Can training on one number sense skill be generalized to overall improved number sense?

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1 Can training on one number sense skill be generalized to overall improved number sense? Results from an intervention study with a tablet game. Maertens 1,2, B., De Smedt 3, B., Elen 4, J., & Reynvoet 1,2, B. 1 Faculty of Psychology and Educational Kulak 2 Experimental Psychology, KU Leuven 3 Parenting and Special Education, KU Leuven 4 Instructional Psychology and Technology, KU Leuven

2 number sense analogue representation mental number line: magnitudes are represented as a Gaussian distribution around the corresponding mental magnitude (Dehaene, 1997, 2001). ability to quickly understand, approximate, and manipulate numerical quantities (Dehaene, 2001).

3 number sense symbolic / verbal representation Arabic symbols or number words to represent numerical magnitudes. drie 3

4 number sense symbolic / verbal representation analogue representation drie 3 link between non-symbolic and symbolic representation of numerical magnitudes. symbolic system is mapped onto the pre-existing ANS (Barth, La Mont, Lipton, & Spelke, 2005; Mundy & Gilmore, 2009). a complete new, exact representational system for symbols is developed, next to the ANS (Carey, 2001, 2004; Le Corre & Carey, 2007).

5 number sense non-symbolic representation maths achievement (e.g. Dehaene, 2001; Feigenson, Libertus, & Halberda, 2013; Von Aster & Shalev, 2007) symbolic representation maths achievement (e.g. De Smedt, Noël, Gilmore, & Ansari, 2013; Holloway & Ansari, 2009; Sasanguie, De Smedt, Defever, & Reynvoet, 2012) the link between both non-symbolic and symbolic representation is important! (Gilmore, McCarthy, & Spelke, 2010; Jordan, Glutting, & Ramani, 2010).

6 number sense paradigms commenly used to address magnitude representations: comparison task o distance effect (e.g. Moyer & Landauer, 1967) 4 8 number line estimation task o log to lin shift (e.g. Siegler & Booth, 2004) o percentage absolute error (PAE) better performance with increasing age and development.

7 number sense is a common underlying mechanism responsible for the findings in comparison and number line estimation? a correlation between performance on both tasks (Laski & Siegler, 2007) yes! no correlation between performance on both tasks (Sasanguie & Reynvoet, 2013) no! further research is appropriate stronger evidence for one of both findings will be found by an experimental intervention study investigating the underlying mechanism of both tasks.

8 design of the intervention study comparison training pretest posttest number line estimation training 70 participants (M age = 5,51 y) data collected with computer tablets

9 number sense measures comparison training pretest posttest number line estimation training number knowledge tasks (non-)symbolic comparison tasks (non-)symbolic number line estimation experimental settings (straightforward, identical for everyone)

10 number sense measures number knowledge tasks (non-)symbolic comparison tasks (non-)symbolic number line estimation

11 number sense measures number knowledge tasks (non-)symbolic comparison tasks o ratio 1,2 1,5 2,0 o 48 trials (non-)symbolic number line estimation o distance 1 4 / symbols 1 9 o 32 trials

12 number sense measures number knowledge tasks (non-)symbolic comparison tasks (non-)symbolic number line estimation o number line 0-10 / dot arrays 1-9 o 18 trials o number line 0-10 / symbols 1-9 o 18 trials

13 tablet intervention game comparison training pretest posttest number line estimation training children were randomly allocated to one of both trainings. 3 weeks of training

14 tablet intervention game Dudeman & Sidegirl: Operatie propere wereld! [Dudeman & Sidegirl: Operation clean world] attractive game environment entertaining story adaptive game setting 2 different training conditions

15 tablet intervention game comparison training pretest posttest number line estimation training 14 levels of 24 trials variation based on: o o stimuli (non-symb, symb, mixed) display duration (UR, 1500 ms) o numerosities (1-4, 1-9, 5-18) progress depends on performance

16 tablet intervention game comparison training pretest posttest number line estimation training 18 levels of 18 trials variation based on: o o stimuli (non-symb, symb, mixed) display duration (UR, 1500 ms) o anchor points (9, 1, none) progress depends on performance

17 intervention study with tablet game comparison training pretest posttest number line estimation training is a common underlying mechanism responsible for the findings in comparison and number line estimation? focus on pre- and posttest data gain scores (posttest score minus pretest score)

18 results non-symbolic comparison task mean pre (SD) mean post (SD) mean gain (SD) comp group (11.81) (10.61) 3.59 (11.83) NLE group (8.88) (10.72) 7.72 (13.13) comp cond t(35) = 1.82, p =.077 nle cond t(33) = 3.43, p =.002* n.s. n.s. * gain scores in both cond do not differ sign F(1,68) = 1.92, p =.171 gain scores in NLE cond differ sign from 0

19 results symbolic comparison task mean pre (SD) mean post (SD) mean gain (SD) comp group (16.29) (16.16) 4.34 (15.94) NLE group (17.22) (15.59) 8.82 (13.62) n.s. comp cond t(35) = 1.63, p =.111 nle cond t(33) = 3.78, p =.001* n.s. * gain scores in both cond do not differ sign F(1,68) = 1.59, p =.211 gain scores in NLE cond differ sign from 0

20 results mean pre (SD) mean post (SD) mean gain (SD) comp group (9.15) (7.38) (9.77) NLE group (9.61) (9.18) (11.95) non-symbolic number line estimation task * comp cond t(35) = -1.38, p =.176 nle cond t(33) = -4,20, p <.001* n.s. * gain scores in both cond differ sign F(1,68) = 5.98, p =.017* gain scores in NLE cond differ sign from 0

21 results symbolic number line estimation task mean pre (SD) mean post (SD) mean gain (SD) comp group (8.60) (10.51).86 (10.55) NLE group (10.52) (8.03) (12.76) comp cond t(35) =.49, p =.628 nle cond t(33) = -6.42, p <.001* n.s. * * gain scores in both cond differ sign F(1,68) = 27.87, p =.001* gain scores in NLE cond differ sign from 0

22 conclusion is a common underlying mechanism responsible for the findings in comparison and number line estimation? COMPARISON SKILLS trend in performance for both groups, but only * gain scores for NLE group * transfer effect NLE group no training effect comp group ESTIMATION SKILLS performance especially for NLE group * training effect NLE group no transfer effect comp group

23 conclusion is a common underlying mechanism responsible for the findings in comparison and number line estimation? absence of training and transfer effect in the comparison group suggests that different mechanisms may play a role in both tasks: additional non-numerical processes moderate performance in the NLE NLE is not a pure reflection of the underlying magnitude representation

24 Questions? Thank you for your attention! Bieke Maertens

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