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

In the present study, the primary objective was to investigate the measurement estimation strategies of fourth-grade students in a classroom setting using concept cartoons. A total of 46 students participated and were presented with realistic problem situations related to weight, length, and area measurements. The students were asked to identify which answer they believed was closest to the correct estimation based on their own understanding and experiences. Furthermore, it was aimed to explore how students would respond if they were faced with the same measurement problem. The idea was to understand students’ personal approaches and thought processes when tackling measurement estimations. By engaging students in this manner, it was aimed to identify their individual perspectives and gather insights into their decision-making processes regarding measurement estimations. This approach provided valuable information on students’ reasoning abilities and problem-solving strategies and their ability to apply measurement concepts to real-life situations.

The aim of using concept cartoons in the present study was to provide students with a means to externalize their mathematical thinking processes, allowing them to express their thoughts freely and establish connections with other ideas in a familiar environment. By presenting realistic problems through concept cartoons, students were immersed in scenario-based situations that motivated them to find solutions. This approach aligns with the principles of RME and concept cartoons, as it promotes active student engagement and the application of mathematical concepts in real-life contexts. The analysis of the measurement estimation strategies provided by the students revealed that, in general, the most favored strategies in all scenarios were “Segmentation/sub-segmentation/fragmentation” and “Unit iteration/separation”. In previous studies, it was also shown that students used the “Unit iteration/separation” strategy at rates ranging from 30% to 97% (Hildreth, 1983; Immers, 1983). Additionally, Lehrer et al. (2003) emphasized the importance of students using the “Reference point/comparison” strategy before employing standard measuring instruments, as it allows them to model the process of unit iteration physically and then mentally. However, it was observed that fourth-grade students showed less interest in this strategy, which contrasts with previous findings indicating its significance. It can be inferred that comparison or reference points are important for estimation, but students tend to use this strategy less frequently (Hildreth, 1983). In a pilot study conducted by Joram et al. (2005) with third-year students, it was also found that the “Reference point/comparison” strategy was rarely utilized for measurement estimation. These findings suggest that there may be variations in the strategies employed by students at different grade levels, highlighting the need for further investigation into students’ understanding and utilization of estimation strategies in the context of measurement. Such variations in findings could be attributed to the mathematics teaching programs and textbooks that each country employs. The extent to which these programs and textbooks emphasize estimation strategies will influence the diversity of strategies students use. Analyzing the results of the research conducted by Bulut and colleagues (2017) on the examination of estimation skills in mathematics teaching programs between 1945 and 2015, it is noteworthy that there are a ‘limited number of studies on estimation’ and ‘insufficiency in the inclusion of estimation skills in the curriculum in Turkey.’ As of 2018, the Ministry of National Education has started to emphasize estimation more in the mathematics teaching program (MoNE, 2018). Consequently, the number of studies conducted on estimation in the country between 2017 and 2019 has increased compared to other years (Bağdat and Yıldız, 2023). Although the concept of estimation is present in the programs, it has been limited to certain grade levels. In particular, due to the necessity for students to have sufficient prior knowledge about the topic, it has been somewhat neglected at the K-4 level. Moreover, research indicates that in textbooks the only estimation strategy mentioned is usually rounding. Additionally, textbooks lack discussions about various estimation strategies and there is a lack of strategy instruction for students.

Another notable finding in the study was the similarity in measurement estimation strategies used by male and female students. While there is limited research specifically exploring gender differences in measurement strategies, Hildreth (1983) conducted a study involving students at different grade levels (fifth, seventh, and university first grade) and found no significant differences in the measurement strategies employed by students based on their gender. These results suggest that gender may not play a significant role in influencing the choice of measurement estimation strategies among students. However, further research is needed to delve deeper into this aspect and explore potential factors that might contribute to variations in strategy preferences.

In a study conducted by Ruwisch et al. (2015) involving fourth-grade students, it was discovered that these students employ a variety of strategies to estimate lengths and areas. These strategies were categorized into three main types: comparisons, division into units, and segmentation/grouping. Interestingly, the students demonstrated equal use of these strategies for both length and area measurement estimations. The students also exhibited spontaneous generation of measurement estimation strategies, including prior knowledge, another solution-oriented approach, reference point/comparison, irrelevant answers, unit iteration/separation, measuring in standard units, and segmentation/subdividing/chunking. This diversity in strategies indicates flexibility in their mathematical thinking, showcasing their ability to adapt different approaches based on the context of the measurement problem (Drijvers et al., 2019). When examining the strategies generated by the students in the present study, it was observed that their approaches to measuring length and area were remarkably similar. However, considering the meaningfulness of mathematical ideas when connected to other concepts and situations (Clements and McMillen, 1996), it was hypothesized that students would be influenced by concept cartoons and potentially develop different strategies in their original responses. Moreover, the observation of students demonstrating equal use of strategies for both length and area measurements implies a certain level of transferability in their problem-solving skills across different mathematical domains. This not only shows the versatility of students’ cognitive processes but also suggests that interventions targeting measurement estimation skills may have broad applications (Desli and Giakoumi, 2017). The spontaneous generation of measurement estimation strategies, including prior knowledge, another solution-oriented approach, reference point/comparison, irrelevant answers, unit iteration/separation, measuring in standard units, and segmentation/subdividing/chunking, underscores the creative and exploratory nature of students’ problem-solving processes. It indicates that students draw upon various cognitive resources, including their existing knowledge, to formulate strategies when faced with measurement estimation challenges (Tambychik and Meerah, 2010).

Notably, the presence of a substantial number of “other solution-oriented options” and “irrelevant answers” in the students’ responses should not be overlooked. These responses highlight the need for cultivating accuracy and relevance in their estimation strategies. As the strategies employed by children play a vital role in problem-solving, they must possess accurate and effective estimation strategies (Peeters et al., 2016). Hildreth (1983) emphasizes the importance of incorporating student discussions during training sessions focused on the utilization of measurement estimation strategies. Classroom examples can be utilized to illustrate each strategy and provide students with a deeper understanding. It is important to note that one limitation of the present study is the use of concept cartoons for evaluation purposes rather than instructional purposes. Consequently, the study lacked the inclusion of desired group activities, discussions, and additional examples based on similar scenarios and new problems. During the study, students were instructed to select the strategy that closely aligned with their own preferences by considering the measurement strategies presented in the speech bubbles of the concept cartoons. In this approach, the aim was to enhance their awareness of their own measurement estimation strategies and potentially inspire the development of new and spontaneous approaches, perhaps influenced by the strategies depicted in the concept cartoons.

In conclusion, in the present study, the measurement estimation strategies employed by fourth-grade students using concept cartoons and realistic problem scenarios were investigated. It was revealed that students utilize various strategies, including comparisons, division into units, and segmentation/grouping, to estimate lengths and areas. The findings emphasize the significance of connecting mathematical concepts with real-life situations. Additionally, research shows that incorporating real-life contexts into mathematical problems can significantly improve student understanding and application of concepts (Adams and Lowery, 2007). The aim of using concept cartoons was to influence students’ original answers and encourage the adoption of different strategies. However, the presence of a notable number of “other solution-oriented options” and “irrelevant answers” in the students’ responses highlights the need for accurate and useful estimation strategies. This suggests an area for instructional focus, emphasizing the importance of guiding students toward strategies that not only showcase creativity but also align with the requirements of the given mathematical problem (Heinze et al., 2009). The research underscores the importance of incorporating student discussions and examples in teaching measurement estimation strategies. By integrating these elements into instructional sessions, students can enhance their understanding and application of various strategies.

Limitations and suggestions

While the study contributes valuable insights into students’ measurement estimation strategies, it has certain limitations. Notably, the focus on evaluation rather than teaching limited the inclusion of group activities, discussions, and additional examples. Addressing these limitations and further refining the study can strengthen its contribution to the field of mathematics education. Overall, the study provides a comprehensive analysis of students’ use of measurement estimation strategies in the context of concept cartoons and realistic problems. The findings underscore the importance of promoting accurate and effective estimation strategies among students, highlighting the potential for further research and instructional improvements in this area.

As suggestions for researchers and future studies, educators, and their practices, several recommendations can be made based on the findings and limitations of the present study:

Suggestions for researchers and future studies:

Several recommendations can be proposed for researchers and future studies based on the findings and limitations of the present study. Expanding the research scope by conducting similar studies with larger sample sizes and across different grade levels can provide a more comprehensive understanding of students’ measurement estimation strategies, allowing comparisons and analysis of developmental changes in strategy choices. Longitudinal studies tracking students’ progression in measurement estimation strategies can shed light on the development and effectiveness of different strategies over time. Qualitative analysis, such as interviews or think-aloud protocols, can supplement quantitative data, providing deeper insights into students’ thought processes, reasoning, and decision-making strategies during measurement estimation tasks. Intervention studies that explicitly target measurement estimation strategies can assess their effectiveness in promoting accurate and useful estimation approaches among students. Comparing the outcomes of different instructional methods or interventions can provide evidence-based guidance for educators. Conducting studies that focus on integrating concept cartoons and realistic problem scenarios into classroom instruction rather than solely using them for evaluation purposes can offer valuable insights into the impact of such interventions on students’ strategy preferences and problem-solving abilities. Investigating potential differences in measurement estimation strategies based on various demographic factors, such as gender, cultural background, or mathematical achievement, can inform personalized instruction and support equitable mathematics education.

Implications for educators

The present study offers valuable insights that educators can use to enhance their instructional practices in the area of measurement estimation strategies. The findings underscore the significance of incorporating realistic problem scenarios, such as those presented through concept cartoons, into classroom instruction. Educators can adopt a pedagogical approach that aligns with the principles of Realistic Mathematics Education (RME) and concept cartoons, promoting active student engagement and the application of mathematical concepts in real-life contexts. By immersing students in scenario-based situations, educators can stimulate their problem-solving abilities and foster a deeper understanding of measurement estimation strategies. Moreover, the study emphasizes the importance of recognizing and addressing the diversity of strategies employed by students. The principles of RME and concept cartoons can guide educators in providing differentiated instruction that accommodates varied learning styles and preferences. The study also highlights the need for explicit instruction and discussions on measurement estimation strategies. Practically, educators can integrate the use of concept cartoons into lesson plans to facilitate discussions and activities focused on measurement estimation. Educators can incorporate classroom activities that encourage students to articulate their thought processes, share their strategies, and engage in collaborative problem-solving. By creating an environment that values diverse strategies, educators can contribute to the development of students’ reasoning abilities and problem-solving skills. Classroom activities can be designed to encourage group discussions, peer interactions, and additional examples related to the concept cartoons presented. In essence, this study opens up avenues for educators to refine their teaching methods, promote a variety of measurement estimation strategies, and create inclusive learning environments that nurture students’ mathematical reasoning.