Mathematical modeling is a cyclical process in which mathematics is used to represent, explore, and better understand real-world situations by mathematizing a problem and validating the results. Unlike traditional word problems, modeling tasks require learners to make assumptions, define quantities, apply mathematics, interpret results, and revise solutions within authentic contexts. Mathematical modeling is increasingly recognized as essential in mathematics education, highlighted in standards such as the Common Core State Standards for Mathematics through mathematical practice 4 (MP4): model with mathematics. This entry explores the evolving landscape of mathematical modeling education. First, it reviews the diverse conceptions of modeling and the various frameworks used to describe the modeling process, including distinctions between holistic and atomistic approaches. Second, it examines the current state of research, including the documented benefits of modeling for student engagement and access, as well as the challenges teachers face in enacting modeling tasks. Finally, the entry discusses implications for future research and practice, emphasizing the need for targeted teacher preparation and continued theoretical refinement to better support the integration of modeling into mathematics instruction.
Mathematical modeling, often shortened to modeling, has become a prominent focus in contemporary mathematics education. At its core, modeling involves using mathematics as a tool to interpret and analyze real-world phenomena, moving well beyond the scope of conventional textbook word problems. Modeling tasks invite learners to grapple with authentic situations by identifying assumptions, specifying relevant quantities, applying mathematical tools, and refining their solutions through interpretation and revision. The importance of this practice is underscored in documents such as the
Common Core State Standards for Mathematics that position “model with mathematics” (MP4) as a central mathematical practice [
1].
This entry examines the growing body of work on mathematical modeling education, with particular attention to developments in Western contexts. It begins by tracing different ways modeling has been conceptualized and the range of frameworks that describe how the process unfolds, from holistic cycles to more fine-grained step-oriented perspectives. The discussion then turns to empirical research, highlighting evidence of how modeling can support student engagement and equitable access to mathematics, as well as the persistent challenges teachers encounter when implementing modeling tasks. The entry concludes with implications for future directions, calling for more robust teacher preparation and theoretical development to strengthen the role of modeling in mathematics instruction.
While this entry primarily attends to perspectives from the West, it is important to acknowledge that research and practice in mathematical modeling education also has rich traditions in Eastern contexts such as China and Japan. Across both regions, modeling is valued for its potential to connect mathematics with real-world problems, develop problem-solving competencies, and prepare students for future science, technology, engineering, and mathematics (STEM) endeavors. Yet differences emerge in emphasis and implementation. In the West, modeling is often framed as an open-ended process of inquiry that supports creativity, collaboration, and sense-making, while in the East it is more commonly positioned as structured application, closely tied to canonical mathematics, competitive contexts, or national curricular goals. These contrasts reflect broader cultural and educational traditions, but they also share a commitment to advancing students’ mathematical thinking. A fuller exploration of Eastern perspectives, however, lies beyond the scope of this entry.
This entry is adapted from the peer-reviewed paper 10.3390/encyclopedia5030138
