In mathematics, sciences and economics, understanding and working with graphs are important skills. However, developing these skills has been shown to be a challenge in secondary and higher education as it involves high order thinking processes such as analysis, reflection and creativity. In this study, we present Interactive Virtual Math, a tool that supports the learning of a specific kind of graphs: dynamic graphs which represent the relation between at least two quantities that covary. The tool supports learners in visualizing abstract relations through enabling them to draw, move and modify graphs, and by combining graphs with other representations, especially interactive animations and textual explanations. This paper reports a design experiment about students’ learning graphs with this tool. Results show that students with difficulty in generating acceptable graphs improve their ability while working with the tool.
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An essential condition to use mathematics to solve problems is the ability to recognize, imagine and represent relations between quantities. In particular, covariational reasoning has been shown to be very challenging for students at all levels. The aim of the project Interactive Virtual Math (IVM) is to develop a visualization tool that supports students’ learning of covariation graphs. In this paper we present the initial development of the tool and we discuss its main features based on the results of one preliminary study and one exploratory study. The results suggest that the tool has potential to help students to engage in covariational reasoning by affording construction and explanation of different representations and comparison, relation and generalization of these ones. The results also point to the importance of developing tools that elicit and build upon students' self-productions
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The current study investigates the effects of the school lockdowns during school years 2019–2020 and 2020–2021 on the achievement scores of primary school students during the COVID-19 pandemic. We analyzed scores for spelling, reading fluency (i.e., decoding speed), reading comprehension, and mathematics from standardized student tracking systems for 5125 students from 26 primary schools in the urban region of The Hague, the Netherlands. Results showed that students in grades 1 through 3 had significant learning delays after the first lockdown. However, results after the second lockdown showed that most students were able to catch up, compared to students from corresponding grades of cohorts before COVID-19. The magnitude of these positive effects was mostly close to the negative effect of the first lockdown. Apparently, during the second lockdown, schools seemed better prepared and able to deliver more effective home schooling and online instruction. The hypothesis that students’ learning from a low SES home environment will suffer most from the school lockdowns could only partly be confirmed. SES effects at the individual level tended to be mitigated by negative effects of SES at the school level, making SES-related differences between schools less profound. The findings of this study offer a broader perspective to evaluate the effects of long-term school closures. Implications for educational practice and issues of inequality between students are discussed.
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