Classification of Mathematical Problems Based on Their Relationship to the Real World: Introducing a Six-Level Continuum

Document Type : Editor's Note

Author

Department of Mathematics Education, Faculty of Mathematics and computer, Shahid Bahonar University of Kerman

10.48310/rme.2026.24484.1175

Abstract

Recently, special attention has been paid to contextualized mathematical problems within the country's educational system, as evidenced by their presence in various forms of assessment. Contextualized mathematical problems are those situated in real-world contexts—a concept with a long-standing history in mathematics education research. Throughout history, most mathematics textbooks have included word problems, which are closely related to contextualized problems. The primary aim of this editorial is to present a theoretical "continuum model" that categorizes mathematical problems based on their relationship with the real world. In this continuum, problems range from pure mathematics to word problems, interpretive word problems, PISA-style problems, modeling problems, and finally, authentic modeling problems. The position of each level is determined by five theoretical dimensions: the role of the real world, the degree of mathematization, the need for making assumptions, the interpretation and validation of the solution, and the problem solver's decision-making autonomy. A brief definition and a sample problem are provided for each level to illustrate the continuum's practical application. This concise overview serves to quickly familiarize teachers, researchers, and curriculum designers with the framework's underlying logic and the distinctions between its levels. It is worth noting that the contextualized problems currently introduced in the national education system largely fall into the category of standard word problems, whereas there is a need to shift toward greater real-world connection (i.e., authentic modeling problems).

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