CEMELA - CPTM - TODOS Conference
Poster Presentation Schedules and Abstracts
Friday Poster Session Abstracts
Title: Latino Families and Mathematics Education: Involvement, Perceptions, and Expectations
Acosta-Iriqui, Jesús M. – The University of Arizona
Civil, Marta – The University of Arizona
Díez-Palomar, Javier – Univesitat Autónoma de Barcelona
Menéndez, José María – Radford University
Quintos Alonso, Beatriz – University of Maryland
Abstract: This poster highlights some of the findings from 5 years of CEMELA1
research with parents at the University of Arizona. Our overarching research
objective was to learn about Latino/a parents’ perceptions of the teaching and
learning of mathematics. We used 3 kinds of activities to open spaces of
communication with parents in mathematics: a) Math For Parents (MFP) series, in
which we engaged with parents in explorations of mathematical topics for 6 to 8
sessions (sometimes their children also participated) with variations in the amount
of Spanish and English used in the different venues; b) “Tertulias Matemáticas” as
focus groups to engage in dialogues about the teaching and learning of
mathematics, often from a critical perspective; and c) Classroom visits and
debriefing, with a small group of parents visiting a mathematics classroom and a
follow-up discussion. Further sources of data were individual interviews with some
parents. We have data from 79 parents from 4 schools (2 elementary, one K-8, and
one middle school), all with a large number of low-income, Latino/a students.
Parents’ level of formal schooling ranged from elementary to college. Our findings
show that parents react to their children’s mathematics education based on their
own experiences as students. Parents tend to apply methods that they learned at
school in their countries of origin. Schooling experiences have an impact on how
parents feel themselves regarding mathematics. Dialogue in the MFP empower
parents’ as mathematical doers and legitimate their practices. Parents’ expectations
include more rigor and discipline in their children’s schooling.
1 CEMELA (Center for the Mathematics Education of Latinos/as) is a Center for Learning and Teaching funded by the National Science Foundation –ESI 0424983. The views expressed here are those of the authors and do not necessarily reflect the views of the funding agency.
Title: TEACH MATH: Developing Teacher Competencies that Integrate Mathematics, Children’s Thinking and Community-based Funds of Knowledge
Julia Aguirre – University of Washington, Tacoma
Mary Q. Foote – Queens College, CUNY
Abstract: The research reported on in this poster is part of a larger research project called TEACH MATH. The central aim of TEACH MATH is to transform preK-8 mathematics teacher preparation so that new generations of teachers will have powerful tools to increase student learning and achievement in mathematics in our nation’s increasingly diverse public schools. One of the ways we are addressing this aim is through studying the iterative refinement of instructional modules for preK-8 mathematics methods courses that explicitly develop teacher competencies related to mathematics, children’s mathematical thinking and community/cultural funds of knowledge. This poster presents background information and some preliminary findings on one of the instructional modules: the Community Mathematics Exploration.
Title: Considerations in Fostering the Delicate Balance Between Language Support and a Challenging Mathematics Curriculum
Presenter: Jennifer M. Bay-Williams, University of Louisville
Abstract: This poster outlines reflective questions that teachers consider as they plan instruction that will support a students’ language and mathematics development. The reflective questions address critical issues in effective classroom teaching, such as how to provide modifications to mathematics tasks without lowering the cognitive demand and when to provide vocabulary instruction to best support student learning.
Title: Reflections on the Negotiation of a Third Space with English Language Learners: Researchers and Students Communicating Mathematical Ideas During Task-Based Interviews
Gabriela Dumitrascu – University of Arizona
Belin Tsinnajinnie -- The University of Arizona
Abstract: Mathematical communication between adult and student requires the bridging of two (or more) separate bodies of knowledge known in the research as the third space (Lipka, et. al, 2005, Lipka, et. al, 2007, Moje, 2004). The third space is a co-evolved discursive navigational space in which different mathematical knowledges are competing to challenge and reshape mathematical literacy, practices, and knowledge. In our study, we examine the third space co- evolving during task-based interviews in which mathematical reasoning and ideas are exchanged, created, and understood between English-speaking adults and students whose first language is Spanish. The purpose of this research project is to document what resources that both interviewer(s) and student(s) use to create a third space and (2) what resources English-speaking adults and students whose home language is Spanish use to co-create a space in which mathematical ideas and reasoning are exchanged. We analyze the interaction of students with Spanish as their home language and English-speaking interviewers. The interactions took place during task-based individual student interviews with 4th and 8th grade students involving proportional reasoning. The data analysis included students’ written work, video data recorded from a camera fixed directly on the student and video data recorded from a handheld camera capturing the interviewer and student interaction with the mathematical task. From our qualitative data analysis, several common themes arose across the various interviews. The findings point to diverse uses of resources to construct the third space for mathematical communication:
Our findings inform both researchers and teachers of potential resources and challenges in the creation of the third space in the mathematics classroom, in particular, classrooms with students whose home language differs from the mainstream language prominent in schools.
Title: Culturally Relevant Teaching in an Elementary Mathematics Classroom
Presenter: Victoria Frost
Abstract: This paper examines culturally relevant teaching in mathematics classrooms in an elementary school in a Mexican-American community. The three main components examined are (1) developing tools for critical mathematical thinking and student engagement, (2) evidence of learning, and (3) orientations to students' culture. The findings are based on a collaborative CEMELA teacher research project.
Title: Analyzing Videotaped Interviews: Building a Story of Co-Constructed Identity
Presenter: Jennifer V. Jones – Rutgers University
Abstract: Research by Martin (2006) has shown that African American students face challenges in developing a mathematics identity that empowers them to fully participate in school mathematics, and pursue or aspire to high levels of mathematics achievement in their secondary schooling and beyond. According to Fordham (1993), Black students struggle with general academic identity and achieving success in school environments, and Steele (1997) argues that “stereotype threat” negatively impacts Blacks and other learners who are members of a domain specific minority group. Martin (2003) and others argue that race is a critical factor in developing mathematics identity and positive racial identity, essential to the well-being of African-American youth, and greatly influenced by context and factors such as power and opportunity (Cross, 1991). Furthermore, Goldin, Epstein and Schorr (2007) and others argue that powerful affect is another critical component to mathematics engagement and learning. The research presented here revolves around data collected during the 2006-2007 school year, relating particularly to one of two “focus” girls in order to better understand how she expressed her identity as a “Black girl” and “doer of mathematics”. Videotaped retrospective interviews are examined to identify “critical events”: affective, social, and mathematical interactions pertaining to identity. Additional data is being collected during the 2009-2010 school year to infer relationships, if any, between mathematics, race, identity, and mathematics learning. Interpretation and analyses draw on critical theories of race in education (Ladson- Billings & Tate, 1995), and Black feminist thought (Collins, 1991). The outcome of the study will be new understandings of Black girls’ mathematics classroom experiences, and “case stories” of racial and mathematics identity development among Black female adolescents.
Title: Secondary School English Learners’ Reading Comprehension of Algebra Items
Presenter: Carl Lager
Abstract: Being able to understand a mathematics problem is the first step towards solving it; however, very little is known about how English learners (ELs) in grades six through twelve individually engage with algebra assessment tasks written in English. Over one-third of the California High School Exit Exam-Mathematics (CAHSEE- M) is algebra. Between 2003 and 2008, CAHSEE-M pass rates for ELs ranged between 35% and 50%. Since all California students must pass the CAHSEE-M and an Algebra I course to graduate high school, these two requirements likely stop many of California’s 600,000 middle and high school ELs from earning their diplomas and advancing to higher education. This study was conducted to examine how Spanish-speaking, high school ELs engaged with CAHSEE-M algebra items in multiple choice and non-multiple choice formats. Findings from this study can help task writers, curriculum developers, and secondary mathematics teachers and teacher-educators better understand how secondary ELs understand and solve written large scale assessment algebra items.
Title: Realistic Considerations and Unit Shifts during Proportional Reasoning
Carlos López Leiva -- University of Illinois, Chicago
Griselda Velázquez -- University of California Santa Cruz
Abstract:Proportional reasoning is one of the mathematical concepts that closely intersects with everyday- real-life situations (Díez-Palomar, Giménez Rodríguez, & Garcia Wehrle, 2007; Lamon, 1995). Lamon (1996) describes an important concept in proportional reasoning as the composition and development of different types of units and how they relate to each other in the context of the problem. In this study we explore students’ realistic considerations as they engage in proportional reasoning, particularly unitizing. In this study, we explore the emergence of students’ realistic considerations as they engage in proportional reasoning, particularly unitizing. We selected a specific student (Leti) that we followed across two proportional reasoning tasks provided in a mathematics afterschool program, documenting and analyzing the resources, strategies, and interactions (with other peers and facilitators) that mediated her mathematical reasoning and social participation.
Title: Teaching the Equal Sign in a Bilingual Context
Presenter: Edgar Romero – University of New Mexico
Abstract: Children's understanding of the meaning of the equal sign is a well- documented challenge in mathematics education. In English, educators aim to get their students to understand the sign as meaning "is the same as." The fact that "igual," the word used for equality in the Mathematics classroom is an everyday word in Spanish, meaning "is the same as," suggests that the equal sign picture is different in a bilingual context. I plan a teaching experiment to explore children's bilingualism as a resource for teaching this essential mathematical topic.
Title: Mathematics Education and Equity: If social equity is the goal will we get there by improving mathematics achievement?
Presenter: Lisa Tsuchiya – University of New Mexico
Abstract: In 2000, the National Council of Teachers of Mathematics (NCTM) published Principles and Standards for School Mathematics ( 2000). This publication “is intended to be a resource and guide for all who make decisions that affect the mathematics education of students in pre-kindergarten through grade 12” (National Council of Teachers of Mathematics, 2000, p. 11). The NCTM 2000, publication has six principles and the equity principle is considered the core element of the total vision. The specific goal of the equity principle is to increase mathematics knowledge and skill for all students. The assumption being if mathematics achievement is raised for under achieving students, then this will provide opportunities for better jobs and a higher standard of living, and thus social equity. This work examines the strengths and weakness of the NCTM equity principle and reviews the literature on whether improved mathematics achievement can achieve this goal.
Title: Mathematical Problem Solving and Discourse in Dual Language and ELL Kindergarten Classrooms.
Erin Turner -- University of Arizona
Sylvia Celedón-Pattichis – University of New Mexico
Mary Marshall – University of New Mexico
Abstract: The study examines the development of Latino/a kindergarten students' participation in problem solving and emerging mathematical discourse in their first and/or second language, with particular attention to the classroom practices and the cultural and linguistic resources that teachers draw upon to facilitate that participation and to support students' mathematical understanding.
Title: Commentary on the Public Discourse of Supporting Teachers ofMathematics with ELLs and the Social Construction of Failure or Success
Presenters: CEMELA -- University of Illinois, Chicago
Abstract: As the demographics of public schools change radically in conjunction
with the rapidly growing student population popularly referred to as English
language learners (ELLs2), there is a growing body of literature designed to help
teachers offer appropriate mathematics instruction to these students. The majority
of ELLs are Latinas/os, who have a history of underachievement in general, and in
mathematics particularly. In fact, Latinas/os comprise the most underserved
student population with the most persistent pattern of poor achievement compared
to all other cultural and racial groups. In light of the fact that public discussion
about teaching mathematics to ELLs is in essence synonymous to teaching
Latinas/os, many questions arise regarding how these students are framed as
learners; how language is framed, both in general and with respect to mathematics;
and what it is that teachers should do in order to capitalize on the strengths and
meet the needs of Latina/o learners. In this presentation, we examine current
books, randomly selected, that specifically address the teaching of mathematics to
ELLs and to explore theoretical and practical approaches put forth in this literature.
2 We use the term ELLs because that is what is used in the texts we discuss. However, this is not a term we ourselves prefer to use. ELL suggests a subtractive perspective of schooling for Latinas/os and does not recognize Latinas/os’ bilingual experiences and knowledge.
Title: Grounded but not Grounded: A Model for Doctoral Education
Authors: CEMELA—University of Illinois, Chicago
Abstract: This poster depicts a model for doctoral education, one that centers on promoting educational equity and justice for Latinas/os. The data presented highlights the experiences of seven doctoral candidates as they progress through a research and academic program that explicitly operates on cultural-historical activity theory principles. Major themes that emerged include challenging dominant educational research paradigms, learning methodological and theoretical perspectives by doing, achieving collectivity while fostering individual growth, and experiencing collaboration that fuels individual success. This work has implications for how Ph.D. programs in education can be structured to address social justice and equity.
Saturday Poster Session Abstracts
Title: Professional Development for Mathematics Teachers of Latino/a Students: Teaching Area and Perimeter with Algebra Blocks
Anhalt, Cynthia - University of Arizona
Ondrus, Matt - Weber University
Abstract: A professional development course in algebra topics for middle school mathematics teachers from schools with predominantly Latino student populations was designed to specifically address mathematics content in the middle grades and issues of language in teaching and learning mathematics. The course allowed teachers to explore the mathematical topics using concrete means. For example, they used algebra blocks to deepen and broaden their own understanding and knowledge of area and perimeter while discussing pertinent issues related to teaching and student learning. In addition, the problems that were explored served as a setting for mathematical discourse among the teachers, and in turn, discussions about discourse development for middle school students. Various research perspectives from the literature will be highlighted. The course was a collaborative effort by a mathematician and a mathematics educator, and discussion of the teaching experience will be shared in addition to comments from the teachers.
Title: Self-Perceptions of Advanced Mathematical Learners: A Focus on Sixth- Grade Latinos/as
Presenter: Cavell, Heather - University of Arizona
Abstract: The purpose of this work was to analyze the impact social and educational context have on students’ mathematical learning, and the understanding of why students’ strategies shift as they moved from the fifth grade into the sixth grade. More specifically, this study addressed the following overarching questions: 1) What makes the relationship between student self-perception and (mathematical) learning specific to these Latino student’s circumstances/experiences? 2)How do students apply their individual prior knowledge, experiences, and beliefs to their situated classroom context and content? a. What are the dimensions that shape student perceptions and engagement in their situated classroom context? b. How do students accept or resist the social structure and mathematical classroom norms of their situated classroom context? c. How does student acceptance or resistance of their situated classroom context impact mathematical learning? 3)What role do student relationships with teachers, parents, and peers have in the development of student self-esteem and self-perceptions?
Data collected in field notes, focal interview transcripts, and questionnaires was analyzed using an ethnographic and constant comparative method in order to develop both descriptive and categorical themes and relationships. Findings suggests that the keys to these student’s mathematical success are: interest in mathematics, making classroom activities challenging and fun, being part of support peer groups, having a supportive teacher, being able to speak in both English and Spanish, being self-motivated, connecting mathematics to their home experiences, and being confident in themselves. Interest in mathematics and self-confidence played a large role in how students perceived their peers and themselves as mathematical learners. Peer relationships were both positive and negative depending on the students; as well as, the relationships that developed between the students, teacher and peers. Resistance and acceptance behaviors were found to be fairly equally used and also student and context dependent.
Presenter: Hayes, Monica
Abstract: Disaggregation of data from the Florida Department of Education showed students of color and other underrepresented students disproportionally represented in the low performing range. This study looked at one specific problem that had not received much attention: do teachers understand the connection between culture and pedagogy when teaching minority and underrepresented students? The research design was a qualitative case study that included structured interviews with study participants and a focus group. Volunteer participants from three counties in Florida, who had participated in at least one College Board-supervised Advanced Placement Summer Institute (APSI) since 2003, were invited to be study participants. The findings support the reality of the connection between beliefs and attitudes. Culture frames ones environment and the findings support the importance of cultural stimuli or the lack of such stimuli and the impact on behavior and maturational development. Study participants articulated that students of color-specifically Black and Latino students—not Asian or Indian students– come to the school setting lacking in the cultural stimuli, the maturity, and an adequate educational preparation to succeed in rigorous academic curricular offerings. While none of the study participants felt the College Board-supervised APSIs they had attended had addressed cultural competency, all agreed that the training had helped them become better teachers. The findings support the need for an emphasis on increasing access and success for minority and underrepresented students and the need to provide more culturally and linguistically competent learning environments for students and educators as well. The results of the study identified the need for education leaders to require training in cultural competency for teachers and other educators.
Title: Re-socializing the Way we do Mathematics: The Case of Three Students Participating in the Zone of Mathematical Practice.
López Leiva, Carlos - University of Illinois, Chicago
Torres, Zayoni - University of Illinois, Chicago
Viego, Gabriel - University of Illinois, Chicago
Abstract: Minority student voices, cultural backgrounds, languages, and out-of-school experiences are commonly subjugated to dominant cultural structures in U.S. schools. This discrepancy is especially prevalent in mathematics classes. In this study, we focus on how Latino students’ resources are validated. This goes beyond simply using their first language, but promoting and strengthening their voices and their active participation in the meaning-making process (Khisty, 1996; NCTM, 2000). We believe that this environment, characterized by its hybrid structure (Gutiérrez, 2002), affords to its participants a ‘zone of mathematical practice’ through joint activities with others (Gonzalez, Andrade, Civil, & Moll, 2001, Vygotsky, 1978) that promote the internalization of new mathematics strategies and practices (Moll, 2001, Moschkovich, 2004). We analyzed the trajectory of three student cases (3rd to 6th grades) as they participated in a mathematics afterschool program at a public school in Chicago: Los Rayos de CEMELA (Khisty, 2004), which is an adaptation of The Fifth Dimension (Cole, 2006) and La Clase Mágica (Vásquez, 2003). Results demonstrated that in this context students take on new roles that cannot be fully realized in traditional classroom settings. Through the use of tools, mathematical talk, social networking and play students have been able to work in ways that enabled them to participate more fully in mathematical meaning-making.
Title: Algebra Academy: Launching Underrepresented Students Toward Success in Math and College
McCormick, Rudy - University of Arizona
Fonseca, José David - University of Arizona
Abstract: What do patterns, windmills, and bottle rockets all have in common? They all provide an opportunity for project-based learning where students, regardless of language capabilities or refugee status, can construct their understanding of fundamental algebraic concepts. The Algebra Academy has been a partnership between the UA Office of Early Academic Outreach and local school districts. Students earn one unit of high school elective credit as they join a small learning community in which they transition to high school, explore algebra, plan for college, and prepare to be professionals in future careers. In the three years of the program, 383 students (85% first-generation college-bound, 68% low-income, 93% minority, 81% Latino, 51% female) have shown increases and improvements in mathematical self-concept, planning on four years of rigorous high school mathematics courses, confidence in future math performance, and college and career knowledge. In the same time, 21 teachers have participated in the program and have expressed that the Algebra Academy is a? life changing? professional development opportunity.
Title: Re-considering Play and Its Role in Socializing Bilingual Latinas/os to Mathematics
Presenter: Radosavljevic, Alex - University of Illinois, Chicago
Abstract: Play in mathematics has typically been dismissed and undervalued in the teaching and learning process. However, play offers enhanced opportunities to problem solve, use multiple modalities of assistance, extend spaces for communication, and shift expert/novice roles (Cole, 2006; Razfar, Khisty, Willey, & Radosavljevic, 2008; Stone & Gutiérrez, 2007; Vásquez, 2003). In essence, play affords opportunities to socialize students into mathematics. Given the well documented achievement gap between Latinas/os and their ‘mainstream’ counterparts, analyzing interactions in informal contexts provides us with a unique opportunity to enhance our understanding of how Latina/o children mathematize using multimodal mediational tools. This study investigates the role of play in relation to mathematics socialization as bilingual Latina/o elementary students collaborate during mathematics-rich games in the Los Rayos de CEMELA after school mathematics club (Khisty, 2004; Khisty & Morales, 2007). Here, mathematical thinking and mathematical discourse is defined as those practices that are primarily used to discuss and understand quantities, shapes, spatial relations, and deductive/inductive reasoning. Through discourse analysis, this work outlines the multiple modalities of assistance, language choice, expert-novice role shifts, repair practices (Razfar, 2005), and tool use to shed light on the role of mathematical game play in socializing students into mathematics. The study presents preliminary findings and examples of how bilingual Latina/o children more fully draw on their knowledge, linguistic, and cultural toolkits to develop mathematical thinking and discourse practices by participating in play. The findings also demonstrate the need to reconsider the role of play in supporting Latinas/os in mathematics.
Title: Making Norms and Activities Relevant for Latino/a Elementary Students in an Afterschool Mathematics Club.
Presenter: Ross, Kathleen - University of Arizona
Abstract: This poster presentation describes how an afterschool mathematics club teacher makes connections that are relevant to the Grade 3-5 students at a predominantly Latino elementary school. These connections supported development of participation and sociomathematical norms. Mrs. Torino also uses tasks with contexts that are relevant to the students and real-world manipulatives. Data, including videotapes of the club sessions and task-based interviews with a sample of five Grade 4 students, conducted while they were participants in the mathematics club, were analyzed to identify features of norms and tasks that were relevant to the students.
Title: Community-Based Problem Posing in the After- School Math Club
Simic-Muller, Ksenija - Pacific Lutheran University
Turner, Erin - University of Arizona
Varley Gutiérrez, Maura - University of Arizona
Abstract: Between spring 2005 and spring 2007, we were the coordinators of an after-school mathematics program (Math Club). Our goal was to connect mathematics to students’ everyday lives, with the belief that a curriculum that is more relevant would positively impact both their attitudes towards mathematics and their learning. In the poster, we will give a description of one Math Club project. The goal of this project was to visit local businesses and investigate their mathematical practices.
Title: Increasing Teachers’ Knowledge of and Attention to Equity Issues in Multiple Settings
Presenter: Strutchens, Marilyn E. - Auburn University
Abstract: The National Assessment of Educational Progress (NAEP), the nation’s primary resource for reporting data across race/ethnicity, gender, and socioeconomic status has consistently reported differential achievement among major groups of students, White, Black and Hispanic (Silver, Strutchens, & Zawojewski, 1997; Strutchens, Lubienski, McGraw, & Westbrook, 2004; Lubienski & Crockett, 2007). These achievement differences indicate that inequities exist in mathematics education. Flores (2007) redefined the gap as an “Opportunity to Learn” gap and shifted the frame from looking at measures of educational outcomes to examining what students actually experience in schools, resulting in a very different way of describing disparities among students. Based on the 1990 – 2050 census trajectories, student populations are becoming more diverse, and the educational community must be able to meet the needs of its multicultural clientele. Thus, it is important for mathematics educators, preservice teachers, and inservice teachers to become knowledgeable of pedagogical strategies that meet the needs of students from diverse backgrounds. Further, teachers need to learn how to help students develop a critical consciousness toward social justice issues through examining issues related to race, ethnicity, gender, and social class, as well as, know mathematics well enough to connect it meaningfully with other issues of concern to students (Sleeter, 1997; Gutstein, 2006). In this poster session, challenges and triumphs experienced when addressing equity in professional development workshops and school embedded professional development will be shared. Specifically, I will discuss a collection of the definitions and related theories used to guide our work when we address equity issues with mathematics teachers involved in TEAM-Math, a partnership of Auburn University’s College of Education and College of Sciences and Mathematics, Tuskegee University, and 14 school districts in east Alabama with the mission of “Transforming East Alabama Mathematics”. Over the past six years, TEAM-Math has received over $12 million to support its systemic change model, which includes professional development, teacher leader development, curriculum alignment, improvement of teacher preparation, and stakeholder outreach.
Title: Perseverance and Students’ Willingness to Struggle With Nontraditional Complex Mathematical Tasks
Presenter: Sutton, Taliesin - University of Arizona
Abstract: Many teachers in the United States do not allow time for students to struggle with a problem, and tend to jump in and assist students at the first sign of trouble, as revealed in Findings from the Third International Mathematics and Science Study (TIMSS) presented in The Teaching Gap (Stigler & Hiebert 1999). Furthermore, the work of Boe, May, and Boruch (2002) linking the TIMSS and Student Task Persistence indicate that the average mathematics classroom may not be fostering a student’s willingness to struggle and engage in multi-step mathematical tasks. These findings are at odds with a growing movement in the curriculum to have students learn how to think mathematically, develop problem solving skills, and explore cognitively demanding mathematical tasks. In order for students to succeed in this new problem-enriched curriculum, it is important that the students are willing and able to persist and persevere through the challenges they encounter. In this paper, we contribute to the growing literature on perseverance and intrinsic motivation. We analyze the students’ willingness to persevere and struggle with cryptograms, cognitively demanding tasks requiring logical reasoning to decode an encrypted message.
In this study, students worked in pairs and participated in two task-based interviews where they were asked to solve several cryptograms employing various strategies and drawing upon multiple resources. Our theoretical framework draws upon Thom and Pirie’s categories of problem solving (Thom & Pirie 2002) and work by Schoenfeld (Schoenfeld 1985), as we analyze the students’ progress on the task together with their capacity to persist and persevere at the tasks. Preliminary findings indicate that students are willing to persist and struggle with a complex mathematical task. We found that the students’ persistence depends on the resources available as they change strategies several times over the course of a problem. We use a robust definition of resources in this study, including peers, interviewers, handouts, and prior knowledge. All of these resources were used by the students in the cryptogram tasks, and often enabled the students to persevere at the task and employ different solution strategies.
It is important to note that these shifts in strategies are not always done in order to persist and engage with the problem. Shifts in strategies can occur when the student is trying to appear engaged with the problem or is trying to employ a strategy in a rote and unthinking way. We analyze the students’ work, strategies, and environment when they exhibit the motions of persistence but are neither refining their work nor actively progressing towards a solution, and tie these unproductive behaviors to the students’ available resources and their agency to employ them as needed.
We found that students are willing to both engage in and persist with complex mathematical tasks. Their capacity for perseverance is dependent on their available resources. Pedagogical implications include stressing the importance that complex mathematical tasks should be presented in a context that fosters and encourages the students to draw on multiple resources.
Title: The Power of Relevant, Real-World Contexts to Support Mathematical Problem Solving Among Latino/a Students: A Case Study
Presenter: Torres, Zayoni N. - University of Illinois, Chicago
Abstract: Research has repeatedly documented an achievement gap between students of color in the United States and their white, middle-class counterparts, a gap that may be attributed to a number of factors, among them, the disconnect students feel between school and their lives/communities. An approach was taken to help students to see the relevance of mathematics to their lives, which was the development of a mathematics club (Math Club) at an elementary school in a predominantly Mexican/Mexican-American community in Southern Arizona. This study investigated the impact of the math club on a group of three fourth grade Latino students. The analysis focused on these students’ participation in a project involving investigating the mathematical practices of a local bakery. Qualitative analysis of transcripts of the math club sessions revealed that a) students had the tendency to draw on school mathematical knowledge more often than they drew on everyday knowledge when solving a mathematical problem; b) relevant, real-world contexts guided the students’ mathematical thinking to some extent; and c) the instruction that pushed the mathematics was the facilitators reframing students questions and posing more mathematical problems.
Title: Analysis of Student Participation in an After School Mathematics Club: Implications for Learning and Identity
Turner, Erin - University of Arizona
Gutiérrez, Rodrigo - University of Arizona
Sutton, Tal - University of Arizona
Abstract: In this study we analyze a diverse group of middle school students¹ participation in ten after school math club sessions focused on solving and discussing challenging problem solving (cryptography tasks). Our analysis focuses on how various instructional practices task structures, teacher/facilitator moves, student moves functioned to position students into particular roles, and how those roles were sustained and/or disrupted both within and across interactions. We contend that better understanding students¹ opportunities to take on these intellectual roles, and in particular, understanding how these roles are sustained both within and across interactions is important because over time, such opportunities have the potential to positively impact the way that students see themselves (e.g., their identities as learners, as students of mathematics) and the discipline (e.g., Boaler & Greeno, 2000; Empson, 2002; Greeno & Gresalfi, 2008).
Title: Racing to the Top Through Stopping to Think: Metaphors in Teacher Talk and National Policy
Wood, Marcy - University of Arizona
Lozano Terán, Guadalupe - University of Arizona
Civil, Marta - University of Arizona
Abstract: The metaphor education as a journey is the predominant conceptual metaphor used in national educational policies No Child Left Behind and Race to the Top. This presentation explores how this national education policy metaphor plays out in teachers' talk. Teachers used two variations of the journey metaphor. These variations foregrounded both teachers' movement and barriers to student progress, but did not focus teachers on student learning. We suggest that another variation of journey metaphor, one used by a nationally recognized educator, might focus teachers (and national policy) on the most important target of education: children's thinking. We suggest we might have better outcomes for students (they could actually race and reach the top) if we stopped to focus on student thinking.