WeBWorK

An Internet-Based System for Generating and Delivering

Homework Problems

Overview

WeBWorK is an internet-based system for generating and delivering homework problems to students. It increases the effectiveness of traditional homework as a learning tool by:

- Providing students with immediate feedback on the validity of their
answers and giving students the opportunity to correct mistakes
*while they are still thinking about the problem*. As one student said, "I can fix my mistakes while [the] problem is fresh in my mind." - Providing students with individualized versions of problems which means that instructors can encourage students to work together; yet each student must develop an answer to his or her own version of the problem.

These are important educational advantages, and WeBWorK is a tool designed to conveniently deliver these advantages to large numbers of students. First used in a single course with 29 students in the fall of 1996, WeBWorK currently serves 900 students at Rochester in seven courses ranging from pre-calculus to second semester calculus and physics. This semester for the first time, WeBWorK is being used at other institutions. Indiana, John Hopkins, and SUNY Stony Brook are teaching courses using WeBWorK. Indiana has approximately 1950 students in WeBWorK courses, John Hopkins 200, and Stony Brook 90.

WeBWorK has been awarded the 1999 International Conference on Technology in Collegiate Mathemnatics (ICTCM) Award for Excellence and Innovation with the Use of Technology in Collegiate Mathematics.

Anyone can try WeBWorK for himself or herself by connecting to
actual courses at ** http://www.math.rochester.edu/webwork**.

Contact Professor Michael Gage (gage@math.rochester.edu) or Professor Arnold Pizer (apizer@math.rochester.edu) for further information.

Student Reaction to WeBWorK

Immediate feedback is a key educational advantage of WeBWorK as recognized by the students themselves. When asked on anonymous surveys:

Does the immediate feedback provided by the WeBWorK system enhance the educational value of solving homework problems? Please provide a number between 1 and 5 where 1 means strongly disagree while 5 means strongly agree.

most students responded with a 5 and made comments such as:

- "Yes. It was very helpful to know if I was wrong and be able to work the problem through until I knew and understood how to get it right."
- "I understand the problems better when given the ability to correct them."
- "I think it’s a better way to learn."
- "I really like finding out right away and being able to rework a problem I got wrong."
- "I loved it. It helped me develop on my skills."
- "Significant increase in motivation [thus] giving students more confidence"
- "It definitely does. I think this is the strongest point of W.W."
- "It was helpful in learning from mistakes & seeing mistakes."
- "Very much so. I don't have to wait for lecture to see if I'm doing it right."
- "Yes. It makes you want to redo it; after finding an answer, you feel accomplished, immediate feedback makes sure you have accomplished something."

When asked on anonymous surveys whether they preferred a section using WeBWorK or a section using a traditional homework system with hand written and hand-graded solutions, almost all preferred WeBWorK sections.

List of current WeBWorK features

WeBWorK’s features make it uniquely suitable for authoring mathematics, physics and engineering problems including problems from calculus, trigonometry and upper-level secondary mathematics courses. The following innovative features stand out:

- Advanced mathematics problems can be authored and displayed and printed with typeset quality.
- WeBWorK produces similar but individualized problems for each student. This makes WeBWorK particularly effective in a group learning setting, since students can collaborate without copying. WeBWorK remembers each student’s problems, so they can connect to WeBWorK, attempt a problem, logout and give the problem more thought, and then reconnect to WeBWorK to attempt their own individualized problem again.
- Flexible mechanisms
are available for handling numeric, symbolic, and string answers. Numeric
answers may (at the instructor’s option) allow elementary functions such as
3*sin(pi/2)+ln(e^2) which WeBWorK will evaluate, or the instructor can require
that the student enter a numeric answer such as 5. Symbolic answers allow for
questions such as:
*enter an anti-derivative for x*Some correct answers are .3333*sin(x^3) or (1/3)*sin(x^3) + 7; however (cos(x))^2 + sin(x^3)/3 + (sin(x))^2 is also correct and WeBWorK will accept that too. WeBWorK will accept^{2}sin(x^{3}).*any**correct answer*. String answers allow for T/F, matching, multiple-choice, and short answer questions. - An instructor can also extend the answer routines to compare a student’s answer with WeBWorK’s answer in new ways without modifying the core of WeBWorK.
- Two partial credit grading mechanisms are provided for scoring multi-part questions. Instructors can also write custom grading mechanisms.
- For physics problems, WeBWorK can check units attached to numeric answers and make the proper conversions.
- Graphs of functions can be generated "on the fly" by a single statement, enabling one to ask individualized questions involving graphs for each student.
- The pg language developed for writing WeBWorK problems is built on the widely used scripting language Perl. Mathematical formulas can be written in TeX (or LaTeX), the mathematical typesetting language, and as with TeX, ease-of-use has been added in the form of macro packages. Even complicated numerical subroutines can be included to help check the answers to problems. Novice problem writers will use these macro packages to write problems, while expert problem writers can extend the capabilities of the language by writing new macro packages. As the new HTML standard syntax for specifying mathematics emerges, it can also be used in writing problems. No change to the WeBWorK system will be necessary.
- Because of Perl's flexibility, it is fairly easy to embed other languages into the pg language. For example, we developed a translator which converts physics problems already written for CAPA to the pg language so that they can be used under WeBWorK.
- GIF illustrations, animated GIF’s, HTML hyperlinks, JavaScript code and Java applets can all be embedded in WeBWorK problems in order to enhance their educational effectiveness.

In addition to these features, which make WeBWorK especially suited for mathematics education, WeBWorK provides standard features found in most CGI/database education solutions.

- Students receive immediate feedback about the accuracy of their answers.
- Students can access WeBWorK from any computer connected to the internet, and instructors can use any computer and browser for management of the assignments.
- The instructor or TA can view the precise version of the problem seen by each individual student, making it easy to answer specific questions from a student via e-mail or in person.
- All pages have a feedback button that sends an e-mail message directly to the instructor(s) (or whomever the instructor designates). Students find this a convenient way to communicate with their instructor, usually requesting help on a particular point. Most student pages also have a help button that provides specific instructions and hints.
- Problem sets are graded automatically, and the results are easily exported to and imported from spreadsheet programs such as Excel.
- The instructor can easily find out the current progress of a class or an individual in correctly completing any assignment.
- Instructors can send e-mail to an entire class reporting individual homework grades, exam grades etc.
- WeBWorK allows great flexibility in administering individual homework. For example, an individual student can be given an extension on an assignment without granting an extension for the entire class. Or an individual student can be granted extra attempts on a problem that has a limit on the number of allowed attempts.

The flexibility of WeBWorK allows its use by instructors with very different teaching styles. For the first year calculus courses at Rochester, we have set up WeBWorK so that:

- Students can attempt a problem as many times as they wish until the due date (unless the instructor desires to place a limit on the number of allowed attempts). Each problem in a set can have a different limit on the number of allowed attempts. For example, instructors may wish to limit the number of attempts on T/F questions while allowing unlimited attempts on problems requiring numeric and symbolic answers.
- Problems can have individualized solutions and/or hints (e.g., solutions can use the same individualized constants each student sees).
- After the due date, students can review the homework, including the answers expected by the instructor. Solutions to problems, if provided by the instructor, are also available after the due date. Students frequently work old assignments to review for exams.