It simply illustrates the qualitative changes much better than I ever could on a blackboard in front of the class. The idea is to make math a subject in which you do experiments, just like biology or chemistry. Goodman never stops stressing the math as the goal of computer lab work. This is still a math class, not a computer class, she emphasized. Hawkins spends less effort de-emphasizing the computer component because she wants her students to approach math with tools that they're already familiar with and will use later in college.
Most undergraduates encounter some math and lots of computer work.
So the goal of the course is to show you how the computer can be used as a tool to solve mathematical problems. One exercise Hawkins poses to students originated in ancient Greece and involves asking them how often they will see a multiple of three among positive numbers. And it stumps them. Hawkins uses the computer to count the prime numbers occurring in the numbers one through 100 and divides that number by 100 - which shows the proportion of primes in the first 100 counting numbers. Then she does the same exercise for 1,000 and 1 million.