Project Activities
The researchers developed and studied the ADSEL intervention in Massachusetts schools with EL students with a variety of mathematical and language backgrounds. Initial work to develop and refine the lessons was informed by interviews with students who are ELs, feedback from collaborating educators, and observations of teachers implementing the lessons. The development of the lessons was followed by a pilot study to investigate how participation in the ADSEL fraction division lessons relates to students' fraction problem solving with diagrams, how knowledge about diagrams and communication develops in relation to the design of the lessons, and how teachers implement fraction division lessons.
Structured Abstract
Setting
The ADSEL fraction division lessons were developed and studied in middle schools from districts in Massachusetts with substantial numbers of students who are ELs.
Sample
During initial development of the ADSEL lesson materials, approximately 50 grade 6 students who are ELs participated in interviews or in lessons taught using lesson materials to support refinement of the lesson materials. Then, 23 grade 6 mathematics teachers and approximately 475 grade 6 students taught by those teachers, including students who are ELs, participated in a study investigating the efficacy of the ADSEL fraction division lessons. Participating ELs represented a variety of English language proficiency levels and home languages.
The ADSEL grade 6 lessons focused on Grade 6 Common Core fraction division content. A series of eight lessons explored fraction division content and diagrams that were useful for problem-solving in fraction division contexts. The lessons integrated support for mathematical communication and academic language, used sample diagrams for students to analyze and learn from, and provided students with frequent opportunities to use diagrams in their problem solving and communication about fraction division. The final lesson materials for the series of 8 lessons included a student book, a teacher edition with examples of student responses, lesson plans, and a teacher guide with additional information.
Research design and methods
The initial design and refinement of the ADSEL fraction division lesson materials were informed by formative research that included interviews with students who are ELs, input from collaborating educators as well as national experts in mathematics instruction and ELs, and observations of and feedback from teachers implementing the lessons in their early draft forms. A pilot study was conducted with twenty-three teachers and their grade 6 mathematics students. Teachers were randomly assigned to treatment or control, using stratified random assignment by school. The research team used assessment data from the participating students to address research questions related to changes in students’ understanding of key ideas about fraction division problem solving with diagrams. The research team also used student written reflections embedded in the lessons as well as interviews with students to understand students’ experiences of instructional strategies. Analyses of lesson observations and teacher surveys provided insight into classroom use of the ADSEL fraction division lessons and into typical fraction division instruction by control group teachers.
Control condition
Control teachers used standard school practices for the Grade 6 fraction division unit in their instruction for their students.
Key measures
Students' fraction problem solving using diagrams was studied through a pre/post fraction problem solving measure administered to treatment and control students. Teacher surveys and lesson observations focused on indicators of key research-based strategies and supported measurement of fidelity of implementation and treatment contrast. Interviews with ELs and written reflections from ELs that were embedded in the ADSEL fraction division lessons supported understanding of ELs' experiences of the lessons and strategies.
Data analytic strategy
Researchers used a series of multilevel regression models with students nested within teachers to analyze quantitative data for student outcomes related to fraction problem solving using diagrams. Qualitative analyses of student written reflections and student interviews, along with analyses of observation of lessons complemented the quantitative findings by identifying key features of the experiences of ELs during fraction division lessons in treatment classes and in control classes where typical fraction division instruction took place.
Key outcomes
The main findings of this project are as follows:
- ELs who participated in the ADSEL fraction division lessons demonstrated their mathematical thinking through flexible use of number lines and area models for both measurement and unit rate approaches to fraction division tasks (Nikula, Neumayer DePiper, & Driscoll, 2019).
People and institutions involved
IES program contact(s)
Project contributors
Products and publications
Project website:
Publications:
Nikula, J, & Neumayer DePiper, J., & Driscoll, M. (2019). Making mathematical thinking visible. Educational Leadership, 77(4), 77-81.
Additional project information
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