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Looking Ahead to CollegeHow do IMP graduates make the transition to college mathematics? The following stories are from informal interviews with college students who were enrolled in IMP in high school and who later studied mathematics in college. This material is not intended to be a representative sample of IMP graduates, nor should it be interpreted as research data. However, these students' comments and observations indicate that taking IMP in high school can open doors to success in college mathematics. Arrissa*Arrissa chose to attend Swarthmore College because it is a good, small liberal arts college with an excellent engineering program. "My major is engineering. I chose it because I like to understand how things work, I like the cooperative nature of the profession, I enjoy math and science, and I like the kind of people that choose to be engineers." Her first college math course was Calculus I, which dealt primarily with differentiation. She says she felt very prepared for the class. She got an A, and in reflecting on IMP's influence on her performance in this course, she said, "I do find that I am much better at solving word problems than my peers. I actually enjoy them more than other problems. Also, our professor wanted us to discuss our answers on our exams, and I didn't have much problem doing that. Engineering is the class I can see my experiences in IMP reflected the most. We do lots of group work, with study groups for our homework, and lab groups. We also solve lots of word problems, and our labs involve extensive explanations of our procedure and calculations." Brandon"Math is my favorite subject," claims Brandon who is now a student at the University of California, Los Angeles (UCLA). Since he scored higher than 700 on the math portion of the SAT and took AP calculus as well as IMP Year 4, he was automatically placed into secondsemester calculus when he entered college. During his first semester, he also took computer science and chemistry. His spring courseload included the continuation of both calculus and computer science as well as physics and English. He worked as a math tutor at his high school and continues to tutor students at the computerscience lab at UCLA. He will most likely major in computer science and engineering. Eventually, he'd like to design computer software and hardware. Brandon states that his high school math courses were critical for college chemistry and physics. He especially remembers the IMP unit on matrices, Meadows or Malls?, and the work on vectors. When asked about the approach used for studying mathematics offered by the IMP curriculum he said, "It makes you think more. We worked out things and came up with the formula ourselves." Brandon thinks college teaching should be more like IMP's, and everyone would benefit. "Students could help each other out. Most of the time students don't ask questions.... They're afraid to ask the professor something." CassieCassie attends Dartmouth College in Hanover, New Hampshire. Like many freshmen, she has not yet declared a major. Her favorite classes so far have been chemistry and English. "I have always done pretty well in math," says Cassie. Based on high school performance and SAT scores, she was placed into firstsemester calculus. She described her class, "Since it was fall term, the class was also my first introduction to huge college lecture classes, and that was quite an adjustment. I did OK in the class. There were no group meetings with a teaching assistant, but there were evening tutorials twice a week that I often attended, and they usually helped me if I encountered a serious problem with the work. The class was a bit teachercentered—actually totally. Students asked the occasional question, but that was about it. I think that my lessthanperfect showing in the class had to do with adjustment to college and to the huge class and the lack of personal attention. But I felt that I was pretty wellprepared by IMP." When asked which high school classes contributed to her current success in college, she replied, "IMP helped me a lot with discipline and being thoughtful.... I think that IMP extends beyond the realm of mathematics, which is important because not everyone plans to devote their life to math. Also, IMP draws correlations between math and other topics, such as physics, business, and sports, which is often not done in high school classes and is essential for a greater understanding of the inner workings of the world." DavidHighly focused as a freshman at the University of California at Berkeley, David was ready to declare his major in Industrial Engineering, Operations Research. His major will require at least eight semesters of mathematics, including four of statistics. In his firstyear calculus course, he earned an A the first semester and an A+ the second semester. He took three years of IMP and AP calculus at an innercity high school. He found IMP challenging. In his high school science classes, he was immediately able to use the statistical analysis and data pattern recognition skills that he learned in IMP classes. David feels that IMP helped him in this course with "thinking critically and applying concepts to solve problems." EmilyEmily attends Haverford College, located near Philadelphia. Emily's current courseload includes biology, computer science, Russian, and education. Although she has no idea what her career goals are at this time, she did identify herself as more of a mathscience person. She was pleased with her high score on the math portion of the SAT. When asked how well IMP prepared her for this test, she said, "I think it did a very good job.... IMP allows you to truly understand the math so that when you see it in a format that you are unfamiliar with—like the SATs—you are more likely to be able to figure it out. She also did well on the math placement test at Haverford, where she was placed into a high secondsemester calculus class. Emily is disappointed with many of her college classes, calculus being only one of them. In the calculus course, Emily reports that the professor talked to the chalkboard the whole time. That situation did not keep her from doing well on the tests and getting good grades. (Her final grade was a B.) Since there are no teaching assistants at Haverford, she persevered with the professor. "I found out about halfway through the semester that he [the professor] was fairly good oneonone, so I went in and saw him during office hours frequently. There was also a math help session once a week that I attended regularly." FionaFiona now attends Stanford University. She attended a rural high school in California, where she earned an International Baccalaureate (IB) diploma. Fiona immediately took the plunge into difficult courses in her freshman year. As a first semester freshman, Fiona took Single Variable Calculus. She enjoyed the course and received a final grade of A. Although the format was quite lectureoriented, the content reminded her of IMP: "The calculus book that we are using focuses heavily on the applications of derivatives, integrals, etc. to problems (physics, economics, etc).... It reminded me a lot of IMP's emphasis on word/application problems. The majority of homework problems were IMPlike word problems, and our midterms were almost always a set of six to seven word problems. IMP has definitely changed my perspectives on the wide range of applications that mathematics has on every aspect of our lives. In that sense, I strongly believe that IMP has given me an appreciation for the beauty of mathematics." GarrettGarrett recently graduated from Howard University, where he majored in biology and minored in computer science. He took four years of IMP in high school. About IMP's effect on his college preparation he says, "IMP prepared me to work in groups, gave me confidence in oral presentations and the expectation of daily homework." At Howard, he worked as a computerlab tutor and had this to say about his peers, "Most of the college students I met were competitively introverted. But I took the initiative to organize study groups and learn collectively." Garrett would eventually like to work in the field of computer graphics/animation. To accomplish this goal, he is considering attending graduate school. *Stories are real but names are not
