WeBWorK Problems

appropriate problem library for Stewart calculus

appropriate problem library for Stewart calculus

by Dana Ernst -
Number of replies: 15
I'm teaching Calculus II this semester out of Stewart's "Calculus" 6e (NOT "Early Transcendentals"). I'm also using WeBWork for the first time (well, technically, I'm not using it yet; our semester begins next week). Can someone tell me which problem library matches up the best with this version of Stewart?


Dana Ernst
Plymouth State University
In reply to Dana Ernst

Re: appropriate problem library for Stewart calculus

by Murray Eisenberg -
This may not be what you or the WeBWorK folks want to hear, but here goes anyway: If you're willing to make your students pay for access to an on-line homework system, then I highly recommend WebAssign (webassign.net). It already has ported nearly all of Stewart's end-of-section problems to its system, of course parametrizing as many as possible. This makes constructing assignments very easy; for example, you can look at the printed versions in the text and then just select the corresponding problems in WebAssign, instead of awkward browsing through the on-line system (which you can nonetheless do, by chapter and section).

My experience is solely with the Stewart Early Transcendentals version, but I believe comparable facilities exist for the "late transcendentals" (?) version you mention.

Stewart's publisher, Cengage, makes bundles available in which the student buys an e-book version of the complete Stewart text (plus a printed copy if desired) along with WebAssign access.

Among the goodies available with the Stewart text are: worked examples presented in the form of tutorials where the student reads actively and has to fill in the blanks instead of just reading the entire example passively; Flash step-by-step tutorials; links to sections of the e-text right on questions; links to animated mini-lectures (with sound); etc.

WebAssign is an up-to-date system, with many rich features that are not yet available in WeBWorK, so far as I am aware. E.g., there is math palette entry for symbolic questions; a symbolic manipulation engine behind the scenes (Maple) which allows full checking of symbolic answers and not just their evaluation at particular real numbers; free-hand drawing tools students can use to supply answers; graphing tools students can use; a sophisticated gradebook that in most cases can completely substitute for what you might do locally in a spreadsheet. WebAssign has a sophisticated, built-in communication system with which students can ask about a particular problem (as with WeBWorK), send other messages directly to the instructor, post to a built-in forums (without any need to set up a Moodle site); and instructors can post announcments directly to the front page students see after they log in (without the instructor having to edit any files).

For the instructor or author, WebAssign has quite a different look-and-feel from WeBWorK. You don't have to bother with files (except when you want to upload or download rosters or scores). I just find it a lot easier to do stuff in WebAssign, whether it's set up a class (for which I need no sysadmin) or to assemble an assignment or to modify an existing problem (e.g., change independent variable from x to t without a cascading series of other changes being necessary as it seems to be with old library questions in WeBWorK). When selecting problems for an assignment by text chapter and section, you can opt to see very short summaries of all the questions, medium-length abridgments of all the questions, or the complete questions; I just find it a lot easier to make my selections with that sort of system.

As a multi-section course chair, with WebAssign I can create a master set of assignments and then propagate it directly to all the other instructors' courses. No export/download/upload/import of .def files required. When students drop one section of the course and add another, we can quickly retrieve their records from the other section for our own. No fussing with files involved: we just do it on-line.

The greater sophistication of WebAssign compared with WeBWorK should be no surprise. While WeBWorK must now rely primarily upon volunteer help, WebAssign, with what I believe is the largest-usage on-line system now available and consequently a lot of development money continuing to flow in for development, can continue to keep abreast of technology and what we expect from contemporary web-based applications.

(I have no financial interest in WebAssign! And I should mention that I've used another on-line homework system, too.)
In reply to Murray Eisenberg

Re: appropriate problem library for Stewart calculus

by joel robbin -
Can you write your own problems in WebAssign?
In reply to joel robbin

Re: appropriate problem library for Stewart calculus

by Bruce Yoshiwara -
Yes, WebAssign faculty users can author problems.

WebAssign is also Perl based, but still quite different from WeBWorK. It is a commercial product and uses a CAS kernel for evaluating expressions.

The company is housed on the North Carolina State campus--the president John Risley is a retired physicist.

But, like WeBWorK, WebAssign is publisher independent. Although WebAssign works directly with Cengage (which owns Brooks-Cole among others), WebAssign also has problems for textbooks under the giant Pearson (MyMathLab) umbrella.
In reply to Bruce Yoshiwara

Re: appropriate problem library for Stewart calculus

by Murray Eisenberg -
Independence from publisher is a real benefit of an on-line homework system -- whether free/open-source such as WeBWorK or non-free/proprietary such as WebAssign.

Our experience with two different publisher-based systems is that, while they can be very good from the student's point of view, they are horrors from the instructor's point of view in providing quick support, handling grade rosters, etc. Typically, one cannot get directly to support but has to go through the publisher's representative (who herself or himself knows from nothing about the technology).
In reply to Bruce Yoshiwara

Re: appropriate problem library for Stewart calculus

by Zbigniew Fiedorowicz -
The postdoc from Oregon who I mentioned in my other post is a very competent programmer in his own right (his research area is computational group theory). He thought it was not too difficult to author problems for WebAssign as long as student answers were not provided by the math palette. If they were provided by math palette, he could not make head or tail of the code used to process the student answers. (The student input from math palette is presented in the form of some horrid XML.)

According to the notes I took during a presentation of WebAssign at OSU last spring, the math palette code was written by a contract programmer hired by the publisher Cengage, rather than by WebAssign staff.
In reply to Murray Eisenberg

Re: appropriate problem library for Stewart calculus

by Dana Ernst -
WebAssign is certainly tempting. However, as an individual who is constantly preaching to others about choosing free and/or open-source alternatives for textbooks, software, etc. when a viable alternative exists, I'd have a hard time asking my students to spend $35/semester. In a perfect world where I had lots of extra time, I'd prefer to spend the extra time futzing around with WeBWork. In my current reality, I'd like to not spend hours choosing WeBWork problems. If anyone has tips and/or advice for streamlining the process for creating assignments, I'd love to hear them.

Actually, I have an even more general question. How are most people that use WeBWork in calculus using it on a day to day basis? How often are people having students use WeBWork? How many problems each time? What percentage of homework is WeBWork based and how much does it contribute to a student's overall grade?
In reply to Dana Ernst

Re: appropriate problem library for Stewart calculus

by Murray Eisenberg -
I can respond to part of what you ask, about how to use the system in calculus, even though I'm using WebAssign there (but I'm using WeBWorK in my differential equations course).

We have one assignment per textbook section, with each assignment having 8 to 12 or so problems. In practice this means from 2 to 3 assignments per week. The key is to allow the students just enough time to work on an assignment but not so much time that the primary pedagogical purposes of the assignments are compromised: (1) to check understanding of what was just taught as soon as possible and reinforce what was learned; and (2) to make sure the student has sufficiently learned what's needed for the new material coming.

(With WebAssign, on an average of once each two assignments, there's a question where the students have to type out their work directly into a big text box on-screen and submit that; then the instructor reads these responses on-line, one student after the one, types comments as desired, and enters a score for each answer. Much quicker than the equivalent on-paper situation. Occasionally, if it would be sufficiently awkward for the student to type the entire solution, there is an option to turn in the work on paper. In any case, such problems are a good measure to take against the temptation for student to let WolframAlpha do their homework.)

Except for multiple-choice or matching questions, the number of tries I allow will vary from 4 to 10, depending on the complexity of the question and how many individual parts it has.

In our calculus courses, the homework counts from 8% to 16% of the overall course grade. (This is up to the individual lecture section instructor. Typically, if that section gives weekly quizzes at recitations, then quizzes count 8% and homework 8%.)

To allow for all contingencies where a short due-date extension won't suffice, I drop the scores from the lowest 20% of homework sets for each student. So if you look at how little one question on one homework assignment counts toward the course score (roughly 4/100 of a point!), it's amazing how long and hard most students will nonetheless work to get the correct answer on each and every question.

Naturally, I (and other instructors) frequently check progress of the class on each assignment. This sometimes results in my e-mailing students to congratulate them for finishing early or getting a harder problem correct with only one or two tries, or to ask them why they haven't even begun an assignment yet, etc.

Ideally, I'd like to add something to this: A short "readiness assignment" on each textbook section, due just before that section is to be covered in class. Such an assignment covers just very basic things a student ought to be able to pick up by reading the assigned textbook section before class -- perhaps a simple concept or technique, with some very basic examples. The assignment checks whether the student has done that reading and gotten anything out of it, and it allows the instructor to spend most of the lecture on that section dealing with more substantial and higher-order matters. I've used such assignments in our "calculus for everybody else" course, to good effect.
In reply to Dana Ernst

Re: appropriate problem library for Stewart calculus

by Zbigniew Fiedorowicz -
We use Moodle as a front end to WeBWorK, via the wwassignment bridge.

In Calculus 2 (integral calculus) we assign 144 WeBWorK problems in 7 problem sets spaced roughly a week apart, spread out over a 10 week quarter. We also grade 48 problems from the text handed in on paper, also in weekly assignments. [We found that if we didn't require paper homeworks, quite a few students neglected to buy the textbook.]

The WeBWorK assignments are worth between 0% and 8%, depending on how they do on quizzes. The formula for the recitation grade (worth 1/6 of the course total) is
where QT is the quiz total and HT is scaled homework total (on a 100 point scale for both QT and HT). For about 70% of the students 0.6*HT+0.4*QT is the higher of the two.

We also have three challenging extra credit projects in WeBWorK which can be worth up to 7% of the course total. About 20-25% of the students do substantial work on these.
In reply to Murray Eisenberg

Re: appropriate problem library for Stewart calculus

by Zbigniew Fiedorowicz -
While WebAssign seems to be a very nice system in principle, in actual practice it appears to be less stellar. For instance last autumn they had serious performance issues due to server overload problems.

The University of Oregon Math Dept was a heavy user of WebAssign and has now switched to WeBWorK due to such issues. One of our current postdocs used to be a TA at Oregon and he reports:

The biggest weakness in WebAssign is its problem bank and specifically within the problems that use this magical math palette. For it is very difficult to create exercise which correctly use this feature especially with randomized values. The majority of exercises which involved these sorts of problems incorrectly graded students inputs with remarkable frequency....
When you mix in a reasonable frequency of actual computer errors (as many WebAssign problems have had) you arrive at an immediate distrust of the entire system. It took very little time for this stigma to spread. We suddenly found that new incoming freshmen had heard of WebAssign in the dorms and already knew "it doesn't work". So they were not willing to learn from it but just dismissed it as busy work.
Faithful reproduction of problems from a text: webwork does not link to specific text. WebAssign does include problem sets which it claims link to Hungerford's pre-calculus, Stewart's Calculus, and other texts. At Oregon we used these problem sets and noticed no obvious correlation between the exercise in the text and those associated to in the WebAssign problems. A particular difficulty was in story problems as VERY OFTEN problems would be missworded, incomplete, or use terminology from other texts and so students could not follow them. It appeared as though the company hired undergraduates to write similar math problems and so the proof-reading and synthesis with the text was non-extant......
Individually these issues might be excused, but not when compared to a product such as WebWork which I found this past term to be incredibly rigorous in its problem sets and without the major distrust that plagued WebAssign.

You might want to write to Hal Sadofsky for more details on Oregon's comparative experience with WebAssign and WeBWorK.

Below are some web links I found, which express less than positive reviews of WebAssign:

NYU student newspaper:
NC State student newspaper:

Better Business Bureau:


In reply to Zbigniew Fiedorowicz

Re: appropriate problem library for Stewart calculus

by Dana Ernst -
Now, it is even easier for me to ignore the temptation of WebAssign. Thanks for posting.
In reply to Zbigniew Fiedorowicz

Re: appropriate problem library for Stewart calculus

by Adam Weyhaupt -
I don't know what this "magical math palette" is, but it made me wonder:

Can DragMath, http://www.dragmath.bham.ac.uk/, be interfaced with Webwork?

If students could enter rational and other expressions in a more visual way, that would, in my opinion, dramatically improve Webwork (which is already great!)

In reply to Zbigniew Fiedorowicz

Re: appropriate problem library for Stewart calculus

by Hal Sadofsky -
Zig pointed out that this dicussion was happening here, so I thought I'd put my two cents in to this complicated question.

Before I launch into my comparison, I want to give my perspective on what homework in lower level math classes (calculus and below) is for. I think homework is to allow students to learn how to do problems, and allow students to test for themselves that they've learned this. I don't believe homework functions well as a way for _us_ to test students knowledge. Because of this, I think multiple choice problems as homework problems are almost always a waste of time (either you allow a lot of choices and the students guess, or you allow very few choices, and then you are assuming students already know how to do the problem and are just testing them).

So I think the best computer graded homework problems are those that force the students to do something to come up with an answer (that they couldn't guess even with a bunch of guesses) and allow the students to keep trying until they get things right.

We used WebAssign quite heavily for a few years, and now we are using WebWork quite heavily. So obviously we think WebWork is a better solution for us, but I emphasize that I'm giving my opinions below, not trying to make assertions of fact. But WebAssign has two big advantages:

1) If you are using a textbook that is well supported by WebAssign, then a lot of the problems will have been coded, with problem numbers from the textbook. So there is a good chance that your instructors can assign homework the way we used to assign it: look at the problems at the back of the book, pick the ones you think are appropriate, and assign those (well, you do have to do the extra step of logging into WebAssign and creating the homework assignment of course).

2) You (or your students more precisely) are paying someone else to take care of the server.

But here is a list of things where WebWork is superior (at least for us) to WebAssign (and I intend no disrespect to WebAssign, which is a good project staffed with many good people).

1) I think the interface to WebAssign nicer looking perhaps, but is harder for instructors to learn. It feels too complicated.

2) [This is a big one for me]: The "email instructor" link in WebWork does, from my perspective, exactly what it is supposed to do. It makes it very easy for me to answer student questions, and provides a huge number of very satisfying (for both me and the student) "teachable moments." WebAssign in my opinion falls down badly on this point.

3) [Another big one for us.] We used WebAssign heavily for College Algebra and Pre-calc. This is a tougher group of students to deal with than calculus students since many of them are very weak on things like order of operation or parentheses and will blame the computer when it interprets 1/2+3 as 3.5 rather than as .2 (which is what they thought they meant).

For these students, it doesn't take a very high proportion of badly coded problems before they turn against the system, thus depriving it of its pedagogical value. The WebAssign problems seem to be mostly coded by people who are not teaching the course (they are being paid to code). As a consequence they often haven't thought through the consequences of coding a problem where the answer is sqrt(2) in such a way that the answer 1.414213 is counted as wrong. In my experience, I can teach students much better at this level if sqrt(3) is counted as wrong for sqrt(2) but if 1.414213 is counted as correct.

We had a high incidence of such problems, especially at the beginning (in their defense, WebAssign was trying to code a new book for us, so they didn't have that much time for testing, but on the other hand, we didn't really demand _that_ many problems be coded).

We also had a high incidence of problems simply being poorly tested and wrong.

And finally, there is a high incidence of problems being coded in ways that are not pedagogically useful. As all of us know, this takes some thought, and I'm sure all of us have made mistakes along these lines.

The WebWork problem library is also (of course) far from perfect. I routinely run across problems that I think are bad problems (for example, virtually all multiple choice problems if considered as homework problems). But I rarely run across problems that have actual errors, and for the most part the problems have been coded to accept correct answers in a way I find pedagogically meaningful.

4) WebAssign is textbook dependent. This can be a good thing, but then when you want to change textbooks you either have to change to a different WebAssign supported book, or convince WebAssign to let you be an alpha tester as they code problems for your new book. In fact even a change in textbook _editions_ can put you in the sudden position of being an alpha tester.

5) I didn't like making the students pay as much extra as they have to pay for this service. It is wrapped into the price of new texts usually, but then students who are trying to save money to buy used texts can't, or they can't save as much money. I'm not accusing WebAssign of being a front for the publishers - again I think they are reasonable people providing a reasonable product, but unintentionally they make it easier for textbook publishers to continue to charge exorbitant prices for textbooks on subjects that haven't changed greatly in hundreds of years.

Of course the tradeoff is that it costs us something to maintain our server. But not that much compared to what students save, and I try to sell this to the dean and the University as a place where we've taken the students finances into account in a small but meaningful way (we're at a state university, so allowing someone to get a used textbook for $80 instead of a new one for $150 is considered to matter).

6) There are people in our department interested in monitoring and helping with instructor use of WebWork. It is easier to track (since we can have emails to instructors go to extra people) and easier to help fix things (since we can put someone knowledgeable on fixing problems quickly) with WebWork than it was for WebAssign (keep in mind that we have 2000+ students using WebWork in any given quarter).

That's the end of the list for me. I'm sure other people have different perspectives on what is important and what I wrote is probably way more than anyone wants to read. I'm not discounting the significant advantages (1 and 2 from my first list) of using WebAssign, and my knowledge is already 2 years out of date, but reasons 2 and 3 from my second list are huge for me.

Back to the question (problem library for Stewart). Last I looked there were lots of 5th edition Stewart problems coded. Stewart is now on 6th edition of course, and there weren't enough 5th edition problem coded for me to be happy with.

We prepared (based on the whole library, not just the Stewart problems) complete homework sets that could be used for someone teaching college algebra, pre-calculus, calculus I, calculus II, business calculus. (We're on quarters, and we haven't dealt systematically with calculus III, which includes sequences, series, Taylor polynomials, power series. This is tougher material for WebWork than differential and integral calculus, though I did teach this once with WebWork with results that I liked.)

In reply to Dana Ernst

Re: appropriate problem library for Stewart calculus

by Adam Weyhaupt -
In my Calculus I course (using Varberg, Purcell, and Rigdon), I create a Webwork assignment for (almost) every section that we cover. Although the length of the assignment varies, these are typically about 12 problems long. (On certain topics, like differentiation using the chain rule, I think they need more practice, so I might give 20 or more in a few section.) I assign these immediately I've covered them in class, and students get 1 week to complete the problem set.

Attempts: I give students unlimited attempts. Much to my surprise, not everyone gets a 100%... Why?!

Grading details: Since I give a LOT of Webwork assignment, I drop the lowest 5 Webwork scores. I DON'T give quizzes, so my grading scale is then:

Webwork: 18% of course grade
Labs: 10%
Four exams: 11% each
Final exam: 28% each

I readily acknowledge that having 18% of my course grade on Webwork means that my scores might be inflated. I'm personally OK with that because I feel that the forced practice is SO important; in my experience students just WON'T practice if it's not a big part of their grade.

Questions: I answer questions by email, but I also often spend the first 20 or so minutes of class answering Webwork questions. Students tell me the number of the problem, and I log into the instructor's account and will work all or most of that problem.

CMS: I've used Moodle before and loved the seamless interaction between Moodle and Webwork. However, our university uses Blackboard, and I decided the last time that I would try to use Webwork with Blackboard. It was a real pain, since I had to take the grades out of Webwork, process them in Excel, and upload them to Blackboard. I did that only 5 times; once right before each exam. Therefore, the students' grades on Blackboard were only totally accurate right after an exam. They seemed OK with that.

On my student evaluations, students generally seem to respond positively to this Webwork setup.
In reply to Dana Ernst

Re: appropriate problem library for Stewart calculus

by Arnold Pizer -
Hi Danna,

If you go to https://math.webwork.rochester.edu/webwork2/
you will see the courses fall09mth161-2 and fall09mth141-3.

The first is our standard two semester first year calculus course taught using Stewart. The second is a three semester sequence covering the same material at the same level, just slower. You can log into any of theses as a guest and look (and/or print out) the weekly assignments. The syllabus will tell you how much they count. Often this is 20% but we find that almost all students get almost full credit, so the 20% doesn't really differentiate between students for final grades.

If you print out the problems since you are a guest, you will not see that actual names of problems. However, if you would find it useful we could send you the setdefnition files for a course and with these you can recreate the sets with a click of the mouse. You can then edit the sets adding/deleting problems, etc.

Also in addition to all the problems in the National Problem Library (many of which will be similar to Stewart type problems) there is a collection of problems from Stewart (not sure what edition) coded at UC Santa Barbara. These can be downloaded from CVS.

In reply to Arnold Pizer

Re: appropriate problem library for Stewart calculus

by Dana Ernst -
Thanks for all of the useful comments and suggestions.