Formative Assessment in Digital Classrooms: Comparison through Bar Model Representations

Abstract

Digital assessment introduces fresh possibilities for evaluating mathematics learning when students' work is created in digital settings. Teachers can modify task structures for remediating students' conceptual deficiencies and align the scope of assessed abilities and skills according to their learning needs. Two key processes underpin effective formative assessment: collecting data on student digital interactions and devising strategies to enhance performance. Among the many contributions of technology to contemporary pedagogy is its capacity to furnish students with an extensive suite of digital tools for exploration, practice, and representation. One such tool is the bar model virtual manipulative. The bar model, a core feature of the model method used in the Singapore mathematics curriculum, is a structured visual representation designed to support students’ understanding of mathematical relationships in problem solving. In line with Bruner’s Enactive–Iconic–Symbolic framework, the bar model occupies the iconic stage of learning, acting as a bridge between hands-on manipulation of objects and abstract symbolic reasoning. By using rectangular bars to represent known and unknown quantities, students are guided to visualise part-whole and comparison structures, comprising two key relational models that underpin many arithmetic and algebraic problems. This visual representation is particularly helpful for students who struggle with abstract concepts in word problems, as it allows them to explore mathematical representations dynamically. Moreover, research has shown that instructional strategy involving the comparison of visual representations effectively supports mathematics learning. A pilot study was conducted to explore the strategy's effectiveness with nine Grade 6 students, employing screen recordings and post-task group discussion as data collection instruments to capture student interactions and fractional reasoning while comparing bar models. Comparison of bar models fosters active learning through interaction with these representations, providing insights into students' mathematical thinking in the process. The study highlights the role of visual modelling and scaffolding to promote student-centred practices, fostering conceptual learning and relational reasoning in mathematics within technology-enhanced settings.