Integrating Popular Digital Contexts into Realistic Mathematics Education - Designing a Hypothetical Learning Trajectory for Arithmetic Sequences and Series

Sep 10, 2026

The integration of popular culture and digital platforms into mathematics learning remains underexplored, limiting the creation of meaningful, context-based instructional designs. This study develops a Hypothetical Learning Trajectory (HLT) for arithmetic sequences and series by integrating TikTok into a digital mathematics classroom. Conducted in the preliminary design phase of design research, it uses literature review, classroom observations, teacher interviews, and expert validation to produce an RME-grounded two-iceberg HLT supporting formula construction and guided problem solving.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages16

Reading Time40 min

AccessFree to download

Introduction

Hypothetical Learning Trajectory (HLT) in digital environments

Arithmetic sequences and series in secondary mathematics

Realistic Mathematics Education (RME) and contextualization

Integrating Popular Digital Contexts into Realistic Mathematics Education: Designing a Hypothetical Learning Trajectory for Arithmetic Sequences and Series Arma Wangsa 1 *, Deti Sri Rahayu 2, Putri Wahdaniah 1, Sitti Mutia Umasugi 2 1 Mathematics Education Department , Universitas Sembilanbelas November Kolaka , Sulawesi, Indonesia 2 Mathematics Education Department , Universitas Negeri Yogyakarta , Yogyakarta , Indonesia * Correspondence: [armawangsa0898@gmail.com](armawangsa0898@gmail.com) Received: 18 September 2025 | Revised: 8 November 2025 | Accepted: 30 December 2025 | Published: 30 December 2025 © The Author(s) 2025 Abstract The integration of popular culture and digital platforms into mathematics learning remains underexplored, limiting the development of meaningful and context-based instructional designs. This study develops a Hypothetical Learning Trajectory (HLT) for arithmetic sequences and series by integrating TikTok into a digital mathematics classroom. The study was conducted within the preliminary design phase of design research using qualitative methods, including literature review, classroom observations, teacher interviews, and expert validation through focus group discussions. The resulting HLT consists of two iceberg models grounded in the principles of Realistic Mathematics Education (RME) . Each model contains six sequential activities comprising one contextual situation and five guided mathematical problems. The first model employs viewer-growth data from the TikTok account @raimlaode94 to support students in constructing the arithmetic sequence formula (Un) through repeated addition and ratio tables. The second model uses engagement data from the TikTok account @jeromepolin98 to guide students in deriving the arithmetic series formula (Sn) using structured tables, ratio columns, and visual folding strategies. Both trajectories are collaboratively implemented using Canva to maximize the pedagogical use of digital devices. This study provides a theoretically grounded and scalable framework that connects students’informal digital experiences with formal mathematical reasoning in technology-enhanced classrooms. Keywords: Arithmetic sequences and series; Rigital classrooms; Hypothetical learning trajectories; Popular contexts; Realistic mathematics education; TikTok Introduction The rapid integration of digital technologies into secondary education has accelerated the implementation of digital classroom program across diverse educational contexts worldwide. In Indonesia, initiatives such as the Year 11 digital classroom program in Kolaka Regency exemplify this transformation by equipping students with tablets, smartboards, and internet connectivity to support technology-enhanced learning. Despite these infrastructural advancements, preliminary classroom observations indicate that mathematics instruction frequently remains pedagogically conventional. Teachers often underutilize interactive digital platforms and collaborative applications, resulting in digital classrooms that merely replicate traditional instructional practices rather than leveraging technology to enhance mathematical reasoning, visualization, exploration, and student-centered inquiry. This condition underscores the urgent need for innovative instructional designs capable of aligning digital infrastructure with theoretically grounded and pedagogically effective learning frameworks. One promising approach for addressing this challenge is the Hypothetical Learning Trajectory (HLT), which conceptualizes learning as a systematically designed progression from informal understanding toward formal mathematical reasoning through sequenced activities, anticipated student thinking, and reflective discourse (Sztajn et al., 2012) . Within digitally mediated environments, HLTs have considerable potential to support the visualization of abstract mathematical relationships, exploratory problem solving, and collaborative modelling t

FAQs

What problem does the study address in digital mathematics classrooms?

Digital platforms are often used conventionally, failing to leverage technology to improve reasoning, visualization, exploration, and student-centered inquiry. The study targets the need for theoretically grounded instructional designs linked to meaningful contexts.

How does the proposed HLT use TikTok for arithmetic sequences and series?

The first model uses viewer-growth data to support constructing the arithmetic sequence formula via repeated addition and ratio tables. The second model uses engagement data to guide deriving the arithmetic series formula using structured tables, ratio columns, and visual folding strategies.

What research method is used to design and validate the learning trajectory?

The study follows the preliminary design phase of design research with qualitative methods, including literature review, classroom observations, teacher interviews, and expert validation through focus group discussions.

Sep 10, 2026

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