I agree with Chris Gregg's answer and want to add some additional thoughts and strategies to it.
Make cheating irrelevant
1) Homework becomes a collaborative venture.
Students can work individually or in groups on all out-of-class assignments. Every student needs to turn in their own copy of the assignment. Every student has to list whom they worked with on the assignment. Homework is a tool for me to give the students to help the students learn the material. Why should I care if they do it in groups or individually? If you encourage students to go to each other for help, then only the most diehard cheaters (whom you cannot stop) will keep going to the faceless masses on the internet. All involved learn more through the interaction. Most "real-world" work is done collaboratively anyway. When I give these kinds of assignments I work very hard to come up with questions and prompts that are not internet searchable - because they must use specific resources, the questions are opinion-based, or the questions focus on specific narrow local events, etc.
- Which of the two figures on the accompanying handout best explains the observation that carbon-carbon single bonds in strain cyclic molecules are weaker than those in unstrained cyclic molecules? Provide a brief rationale.
- Use the data in Table 8.1 on page 115 to determine which of the the following is growing faster: China's population, China's per capita GDP, or China's per capita energy consumption. Do a similar analysis for the US 100 years ago (use the data on the handout). Comment on any similarities.
- What are the three key points of the speech given last week by the Dean of the College? With the information I've given you about the budget of the College, which of the Dean's action priorities for this year are financially feasible? Which action priority are you most interested in seeing completed?
The third one on my list would be very challenging for someone to get outside the institution help on.
If the out-of-class projects are significant, then you can encourage the students to keep each other honest. On big collaborative projects, I have the students rate (not grade) each other on the following questions. Trends appear when someone has not pulled his/her own weight:
- This person contributions to the project were (less than, the same as, greater than) mine.
- This person deserves a grade on the project that is (less than, the same as, greater than) mine.
- This person's greatest contribution to the project was _______.
- The hardest thing about working with this person was _______.
2) As Chris Gregg said - make exams worth much more than homework.
- Homework 20%
- Midterm Exam 1 20%
- Midterm Exam 2 20%
- Midterm Exam 3 20%
- Final Exam 20%
In this scenario, exams count for 80% of the grade (and so cheating on homework will not have a huge impact), but homework still counts for something. If you phrase your grading descriptions as "homework counts as much as an exam", then you get students to take it seriously. One instructor I know even goes the extra step to rename his homework assignments as "Take-home Exam Part 1, 2, 3, etc." (and then treat them like the collaborative homework I described above. If a student has been cheating on the assignments, then he/she will not do well on the tests, and course grades will follow.
Both of these strategies focus on the purpose of the homework (to guide student learning and studying) which is different from the the purpose of tests (to assess student knowledge, skills, etc.). If homework is a guiding assignment and exams are an assessment assignment, then worry about cheating on exams (easier to spot and control) and ignore cheating on homework. Some students will not be guided the way you want them to be. Just as you cannot make an individual student learn, you also cannot make an individual student learn in the fashion you choose.