Reflections on Instructional Strategies for English Language Learners
Milton Rosa
Encina High School, Sacramento, California
Daniel Clark Orey
California State University, Sacramento
Introduction
Often diversity is seen as a problem to overcome. However, diversity can, indeed, be a powerful tool for learning and enrichment that will allow students traditionally labeled as “at-risk”, or English Language Learners (ELL) to explore mathematics concepts extending beyond traditional curriculum contexts. ELL students can improve their understanding of how mathematics applies to real-world experiences and concepts, strengthen their algebra skills, and enhance interest in mathematics while improving English skills. All this leads to, and helps them to enroll in higher-level mathematics classes.
Newly arrived immigrant students can be engaged in meaningful mathematics experiences if these experiences are designed to increase both their language and mathematical reasoning. The students should also be challenged to participate in activities where they learn by using demonstration, observation, manipulation, mechanics, practice, application, and experimentation to become fully engaged in and involved in mathematics, all concepts useful in developing and improving English language facility.
Problems of performance and engagement by under-represented minorities indicates a tendency towards these students who often see their own ethnic identity as antagonistic to the traditional school culture (which includes the traditional mathematics curriculum) because it does not enable them to see how they connect, or worse yet, how all cultures use complex mathematical ideas and practices. As well, as diversity increases in our schools, many teachers now lack the access to resources and receive little if any practical training in how to differentiate instruction and use different strategies and methodologies for the students in diverse classrooms.
Culturally Sensitive Instruction
One attempt to differentiate instruction is to apply Culturally Sensitive Instruction with students from different cultural backgrounds. Because of space and time, we will reserve our discussion and observation about how many newly arrived immigrant students have difficulty with this diversity at first as well, as they often originate in what we refer to as extreme monocultural environments. Protherose & Turner (2003) state that “culturally sensitive instruction aims to facilitate the ability of all students to meet high standards, using approaches best suited to meeting students’ individual needs” (p.2). This perspective meets one of the goals of multicultural education. D’Ambrosio (2001) has talked about how many children of color have not yet quite realized the same level of mathematical success as European American students in our classrooms, they are often underrepresented in higher-level mathematics courses and professions requiring significant mathematical competence. Studies indicate that African-American, Hispanic/Latino, Pacific Islander, and Native American student’s sub-groups currently average relatively low in regards to mathematics performance. Cross-disciplinary work provides dramatic evidence that people of all cultures use complex mathematical ideas and it is possible to use Culturally Sensitive Instruction to begin adapting these ideas in the unique context found in highly diverse school settings.
This also includes the development of improved mathematical strategies for English Language Learners and low-performing school students. To do this work, a number of tools and instruments are used to make the bridge between Culturally Sensitive Instruction and the formal curriculum in mathematics. These include the use of games, recreational mathematics, and the exploration and incorporation of mathematics found in arts and crafts. As well, as the use, demonstration and inclusion of their home language(s), the study and use of critical hands-on experiments, manipulatives, interdisciplinary connections, cooperative learning, and other sheltered and SDAIE techniques have been found vital to the success of work with adolescent ELL students. However, how to organize this into a coherent whole in an atmosphere of standards-based instruction, assessment and accountability is an important question to explore in future discussions.
Goals and Objectives
There are two objectives when implementing Culturally Sensitive Instruction in classrooms we work in:
- The first objective is to increase the awareness of current mathematics teachers in relation to the mathematical practices of the cultural heritage of the students they teach, by:
a) Increasing under-represented minority student engagement in mathematics; and by
b) Increasing the awareness of all students, no matter their gender, linguistic, cultural or ethnic backgrounds, of the sophisticated mathematical practices embedded in these cultures.
· The second objective creates rigorous culturally based lessons, which allow teachers to introduce the use of interactive technologies in the teaching of culturally derived mathematical concepts, and thereby increasing the information technology skills in under-represented minority students.
Seen in this context, the most important objective of this methodology is the enhancement of teaching strategies that implement activities which make use of the culture and day to day activities found in the student’s community. In so doing, teachers should develop longstanding commitments to the local cultural communities they represent, to the knowledge of mathematics, and to the national, state, and local standards in mathematics. School districts should offer encouragement for teachers to live in the community, to learn second and third languages, to make home visits, for example. Classroom settings will be attentive to teachers’ needs in a range of cultural contexts because they seek to understand how Culturally Sensitive Instruction can be used to enhance student interaction with mathematics and increase students’ understanding of the role that mathematics plays in the activities of all cultures. These activities offer examples of non-trivial ideas and practices, which is an inclusion of mathematics that directly opposes the common stereotypes of at-risk minority students’ heritage and culture while encouraging them to include, study and to share and report on what their own families’ culture and language groups successfully accomplish and contribute to the community they live in (D’Ambrosio, 2006). Activities must be designed to provide a deeper interaction, rather than passive presentations, and should allow teachers to link activities to the mathematics curriculum by providing respect and understanding of local cultural contexts.
Methodology
Culturally Sensitive Instruction motivates minority students to see mathematics as a powerful cultural tool worth the mental labor required to master it. Establishing cultural connections by making mathematics a significant part of a student’s identity and heritage is an important development in new mathematics teaching strategies. These kinds of lessons can be especially useful in highly diverse classroom environments as found in many urban areas of the United States. Culturally Sensitive Instruction possesses connections to multicultural mathematics, whose positive results in classrooms in general have also been reported in African American, Latino, and Pacific Islander students.
In the light of the above, students must be given opportunities to explore mathematical concepts that enable them to make connections between mathematics and their daily life. In this methodology, students talk, discuss, explain, and write about the mathematics they encounter and learn, they work individually and/or with partners, and they also learn how to share experiences, ideas, and opinions. They will learn how to justify their thinking, by applying an interdisciplinary strategy whereby the students make connections among different school subjects and to their prior experiences in other environments.
Lessons Based on Culturally Sensitive Instruction
Below are four lesson titles and a brief description of the major activities each.
1) The Vocabulary Wall
Using 5x7 index cards a collection of the important mathematical vocabulary is shared and developed with English being accompanied by the translations of the terms in all the languages found at the school site, or in the classroom. See: http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/Alg.html
2) The Flag Lesson
Teachers will begin this lesson by asking questions about flags from the student’s home country. After this discussion, teachers introduce the flags by linking the student’s home country and its flag. Students identify geometric forms present in each flag. The names of the geometric forms will be written on English on cards, and placed on the vocabulary wall, and entered in the spreadsheet. The cards will be posted on the wall. Teachers will work with ratio, rate, percentages, probability, and geometry.
3) The Map Lesson
The xy-coordinate system should be placed on poster graph paper before class. Have the large poster graph paper up and ready in the classroom for students to plot their (x, y) points while doing the activity with their partners. Alternatively, teachers could use chalk to mark and label the axes on the black/white board. Students will receive a first paper sheet to graph points on a xy-coordinate system. Each student must make his or her own graph. Each student will receive sticky dots to plot their point or points on the poster graph paper. The graph is the map of the United States. Each student will receive a second paper sheet to answer questions related to their graphs. They will discuss and analyze questions and arrive at solutions. The objective of this activity is to help students to explore and use the xy-coordinate system, to expose them to different-shaped graphs, and to practice sharing their findings in English.
4) The Birthday Party Piñata Lesson
This activity is introduced to show the students the kind of ideas that they will research in relation to customs brought to California by recently arrived immigrant students. By applying Multicultural Activities, students will share of cultural knowledge. This perspective will encourage respect among the students for one another, as well as for the members of the community and peoples of the world. The students are given a handout that describes the history and use of the Piñata, with the additional mathematical problems related to the Pythagorean Theorem.
5) Student Investigation Lesson
Students interview adults in their own language and cultural community about alternative algorithms, customs, and games used to solve problems and develop a presentation and poster to be shared with the rest of the school.
Final Considerations
As a basic tenet of Culturally Sensitive Instruction, the authors believe that if teachers are allowed to explore the diverse backgrounds of their charges that the students can to learn more than just the traditional mathematical algorithms. The activities that are briefly outlined above are excellent in that they encourage dialogue, which is fundamental in improving language as well as mathematical skills. All students need to extend their understanding to include how mathematics connects to other disciplines, to problems in society and the environment, and to the traditions and customs of diverse people around the world. Teachers need to help students to discover the relationship between mathematics, the real world, and daily life. All students need to be encouraged to develop and apply higher-level critical thinking skills. In so doing, they must learn mathematical concepts, they need to learn to question, to take risks, to verbalize ideas, to listen to other peoples ideas, and to critique their own and other's ideas. This form of critical thinking must be practiced regularly. The authors believe that one of the best ways to practice critical thinking in students is to explore and study new technologies, methodologies, and strategies in the teaching of mathematics.
Bibliography
D’Ambrosio, U. (2001, February). What is ethnomathematics, and how can it help children in schools? Teaching Children Mathematics, 308-310.
D’Ambrosio, U. (2006) Ethnomathematics: Link between traditions and Modernity. Sense Publishers: Rotterdam. (ISBN: 9077874763).
Protherose, N., Turner, J. (2003). Culturally sensitive instruction. The Informed Educator Series, 1-12.