Research on solving mathematical word problems suggests that students may perform better on problems with a close to real-life representation of the problem situation than on word problems. In this study we pursued real-life representation by a mainly depictive representation of the problem situation, mostly by photographs. The prediction that students perform better on problems with a depictive representation of the problem situation than on comparable word problems was tested in a randomised controlled trial with 31,842 students, aged 10–20 years, from primary and secondary education. The conclusion was that students scored significantly higher on problems with a depictive representation of the problem situation, but with a very small effect size of Cohen’s d = 0.09. The results of this research are likely to be relevant for evaluations of mathematics education where word problems are used to evaluate the mathematical capacity of students.
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The aim of this study is to contribute to the body of knowledge on the use of contextual mathematical problems. Word problems are a predominant genre in mathematics classrooms in assessing students’ ability to solve problems from everyday life. Research on word problems, however, reveals a range of difficulties in their use in mathematics education. In our research we took an alternative approach: we designed image-rich numeracy problems as alternatives for word problems. A set of word problems was modified by systematically replacing the descriptive representation of the problem situation by a more depictive representation and an instrument was designed to measure the effect of this modification on students’ performance. The instrument can measure the effect of this alternative approach in a randomized controlled trial. In order to use the instrument at scale, we made this instrument also usable as a diagnostic test for an upcoming nationwide examination on numeracy. In this article we explain and discuss the design of the instrument and the validation of its intended uses.
Designing non-routine mathematical problems is a challenging task, even for excellently performing prospective teachers in primary teacher education, especially when these non-routine problems concern knowledge at the mathematical horizon (HCK). In an experimental setting these prospective teachers were challenged to design non-routine HCK-problems. Acquiring HCK, the perspective of the problem solver in terms of heuristics, a cyclic design process, experts struggling themselves in designing problems were the most important effective characteristics of the learning environment that rise from this explorative study. In Stylianides, G. J., & Hino, K. (Red.). Research Advances in the Mathematical Education of Pre-service Elementary Teachers: An International Perspective. Springer, New York.
