# Activities for the 2007-2008 School Year at The University of Arizona

**Teacher Study Group**- Teachers in the study group will:
- Engage in mathematical problem solving that focus on multiple strategies for operations in number sense and fractions
- Use hands-on concrete materials to look at various ways of representing the operations
- Analyze their students’ work to reflect on their practice, pose questions and engage in discussions on articles related to their inquiry which may include math talk, Latino students, and reform teaching strategies.

- Teachers in the study group will:
- Analyze samples of students’ work to look for possible topics to pursue. (Eventually, we would like to look at samples of students’ work across sites, that is among the different CEMELA study groups.)
- Engage in explorations of mathematics to enhance their own understanding of some topics.
- Discuss relevant resources that look at the interaction among language, culture and mathematics, particularly as it applies to working with Latino students.
- Use an array of hands-on materials, exemplary and innovative curriculum materials, and video cases for professional development.
- Have the opportunity to engage in action-research.

During the academic year 2007-2008, 6 teachers from two Elementary Schools (Tucson Unified School District) participated in nine 2-hour sessions each semester. The goal of the study group is to provide a supportive environment for teachers to engage in reflection on their own practice. For example, the teachers in a study group may choose to work on strengthening their students’ understanding of a specific topic in mathematics, or they may be interested in developing their students’ ability to use writing in mathematics. The connection between culture, language and mathematics is an ever-present theme throughout the sessions. The teachers have a central role in deciding the mathematical topics to be explored. This academic year the focus included number sense and fractions, both of which were featured in the reform curriculum within the school district.

While the TSG remains committed to strengthening the mathematical pedagogical content knowledge of the teachers, the structure has changed from a focus on mathematics to include also a focus on language. First, each session opened with scheduled time for the teachers to reflect back on their interactions with students on mathematics and language. The teachers shared work and anecdotes about their students’ interactions with activities that were generated through the study group or came through different resources. The engagements over the months included only two areas of mathematics, number sense and the strategies related to the four operations and the exploration of fractions. In both areas we provided published articles to augment our conversations.

- Teachers in the study group will:
**Math For Parents Workshops**Bringing together all interested parties (i.e. parents, school personnel, and students) is fundamental to CEMELA's holistic vision. CEMELA's work with parents and families builds on our previous projects (Funds of Knowledge for Teaching, Bridge, and MAPPS (Math and Parent Partnerships in the Southwest). Since 2005 four schools from two school districts have participated in the Math for Parents workshops. As of the spring semester of 2008, the CEMELA Math for Parents workshops consisted of two learning models: the Middle School model serving grades 6-8, and the Elementary/Middle School model serving grades Pre K-8.

*The Middle School Model*

This model consists of modules containing seven sessions each. CEMELA, with support from the middle school personnel, facilitates the

*Tertulias matemáticas*where parents gather once a week at the school facilities for about one and a half hours to participate in hands-on mathematics activities, to share their experiences as parents of school-aged children, and to build a community of supportive adult learners. The content of the math activities has varied over time to adapt to the school reform-based curriculum, and to respond to parents’ interests in their understanding of and familiarity with school mathematics strands for grade Pre K-8, including: graphs of linear functions; data representation; and fractions and proportional reasoning. Although initially we began meeting only with parents in the mornings, after the parents dropped off their children at school, we currently meet in the evenings in order to accommodate the fathers’ participation. Additionally, per the parents’ request, beginning with the spring semester 08, the children (grades 6-9) joined their parents in the Tertulias. This has allowed us to continue looking at parents-children interactions in the learning of mathematics that we had started to study a year earlier at one of the elementary schools. We usually have about 10 parents in attendance and 7 children.*The Elementary/Middle School Model*

This model is similar to the middle school’s model, and consists of modules containing seven sessions that meet once a week. Quite often parents are called upon, or are expected to help their school-aged children with their mathematics homework. However, given that the parents are often far removed from the current reform-based mathematics curricula and the corresponding instructional practices, they need to familiarize themselves anew with the fundamentals of the mathematics being taught. To assist them bridge this chasm, the CEMELA Mathematics for Parents learning modules are designed to parallel the mathematics topics that children are actually learning in the classroom. The concept of numbers, fractions, and proportional reasoning is probably the first topic that needs considerable attention in the early years of children’s mathematics education. For this reason, the learning modules emphasize the conceptual understanding of operations on whole numbers and rational numbers (e.g., addition, subtraction, multiplication, and division of fractions). The learning modules develop a conceptual understanding of fractions using geometric shapes such as Tangram fractional pieces and Pattern Block manipulatives. Furthermore, the modules use contextualized problem-solving activities in everyday’s applications of mathematics.

The last component of the CEMELA Math for Parents model consists of a classroom observation by the parents. One of the objectives for the classroom observation is for the parent to witness for themselves what goes on inside the classroom, particularly in terms of the reform-based curriculum being taught, and how it is being taught. There are typically two parents’ classroom observations in a seven-session module. The classroom observations are usually complemented with debriefing sessions.

**After School Program**The after-school math club (ASMC) at a local Tucson middle school is a program run by CEMELA to provide access to high level mathematics that students otherwise may not have the opportunity to study. The project for the Fall of 2007 posed logically and linguistically challenging tasks to the students following a theme of cryptography. During the activities, the facilitators fostered a safe environment for dialogue, and the tasks were designed to encourage student interaction by virtue of their complexity. In the Spring of 2008, students discussed issues of importance in their school and community with the assistance of the Social Justice Education Project. As a result, they created a school and community safety survey that they administered to the majority of their school. Their analysis was presented to school faculty and families with hopes of creating change in the coming years. Throughout the year, participants in the the ASMC meet once a week for an hour and a half.

The continued work at the after-school math club (ASMC) at a local Tucson elementary school, is now a mathematics club for girls. This mathematics club is headed by CEMELA fellow Marua Varley who is also using the club as her dissertation site. Her study, entitled

*Voices of Young Latinas Speaking to Equity in Mathematics Education and Society: Understanding Social Justice Mathematics,*seeks to give a 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. The research questions Maura seeks to answer in this after-school girls' mathematics club are:

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.