Ankerpuntstrategieën in de getallenlijntaak

During the past 15 years, the number line estimation task has gained a lot of research attention. In this task, participants are asked to estimate the spatial position of a target number on an empty number line with labelled endpoints (e.g., 0 and 1,000). Developmental studies have shown age-related improvements in number line estimation performance which are traditionally explained by a shift from a logarithmic mental magnitude representation towards a linear one. Recently, however, some authors have argued that these developmental changes might stem from improvements in the use of strategies based on benchmarks. More specifically, children’s strategy use seems to gradually develop from relying on one external benchmark at the origin for estimating all target numbers, to two external benchmarks i.e., one at the origin to estimate numbers in the lower range of the number line and one at the endpoint to position numbers in the upper range of the number line. Later on, children are able to generate a third, internal benchmark at the midpoint for locating numbers in the middle range of the number line. This doctoral research project aims at: (a) providing a systematic picture of children's and adults’ benchmark-based strategy use and its development, (b) investigating whether the degree of sophistication in this benchmark-based strategy use is positively related to number line estimation performance and to mathematics achievement, and (c) examining the extent to which certain task characteristics in the number line estimation task affect the use of these benchmark-based estimation strategies, and, correspondingly, estimation performance. In Chapter 1 of this dissertation, we present a general introduction in which we provide an in-depth description of the number line estimation task and its variants, followed by a discussion of three theoretical accounts that try to explain the observed developmental changes in number line estimation performance (i.e., the log-to-lin shift, the two-segmented linear, and the proportional judgment account). Next, we provide an overview of the different sources of evidence in favour of benchmark-based strategy use in number line estimation. We conclude this chapter with the research objectives and the outline of the dissertation. In Chapter 2, we report a first study in which we investigated, by means of trial-by-trial verbal strategy reports, whether the provision of additional unlabelled benchmark support on the number line stimulates second graders’ benchmark-based strategy use and, correspondingly, improves their estimation performance. Results indicated that an additional external benchmark at the midpoint had a beneficial effect on children’s midpoint-based strategy use and estimation performance while three additional external benchmarks (at 25, 50, and 75%) had a detrimental effect. Furthermore, a more frequent use of benchmark-based strategies was positively related to more accurate estimates and to higher mathematics achievement scores. In Chapter 3 and 4, we present two closely related studies in which we examined whether the development of benchmark-based strategy use in number line estimation goes beyond the creation of an internal benchmark at the midpoint. More specifically, we examined the extent to which adults (Chapter 3) and third and fifth grade children (Chapter 4) needed additional benchmark support to apply quartile-based strategies by varying the number of additional unlabelled benchmarks on the number line. Results indicated that the spontaneous application (i.e., without any external benchmark support) of quartile-based strategies increased with age. Moreover, with an increasing number of external benchmarks on the number line, adults were able to further refine their benchmark-based strategy use by applying octile-based strategies and also their estimation performance improved. Similarly, fifth graders’ quartile-based strategy use and estimation performance improved with an increasing number of external benchmarks on the number line. In contrast to adults and fifth graders, third graders benefited less from the external benchmark support as they resorted more to idiosyncratic strategies as the number of benchmarks on the number line increased. This was especially true when three additional unlabelled benchmarks at 25, 50, and 75% of the number line were provided. As a result, third graders’ use of quartile-based strategies and estimation accuracy did not improve as the number of external benchmarks increased. Results further indicated that the accuracy of participants’ estimates was positively associated with the number of benchmark-based strategies into their repertoire and with the frequency of use of benchmark-based strategies. Similarly, having a broader strategy repertoire and a more frequent use of benchmark-based strategies correlated positively with children’s mathematics achievement scores. After revealing in Chapter 4 that the provision of additional unlabelled benchmarks at 25, 50, and 75% of the number line only positively affected fifth graders' and not third graders’ number line estimation performance (nor second graders’ estimation performance, as explained in Chapter 2), Chapter 5 reports a study that examined whether providing additional labelled, in contrast to unlabelled, benchmarks at 25, 50, and 75% of the number line would positively affect third and sixth graders’ quartile-based strategy use and estimation accuracy. Findings indicated that labelling the benchmarks at 25, 50, and 75% of the number line enhanced children’s quartile-based strategy use and estimation performance. Specifically, third graders greatly benefited from the provision of labelled benchmark support while labelling the benchmarks had no additional beneficial effect on sixth graders’ quartile-based strategy use and estimation performance. Additionally, having a broader strategy repertoire and applying quartile-based strategies more frequently was positively related to higher estimation accuracy and to higher mathematics achievement scores. In Chapter 6, we report a final study in which we varied the nature of the endpoints in order to disrupt fifth graders’ and adults’ ability to determine internal benchmarks and examined the extent to which this affected their number line estimation performance. More specifically, we compared fifth graders’ and adults' strategy use and number line estimation performance in a typical 0-1,000 and an atypical 367-1,367 number line estimation task. We reasoned that the round endpoint values typically used in the number line estimation task (e.g., 0 and 1,000) might be of central importance when determining internal benchmarks on the number line. Results indicated that hindering the application of benchmark-based strategies negatively affects children’s and adults’ number line estimation performance. The dissertation ends with Chapter 7, in which we provide the main conclusions that can be drawn from the set of studies that were conducted. Next, we discuss some broader theoretical implications of our findings. Thereafter, we address some methodological considerations. Finally, we propose some suggestions for further research and end with a few educational implications.status: publishe