Publication Type: Poster
Abstract: This paper examines cognitive structures activated as learners re-present verbal problem statements as algebraic experiences. Symbolization is viewed as a dynamic interaction among three knowledge structures. Capacity to write equations is related to the congruence among these structures. Participants’ responses are analyzed to uncover the nature of the activated knowledge. The results provide insight into learners’ cognitive structures and activity.

Publication Type: Research Report
Abstract: This report explores developing problem solving skills of first-semester calculus students (n=202) at a midsize (25,000 students) university in the southwest with one-fourth of the student body enrolled at the graduate level. The study was designed to determine base-line problem solving performance among the first-semester calculus students and then measure any change in problem solving performance over the course a fifteen-week semester. Also, an experimental group (n=73) worked 1.5 hours per week in addition to regular class time on challenging group problem solving activities. Findings suggest that students moved from an emergent or developing performance to a proficient performance over the course of the semester at each level of sophistication studied.

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: This paper looks at a new version of the old “not our problem” dynamic, under which activist organizations ignore social issues important to subgroups of their target community, arguing that those issues are outside the scope of their activism. Our concern is the “not our problem” posture that mainstream U.S. opponents of female circumcision take when faced with the issue of intersex surgery. In the paper, we argue that the harms of intersex surgery (cosmetic procedures performed to “normalize” the genitals of infants and young children) are similar to those posed by the African genital cutting practices commonly critiqued by such feminists. The distinction those feminists draw between the two practices is premised upon problematic attitudes that disparage African procedures as harmful, patriarchal cultural rituals while justifying intersex surgery as a legitimate medical response to bodily abnormality. What that distinction obscures is the cultural dimensions of intersex surgery – such as its enforcing of patriarchal gender norms and its reification of the notion of “disability.” The appeal of the “not our problem” stance in this context lies, perhaps, in the fact that it reaffirms the racial superiority of those drawing the comparison. In short, their position can be seen as revealing a Faustian willingness to sacrifice the interests of some females (intersex children raised as girls) in order to preserve the racial privilege of other females (the feminists making the anti-circumcision critique). Ultimately, however, the failure of North American feminists to see the problematic cultural dimensions of intersex surgery undermines their efforts to eliminate harmful genital cutting, for it perpetuates patriarchal gender norms and ignores the plight of victims here in this country, as well as opening their movement up to criticisms of hypocrisy and orientalism abroad.

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: New Olympiad problems occur to us in mysterious ways. This problem came to me one summer morning of 2003 as I was reading a never published 1980s manuscript of a Ramsey Theory monograph, while sitting by a mountain lake in Bavarian Alps. It all started with my finding a hole in a lemma, which prompted a construction of a counterexample (part b of the present problem). Problem (a) is a corrected particular case of that lemma, translated, of course, into a language of a nice “real” story of a chess tournament. I found three distinct striking solutions of (a) and an even more special solution of (b). As a result, this problem became the most beautiful Olympiad problem I have ever created. What is more, the journey that lead me from Ramset Theory to problems of mathematical Olympiads, continued to finite projective planes!

Chess 7 7 (21st Colorado Mathematical Olympiad, April 16, 2004, A.Soifer).
(a) Each member of two 7-member chess teams is to play once against each member of the opposing team. Prove that as soon as 22 games have been played, we can choose 4 players and seat them at a round table so that each pair of neighbors has already played.
(b) Prove that 22 is the best possible; i.e., after 21 games the result of (a) cannot be guaranteed.
I will present beautiful solutions of this problem, and show its link with "real" mathematics.

Publication Type: Short Oral Report
Abstract: The study examines an impact of instructional setting, problem posing, and language on elementary school students' ability to solve word problems. Research sample consisted of 141 second graders from an urban southwestern public school with predominantly Hispanic student population. Data collection conducted through the use of a short and extended version of a ‘trick’ word problem which was posed in English in a monolingual class, and both English and Spanish – in a bilingual class. The short version was introduced as a mathematics word problem whereas extended version was presented as a reading assignment. In some of the groups (both monolingual and bilingual) a brief direction statement “Read everything carefully!” was given to the students. The paper discusses the results of this study with regard to impact of different variables on students' problem solving performance.