Center for the Mathematics Education of Latinos/as
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Research on Teacher Education

Background notes

Throughout this document, phrases like the "four of us" may appear. It should be noted that such phrases refer to the four institutions: UA, UNM, UCSC, and UIC. There is no intention of implying only four individuals.

Also, this developing document is to make concrete where we are, how we might think about the research and its process, and what needs to be done. It has emerged after many conversations between and among representatives of the four CEMELA institutions over almost a year or more. This document is what we have negotiated thus far as our common endeavor and objective; however, it is still a work in progress.

Overarching CEMELA-wide Teacher Education research question:

What are the issues and/or challenges teachers face as they adapt or create instruction in mathematics to meet the needs of Latinos, particularly in light of language and culture?

Sub-questions that might be addressed under this umbrella question:

  1. How do teachers understand (or view) the role of language and the cultural resources of Latino students and parents in the learning of mathematics?
  2. How do teachers recognize and use these resources to adapt their mathematics instruction (e.g., lesson design, implementation, revision, curriculum selection) to meet the language and cultural needs of students?
  3. How do school/district policies (i.e. those related to language, accountability, high-stakes assessments) affect teachers' understandings about the role of language and culture in their teaching of mathematics?
  4. How do teachers' understandings and use of the language and cultural resources of Latino students and parents change over time as they are involved in professional development?
  5. What impact does an inquiry approach to teaching mathematics have on enriching teachers' understanding of teaching mathematics to Latino students?
  6. What are the issues of language and culture with which teachers grapple while engaged in reflecting on Latino children's thinking about mathematics?

Sample methods

  1. Qualitative examination of patterns that emerge in teachers' naturalistic discussions around planning, doing, and thinking about lessons, around studying student thinking as represented in mathematical writings; content analyses of teaching and planning artifacts such as lesson plans, written discussions of student work, the kinds of questions teachers raise, etc.
  2. Long-term recording of teacher discussions in courses, lesson study, study group, and inquiry group contexts.
Data sources

  1. Video- and audio-tapes of teacher meetings in classes, lesson study groups, teacher study groups, and inquiry groups.
  2. Artifacts of teachers' lesson planning, assessment of student work, etc.
  3. Possible more structured data, for example, specific teacher analyses of a given videotape of classrooms from other sites, classroom observations, and/or assessment of hypothetical lesson plans or student work that we ask teachers to comment on with specific prompts.
  4. Student achievement data (e.g., AIMS, district assessments, etc.)

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Research Study 1

Language and Mathematic Problem Solving: Exploring the Complexities of Bilingual Teachers' Growth

Recent research on teacher growth has explained that teachers develop understanding of their practice as they deepen their comprehension of student learning (Franke et al, 1998). Current discussions about teachers’ professional development highlight the potential of generating learning communities in which teachers strengthen their content knowledge and instructional practices by engaging in active reflection and analysis of student work (Kazemi & Franke, 2003). Moreover, in the area of mathematics education, research has shown the connections between teacher knowledge and the decisions teachers make in relation to their mathematic instruction (Aguirre & Speer, 2000) and the role of language and teacher talk in Latino student mathematics learning (Khisty & Chval, 2002). Understanding how students solve problems, how their thinking develops and how language impacts learning can foster teacher understanding of how instruction can promote mathematical learning. This study describes the highlights of a professional development initiative in which two first grade bilingual teachers engage in learning about Cognitive Guided Instruction (Carpenter et al., 1999) and the importance of problem solving in mathematics learning. This approach argues that children even in the early grades should be afforded repeated opportunities to solve a variety of word problems and communicate their thinking about their solutions.

Research Objectives

Recent reform initiatives stated the importance of teachers understanding students’ mathematical thinking (NCTM, 2000). This study contributes to comprehending teacher change as both teachers engaged in joint practice and ongoing conversations about Latinos/as’ student thinking, problem solving, issues of language, and adaptation of instruction to meet students’ needs. Specifically, the study explores:

  • (a) the impact of professional conversations and student work analysis on enriching teachers' understanding of teaching mathematics to Latino students; and
  • (b) issues of language and culture with which teachers grapple while engaged in reflecting on students’ thinking about mathematics.

    Two bilingual first grade teachers from an elementary school in a city in the southwest of the United States participated in the study. The school population is culturally and linguistically diverse: Hispanic 86.3%, Native American 6.4%, Anglo 4.3%, African American 1.5%, Asian 0.8%, and other 0.9%. Both teachers teach in Spanish 90% of their curriculum.

    Research Area(s)

    1. Teacher Education

    Timeline

  • Started 9/06.
  • Projected Completion: May 08

    Site Involved

    1. University of New Mexico

    Research Team

  • Sandra I. Musanti, Postdoctoral Fellow, University of New Mexico
  • Mary E. Marshall, Doctoral Student, University of New Mexico
  • Sylvia Celedon-Pattichis, Faculty and Co-PI, University of New Mexico
  • Libni Berenice Castellon, Master’s Student, University of New Mexico

    Methods and Data Collection Techniques

    This qualitative study describes a year-long collaboration involving two first grade bilingual teachers and three researchers. Together we engaged in exploring the nuances of students thinking and the role of language and culture in mathematic instruction, and collaborated in planning and delivering mathematics lessons focused on developing students’ problem solving strategies as well as their capabilities to communicate mathematical reasoning in their first language (Spanish). Participating teachers and researchers engaged in a collegial and inquiry based approach to professional development. This approach involved joint planning of problem solving lessons, lesson implementation on a weekly basis, and debriefing sessions to reflect on the outcomes of the lesson and to analyze student work. Data collection included detailed field notes of each of the problem solving lesson in each first grade class, audio-recording of the debriefing sessions and two interviews with each teacher to explore their beliefs and knowledge on issues of language and mathematics.

    Preliminary Findings and Implications

    Through this approach to professional development teachers developed increasing understanding of how students’ pictorial representations and verbalizations of their solutions to problems gave insight into students’ thinking about mathematical problems. In addition, their instruction became progressively more informed with the importance of introducing specific mathematical language while encouraging students’ oral or written representation of their reasoning. Ongoing reflection, collegial conversations with researchers, and a focus on analysis of student work contributed to teachers’ understanding that when students had access to explanations and representations of their peers, they appropriated additional problem solving strategies to add to their toolkits. They also found that careful scaffolding in oral and written communication and their expectation that students’ would always need to explain their thinking helped them to develop the mathematical process skills fundamental to success in reform mathematics. This study contributes to the actual body of research that explores the analysis of student work as a source for teachers’ reflection and exploration of the different dimensions and complexity of student learning.

    References

  • Aguirre, J. & Speer, N. M. (2000).Examining the relationship between beliefs and goals in teacher practice. Journal of Mathematical Behavior, 18(3), 327-356.
  • Carpenter, T., Fennema, E., Franke, M., Levi, L., & Empson, S. (1999). Children’s mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann.
  • Kazemi, E. & Franke, M. L. (2003). Using student work to support professional development in elementary mathematics [Working Paper]. University of Washington: Center for the Studies of Teaching and Policy,
  • Khisty, L. L. & Chval, K. B. (2002). Pedagogic discourse and equity in mathematics: When teachers’ talk matters. Mathematics Education Research Journal, 14(3), 4-18.
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.

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    Research Study 2 (Dissertation Study)

    Culture, Pedagogy, Mathematics: Multiple Perspectives in a Latino Community

    This is a dissertation study being conducted by University of Arizona, CEMELA Fellow Beatriz Quintos-Alonso.This study is a qualitative research study at an elementary school within one fifth-grade classroom. The purpose of this study is to explore the influence of a culturally relevant teacher and teaching practice on Latina/o students’ mathematical learning and attainment. This study draws on a multi-level framework to explore the influence of a culturally relevant teaching practice on Latina/o students’ mathematical learning. First, Beatriz will examine the socio-cultural context of these learning experiences. The analysis includes a description of the social and political context that relates to the local context based on literature. The second level in this study identifies key features of the teacher’s mathematics teaching and their interplay. Beatriz will explore the teacher's practices and beliefs through classroom observations and interviews throughout the year. In the third level, Beatriz will incorporate students’ parents. Their beliefs and values will be explored through interviews and household observations. Finally, students’ perspectives will provide an emic perspective about the interplay of factors that influence their learning and academic attainment. For this fourth level, Beatriz will do classroom observations in which she will take field notes, transcriptions from selected classes, collect sample work and will interview the children in the case studies. The significance of the study is to provide a holistic perspective of Latino student learning experiences that is critical in our local context as well as in the picture of the country; Latinos mathematical learning and achievement have not been systematically researched.

    Research Area(s)

    1. Student Learning
    2. Parents
    3. Community

    Timeline

  • Began: May 2005
  • Completion Date: May 2008 (Expected)

    For more information please contact Beatriz Quintos-Alonso.

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    Research Study 3 (Dissertation Study)

    Currently, Eugenia Vomvoridi-Ivanovic is focusing on her dissertation which is concerned with investigating how prospective teachers who are Latinas/os and bilingual use their own language and cultural knowledge to mediate the mathematics engagement of Latina/o children. Her dissertation findings should contribute to CEMELA's research goals for teacher education. She recently presented a research report from her pilot study at the North American Chapter of the International Group for Psychology of Mathematics Education (PME-NA) Annual Conference, in Lake Tahoe, NV, (October, 2007) entitled The Multidimentionality of Language in Mathematics: The Case of Five Prospective Teachers.

    Research Area(s)

    1. Teacher/Preservice-Teacher Education

    For more information please contact Eugenia Vomvoridi-Ivanovic.


    Research Study 4

    Measuring Pre-Service Teachers’ Preparation for Academic Language, English Learners, and Mathematics: The Performance Assessment for California Teachers (PACT)

    Description of Study and Preliminary Findings and Implications The Center for the Mathematics Education of Latinos/as (CEMELA) crafted five research questions to investigate mathematics instructional practices in classrooms serving Latino/a youth:
    • How do teachers understand the role of language and culture in learning mathematics for Latino/a students?
    • How do teachers recognize and adapt their mathematics teaching/curricula to include attention to language use, language development, and cultural resources?
    • What cognitive and social resources do they draw upon to adapt their instructional practice (i.e. beliefs/knowledge and teacher/school norms.)?
    • How are teachers’ understandings and mathematics teaching about the role of language and culture affected by school/district policies (i.e. accountability reforms, policies related to language)?

    We investigated a subset of these questions in relation to new teacher development. We specifically wanted to examine how pre-service teachers understand the role of language in learning mathematics for Latino/a and English learners and the level of attention to language use, language development and cultural resources in their instructional vision and planning processes. The study is situated in a policy context unique to California advancing a high stakes teacher performance assessment that explicitly addresses the role of language in instruction and the needs of English learners. The following is a brief description of the study and some significant findings.

    As the number of English Learners (ELs) increases, teacher preparation programs across the United States must prepare preservice candidates for educating students from a wide variety of linguistic backgrounds. This is especially important for meeting the needs of Latino students and other minority groups traditionally failed by schools, especially in subjects such as mathematics that have often been erroneously considered to be “language-free”. One way to ensure that candidates and their teacher education programs work toward meeting the needs of ELs is to require candidates to address the teaching of ELs on assessments required for state licensure. Yet assessing the preparation of preservice candidates for quality teaching requires reliable and valid assessments that pay close attention to context, process, and reflection, factors that traditional evaluations of teaching either ignore or undervalue.

    The Performance Assessment for California Teachers (PACT), currently used in a number of teacher preparation programs throughout California, is a comprehensive assessment of knowledge and skills in which candidates analyze and reflect on their own instruction and their students’ learning during a “Teaching Event” in their student teaching placements. We documented how 8 elementary teacher candidates discussed issues related to language and mathematics for ELs in their extensive written materials submitted as part of the PACT.

    We found that candidates, in response to the PACT prompts, articulated a variety of perspectives on the nature of academic language, the role of language in mathematics teaching and learning, and the language demands facing Latino and EL students. They advocated for a variety of instructional supports for ELs, including using multiple representations to make mathematics concepts comprehensible, promoting the use of mathematics vocabulary and discourse, and using students’ home experiences and language as a resource. Candidates also discussed various sources of challenge, from factors associated with students’ attributes and behaviors to instructional contexts.

    Preliminary findings suggest that the PACT, beyond its function as a high-stakes examination, has the potential to provide important formative information about candidates’ preparation for working with ELs that can be used by both candidates themselves and by teacher educators.

    Site Involved

    University of California, Santa Cruz

    Research Team

    George C. Bunch, Assistant Professor, U.C. Santa Cruz
    Julia M. Aguirre, Assistant Professor, University of Washington, Tacoma
    Kip Téllez, Assistant Professor, U.C. Santa Cruz

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