Thematic analysis of students’ talk while solving a real-world problem in geometry

Abstract

From a social semiotic perspective, students' use of language is fundamental to mathematical meaning making. We applied thematic analysis to examine students' use of geometric and contextual ideas while solving a geometry problem that required them to determine the optimal location for a new grocery store on a map of their local community. Students established semantic patterns to connect the problem context to geometry. Groups differed in how they used geometry in their discussion of the solution, in particular with how students used distance to describe the location of a new grocery store. Overall, students' knowledge of the problem context served as a resource for them to establish geometric meanings. Thematic analysis, which describes the connections in students' talk between out-of-school and discipline-specific knowledge, highlights ways in which instruction can build upon students' prior experiences for the purpose of learning in school.

Interpretations of Slope Through Written and Verbal Interactions Between a Student and Her Tutors in Algebra 1

“…After transcribing the interactions between Tanisha and her tutors, we enumerated the semantic relationships (Halliday & Matthiessen, 2014;Lemke, 1990) between terms and phrases related to slope. The first step in this analysis was to identify the key phrases, which are defined as the nouns and noun phrases that Tanisha and her tutors used to discuss linear functions (DeJarnette & González, 2016;Herbel-Eisenmann & Otten, 2011). To identify these key phrases, we made passes through the transcripts to note the specific language used by Tanisha and her tutors to discuss the tasks at hand.…”

“…Thematic analysis is a method within the theory of SFL (Halliday & Matthiessen, 2014) that focuses on the ways ideas are connected to one another in a text (Lemke, 1990; see also Chapman, 1993;DeJarnette & González, 2016;Herbel-Eisenmann & Otten, 2011;O'Halloran, 2005;Webel & DeLeeuw, 2016). The primary assumption guiding thematic analysis is that meaning is given to words and phrases through the ways in which they are connected to other words and phrases.…”

“…It is often taken for granted that a shared visual representation can serve as an anchor to clarify spoken communication, however this was not the case here. Although studies using thematic analysis have illustrated ways in which ideas become connected through verbal text (DeJarnette & González, 2016;Herbel-Eisenmann & Otten, 2011;Lemke, 1990;Webel & DeLeeuw, 2016), there is a need for more research to articulate the role of visual and symbolic representations in supporting, or inhibiting, those connections.…”

Contextualización en matemáticas: uso del teorema del ángulo inscrito en la geometrización de la percepción visual

“…Ahora bien, Freudenthal (2002), al plantear que la enseñanza de la matemática debe situarse en contextos o situaciones realistas, considera que un fenómeno puede provenir tanto del mundo real como de las matemáticas, refiriéndose de manera amplia a dominios de actividad en los cuales se revela al estudiante algún aspecto que debe ser matematizado. Desde nuestra perspectiva, al referirnos a contextos de uso, hacemos referencia específica a la incorporación a la escuela de ámbitos de uso del conocimiento que provengan del mundo real del aprendiz (Montiel y Jácome, 2014;DeJarnette y González, 2016).…”

Teachers' Understandings of Realistic Contexts to Capitalize on Students' Prior Knowledge

“…The problem is situated in the context of Hopi and Pueblo pottery and support students' discovery of the symmetry line as the perpendicular bisector of the segments that connect corresponding points in the pre‐image and the image. In the “grocery store problem,” students have to recognize the perpendicular bisector as a set of points equidistant from two given points (DeJarnette & González, ). Students find the best location for a new grocery store by using a map with points representing the locations of existing stores.…”