Fermi problems, initially introduced by Nobel Prize–winning physicist Enrico Fermi, are defined as "open, non-standard problems requiring the students to make assumptions about the problem situation and estimate relevant quantities before engaging in, often, simple calculations." (Ärlebäck, 2009, p.131). Fermi problems differ from traditional mathematical problems in that they seem ambiguous and require limited information, as illustrated by the question, "How many technologically advanced civilizations exist in our galaxy?" (Efthimiou & Llewellyn, 2007, p. 255).  These complex problems can be solved using estimation without exact calculation (Chandler, 1990), enabling quick approximate answers (Carlson, 1997). According to Ärlebäck (2009), Fermi problems are characterized by their accessibility to learners across different educational levels, their grounding in meaningful real-world contexts, and their open-ended nature, which involves neither predetermined solution strategies nor given numerical data; instead, they require students to identify relevant information, make reasonable estimates, and engage in discussion by drawing on prior knowledge and experience. These rich and meaningful features lead to its frequent usage in both physics and mathematics education. In this sense, solving Fermi problems can require examining models and principles in physics (Robinson, 2008) and doing mathematics (Meyer & Greefrath, 2025) without reaching the exact answer. The real-life context of its (Peter-Coop, 2009) can enable the construction of a bridge between different subjects, as it has an interdisciplinary nature (Sriraman & Lesh, 2006).

Although Fermi problems were initially employed primarily in science contexts, following Ärlebäck's (2009) study on their potential for introducing mathematical modeling, they have been increasingly used in mathematics education research, specifically focusing on students' mathematical modeling and estimation skills.  The scope of the recent studies comprises examining students' Fermi problem-solving process, larger number estimation and modeling skills (Albarracín & Gorgorió, 2019), mathematical model development process (Albarracín, 2021; Brunet-Biarnes & Albarracín, 2024), and measurement estimation skills (Er & Sezer, 2025; Segura et al., 2025).  Within this scope, Fermi Problems enhanced students' mathematical skills across grade levels from primary school to high school.

However, Fermi problems, which support students’ various mathematical competencies, need to be more widely recognized and used at the global and international levels. Thanks to their flexible structure, Fermi problems can be used in various mathematical contexts and foster a range of skills in students. In this respect, determining the research trends in existing studies on Fermi problems in mathematics education and identifying existing research gaps can provide an important roadmap for future studies. In the literature we reviewed, we encountered only one review study, conducted by Ärlebäck and Albarracín (2019), that examined the use of Fermi problems. However, this review primarily focused on the development of twenty-first-century skills and examined STEM disciplines broadly. Consequently, there remains a clear need for an in-depth examination of the use of Fermi problems, specifically within the field of mathematics education, with particular attention to publication trends over time, research methodologies, participant characteristics by countries and educational levels, and how Fermi problems are addressed in different mathematical contexts.

In this regard, the purpose of this study is to systematically examine the studies that focus on the use of Fermi problems in mathematics education published in Web of Science (WoS), Educational Resources Information Center (ERIC), and Scopus databases with the following research questions:

1) What are the research trends in studies on the use of Fermi problems in mathematics education in terms of publication years, research methodologies, participant characteristics by countries, and educational levels?

2) How have Fermi problems been addressed and utilized in mathematics education research?

In this study, the PRISMA (Preferred Reporting Items for Systematic Review and Meta-Analysis) framework (Moher et al., 2009) was used to systematically review studies through the following steps: identification, screening, eligibility, and inclusion. WoS, Scopus, and ERIC databases were selected for their inclusion of high-quality education journals. In December 2025, each database was searched using the following strings: “Fermi problems AND mathematics”; “Fermi problems AND modelling OR modeling”; “Fermi problems AND estimation”. As a result of this search, 110 studies were obtained. After duplicates were removed, 76 records remained for screening. To systematically identify and select studies on Fermi problems in mathematics education, inclusion and exclusion criteria were established. Thus, 52 studies conducted outside the field of mathematics education, published in languages other than English, systematic reviews, book chapters, theses and dissertations, non-peer-reviewed publications, and conceptual, theoretical, or descriptive studies without empirical data were excluded. Accordingly, 24 English-language, peer-reviewed journal articles and conference papers on Fermi problems in mathematics education remained. During the eligibility assessment, three additional studies were excluded as they did not report empirical data. Thus, 21 studies that met all inclusion criteria were included for the data analysis. To ensure transparency and consistency, data were extracted using a structured coding sheet developed by the authors. Information was recorded on this sheet, including bibliographic details (author(s), title, publication year, document type), research aims, methodological characteristics (research design, participants, data collection, data analysis), key findings, and how Fermi problems were addressed in each study. Descriptive and qualitative content analysis methods were used to analyze data. Descriptive analyses were employed to determine the studies’ research design, publication years, participant characteristics by country, and education level. Then, a qualitative content analysis was used to identify the mathematical contexts of studies and how Fermi problems were addressed. During this process, each researcher independently reviewed and categorized the studies. They then met to compare their analyses, resolving any discrepancies through discussion until a consensus was reached. This categorization provided a systematic comparison of each study, illustrating how Fermi problems are conceptualized and utilized within mathematics education research.

Descriptive analysis showed that studies predominantly used a qualitative approach (71%), followed by mixed-method (24%) and quantitative studies (5%). Annual publication trends indicate that research on Fermi problems increased following Ärlebäck's (2009) study, which used Fermi problems to introduce modeling, with a notable rise in recent years, including five studies in 2021 (24%) and four in both 2023 and 2025 (19% each). The participants' characteristics of the studies showed that the vast majority (71%) were from Spain. Turkiye (14%) and Sweden (10%) follow Spain. In most studies, participants were pre-service teachers (33%), high school (33%), and middle school (24%). students. Considering the real-life context of Fermi problems (Peter-Coop, 2009) and their positive effect on students' estimation and modelling skills (Albarracín & Gorgorió, 2019), it is recommended to conduct further studies with primary school students. Content analysis demonstrated that Fermi problems were used in studies in two ways: either as the study's research objective, focusing on the Fermi problems themselves (e.g., solution processes, strategies, and errors), or as a tool to develop or examine a skill. While Fermi problems were used as a research objective in 10 studies (48%), 11 studies (52%) used Fermi problems as a tool. Studies that used Fermi problems as a research objective focused on problem-solving (PS) skill, specifically on PS processes (20%), PS strategies (30%), PS misconceptions and mistakes (30%), and PS flexibility and performance (20%). Studies that used Fermi problems as a tool examined a skill (73%) or supported a skill (27%). Predominantly, students' mathematical modeling skill was examined or supported using Fermi Problems as a tool. Future research could leverage the open-ended nature of Fermi problems (Ärlebäck, 2009) to foster a broader range of mathematical skills, with a stronger emphasis on their instructional potential rather than solely on examining skills.

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