Teachers' Selections of Tasks for English Language Learners

The U.S. achievement gap in mathematics has received a lot of attention. English language learners (ELLs) have historically been at the lower end of this gap (Fry, 2008). Finding strategies to improve the educational outcomes of these students is imperative as ELLs are the fastest growing segment of U.S. students (Thomas & Collier, 1997). As the number of ELL students increases, there have been changes in U.S. mathematics curricula. Many new curricula are so-called reform oriented curricula, which stem from the shift toward standards based learning. These reform-oriented curricula are more student-centered, have increased demands in terms of reading, verbal, and written communication, and center on rich mathematical tasks.

Perspectives

The selection of tasks is an important part of a teacher's practice and student learning. Kloosterman and Walcott's (2010) examination of NAEP results concluded there exists a “positive relationship between what is taught and what is learned” (p. 101). This implies the types of problems enacted impact the type of learning that occurs. Several studies have examined teachers' uses of mathematical tasks (e.g. Stein, Smith, Henningsen, & Grover, 2009); however, a review of the literature found no studies specifically examining teachers' selection and use of tasks with secondary ELL students.

This study examines high school ELL teachers' selection of mathematical tasks. Stein and Smith (1998) proposed three phases of task implementation. I developed my research question to correlate with the factors influencing the first phase, the tasks as they appear in the curriculum materials. The following research question relates to this purpose:

1. How does this sample of high school mathematics teachers choose tasks for use with ELL students?

1. What are the characteristics of the tasks selected?

2. What factors influence the teachers' selection of tasks?

Methodology

The theoretical framework builds on Stein et al.'s (2009) work on cognitive demand of mathematical tasks. I employed a qualitative, single case study methodology. The participants — Ms. Thomas, Ms. Hunter, and Mr. Dubois — are secondary mathematics teachers who teach a ninth grade, sheltered mathematics class for ELLs. I purposefully selected these teachers because of their role as sheltered mathematics teachers.

The primary data sources are interviews and classroom artifacts. I conducted daily interviews with each of the teachers prior to observing their teaching and then two extended interviews after the two weeks of observation. The classroom artifacts included the tasks presented to the students. Secondary data sources include the classroom observations and a background survey. I analyzed the data using the constant comparison method decoupled from grounded theory.

Summary of Results

            Characteristics of tasks. After classifying each of the tasks the teachers implemented with students, I found the vast majority of the tasks chosen were low cognitive demand tasks (Stein et al, 2009). These tasks were highly repetitive and focused on procedural learning. The problems centered certain procedures and did not contain any real world or contextual applications of such procedures. The teachers stated they thought these tasks were important for their ELL students as they needed the repetition to learn the mathematics. None of the teachers successfully implemented high cognitive demand tasks with students, although two of the teachers had included high cognitive demand tasks in their lesson plans. When asked about these tasks the teachers cited lack of time for students to engage in them or skipped them because they saw the more procedural tasks as the priority.

            The teachers did not select tasks from textbooks. Ms. Thomas either created tasks or found tasks by searching the internet. Both Ms. Hunter and Mr. Dubois selected tasks from a test generator and built their lesson around these tasks. The vast majority of tasks on these test generators were low cognitive demand. All three teachers had access to tasks released by the state and tasks in a textbook that were more high in cognitive demand, though none of the teachers accessed these resources during my time in their classrooms. When asked about these resources the teachers stated they did not use these resources because they were too difficult for students and took too much time to implement.

Factors impacting task selection. The teachers thought ELL students required simplified tasks. The teachers often stated they had to “cut out a lot of words” or “simplify” the tasks for their sheltered class in ways they would not for a class with native English speakers. To make tasks appropriate for their students, the teachers thought it important to make the tasks simpler both in terms of the mathematics and language.

When explaining their choice of problems, each of the teachers referenced the state standards as an important factor. The problems I examined during my time in their classrooms focused on the standards for the day and avoided problems addressing other standards. This strict adherence to the standards prevented teachers from choosing tasks connecting to other ideas or concepts. The teachers also thought the curriculum materials and resources they had were insufficient for teaching ELL students. The teachers also cited a lack of collaborative opportunities in the school and district.

Importance

Knowing how to select or modify tasks in ways that maintain the mathematical rigor is important for students to build mathematical understanding. This research will allow curriculum developers to understand the factors teachers consider when selecting curriculum materials with ELLs. This understanding can lead to improvement in curriculum materials that support teachers of ELLs. Finally, teacher educators and professional developers can build on the findings of this research to develop strategies to better prepare teachers for this rapidly increasing population of students.

Organization of the Session

            I submitted this proposal as an interactive paper session. During the first 15 minutes of the session, I will present a summary of the study, including the results, through a PowerPoint accompanied presentation. I will close the presentation with possible questions for the audience to consider as they enter the discussion. It is my hope NCTM members attending this presentation will gain insight into this little researched area of mathematics education.

References

Fry, R. (2008). The role of schools in the English language learner achievement gap. Washington, D.C.: Pew Hispanic Center.

Kloosterman, P., & Walcott, C. (2010). What we teach is what students learn: Evidence from national assessment. In B. Reys, R. E. Reys, & R. Rubenstein (Eds.), Mathematics curriculum: Issues, trends, and future directions (pp. 89-102). Reston, VA: National Council of Teachers of Mathematics.

Stein, M.K., Smith, M.S., Henningsen, M.A., & Silver, E.A. (2009). Implementing standards-

based mathematics instruction: A casebook for professional development (Second Edition). New York, NY: Teachers College Press.

Stein, M.K., & Smith, M.S. (1998). Mathematical tasks as a framework for reflection: From

research to practice. Mathematics Teaching in the Middle School, 3(4), 268–75.

Thomas, W. P., & Collier, V. (1997). School effectiveness for language minority students. Washington, D.C.: National Center for Bilingual Education.