The Hampshire College Summer Studies in Mathematics (HCSSiM) is an intensive six-week residential program that trains high ability high-school students in the mathematical sciences and mentors undergraduate and graduate students in teaching, research, and career navigation. Our primary goal is to identify, invite, and prepare motivated high-school students to pursue mathematics and mathematical vocations. We seek:
- To enlist the support of the secondary school mathematics community in the identification of talented and highly motivated students.
- To engage participants actively in the processes of mathematical thought, emphasizing the methods of discovery, proof, and modeling (rather than merely accumulating results).
- To create an atmosphere in which the enterprise of sharing of insights, knowledge, and mathematical enthusiasm overshadow distinctions between teachers and students and competitiveness among students.
- To explore active, accessible, and applicable areas of mathematics—for example, graph theory, dynamical systems, knot theory, and cryptography.
- To provide varied role models of mathematical exposition and both guidance and encouragement for participants to develop their oral and written expository skills.
- To encourage students to experiment with the learning process, take an increasing role in shaping their own education, and to evaluate their own goals, tastes, and growth regularly.
- To encourage undergraduate and graduate junior staff to experiment with the teaching process.
- To increase participation in mathematical activities by underrepresented students, including women, ethnic minorities, and economically disadvantaged students.
- To introduce students to the larger mathematical community and to help them to an understanding of the joys and options it offers.
- To provide continuing support for our students and their teachers.
The HCSSiM structure allows for vertical integration of mathematical mentoring. Faculty, graduate students, and undergraduate students mentor the high-school students in learning mathematics, in joining the mathematical community, and in planning their futures. Faculty serve as mentors and models to the junior staff members and high-school students; high-school students learn about applying to college, college students are guided in the transition to graduate school, and graduate students receive advice for their professional careers. Some of the undergraduate and graduate staff are alumns of HCSSiM, which allows for long-term mentoring; other staff are new to the program, which produces a broader impact in mentoring.
All HCSSiM instructors keep foremost in mind those aspects of presentation that will pique students’ curiosity and draw them further into mathematical study; it is an intense and supportive teaching environment. The pedagogical style is highly exploratory, encouraging generalization, collaboration, and question-asking. Both graduate and undergraduate junior staff teach several hours each week under the supervision of faculty. Undergraduate and graduate junior staff members acquire rich experience in teaching, mentoring, and leadership by assisting with collaborative learning and presenting material in classes under the supervision of faculty; by the end of the program, they are designing and teaching their own mini-courses. Each staff member is expected to deliver a Prime Time sometime during the summer in order to practice presenting expository mathematics or the staff member’s own research results. The material must be placed in context for it to be effectively communicated to high-school students.
By providing models, practice, and feedback, HCSSiM helps participants become outstanding communicators. Everyone spends time at the board, shares questions and insights in small groups, and regularly writes up mathematics—and receives, almost immediately, praise, suggestions, and advice. In this way, the junior staff members learn to use discovery-based active-learning methods. Both students and staff take these skills, and a lot of mathematics, with them when they depart Hampshire. Many junior staff members later become teachers at the secondary, collegiate and graduate levels, and practice the engaging and empowering pedagogy learned at HCSSiM.