# Research on Student Learning

Research studies in this area address questions about student thinking, reasoning, and learning. Research is currently being conducted in several settings, such as after school projects and classrooms. We are also planning to conduct research in the future in local and trasnational community settings.

**Overarching Research Question: How do language, discourse practices, and everyday mathematics mediate mathematical reasoning,
understanding, and learning for Latino/a learners?**

*Connecting research across sites:* We are planning to connect research analyses at the four CEMELA campuses by developing data
based “Working Case Studies” to be shared and discussed across sites. We expect Fellows and Faculty who are conducting research on student
learning to develop a “Working Case Study” with the goals of a) developing common ways of talking about how students use language(s)
(one or more) when doing mathematics and describing mathematical reasoning, mathematics learning, mathematical discourse; b) sharing
and refining theoretical perspectives on language and mathematical reasoning, learning, and discourse; and c) developing new analytical
themes and schemes that address our overarching research question.

**CEMELA is currently develping the following five studies related to Latino learners and mathematics:**

**Research Study 1**

The after-school study is currently being conducted at two sites: University of Arizona and University of Illinois at Chicago. The main goal of the after-school math clubs is to engage students in mathematics in ways that are perhaps not possible in an “ordinary” classroom setting. The study will document student discourse around mathematical activity and the multiple resources students and facilitators (undergraduates, parents, teachers, etc.) use as they are involved in mathematics activities and projects. We will also explore student mathematical identities and how these develop, including student perceptions of academic expectations at school, their views of school mathematics curriculum, and their goals for the future. Because the after-school Math Club allows students to take an active role in their learning, through student-driven projects, hands-on activities, or developing strategies for mathematical games, the study will especially focus on comparing student attitudes, participation and sense of agency in the classroom and in the math clubs.

** Research Area (s):**

**Timeline:**

**Site Descriptions:**

The after-school program **Los Rayos de CEMELA at Whittier elementary ** (a Chicago Public School) is a general adaptation of two after-school projects: Fifth Dimension (e.g., Cole, 1996)
and La Clase Mágica (Vásquez, 2003). The project involves undergraduate facilitators (UGs), participant researchers, 18 Latina/o 3rd,4th, and 5th graders, teachers and parents.
The after-school project, Los Rayos de CEMELA (Khisty, 2002), is designed to better understand the language and cultural resources Latinas/os use as they do mathematics; and it maps the development,
influences, and beneficiaries of networks consisting of different generations that come together in the math club. Students do high level mathematics(e.g., probability , algebraic thinking, proportional reasoning,
advanced geometry) that they are unlikely to encounter in classrooms. Bilingualism and dialogue among all participants (students, El Maga, researchers, facilitators, etc. ) are highly valued and fostered.
Participants meet twice a week for an hour and a half each session.

The **after-school math club (ASMC) at Ochoa Elementary School** worked in parallel with Los Rayos de CEMELA in Chicago in the Spring
of 2007. Both after-school programs focused on having the participants discover mathematics within their community and report on what they found
by producing a "digital story " about what their experiences and conversations with people in their community about the mathematics they encounter
in the course of their work. Some of the findings from this joint project will be reported on in the 2008 AERA national conference.

The **after-school math club (ASMC) at Safford Middle school** is a program run by CEMELA to provide access to high level mathematics to students
that they otherwise may not have the opportunity to study. Furthermore, the researchers continue to work with math club participants from Ochoa Elementary School.
As more students from the Ochoa ASMC graduate to Safford, the researchers hope to follow up on previous projects conducted at Ochoa. The project for the Safford ASMC
for the Fall of 2007 is to pose logically and linguistically challenging tasks to the students following a theme of cryptography. During the activities, the facilitators
foster a safe environment for dialogue, and the tasks are designed to encourage student interaction by virtue of their complexity. For the Fall of 2007, the Safford
ASMC meets once a week for an hour and a half.

The **after-school girls' math club, Mathematigals, at Ochoa Elementary School** is a smaller continuation of math clubs in previous years at Ochoa.
This setting provides a space to investigate social justice mathematics with elementary-aged Latinas based on topics of interest to the participants. The participants engage
in significant mathematics through community based and social justice oriented projects. They meet once (Fall 2007) or twice (Spring 2008) a week for two hours.

**
The research will focus on the overarching research question for the student learning research group, and also more specifically on the
following related questions: **

**Cross-Site Questions about Learning\Understanding\Language\Participation**

- What is the nature of Latino\a students' mathematical understanding, language use, and participation in an after-school setting?
- What linguistic, cultural, and social resources do students use as they engage in learning (standards-based non-remedial) mathematics?
- How do bilingualism and bi-literacy influence mathematical reasoning and learning?

**Research questions at the University of Illinois-Chicago**

- What role do cross-generational networks and interactions with undergraduate students and parents play in the development of mathematical identity?
- How do students support each other's reasoning and learning of mathematics, language, and literacy in an after-school setting?
- How do the after-school facilitators' (undergraduate students) conceptions about mathematics learning evolve through their experience in the after-school math club?

**Research questions at the University of Arizona**

- How do students use language, and draw on what they know about language to reason about language intensive problems (e.g., cryptograms, logic tasks)? For bilingual students, how does their use of language compare with English versus Spanish tasks?
- To what extent does a student’s willingness to struggle with challenging tasks change over time? What factors seem to contribute to shifts in a student’s willingness to struggle?
- What roles do students take on as they participate in a variety of mathematics projects, and how does their after-school participation (in particular the roles they take on) compare to their participation in regular mathematics class?
- In the context of “Teaching Math for Social Justice,” what is the nature of students’ mathematical identity, their mathematical learning, sense of socio-political agency, and beliefs about the discipline?
- How can we support Latino/a students’ sense of mathematical agency and the development of strong mathematical identities
- How do students enact a sense of mathematical agency in the ASMC? How does their sense of agency develop over time, and how does it compare across contexts (ASMC vs. classroom)?
- What is the relationship between the development of mathematical power (understanding) and the development of students’ sense of socio-political agency? How might one support the other?
- What is the nature of students’ beliefs about mathematics and its relevance to their lives and communities? How does teaching mathematics for social justice impact
**students’ beliefs**about the discipline of mathematics and its relevance to their lives and to their community? How do these beliefs shift over time? - What tensions arise and how are they negotiated?

** Data Collection:**

- All the after-school sites collect data by videotaping all of the activities (although in some cases only audio taping due to the lack of video cameras)
- All of the after-school sites collect field notes written by the facilitators as well as student work.
- Los Rayos de CEMELA also collect messages written to El Maga (RE: The Fifth Dimension).
- The Safford ASMC has video data of pre-assessment and post-assessments done with pairs of students.
- The Safford ASMC has audio data of student interviews pertaining to the student's sense of identity and agency and their beliefs about mathematics.

**For more information about this study please contact:**

**Research Study 2**

In this study, we will examine the nature of Latino middle school students’ mathematical reasoning and communication as they relate to the students’ linguistic repertoires and cultural funds of knowledge. We will begin by examining communication and reasoning within small groups of students in four middle-school mathematics classrooms. Each classroom community, with its evolving norms and mathematical practices, will be taken as the unit of analysis, as actions are only meaningful in relation to the social and cultural contexts in which they are embedded. Data sources for the study will include classroom observations, videotape of small groups, field notes, teachers’ lesson plans, and copies of student work.

**Related Research Questions:**

- How do middle school Latino students, including English Language Learners, use their linguistic repertoires and every-day funds of knowledge to communicate about mathematics and engage in mathematical reasoning?
- How do the discursive structures of classroom communities influence students’ methods of communication and reasoning?

**Research Study 3**

Students' Mathematical Ideas Organization Based in the Connecting Math Program Structure

The purpose of this study is to keep track of the way in what sixth grade Latino students organize their mathematical ideas in different ways (e.g. writing, speaking, drawing, and so forth) and settings (e.g. individual work, group work, and class). Therefore look if organization affects in any way their achievement. In all these aspects will be an especial attention to language issues.

**Research Team:**

**Sites Involved:**

** Research Area (s):**

**Timeline:**

**Related Research Questions:**

- How mathematics curricula in English, Spanish, or both languages affect mathematics learning and teaching? (CEMELA-research question)
- How the design of the connecting math program influences students' organization of their mathematical thinking?
- How does students' organization of mathematical ideas play out within language and culture to influence their achievement?

**Data Collection:**

This research is a case study of a group of 13 Latino/a sixth grader students in “Escuela Luz del Mundo”. The sample consist in all Latino students in the class (13 out of 18). Data collected includes:

- Students Work
- Collection of samples of students work produced during class: individual and group
- Copies of students homework
- Description of students notebook
- Video-taping of classes. (At least one a month)
- Student Assessments
- Copies of students pop-quiz, test, and non-programmatic assessments in class
- Students interviews
- Individual interviews. (At least two a year)
- Group interviews to see the interaction and the progress when their share with their peers. (At least two a year)

**Research Study 4**(Dissertation Study)

This is a dissertation study being conducted by University of Arizona, CEMELA Fellow Maura Varley. This research seeks to give voice to young Latinas regarding equity in mathematics education and society. As Latina youth are marginalized from classrooms and in society where their language, culture, practices, and community are seen as “problems,” and particularly in mathematics classrooms where a dominant culture further excludes girls, there is an exigency to understand how in fact Latina students could experience education as empowerment. A critical educational paradigm has been put forth in which the purpose is to develop critical literacy in students where they make apparent and challenge oppressive societal structures. This critical ethnographic research study seeks to gain a more nuanced understanding of how young Latinas experience social justice mathematics through the facilitation and research of an after-school mathematics club. More specifically, data in the form of field notes, videotaped sessions, classroom observations, collection of student work and interviews offers a rich source for analysis of their participation in the learning environment, their perceptions of mathematics, themselves as learners of mathematics and as people who can make changes in their lives, communities and in the world. This understanding will inform arguments for seeking equity in society through mathematics education and education in general.

** Research Area (s):**

**Timeline:**

**Research Questions:**

With this research, Maura seeks to answer the following broad question:

As they participate in a social justice mathematics learning environment, what are young Latinas’ perceptions of mathematics and themselves as doers and creators of mathematics, and their capacity to contribute to or impact change in their lives, communities, and/or worlds?

More specifically, she will focus on the following sub-questions:

- In the context of this learning environment, how do these young Latinas enact or express mathematical agency and sociopolitical agency?
- What is the interplay/relationship between the two?
- What is the nature of the opportunities that arise for the Latina participants to do/engage in significant mathematics and activism in this learning environment?

For more information please contact Maura Varley.

**Research Study 5**(Dissertation Study)

In this dissertation study, CEMELA post-doctoral student Higinio Domínguez, Ph.D., examined students’ bilingualism and multicultural experiences as cognitive resources for mathematization. Capitalizing on the view of language as action, and on students’ familiarity with certain experiences through direct participation, the study includes a conceptual framework, never used with bilingual mathematics learners, to investigate how bilingual students organize and coordinate actions to solve mathematical problems about familiar and unfamiliar experiences in English and Spanish.

**Supervisor:** Susan Empson

** Research Area (s):**

**Research Questions:**

The study used a research methodology to investigate two questions:

**Findings:**

Findings show important differences. In problems about familiar experiences, students generated more productive actions, more reflective actions, and less unproductive actions than in problems about unfamiliar experience. As for the bilingualism, students used Spanish and English differently. When solving problems in Spanish, they framed actions more socially by including partners or sharing the action with partners, whereas in English they framed actions more individually, more depersonalized, excluding partners and instead relying on words in problems to justify their individual actions. This suggests that reinventing mathematics and themselves as mathematical thinkers is part of using their bilingualism and experiences as cognitive tools, and attention to how they use each language for each type of problem can reveal substantial knowledge about how bilinguals learn mathematics.

For more information please contact Higinio Domínguez,Ph.D.