Purpose - This study explores variation theory-based interventions' contribution to enhancing preschoolers' subitizing abilities during iterative lessons. Results are presented according to low, middle and high achievers, focused on those with prominent challenges. Design/methodology/approach - In total 68 Swedish preschoolers participated. They were randomly assigned to one of the intervention/control groups: 23 mixed design, 24 variation theory design and 21 controls. Data from 59 pupils were analyzed. A learning study with three lesson designs for each intervention group was used in autumn 2022 and spring 2023, respectively. The mixed design met ordinary textbook material and variation theory (VT) group instructions designed by VT during autumn, whereas all met instructions designed by VT in spring. Each group was divided into two subgroups. The controls followed business-as- usual math teaching. Two tests assessed pupils' results before and after the interventions. Findings - All groups showed significant improvements between pre- and post-tests. Pupils in the mixed and VT groups developed more knowledge than the controls. The low-achieving group developed the most. The VT group exhibited a more complex pattern of variation and a greater increase than the mixed group. The intervention groups showed a greater improvement in both tests' results than the controls. Originality/value - There is agreement on the importance of subitizing abilities as a predictor of future mathematical development; however, lesson design and research on pupils' development regarding lessons offered are limited.

The focus in this study is methods for screening young children’s, subitizing abilities. Subitize is in this project defined as identifying the number of things in a setsimply by quickly looking at them and without counting them one by one. The aim of the study is to compare two different screening instruments for identifyingchildren’s subitizing abilities, individually and in groups of children, in a Swedish preschool class context. In total, data from 44 children is collected, who havetaken one group test (Ability to Quickly See Quantity - AQSQ), and an individual test (Number Set Test - NST). The research question was if the children’sresults correlate with each other, or not, no matter of test conditions (individual/group). The results show a moderate to strong positive correlation, usingPearson and T-test Pair Samples Correlation (r=.559 p=

It has been argued that the Mainland Scandinavian languages differ from English in that they permit filler-gap dependencies into adjunct clauses (Anward, 1982; Hagström, 1976), which are standardly treated as strong islands for extraction(Huang, 1982). A closer look suggests that extraction from adjunct clauses is also possible in English, provided that a coherence relation (e.g., a causal, as opposed to a purely temporal relation) holds between the events referred to by the matrix and the adjunct clause (Truswell, 2011). The same restriction appears to hold in Swedish. However, English contrasts with Swedish in that it has been argued to disallow extraction from finite adjuncts. Observations like these raise important questions regarding filler-gap association in island domains and cross-linguistic variation. First, if coherence matters for extraction from adjunct clauses, then adjuncts appear to contrast with other island domains, in which filler-gap association has been claimed to be suspended, such as in relative clause islands in English (e.g.,Traxler & Pickering, 1996). Second, if finiteness is a potential locus of variation, then this must be explained and related to other evidence of cross-linguistic and inter-individual variation (Kush et al., 2017; Phillips, 2013; Sprouse et al., 2016). 

We conducted two acceptability judgment experiments, one for English and one for Swedish, to investigate the hypothesis that semantic coherence facilitates extraction in both languages, whereas finiteness degrades extraction, but only in English. In our materials, we first manipulated the telicity of the matrix verb such that sentential coherence was either augmented(coherent, 1a and 2a) or impeded(non-coherent, 1band 2b), and then manipulated the finiteness of the adjunct clause ([finite/non-finite] in 1and 2). Long-distance dependencies were tested in the form of question formation in English (1) and topicalization in Swedish (2).

Forty sets of items were created and distributed across four presentation lists, interspersed with 80distractor sentences. Fifty-seven Swedish and 72 English mono-lingual, native speakers rated the sentences using a 7-point Likert scale(1 = “completely unacceptable” to 7 = “completely acceptable”), as presented using Google forms.The z-score adjusted responses for each condition in the two languages are presented in Figure1 and 2. Linear mixed models were used to analyze normalized z-score responses. As expected, coherence significantly improved extraction for both Swedish (β= 0.191, t = 4.792, p<.001) and English (β= 0.121, t = 3.853, p< .001). Furthermore, a significant finiteness by coherence interaction was found for English, in which finiteness was seen to degrade coherent, but not non-coherent structures(β= -0.050, t = -2.159, p< .05). Swedish showed no effect of finiteness or finiteness by coherence interaction.

Our results demonstrate that coherence improves extraction from adjuncts in both Swedish and English, which suggests that filler-gap association is not suspended in adjunct clauses. Furthermore, we show that finiteness reduces the acceptability of coherent structures, but only in English, thus pointing to one case of cross-linguistic variation.One possible explanation for this variation is that finite and non-finite adjuncts in English differ in terms of syntactic complexity: Non-finite after-adjuncts in English have a participial structure and can be assumed to lack a contentful CP-domain. Extraction from such structures thus requires fewer intermediate steps in successive-cyclic movement and a corresponding lower processing cost than extraction from their finite counterparts(see Wurmbrand, to appear, for a similar account for quantifier raising in English). In contrast, Swedish non-finite after-adjuncts involve a complementizer and an infinitive and can be assumed to be similar in structural size to their finite counterparts, requiring equally many movement steps and hence similar processing costs for extraction.

1) 

a. coherent | non-finite/finite

Which beer did he almost stumble [after chugging / after he chugged]?

b. non-coherent | non-finite/finite

Which beer did he stroll a little [after chugging / after he chugged]?

(2) 

a. coherent | non-finite/finite

Den medicinen däckade han alltid [efter att ha tagit / efter att han hade tagit].

that medicine fell-asleep he always after to have taken / after that he had taken

‘He always fell asleep {after taking/after he took} that medicine.’

b. non-coherent | non-finite/finite

Den medicinen stannade han lite [efter att ha tagit / efter att han hade tagit].

that medicine stayed he a little after to have taken / after that he had taken

‘He stayed a little {after taking/after he took} that medicine.’

Figure 1. z-adjusted ratings for Exp. 1 (English) 

Figure 2. z-adjusted ratings for Exp. 2 (Swedish)

References

Anward, J. (1982). Basic Swedish. In E. Engdahl & E. Ejerhed (Eds.), Readings on unbounded dependencies in Scandinavian languages (pp. 47-75). Stockholm: Almqvist & Wiksell.

Hagström, B. (1976). Om satsflätans förutsättningar. En skiss. In L. Svensson, A. M. Wieselgren, & Å. Hansson (Eds.), Nordiska studier i filologi och lingvistik. Festskrift tillägnad Gösta Holm på 60-årsdagen den 8 juli 1976 (pp. 138–150). Lund: Studentlitteratur.

Huang, J. C.-T. (1982). Logical Relations in Chinese and the Theory of Grammar. PhD. Dissertation, MIT, Cambridge, Mass.

Kush, D., Lohndal, T., & Sprouse, J. (2017). Investigating Variation in Island Effects: A Case Study of Norwegian Wh-Extraction. Natural Language & Linguistic Theory. doi:https://doi.org/10.1007/s11049-017-9390-z

Phillips, C. (2013). On the Nature of Island Constraints. II: Language learning and innateness. In J. Sprouse & N. Hornstein (Eds.), Experimental syntax and island effects (pp. 132-157).Cambridge: Cambridge University Press.

Sprouse, J., Caponigro, I., Greco, C., & Cecchetto, C. (2016). Experimental syntax and the variation of island effects in English and Italian. Natural Language & Linguistic Theory, 34, 307–344.

Traxler, M. J., & Pickering, M. J. (1996). Plausibility and the processing of unbounded dependencies: An eye-tracking study. Journal of Memory and Language, 35(3), 454-475.

Truswell, R. (2011). Events, phrases and questions. Oxford: Oxford University Press. 

Wurmbrand, S. (To appear). The cost of raising quantifiers. To appear in Glossa.

The current study compares controlled acceptability judgments for Swedish relative clause extractions to extractions from <i>that</i>-clauses and extractions from non-restrictive relative clauses. It also compares each structure in both extracted and non-extracted form. The reported possibility of relative clause extraction in Swedish (and the other Mainland Scandinavian languages) has long presented a challenge to universal theories of constraints on extraction because the phenomenon is cross- linguistically very rare. In the off-line judgment data presented here, relative clause extractions are shown to pattern with extractions that are assumed to involve an island-like violation (non-restrictive relative clause extraction), thus contrasting with informal judgments reported in the literature. The data also appear to present a counterpoint to the conclusion reached in Tutunjian, Heinat, Klingvall and Wiklund (2017) from on-line eye-tracking measures, regarding the representational status of this structure as being more in line with that of a licit extraction. Potential explanations for the obtained patterns of the result are discussed, presenting avenues for further investigations.

Relative clauses are considered strong islands for extraction across languages. Swedish comprises a well-known exception, allegedly allowing extraction from relative clauses (RCE), raising the possibility that island constraints may be subject to "deep variation" between languages. One alternative is that such exceptions are only illusory and represent "surface variation" attributable to independently motivated syntactic properties. Yet, to date, no surface account has proven tenable for Swedish RCEs. The present study uses eyetracking while reading to test whether the apparent acceptability of Swedish RCEs has any processing correlates at the point of filler integration compared to uncontroversial strong island violations. Experiment 1 tests RCE against licit that-clause extraction (TCE), illicit extraction from a non-restrictive RC island (NRCE), and an intransitive control. For this, RCE was found to pattern similarly to TCE at the point of integration in early measures, but between TCE and NRCE in total durations. Experiment 2 uses RCE and extraction from a subject NP island (SRCE) to test the hypothesis that only non-islands will show effects of implausible filler-verb dependencies. RCE showed sensitivity to the plausibility manipulation across measures at the first potential point of filler integration, whereas such effec.ts were limited to late measures for SRCE. In addition, structural facilitation was seen across measures for RCE relative to SRCE. We propose that our results are compatible with RCEs being licit weak island extractions in Swedish, and that the overall picture speaks in favor of a surface rather than a deep variation approach to the lack of island effects in Swedish RCEs

Swedish relative clause (RC) extractions are allegedly acceptable despite a universal constraint on NP extraction (Erteschik-Shir, 1973). In two eye-tracking experiments, we investigated the processing of RC extractions in Swedish by manipulating the plausibility of NP fillers relative to RC predicates. A similar study on English RCs (Traxler & Pickering, 1996) found plausibility effects in English for non-island but not island conditions, indicating a lack of integration in islands.

Experiment 1 tested for plausibility effects in extractions from RCs (alleged non-islands), that-clauses (non-islands), and non-restrictive RCs (islands; Engdahl, 1997). We expected that only the first two would show sensitivity to plausibility. Surprisingly, we found effects, and thus integration for all three structures. Experiment 2 tested for plausibility effects in RCs embedded in subjects (islands) vs. objects (non-islands). The RC verbs (optionally transitive) provided a potential gap and were hypothesized to allow for integration in the object condition only. A following clause provided the real gap. Again, we found plausibility effects for both conditions at the RC verb, suggesting integration. Our study calls into question the correspondence between acceptability- and processing-based metrics of Swedish islandhood and raises the possibility of cross-linguistic variation with regard to the processing of island violations.