Learning Trajectory-Based Formative Assessment and Sequenced Digital Learning Activities in Math Class

Introduction

In the last two years, education systems have seen unprecedented and rapid technology integration for teaching in the wake of COVID-19. Teachers and students in schools across the United States increased the use of educational technology dramatically, spending entire days on online platforms over periods of weeks and months at a time. As many classes transitioned to an online-only format, educators had to integrate technology into their lessons without having time or training to explore the best practices for technology integration. Some choices did not come from intentional and informed decision-making but from necessity. Even as we transition back to the classroom, we have urgency in supporting students whom the COVID disruption has most impacted, and the need to differentiate has been amplified. One strategy we propose is leveraging the widespread adoption of technology and providing teachers with guidance on how to most efficiently and effectively evaluate technology that targets mathematics instruction along a learning continuum to better meet students’ diverse needs. This strategy aligns with the goals articulated in the Association of Mathematics Teacher Educators’ (AMTE, 2017) Standards for Preparing Teachers of Mathematics (SPTM) which advocates preparing teachers of mathematics to be “proficient with tools and technology designed to support mathematical reasoning and sense making, both in doing mathematics themselves and in supporting student learning of mathematics” (p. 11). In order to prepare teachers of mathematics to be proficient, Foulger et al. (2020) recommend a systemic and sustainable approach that moves beyond technology integration to technology infusion where teacher preparation programs help teachers candidates to effectively teach with technology by “redesigning experiences, systems, and cultures of teacher education systems rather than focusing on stand-alone technology courses or tool specific application” (p. xix). This chapter will focus on rich experiences for teaching and learning with technology to be systematically evaluating their uses to promote equity. More specifically, we detail learning experiences to support PSTs in using technology judiciously through formative assessments and bridging activities aligned to the learning trajectories to support better diverse learning needs and position technology as a significant lever for equity and pandemic recovery.

The lead author designed an assignment called Learning Trajectory-based Formative Assessment & Sequenced Digital Math Activities. In this assignment, PSTs planned and enacted asset-based solutions that included digital tools assessment tasks. The goal of the tasks was to re-engage students in mathematics as the students worked to develop their sense of agency, identity, and ownership in their mathematical learning. Our chapter focuses on how PSTs used learning trajectory research to analyze formative assessment data and then sequenced bridging activities using digital technologies to enrich mathematics instruction for individual and collective learning. PSTs also learned to use digital technology teacher dashboards, which allowed them to be responsive by providing ease of analysis of student proficiency, facilitating immediate feedback, and providing information to form targeted small groups to support student learning. The Learning Trajectory-based Formative Assessment and Digital Math Activities assignment was designed using two important frameworks, Learning Trajectory Based Instruction (LTBI, Sztajn et al., 2012) and Technological Pedagogical Content Knowledge (TPACK, Mishra, P., & Koehler, M. J., 2006)). In many academic and practitioner resources, the terms Learning Trajectories (LTs) and learning progressions are used interchangeably, emphasizing the developmental progression of levels of thinking within a conceptual domain. Confrey’s notion of LT/progression is described as