Response to Gutstein Generalized- A Philosophical Debate

It is a pleasure, challenge, and an honor to respond to the thoughtful and innovative debate started by Braver, Micklus, Bradley, van Spronsen, Allen, & Campbell on teaching mathematics for social justice. They take seriously the issues in, and raise many interesting views about, my article, Teaching and Learning Mathematics for Social Justice in an Urban Latino School (JRME, January, 2003). I would like to respond to (connected) two points in particular: the relationship of functional to critical literacies, and the relationship of “critical thinking” in mathematics to learning mathematics for social justice. However, I would first like to clarify certain points about my article

The Political Context of the National Mathematics Advisory Panel

The National Mathematics Advisory Panel needs to be situated in its broader political context to more fully understand it. Who created it, for what purpose, and who will (and will not) benefit from it are key questions I address in this article. My argument is that the NMAP, as part of a larger initiative undertaken by the Bush Administration and US financial/corporate elites, serves capital’s efforts to shore up the US’s weakening economic global position and does not benefit the majority of the US people—particularly marginalized and excluded students of color and low-income students

Exploring different theoretical frontiers – A symposium

Providing for a praxis of uncertainty, theoretical traditions that undercover how knowledge, power, and identity are interwoven and constituted in and through socio-cultural and -political discourses characterize the sociopolitical-turn moment in mathematics education research. Researchers who work in the sociopolitical-turn moment pull from a variety of theoretical perspectives most often located in the emancipate and/or deconstruct paradigms of inquiry. In this symposium, panelists discuss how different theoretical traditions available to researchers in the sociopolitical-turn moment provide new productive ways to think and rethink mathematics teaching and learning

Krytyczne badania w działaniu z młodzieżą miejską: badanie rzeczywistości społecznej przez matematykę

This paper describes a long-term action research project (over 15 years) on critical mathematics—a study of urban, public school students (ages 11 to 19) in the U.S. who used and learned mathematics to simultaneously learn about their social reality. Two major questions were: How does one teach critical mathematics? and What do students learn? The theoretical framework builds on Paulo Freire’s concepts, epistemology, and theory of political change. The settings were two schools in low-in- come, working class Latino and African American communities. Students were active co-research participants and contributed to every aspect of the project.Niniejszy artykuł przedstawia długofalowy (trwający piętnaście lat) projekt dotyczący matematyki krytycznej przeprowadzony metodą badań w działaniu. Dotyczy on uczniów (w wieku od 11 do 19 lat) szkół publicznych w dużym amerykańskim mieście, którzy uczyli się matematyki używając jej jednocześnie w celu zrozumienia otaczającej ich rzeczywistości społecznej. Główne pytania badawcze brzmiały: W jaki sposób można uczyć krytycznej matematyki? oraz Czego uczą się uczniowie? Podbudową teoretyczną projektu były koncepcje Paulo Freire’go, epistemologia oraz teoria zmiany politycznej. Projekt został przeprowadzony w dwóch szkołach w dzielnicach zamieszkanych przez latynoamerykańskie i afro-amerykańskie społeczności robotnicze o niskich dochodach. Uczniowie byli aktywnymi współbadaczami uczestniczącymi w każdym aspekcie projektu i wnoszącymi weń swój wkład na każdym jego etapie

Learning From Students To Improve An Intelligent Tutoring System

SIFT, a Self-Improving Fractions Tutor, is an intelligent tutoring system which learns from its interactions with the students it tutors. Its learning module takes transcripts of tutoring sessions as input. It analyzes the results of its work and modifies its knowledge bases in domainspecific ways, creating new tutorial rules and extending its domain knowledge. To produce its transcripts, SIFT tutors student-simulations which interact with the tutor to solve problems. SIFT generates a rule for each hypothesis that could possibly explain why it took inappropriate or wrong actions, although not all hypotheses are ultimately valid. It initially assumes that new rules have equal correctness probability. It then continues to tutor (using its probabilistic conflict-resolution rule-selection algorithm) and uses feedback from its rule applications to modify probabilities with the Dempster-Shafer theory of evidence. Initial results show that (1) SIFT learns more rules than it uses, but eventual..

Abstract LEARNING FROM STUDENTS TO IMPROVE AN INTELLIGENT TUTORING SYSTEM

SIFT, a Self-Improving Fractions Tutor, is an intelligent tutoring system which learns from its interactions with the students it tutors. Its learning module takes transcripts of tutoring sessions as input. It analyzes the results of its work and modifies its knowledge bases in domainspecific ways, creating new tutorial rules and extending its domain knowledge. To produce its transcripts, SIFT tutors student-simulations which interact with the tutor to solve problems. SIFT generates a rule for each hypothesis that could possibly explain why it took inappropriate or wrong actions, although not all hypotheses are ultimately valid. It initially assumes that new rules have equal correctness probability. It then continues to tutor (using its probabilistic conflict-resolution rule-selection algorithm) and uses feedback from its rule applications to modify probabilities with the Dempster-Shafer theory of evidence. Initial results show that (1) SIFT learns more rules than it uses, but eventually converges on correct and minimal rule sequences, (2) it learns what one would want it to given the type of student who uses it, and (3) its learning patterns are intuitively plausible in terms of human tutors