Exploring measurement estimation strategies through concept cartoons designed with Realistic Mathematics Education

The study examines how fourth-grade students estimate measurements when engaging with concept cartoons designed within the Realistic Mathematics Education (RME) framework. Visual representations, including concept cartoons, can concretize abstract mathematical ideas and foster discussion. RME emphasizes connecting mathematics to meaningful, real-life contexts and supports horizontal and vertical mathematization. Measurement estimation is both a practical life skill and foundational to elementary mathematics, yet primary-level understanding and strategy use remain underexplored. This study aims to identify the estimation strategies students use in weight, length, and area problems presented via RME-aligned concept cartoons, explore gender differences, and document strategies students generate themselves.

Prior work highlights the importance of visual representations in mathematical reasoning and instruction (NCTM; Jitendra & Woodward). Concept cartoons, as illustrated arguments, promote engagement, discussion, and critical thinking (Dabell) and align with RME’s focus on meaningful contexts and mathematization (Freudenthal; Treffers; Van den Heuvel-Panhuizen). Estimation is essential in curricula for developing mental references of units and practical measurement skills (NCTM; Levin; O’Daffer; Coburn & Shulte; Davydov & Tsvetkovich). However, research on measurement estimation largely targets upper grades (Sowder), with limited knowledge at the primary level (Ruwisch et al.). Typical strategies include reference point/comparison, unit iteration, and segmentation/chunking (Joram et al.; Hildreth; Lehrer et al.). In Turkey, estimation has historically been underemphasized in curricula and textbooks, though emphasis has increased since 2018 (Bulut et al.; MoNE). The explicit alignment between concept cartoons and RME principles has been underexplored, motivating this study.

Design: Qualitative case study of fourth-grade students’ measurement estimation strategies within concept cartoons. Participants: 46 fourth-grade students (23 girls, 23 boys), ages 9–10, from two classes in a middle-SES school in Adana, Turkey (2021–2022). Selection used purposeful random sampling based on teacher willingness. Students with special education needs or exceptional achievements were excluded; participants shared similar language and literacy levels. Instruments: RME-Supported Concept Cartoons developed by the researcher, explicitly aligned with RME principles (meaningful contexts; horizontal/vertical mathematization) and focused on weight, length, and area estimation. Each scenario presented multiple student statements embodying different strategies (e.g., prior knowledge, unit iteration/separation, segmentation/chunking, comparison). Procedure: Over four weeks, during scheduled measurement units, teachers introduced and then administered weekly worksheets with realistic problems. Students selected the statement they believed used the most appropriate estimation strategy and wrote any alternative strategies of their own. Ethical procedures included parental consent, voluntary participation, confidentiality assurances, and the right to withdraw. Analysis: Descriptive analysis (Yıldırım & Şimşek) coded students’ selected strategies from worksheets, examined frequencies and gender differences, and analyzed self-generated strategies. Reliability: An independent mathematics education researcher conducted a second analysis. Inter-rater reliability using Miles and Huberman’s formula yielded 98% agreement, indicating high reliability.

Overall strategy use across all problems (Table 1 totals): Segmentation/subdividing/chunking 53 (38.4%); Unit iteration/separation 32 (23.1%); Reference point/comparison 29 (21.0%); Prior knowledge 24 (17.3%). By context: Weight—Segmentation/chunking was most frequent 26 (56.5%), followed by comparison 12 (26.1%), prior knowledge 5 (10.9%), unit iteration 3 (6.5%). Length—Unit iteration/separation was most frequent 20 (43.5%), followed by segmentation/chunking 11 (23.9%), comparison 9 (19.6%), prior knowledge 6 (13.0%). Area—Segmentation/chunking was most frequent 16 (34.8%), followed by prior knowledge 13 (28.3%), unit iteration 9 (19.6%), comparison 8 (17.4%). Gender: No significant differences in strategy use by gender across weight, length, or area (Weight χ2=0.912; Length χ2=0.300; Area χ2=0.423). Student-generated strategies (Table 3): Weight—emphasis on prior knowledge (f=5) and many ‘another solution-oriented option’ responses (f=9), with some comparison (f=3), irrelevant answers (f=2), and unit iteration (f=1) (total 20). Length—students favored unit iteration/separation (f=10) and measuring with standard units (f=6), with few segmentation (f=1), comparison (f=1), another option (f=1), and irrelevant answers (f=2) (total 21). Area—more responses involved measuring with standard units (f=3) and irrelevant answers (f=3), with unit iteration (f=2), comparison (f=2), segmentation (f=2), prior knowledge (f=1), and another option (f=1) (total 14). Students predominantly used unit iteration and segmentation/chunking; reference point/comparison was less used. Many alternative solution-oriented and irrelevant responses appeared in self-generated strategies.

Findings show that fourth graders prefer segmentation/chunking and unit iteration/separation across measurement contexts, with a shift toward unit iteration for length and segmentation for weight and area. The relatively infrequent use of reference point/comparison contrasts with some recommendations that emphasize its role before standard measurement, echoing prior reports of limited use at these grade levels. The patterns may reflect curricular emphases and textbook treatments of estimation. Students’ similar approaches to length and area suggest some transferability of reasoning across attributes. The notable presence of ‘another solution-oriented option’ and ‘irrelevant answers’ indicates a need to cultivate accuracy and relevance in estimation, and to explicitly teach and discuss strategy selection and justification within realistic contexts, consistent with RME principles of activity, interaction, and mathematization.

The study contributes evidence that concept cartoons aligned with RME effectively surface primary students’ measurement estimation strategies, revealing predominant use of segmentation/chunking and unit iteration/separation and limited use of reference point/comparison. No gender differences were found. The results underscore the value of realistic, context-rich tasks for eliciting and developing estimation strategies and the need for explicit classroom discussions and examples to refine accuracy and appropriateness. Future research directions include expanding samples and grade levels, conducting longitudinal studies of strategy development, using interviews or think-alouds to probe reasoning, integrating concept cartoons into instruction (not only evaluation) to assess instructional impact, testing targeted interventions to improve estimation strategies, and exploring demographic or achievement-related differences in strategy preferences.

A primary limitation was using concept cartoons for evaluation rather than instructional purposes, which limited group activities, discussions, and additional examples based on similar scenarios and new problems.