey
MOOCs are very new. I think this is the first time anyone has given a mathematics transition course in MOOC format. Because the focus is on the difficult transition from high school math to university-level mathematics, which is very different, I am working with two researchers from Stanford's School of Education, who want to find out what and how people learn in this kind of environment, and in particular how their attitudes to mathematics affect their performance and how those attitudes change as a result of taking a course such as this. This is very non-invasive research. All we ask you to do is fill out an online survey now, at the start of the course, and then again at the end. It should not take more than a few minutes. One benefit to me, as instructor, is that the results we get can help me improve the course when I give it again next year. You will find the survey here. (Please ignore the stated due date; that's a Coursera system default that they have not had chance to fix. We'd like you to complete the questionnaire right away.) One of the questions asks you if you are willing to serve as a "Community TA". Please check out what this entails in the appropriate section of the course website. Many thanks.
-- KD (for me, Molly, and Paul)
-- KD (for me, Molly, and Paul)
Sat 15 Sep 2012 10:30:00 PM PDT
What is a mathematics transition course?
This course is an example of what is generally called a "mathematics transition course," designed to assist students make the transition -- which most of us find difficult -- from high school math to university-level mathematics. Many colleges and universities offer such a course to the incoming class. There is an informative recent blog about such courses here.
Several of the comments are from instructors who have given such courses (as did the blogger - at Harvard). Those comments make it particularly interesting. Definitely worth a read. For one thing, when you reach the stage of thinking you are totally lost (a very common reaction), you will know that you are not at all alone -- it's part of making the transition!
Incidentally, if you are wondering what "mathematical thinking" is, check out this article.
-- KD
Several of the comments are from instructors who have given such courses (as did the blogger - at Harvard). Those comments make it particularly interesting. Definitely worth a read. For one thing, when you reach the stage of thinking you are totally lost (a very common reaction), you will know that you are not at all alone -- it's part of making the transition!
Incidentally, if you are wondering what "mathematical thinking" is, check out this article.
-- KD
Sat 15 Sep 2012 10:15:00 PM PDT
Meet the Team (two short videos)
Three weeks before the course launch date, I went into the campus TV studio with my two course assistants to record a short video to introduce you to the two people who will be working hard to keep the course running smoothly. (You'll see a lot of me, but Paul and Molly will be working behind the scenes, though you are likely to see Paul's contributions to the forum discussions.) You'll find the seven minute video we recorded in the Videos section of the course website (which is where you will also find the lectures and solutions to some of the assignments, when they are released).
During the course of recording that introduction, the three of us got into a discussion about our backgrounds, our motives in giving this MOOC, and our views on mathematics, science, education, and our expectations for the MOOC format. The camera was rolling all the time, so we were able to select a few parts of that discussion. This video is not a planned part of the course, but we felt it might interest you to know more about our thinking as we designed this course. (You can also find out about my own experiences in putting this MOOC together from my blog MOOCtalk.org.)
You can find out more about Molly, Paul, and myself in the About Us section of the course website.
--KD
During the course of recording that introduction, the three of us got into a discussion about our backgrounds, our motives in giving this MOOC, and our views on mathematics, science, education, and our expectations for the MOOC format. The camera was rolling all the time, so we were able to select a few parts of that discussion. This video is not a planned part of the course, but we felt it might interest you to know more about our thinking as we designed this course. (You can also find out about my own experiences in putting this MOOC together from my blog MOOCtalk.org.)
You can find out more about Molly, Paul, and myself in the About Us section of the course website.
--KD
Sat 15 Sep 2012 10:00:00 PM PDT
Welcome!
Welcome to the course on Mathematical Thinking. This page is where you will find notifications of upcoming assignments, submission deadlines, course updates, and messages from me and my TAs, Paul and Molly.
-- KD
-- KD
Sat 15 Sep 2012 9:45:00 PM PDT
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