Traditional Cone-Shaped Hats Reveal How Learning Styles Shape Indonesian Students’ Math Literacy

In a junior high school classroom in Magetan, East Java, a woven bamboo hat known as the caping is doing more than shielding farmers from the tropical sun. It is becoming a mathematical object, a cultural artifact pressed into service to teach one of geometry’s most stubborn topics: the surface area of a cone. A new study published in SN Social Sciences by researchers at Universitas Sebelas Maret examines how students interpret this traditional hat through the lens of mathematical literacy, and how their individual learning styles, whether visual, auditory, or kinesthetic, shape the way they engage with the underlying geometry. The findings arrive at a moment when Indonesia is searching for new ways to lift its performance in international assessments, and they suggest that culture alone is not enough; instruction must also be tuned to how individual students actually absorb information.

The stakes of the research are rooted in a persistent and well-documented problem. Mathematical literacy, the capacity to formulate, apply, and interpret mathematics in real-world contexts, is a central construct of the Programme for International Student Assessment, better known as PISA. Indonesian students have consistently ranked near the bottom of the PISA league tables, a result that researchers in mathematics education interpret as evidence of generally low mathematical literacy across the country’s school system. Students may learn to compute mechanically, the argument goes, but they struggle to translate a situation from daily life into mathematical terms, to select appropriate procedures, or to reason about what a result means once it has been obtained. This gap between procedural fluency and genuine mathematical understanding has motivated a decade of experimentation with context-based and culturally grounded teaching approaches.

One of the most influential of these approaches is ethnomathematics, a field pioneered by the Brazilian mathematician Ubiratan D’Ambrosio in the 1980s. Ethnomathematics rests on the observation that mathematical ideas are not confined to formal schooling; they are embedded in the practices, crafts, architecture, and rituals of every culture. By surfacing the mathematics hidden in familiar cultural objects, educators hope to make abstract concepts concrete and to signal to students that mathematics belongs to them, rather than being a foreign import. In Indonesia, a country with extraordinary cultural diversity, researchers have explored ethnomathematical modules, learning tools, and realistic mathematics education designs built on regional traditions. Meta-analyses of this work suggest that ethnomathematics-based learning can have positive effects on both problem-solving skills and mathematical literacy, which helps explain why the approach continues to attract attention.

The caping offers a particularly elegant case. The hat’s conical form is not merely decorative; it embodies the geometry of a right circular cone, a solid whose surface area depends on the radius of its circular base and the slant height running from the apex to the rim. Unroll the lateral surface of a cone and it flattens into a sector of a circle, whose area can be derived with basic formulas. For a hatmaker, the practical problem of how much woven bamboo is needed to cover the head is, in effect, a cone surface area problem solved with inherited craft knowledge. Previous literature reviews of caping ethnomathematics had already flagged its relevance to teaching cone material, but the Universitas Sebelas Maret team, led by Nuri Wahyu Widayanti with Rubono Setiawan and Laila Fitriana, wanted to go further: to observe how real students actually use the caping model to construct mathematical literacy, and whether that construction differs depending on how they learn.

The researchers adopted a qualitative phenomenological approach, a methodology designed to capture the lived experience of participants as they encounter a phenomenon. Rather than testing large samples with standardized instruments, phenomenological studies gather rich, detailed data from individual students, typically through written work, task-based problem solving, and observation, and then analyze that material thematically to reveal the structure of the experience. In this study, the data consisted primarily of students’ written work on problems involving the surface area of a cone, contextualized through the caping. The research was conducted at SMP N 1 Ngariboyo in Magetan, with formal permissions from both the university’s Faculty of Teacher Training and Education and the school’s principal, and with informed consent from all participants whose work was anonymized for analysis.

Central to the study’s design is the concept of learning styles, a framework popularized in educational practice by works such as DePorter and Hernacki’s quantum learning model. The framework classifies learners into three broad modalities. Visual learners prefer to process information through images, diagrams, and spatial representations. Auditory learners rely on verbal explanation, discussion, and hearing ideas articulated. Kinesthetic learners learn best through physical activity, manipulation of objects, and direct bodily engagement with the material. The hypothesis is straightforward: a culturally embedded model like the caping, which can be looked at, described, or handled, might interact differently with each modality, producing different levels of engagement with the three indicators of mathematical literacy that the study tracks.

Those three indicators, drawn from the international literature on mathematical literacy, involve the ability to formulate a real-world situation mathematically, to apply mathematical concepts and procedures to solve the resulting problem, and to interpret and evaluate the solution in terms of the original context. In a cone surface area problem framed by the caping, formulating means recognizing the hat as a cone and identifying the relevant dimensions; applying means correctly deploying the surface area formula and its derivation through the circular sector; interpreting means connecting the computed area back to the practical question of material or coverage. A student who is fully mathematically literate in this domain should demonstrate competence at all three stages, not merely at the computational middle.

The study’s central findings reveal a clear asymmetry. Visual and auditory learners demonstrated proficiency across all three indicators of mathematical literacy when solving the cone surface area problems built on the caping model. For visual learners, the hat’s distinctive silhouette and its unrolled sector diagram provided the spatial scaffold needed to formulate the problem and verify the sensibility of results. Auditory learners, meanwhile, could talk themselves through the formulation and interpretation stages, using verbal reasoning to connect the cultural context to the formal mathematics. Kinesthetic learners, by contrast, struggled to fully achieve all three indicators. Although the caping is a physical object that might seem ideally suited to hands-on learners, these students did not consistently reach the formulation and interpretation stages through the model as presented, suggesting that merely introducing a cultural artifact does not automatically guarantee that every learner will translate it into formal mathematics.

The practical implication the researchers draw is that culturally integrated mathematics instruction must be designed with learning styles explicitly in mind. A single ethnomathematical model, however vivid, will land differently across a classroom of students, and teachers who want to raise mathematical literacy effectively should offer multiple pathways into the same cultural-mathematical context: visual representations for those who think in pictures, structured verbal discussion for those who think in words, and carefully designed hands-on activities, possibly involving actual manipulation and measurement of the object itself, for kinesthetic learners. Without this differentiation, the benefits of ethnomathematics may flow disproportionately to students whose styles happen to match the presentation format, leaving the very students who most need concrete, embodied learning experiences behind. The finding is especially relevant to Indonesia’s broader reform efforts, where ethnomathematics is increasingly promoted as a national strategy for improving PISA-related competencies.

The study also contributes methodologically, showing how a phenomenological approach can illuminate the fine-grained texture of mathematical thinking that standardized tests flatten out. By examining students’ written work closely, the researchers could trace where in the formulation-application-interpretation chain each type of learner stumbled, offering a diagnostic precision that a test score alone cannot provide. The authors note limitations inherent to the design: the data derive from written work rather than publicly archived datasets, in order to protect participant confidentiality, and the qualitative scope means the findings speak to the structure of the experience rather than to population-level effect sizes. Even so, the message is compelling. A humble farmer’s hat from Magetan, when treated as a mathematical model, can open a window onto the geometry of curved surfaces and, simultaneously, onto the diverse ways students make sense of mathematics. Bridging Indonesia’s literacy gap, the study suggests, will require both the wisdom of cultural heritage and a sharper attention to the individual minds sitting in the classroom.

Subject of Research: Ethnomathematics-based mathematical literacy in cone geometry analyzed through students' learning styles

Article Title: Mathematical literacy analysis based on ethnomathematics modelling of caping and learning styles: study in Magetan, Indonesia

Article References: Widayanti, N. W., Setiawan, R., & Fitriana, L. (2026). Mathematical literacy analysis based on ethnomathematics modelling of caping and learning styles: study in Magetan, Indonesia. SN Social Sciences, 6(9), Article 373. https://doi.org/10.1007/s43545-026-01665-5

Image Credits: AI Generated

DOI: 10.1007/s43545-026-01665-5

Keywords: mathematical literacy, ethnomathematics, caping, learning styles, cone surface area, PISA, Indonesia, phenomenology, mathematics education, Magetan, visual learners, kinesthetic learners