STRENGTHENING MATHEMATICS TEACHERS ’ PEDAGOGICAL CONTENT KNOWLEDGE THROUGH COLLABORATIVE INVESTIGATIONS IN COMBINATORICS

teachers in collaborative, combinatorics problem-solving experiences during an intensive four-week summer institute. The program challenged participants ’ pedagogical content knowledge and their views about collaborative problem solving as evidenced by statistically significant gains in test scores, their self-reported ratings on content and problem-solving abilities, and excerpts from journal writings. According to Freudenthal (1991), only a small minority learns when mathematics is taught as a ready-made subject in which students are given definitions, rules and algorithms from which they are expected to proceed. Instead, learners should be given opportunities to reinvent mathematics in the manner that mathematicians create mathematics. Within professional development settings, in order for teachers to reinvent mathematics in this way and experience disequilibrium as their students do, the content should be in a domain which teachers typically do not know deeply. Through a combinatorics domain problem-solving approach, the NSF-funded Rice University Mathematics Leadership Institute (MLI) (1) provided teachers opportunities to reinvent their mathematics pedagogy and knowledge. This allowed teachers to experienc