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Sizing up numbers: Exploring individuals’ numerical magnitude understanding of natural and rational numbers using eye tracking

Boek - Dissertatie

It is a well-established finding that the numerical magnitude of natural numbers (e.g., 250) is better understood than that of rational numbers (e.g., ¼ or 0.25; Vamvakoussi, Christou, & Vosniadou, 2018). Consequently, number type (i.e., natural vs. rational) can be regarded as source of difficulty in numerical magnitude understanding. However, research has shown, within the class of rational numbers, that the numerical magnitude understanding of decimals is better than that of fractions (e.g., Iuculano & Butterworth, 2011). Since number type as a source of difficulty cannot explain these results, we proposed that the structure of the notation system (i.e., the way in which a number is written) might be an additional source of difficulty in numerical magnitude understanding. Specifically, we posited that numerical magnitude understanding is better for notations in which each digit can be related to multiples or powers of 10 (i.e., place-value-based) than for notations in which this is not the case (i.e., non-place-value-based). The main goal of this dissertation was to investigate the effect of these two sources of difficulty in individuals' numerical magnitude understanding. The central task in all our studies was the number line estimation (NLE) task in which participants had to estimate the position of a given target number on a bounded number line, while performance and eye-tracking data were gathered. The first study served as a methodological control study for the other empirical studies of the dissertation and directly compared responding with the mouse cursor and with eye fixations in the NLE task. As aimed for, the well-known findings from previous NLE studies could be replicated when participants responded with their eyes instead of the mouse cursor. These results allowed participants in each of the subsequent studies to respond with their eyes, which enabled us to record eye movement behaviour related to the participants' NLE solution process without capturing eye movement behaviour related to moving the mouse cursor, since moving the mouse cursor involves hand-eye coordination. Studies 2, 3, and 4 investigated the impact of number type and structure of the notation system on the numerical magnitude understanding in adults, adolescents, and children, respectively. These studies showed that fractions (which are rational numbers and non-place-value-based), individuals from each age group have the most difficulty understanding their numerical magnitude. Moreover, when a rational number is place-value-based or a natural number is non-place-value-based, it is less well-understood than a when a natural number is place-value-based. We concluded that not only does number type play a role in numerical magnitude understanding as previous studies have shown (e.g., Vamvakoussi et al., 2018), but also the structure of the notation system. The general discussion focusses on a comparison of the findings of the three age groups as well as the theoretical, methodological, and educational implications from this dissertation.
Jaar van publicatie:2021
Toegankelijkheid:Closed