Retrieving information from memory can—under many circumstances—strengthen one’s memory of the retrieved information itself. The strategic use of retrieval to enhance memory and help long-term retention is known as retrieval practice. However, it is unclear whether its effect also holds true in the case of learning mathematics. This research is an exploratory case study, where we test a method— using test-enhanced learning as formative assessment—in a high-needs vocational school. Since the literature on how this method works in classroom settings in mathematics is limited, the purpose of our case study was to get a better view and to lay the groundwork for further experiments. The experimental group and one of the control groups were from the vocational school, while the other control group was from an elite grammar school. On the final test members of the experimental group outscored their schoolmates and reached statistically the same scores as the control group from the elite grammar school. By means of the method, we were able to reduce the performance gap in long-term retention between students from the elite grammar school and students from the urban high-needs school.
It is a common assumption that taking a mathematics course and passing the exam means that one has mastered the course requirements and gained a sufficiently deep understanding of the course material. According to the communication part of the Van Hiele Theory, if someone does not reach the expected entry-level, they won't be able to develop during the course.In our research, we investigated this contradiction in the field of geometry. We examined this phenomenon with mathematics major and pre-service mathematics teacher students during their first geometry course.
Modelling and dressed-up problems play an inevitably unavoidable role in mathematics education. In this study we would like to point out how dangerous is it to dress up mathematical problems. We go back to the principle of De Lange: The problem designer is not only dressing up the problem, but he is the solution designer, as well. We show three examples selected from Hungarian high school textbooks where the intended solution does not solve the problem, because the dressing changes the context and changes the problem itself.
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