Analysis of real-world math problems: Theoretical model and classroom applications

Abstract

The Russian education standards stress the importance of real- life applications of mathematics. However, the educational outcome standards do not provide a clear idea of how a math teacher should organize their syllabus to develop relevant skills in students. As long as there is no universal definition of a real-world math problem, it is rather difficult to qualify the problems that teachers use in the classroom. We analyzed algebra problems that teachers give to secondary school students. Using three parameters, 83 word problems were coded: situational relevance, mathematical modeling, and non-triviality. We carried out a cluster analysis to identify typical categories of mathematical problems. As a result, we determined three types of problems differing in the abovementioned characteristics. Only one cluster appeared to feature all three characteristics typical of real-world problems. Therefore, a portion of the tasks that teachers give students as real-world fail to qualify as such according to the proposed theoretical model.