Alma Nuñez Helen S. & Alexander W. Astin Civic Engagement Scholar, UCLA

Engaging Students as Mathematicians

According to Paulo Freire, education is a state of suffering because students are passively listening as teachers are imparting knowledge on the student. Within this model, students are not be engaged in their learning and as a result many are not able to reach their maximum learning potential. In particular, this model is detrimental to students of color as they are not succeeding in the math classroom.

Background and Introduction: According to Freire's (1973) theory of a 'banking' model of educational practice, students are passively listening as teachers are imparting knowledge on the student. Within this model, students are not engaged in their learning and as a result, many are not able to reach their maximum learning potential. In particular, this model is detrimental to students of color as they are not succeeding in the math classroom. Within the math classroom, there is a culture that organizes the learning. Nieto (1999) notes that a culture implies a specific language, a certain way of doing things, and a particular way of being within an environment. For some students, the culture used within the school environment is familiar because it matches their home culture. However, Howard (2010) indicates that for other students, like students of color, the school culture is unfamiliar; thus, creating a cultural mismatch and a learning discontinuity between the home and school. Additionally, students walk into the classroom with different types of knowledge, but when it does not match the academic set of knowledge used within the classroom, students are often labeled as deficient, affecting students’ perceptions of their abilities and their academic performance. Therefore, students’ funds of knowledge should be incorporated as a way to build on what the student already knows and as a way to build bridges to new knowledge (Gonzalez, Andrade, Civil, and Moll, 2001).

Abstract: This case study looks at different aspects of the classroom that support students to grow and develop as mathematicians. Through classroom observations and student interviews, students responded to a teacher who created a positive learning environment that consisted of a variety of activities, where respect and responsibilities were shared between the students and teacher.

Many math classrooms have a fallen in the “banking method” of education where common plug-and-chug worksheets are mainly used for students to master skills. However, this model does not capitalize on students‟ maximum potential. This study examines a particular classroom where the teacher and the students co-construct learning as a process that utilizes other students as multiple teachers. This case study looks at different aspects of the classroom that help the students to grow and develop as mathematicians. Through classroom observations and student interviews, it has been confirmed that students are more likely to respond to a teacher who creates a positive learning environment that consists of a variety of activities.

Research Question:

How can we engage students as

mathematicians? What class room activities are the most effective in

students’ learning and development? More specifically,

what does it look like when a student is involved and engaged in

his/her learning?

Methods: Participant observer – Since the beginning of the school year, I was integrated into a class of ninth grade Algebra 1 students whom had already taken Algebra 1 but received a letter grade of “C” or lower. Interviews – Midway through the year, I interviewed students with different levels of mathematical abilities that volunteered to help me in this study.

Recommendations from the Students: 1) Peers & Learning Learning is an interactive process among peers that is vital for students to learn, teach, re-learn and re-teach. Due to the similarities in age, habits and often thinking, peers are great teachers that supplement the teacher within the classroom. 2) Variety of Activities Students become distracted easily, especially with repetition. Thus, practicing the same skills in different ways not only helps students master the skill, but also keeps the students engaged. 3) Assets Based Thinking Students walk into the classroom with already gathered knowledge, but connecting new material to this is difficult. Therefore, using what students already know as assets facilitates the introduction of new material. Students also need support in this process of synthesizing new knowledge, especially when they encounter problems and do not believe in themselves.

A variety of different activities engage the students in the material as a way to practice a specific skillset in order to master it. In particular, students respond well to activities that combine movement, interaction, and competition. (They get even more excited and pumped for an activity when there are small prizes.)

When asked to name 3 different activities that they enjoy and learn from, each student named the index card activity. Within this specific game, students are able to choose from 3 different level cards: red for challenging, yellow for mild, and green for basic. The students receive points for each card they complete in their notebooks correctly.

Acknowledgments: Special thanks to Professor Megan Franke, Denise Pacheco, Doug Barrera, and Amy Pojar for all their genuine encouragement, guidance, and suggestions. I would especially like to thank Mr. Madathian and his students for allowing me to become a part of their classroom.

References: Freire, P. (1973). Pedagogy of the Oppressed. New York: Continuum Press. González, N., Andrade, R., Civil, M., & Moll, L. (2001). Bridging Funds of Distributed Knowledge: Creating Zones of Practice in Mathematics. Journal of Education for Students Placed at Risk, 6 (1 & 2), 115-132. Howard, T.C. (2010) Why Race and Culture Matter in Schools: Closing the Achievement Gap in America’s Classroom. New York: Teacher’s College Press. Nieto, S. (1999). The Light In Their Eyes: Creating Multicultural Learning Communities. Ch. 3 Culture and Learning. Teachers College Press, pgs.47-71.

Freire, P. (1973). Pedagogy of the Oppressed. New York: Continuum Press, 25-67.

Finding #1: Teacher’s Pedagogy Respects Students

The teacher is able to relate the math concepts to the students. The teacher also respects the different cognitive and ability levels of each student. As a result, the students trust that the teacher will help them develop their mathematical skills because he does not lose faith in their abilities even when the students do not believe in themselves.

“He makes it interesting, the way that he teaches

it, in my lingo, it caught my attention when he

said it like that.”

“Some times I don‟t get the chance the to finish

the entire worksheet and sometimes it frustrates

me when they tell me, „Oh you‟re going to have

to do this for homework,‟ and I‟m like, „Aww,

what? Now I have more homework!‟ but the

teacher says, „Just show me that you‟re actually

putting in the effort.‟ ”

Finding #3: Balancing Control and Comfort Within

the Classroom Environment The type of environment created affects the way that the students learn and work on their own. A balanced atmosphere must be created where the teacher has control of the students, but they feel comfortable enough to be themselves while working hard. “…show your kids respect and they‟ll show you

respect back for sure. At times have fun, but you

also have to show them who‟s boss. You can‟t let

them run over you.”

“He trusts us. When we‟re doing the warm-up

he‟s not like other teachers. He lets us walk

around and ask for help or help other people,

when usually other teachers are like „Okay, sit

down, be quiet!‟ They don‟t let us share different

ideas about how to do the math or help.”

Finding #2: Students as Teachers Students respond well to being treated as adults in being responsible for not only themselves and their learning but also their peers’ learning. Multiple teachers within the classroom allows for students to learn, teach, re-learn and re-teach mathematical concepts.

“If they get it, I like it because now they get it

and they don‟t have to ask anybody else. I‟m

like „Oh that‟s cool, I just helped somebody do

math.‟ Was it ever something that you thought

you could ever do? Help somebody else with

math? No, I never thought I could give help to

someone in math.”

Finding #4: Activities Allowing For Different Student Participation

A variety of different activities engage the students in the material as a way to practice a specific skill set. In particular, students participate more in activities that combine movement, interaction, and competition. When asked to name 3 different activities that

the students enjoy and learn from, each student

named the index card activity. Within this

specific game, students are able to choose from

3 different level cards: red for challenging,

yellow for mild, and green for basic. The

students receive points for each card they

complete in their notebooks correctly. (See

pictures above) Different stations of the casino game where students must solve problems for a chance

to gain more tickets and then try their luck. The students with the most tickets at the end

win a 1st, 2nd, or 3rd place prize.

Above – An activity done in pairs where the Boss

tells the Employee what to do.

Left – Business profit bar graphs created by

students in small groups.