Ilana Horn
Assistant Professor of Mathematics Education
Current research projects:
Adaptive Professional Development for High School Mathematics Teachers
In the current educational climate, high schools are being pressed to support all students’ success in the college preparatory mathematics curriculum. Yet students’ historically high attrition from mathematics exacerbates this challenge. The situation places great demands on mathematics teachers, many of whom have not been trained to support the learning of their diverse students. New inquiry-based teaching methods require teachers to reconsider their understandings of mathematics, pedagogy, and student learning.
To support teacher learning, effective professional development is needed. Yet most standard approaches to professional development (e.g., the one-day workshop) have been shown ineffective in supporting the deeper level of teacher learning that this situation requires. In partnership with a local school district, we are using a professional development approach we call “adaptive professional development” –– that is, building activities both within and outside of the school setting that respond to the perceived needs of the teachers and districts, while drawing on our team’s expertise. This study will contribute to our understanding of teachers’ learning through participation in various professional development activities, as well as documenting the conceptual and practical obstacles to ambitious and equitable teaching.
Funded by the National Science Foundation
Identity and interest development in learning to teach
The purpose of the study is to investigate the role of social contexts in the development of students’ interest in learning and the development of their identities as teachers. In the TEP, learning occurs in multiple social contexts, including methods classes, foundations classes, and the field. Interest (and disinterest) in learning from the program is channeled (canalized) in different ways in these contexts by interactions with individuals, participation in social groups with different values, and by experiences in the social context of the classroom itself. These experiences often result in TEP students having to resolve conflicting ideas about what is important to learn in becoming a teacher. Students’ entering and developing notions of their identities as teachers also develops and is likely to be closely related to what they find interesting and important to learn. To explore these changes, we are following one cohort through the five quarters of their program, and hope to continue to follow them through their first years as teachers. Students in our study come from different subject areas (math and social studies), and we are capturing the variation in their views of how close the learning and learning activities in the three contexts fit their image of teaching.
Funded by Teachers for a New Era project
Urban Teacher Scholars
The primary goal of this project is to overhaul the secondary mathematics methods courses to better articulate theory and practice. While many field experience assignments strive to do this, they are limited for a number of reasons. First, the field placements vary widely in their alignment with our program’s notions of “good teaching.” Second, the variations that would be inherent in even the most ideal settings does not allow preservice teaching students and instructors a “common text” to interpret and make sense of. Relatedly, when students do bring representations of their field experiences to our classrooms, we must rely on their reports, which are limited by what is salient to them, even with the remote mediation of course assignments. In addition, although tools like video cases may seem to alleviate many of these problems (e.g. they allow instructors to represent “good practice” while providing a common text for students and instructors to interpret), they lack the complexity and immediacy of students’ field experiences, in which the stakes are raised, exposure is richer and longer, and the people are real. Finally, our program does not provide consistent support in helping our students understand firsthand issues in urban education. To provide for mediated experiences of real life/real time teaching, we areholding portions of the secondary math methods courses at a local urban high school that is undertaking serious renewal work in its math department. This will allow for common, complex experiences of practice to be mediated by university faculty thereby focusing the preservice teacher students’ attention on the important aspects of what they see and experience. By attending selected classes over the course of two quarters, TEP students will also participate in the unfolding of the class’s history, understanding the complex and multilayered settings of teaching practice. To facilitate our presence in the math department, grant funds support a first-year teacher (a TEP grad) in the department who serves as a “bridge” between the university and the department, actively consulting with the preservice TEP students and course instructor, while simultaneously releasing some of the department’s teachers from their teaching load, making them more accessible to our students as well.
Funded by Teachers for a New Era project
Selected chapters & articles:
Horn, I.S. (In press). Accountable argumentation as a participation structure to support mathematical learning through disagreement. In D. Ball & A. Schoenfeld (Eds.) A Study of Teaching: Multiple Lenses, Multiple Views. Journal for Research in Mathematics Education monograph series. Reston, VA.
Recent emphasis on discourse in mathematics classrooms (e.g. NCTM, 1991, 2000) has spurred a line of inquiry about different forms of talk in these settings. If mathematical thinking is understood to be a set of practices that include mathematical discourse, argumentation, which has an especially important role in mathematics, requires analytic attention. In particular, the following questions arise: How can classroom discourse be organized to support mathematical disagreements that (a) are intellectually productive, and (b) minimize social discomfort? This paper investigates the interactional organization of public disagreements in Deborah Ball’s third grade classroom by describing a participation structure called accountable argumentation. The norms, expectations, interactional roles, and use of history employed during accountable argumentation are explicated and then applied to the analysis of two public peer disagreement episodes that take place during the same whole-class discussion. These two episodes illustrate the ways in which accountable argumentation supports mathematical learning through disagreement, while mitigating the potentially uncomfortable feelings typically expected in such interactions.
Little, J.W. & Horn, I.S. (In press). Resources for Professional Learning in Talk about Teaching: From "Just Talk" to Consequential Conversation. To appear in L. Stoll & K. Seashore (Eds.) Professional Learning Communities: Divergence, Detail and Difficulties. London: Open University Press.
This paper draws on "close up" records of talk among teachers to suggest how out-of classroom dialogue among teachers can generate professional learning and strengthen classroom practice. Even among groups of teachers who are attracted to collaboration and committed to reform, time spent together may yield little new insight into teaching and learning: it may be "just talk." Research suggests a number of possible explanations, among them: the inability of experienced teachers to explicate tacit knowledge to one another or to novice teachers, difficulty in confronting normative constraints; the slow evolution of group relationships, and insufficient structural supports. Yet only in a few cases have we begun to look at the dialogue among teachers to locate evidence about why some groups are more successful than others in pushing the boundaries of ambitious teaching. How is "just talk" different from "consequential conversations"?
We use extensive records of discussions in collaborative teacher groups to illustrate the kind of dialogue that supports close attention to student learning and teaching practice. One "existence proof" -- a group of secondary mathematics teachers who have succeeded in fostering high of student participation, confidence and achievement – is analyzed in-depth. In brief, their talk is "consequential" because it (a) is closely tied to student experience and learning; (b) exploits discourse and material resources to represent classroom practice with a high degree of specificity; (c) displays a normative disposition and particular discourse resources for examining assumptions and alternatives; (d) exhibits mutual support linked to ambitious conceptions of mathematics teaching and learning; and (e) embodies leadership initiative rooted in teaching purpose and practice. This case is compared with other groups in our data to generate a framework that relates dimensions of professional dialogue in relationship to professional learning. In particular, we propose a framework organized in terms of the cognitive, social, material and normative resources that the teachers marshal in support of their own learning and their efforts to improve student learning.
Horn, I.S. (2006). Lessons learned from detracked mathematics departments. Theory Into Practice, 45(1), 72-81.
Students’ mastery of and achievement in high school mathematics is considered pivotal to their opportunities for and within post-secondary education. For this reason, many educators have attempted to implement equity-geared reforms, including detracking, that affect the organization and instruction of high school mathematics. This article describes how schools with successful detracked mathematics programs share four characteristics: (1) a view of subject that focuses on connections and meaning; (2) a curriculum focused on important mathematical ideas; (3) a balance of coordination and professional discretion for teaching decisions; and (4) clear distinctions between doing math and doing school in both the structures of the classroom and the evaluation of students’ thinking. This analysis can support other schools’ attempts to detrack mathematics.
http://muse.jhu.edu/journals/theory_into_practice/
Horn, I.S. (2005). Learning on the Job: A Situated Account of Teacher Learning in High School Mathematics Departments. Cognition and Instruction, 23(2). 207 - 236.
To investigate teachers’ everyday on-the-job learning, I used a comparative case study design and examined the work of mathematics teachers in 2 high schools. Analysis of interviews, classroom observations, and teachers’ conversations highlighted 3 key resources for learning: (a) reform artifacts oriented the teachers’ attention to key concepts of a reform, whereas the interactions surrounding them established local meanings; (b)conversation-based classification systems communicated pedagogical assumptions; and (c)the rendering of classroom interactions in conversations shaped opportunities for teachers to consult with and learn from colleagues. Taken together, these learning resources provide a conceptual infrastructure for teachers to make sense of their practice. This research highlights the social and situated nature of teachers’ pedagogical reasoning and specifies the role of teacher community in teacher learning.
http://www.leaonline.com/loi/ci
Horn, I. (2004, November). Why do students drop advanced mathematics? Educational Leadership, 61-64.