For anyone who has ever learned or attempted to learn a different language, the experience can range from exhilarating to exasperating and every emotion in between. Now, add to the language equation the challenge of developing mathematical reasoning.
That’s the problem Heather Johnson, PhD, mathematics education assistant professor, School of Education and Human Development is continuing to examine. This spring, with grant support from the Center for Faculty Development, she will extend earlier work conducted through the Denver Public Schools (DPS) - University of Colorado Denver Research Collaborative.
Last year, Johnson participated with researchers studying DPS schools with a high density of learners of English as a second or additional language and high numbers of students who qualified for a free or reduced-price lunch that were experiencing the most success with English language learners (ELL students). “The goal,” Johnson said, “was to identify school-wide practices that have been successful in supporting the achievement of these students.”
The next phase for Johnson is to look at how middle school ELL students engage in mathematical reasoning about quantities involved in rates of change. Johnson noted, “Mathematical reasoning has been identified as a process essential to developing understanding in mathematics.” Informed by the work of other researchers, Johnson’s grant proposal stated, “By examining rate of change in different contexts, students can better understand important ideas in the world around them.”
Johnson started by consulting with a middle school math teacher from a school connected to the DPS-ELA Exemplary Schools study. Her plan is to conduct classroom observations this spring, then teach a series of six lessons that require students to makes sense of quantities that change together. After the lessons, Johnson will interview pairs of students to investigate their mathematical reasoning related to quantities involved in rate of change. During the interviews, students will work together on mathematical problems that build from the tasks they worked on during the classes Johnson taught.
Anticipated results include characterizations of students’ reasoning about quantities involved in rate of change and explanations marking distinctions in students’ reasoning related to rate of change. “Tasks and questions used in this study could inform the development and implementation of mathematics curricular materials related to rate of change,” Johnson explained.