Supporting Students' Mathematical Higher Order Thinking Through an Embodiment Approach to Graphing

• In Event: Higher Order Thinking in Primary School Mathematics Education

Abstract

Graphs are essential tools to represent mathematical relationships between variables and, in particular, data changing over time. Yet, understanding graphs is difficult for many students, who are prone to focus on surface characteristics, such as slope or height, instead of the deeper connections underlying the represented data (e.g., Glazer, 2011). Being able to make connections between variables and becoming proficient in graphing is key in higher-order thinking activities within mathematics and science education. In our research, we make use of embodiment theory to promote students’ graphical understanding. Embodiment theory proclaims the fundamental coupling of action, perception, and reasoning for mathematical cognition (Abrahamson, 2017). This leads to the assumption that perceptuo-motor experiences are necessary when developing mathematical knowledge (Glenberg & Gallese, 2012). When the focus is on mathematical higher-order thinking in the context of graphing, this means reasoning about graphs, i.e. interpreting, constructing, changing, combining, and comparing graphs. To elicit such domain-specific mathematical higher-order thinking, we created an experiential context in which students have the opportunity to actively engage in dealing with dynamic data. Students create distance-time graphs describing their own movements in front of a motion sensor, hereby coupling action and perception, which implies a strong grounding of the mathematical concept of change in the bodily based experience of moving through space (Ferrara, 2014; Nemirovsky et al., 1998). The resulting graphical representation will no longer be an abstract entity, but a reference to actual personal experiences within the classroom environment. Moreover, students are given ample opportunities to reason about the resulting graphical representations, following the notion that embodied action and mathematical reasoning are intricately linked (cf., Abrahamson, 2017; Nathan et al., 2014). In this paper, we present empirical evidence regarding how an embodied approach to graphing in a classroom setting can contribute to developing higher-order thinking. Consequently, this evidence is used as a basis for a domain-specific conceptualization of higher-order thinking, focusing on graph interpretation and graph construction as two core components.
Method
The intervention consisted of six lessons on graphing change. In total 72 students, divided over three fifth-grade classes, participated. Two types of data were collected: Micro-genetic data consisting of students’ answers after each lesson on test items on graphing change, and macro-genetic data, consisting of students’ responses to a mathematical higher-order thinking pre- and posttest. These data were analyzed on two central graphing components: interpreting and constructing graphs. For each of these components a coding scheme was developed.
Results and significance
Overall, we expect to find that, by providing students with rich embodied experiences, graph comprehension on both core higher-order thinking components can be fostered. Understanding the embodied processes valuable for graph learning is key to enhance students graphical understanding. The data will provide evidence that has the potential to advance current conceptual, theoretical, methodological, and analytical frameworks related to the development of higher-order thinking within an embodied approach to teach graphing. This domain-specific conceptualization of higher-order thinking, illustrated by examples from student work, will allow researchers to design effective embodied graphing tasks within learning environments.

Authors

• Carolien Duijzer, Freudenthal group FSW, Utrecht University

• Marja Van Den Heuvel-Panhuizen, Utrecht University, the Netherlands; Nord University, Norway

• Michiel Veldhuis, Utrecht University

• Michiel Doorman, Utrecht University

• Paul P.M. Leseman, Utrecht University