Integrating Dynamic Mathematics to Advance Learning of Computing Concepts for Diverse Student Populations

• In Event: 41.049 - Stories From the Field: Integrating Computational Thinking Across Curricular Domains

Abstract

Purpose and Theoretical Framework. Learning to program is a central feature of introductory CS curricula in K-12 classrooms. Research suggests that deeper conceptual learning of programming is difficult (Robins, Rountree & Rountree, 2003). Past research also shows a correlation between learning outcomes in introductory programming and prior mathematics preparation (Grover et al., 2016; Lewis & Shah, 2012). Weak mathematics preparation can be a barrier to successful learning of CS.
To prevent achievement gaps in mathematics from being replicated in CS, our project explores the potential impact of educational technology approaches drawn from contemporary mathematics education—particularly, dynamic mathematics technologies (Drijvers et al., 2009)—on middle school dynamic conception of variable supported by such environments. In addition to subtly repositioning students’ understanding of variables (V), we see dynamic technology approaches as relevant to expressions (E), looping (L), and the ubiquitous idea of abstraction (A) across data and control architecture (hence the acronym VELA). Our larger ambition is to drive conceptual reconfigurations of quasi-mathematical components appearing at the very start of middle school computing curricula, and in doing so, first, to level wide differences in mathematical preparation that students bring to programming—differences that frequently play out along socioeconomic spectra—and, second, to expand the operative and predictive usefulness of students’ understanding of these foundational ideas.
Methods and Data.
VELA Activities and Curriculum Design entails conceptualization, design, and development of digital and non-digital activities for introductory CS middle school curricula that will serve as precursorial conceptual sandboxes to explore VELA before employing these concepts in programming. The activities have been designed with inputs from classroom teachers from a large, diverse urban school district in Northern California in a participatory design model.
Data Sources. The beta versions of the VELA activities are currently being piloted in lab-settings as well as a local summer camp in Northern California in 1-1 and small group sessions with ~10 middle school children that represent varied levels of prior math preparation. Roughly 10 more students will participate in thinkaloud sessions in the Fall of 2016. These activities are slated to be used by 3 middle school CS teachers in a large, diverse, urban school district in Northern California with a total of 100 students in Jan 2017. Data collection and mixed-method analyses will include pre-post tests and case studies (using a maximum variation strategy (Flyvbjerg, 2006) to select case study students) that examine the CS & CT learning experiences of a diverse subset of students.
Results. The anticipated result is a curriculum that will build better conceptual foundations for key computing constructs in introductory programming with which learners typically struggle, and especially those with lower math achievement. The case studies will reveal how well the activities helped diverse learners build the necessary conceptual bridges for succeeding in programming.
Significance. “CS for All” in K-12 requires that curricula be designed so all learners succeed in deeper learning of computing regardless of prior academic preparation. This current work attempts to achieve that by exploiting the synergies between key concepts in middle school math and programming.

Authors

• Shuchi Grover, SRI International

• Nicholas Jackiw, SRI International