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eneral and specific thinking skills and schooling: Preparinghe mind to new learning
ari-Pauliina Vainikainen ∗, Jarkko Hautamäki, Risto Hotulainen, Sirkkuupiainen
niversity of Helsinki, Department of Teacher Education, Centre for Educational Assessment, Finland
r t i c l e i n f o
rticle history:eceived 3 October 2014eceived in revised form 17 April 2015ccepted 23 April 2015vailable online xxx
eywords:hinking skillsognitive developmentormal thinkinglass-effect on thinking skillsested multilevel factorial models
a b s t r a c t
Enhancing thinking skills is an important goal of formal education. It is often embeddedin national curricula, which, however, are seldom based on theoretical understanding ofthe structure of the skills or how they should be taught. Accordingly, there is only limitedinformation available about schools’ success in this important task. The present study hastwo goals: firstly, to find support for the theoretical assumption of the nested structure ofthinking skills with a core factor of formal thinking and specialised structures for verbal andquantitative reasoning; and secondly, to test the differentiated development of these skillsin school. This was done by studying class-level variation of sixth graders’ thinking skills ina multilevel factor analysis when initial between-class differences at grade three had beentaken into account. The data (N ≈ 1543) were drawn from a learning to learn panel study inone of the major cities of Finland. The results showed that the core factor for formal thinkingcould be identified at both the individual and the class level, and that at the individual levelthere were statistically significant residual factors for verbal and quantitative reasoning.Initial between-class differences explained only a third of the variance of class-level formalthinking. This was interpreted to indicate the effect of schooling.
. General and specific thinking skills and schooling
Discussions of current working environments and of the skills necessary for work call for a new approach towardsearning. In the continuously changing work environments people need to make coherent decisions with access to unlim-ted information in a limited time, to think creatively, to adjust their actions and attitudes according to possible risks androblems, to learn quickly, and to trust their problem solving skills (Halpern, 2008). Hence, educational policy makersorld-wide have lately become interested in concepts, such as learning to learn, thinking skills, and 21st century skills
Recommendation 2006/962/EC of the European Parliament and of the Council, 2006; Rocard et al., 2007; Organisation forconomic Co-operation and Development (OECD), 2013a).
Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparingthe mind to new learning. Thinking Skills and Creativity (2015), http://dx.doi.org/10.1016/j.tsc.2015.04.006
The common core for the new or newly introduced concepts is that they all tap underlying cognitive competences andon-curricular domain-general skills that regard an individual’s overall learning preparedness. Depending on the framework,hese skills are referred to as cross-curricular, learning to learn (LTL), transversal, or 21st century skills (Deakin Crick,tringer, & Ren, 2014). Regardless of the term, these definitions emphasise the importance of developing thinking skills as
∗ Corresponding author at: Centre for Educational Assessment, University of Helsinki, P.O. Box 9, 00014 Helsinki, Finland. Tel.: +358 503465050.E-mail address: [email protected] (M.-P. Vainikainen).
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a basis for future learning from core processes and specialised structural systems to critical thinking (Demetriou, 2014).Enhancing thinking skills have been considered as a central goal of education already for decades (Resnick, 1987), but itis still quite rare that educational systems promote such development deliberately (an interesting exception is Hungary,where new frameworks in reading, mathematics and science are all based on ideas of general and specific thinking as anexplicit part, see Csapó & Szapo, 2014). Even though thinking skills are expected to improve when pupils proceed throughtheir formal schooling, strategies for evaluating educational outcomes and effectiveness of schooling mainly centre on themeasurement of subject-specific knowledge and skills or at best their application. In Finland, the assessment of generalcognitive competences and the affective factors which support their effective use, together labelled LTL, were defined as oneof the measurable outcomes of education already in the 1990s (Hautamäki et al., 2002; National Board of Education, 1999).Since then, they have been used as one indicator for monitoring the effectiveness of education.
LTL is defined as the cognitive competence and willingness to adopt to novel tasks and new learning (Hautamäki et al.,2002; Hautamäki, Hautamäki, & Kupiainen, 2010). In empirical assessment of LTL, the assessment tasks are seen to activatea complex of interrelated competences and beliefs, leading to an attempt to solve the tasks. Competence refers to theapplication of general cognitive schemas and the already acquired knowledge or scholastic achievement to new situations.Beliefs refer to anticipated emotions which, once activated, lead to commitment or refusal. Defined this way, LTL competencesare related to intelligence, understood in a Piagetian framework as the active use of formal operational schemas. From thisfollows the hypothesis that the cognitive LTL tasks measure general thinking skills (see Adey & Csapó, 2014). LTL as aneducational goal is an explicit part of the EU definition of key competences and of the 21st century skills in the global context.However, neither of the two presents an empirically tested model to measure the competences. The Finnish LTL Frameworkand scales are one of few attempts to offer a tool to assess both the cognitive and the willingness- or commitment-relatedcomponents of LTL (Deakin Crick et al., 2014).
The aim of the present study is on the one hand to test the theoretical assumption that the thinking skills measured withthe Finnish LTL construct have a nested structure (cf., Härnqvist, Gustafsson, Muthén, & Nelson, 1994) with formal operationalthinking (see Shayer, 1979) at its core and with specialised residual factors for verbal proportional and quantitative reasoning(see Demetriou, Spanoudis, & Mouyi, 2011). On the other hand, the aim is to evaluate whether schooling has an effect onthese skills in the Finnish context, where thinking skills are defined as a goal embedded in all school subjects in the nationalcore curriculum (National Board of Education, 2004) but details regarding their teaching are missing.
1.1. Development of thinking
Developmental psychologists have long studied the development of thinking. The theory of cognitive development pro-posed by Demetriou et al. (2011) and Demetriou (2014) involves both central and general mechanisms, and specialisedcapacity systems for different domains of knowledge or relations. The spatial, verbal, quantitative, categorical, causal, andsocial reasoning systems have been identified by methods from different theoretical origins, and they are considered asautonomous domains of understanding, thinking, and problem solving. A critical feature of this theory is that the develop-ment of the specialised systems is both limited by and is the route into the development of the general intellectual processorand its executive control (self-regulation). That is, the general factor is also amenable to educational influence. There is evi-dence from other theoretical backgrounds that high performance on a general level facilitates the acquisition of new domainspecific skills especially on the early phases of the learning process (Francis, Fletcher, Maxwell, & Satz, 1989; Gustafsson,2008). But when learning is based on already acquired skills, the gains are more likely to depend on earlier domain-specificknowledge. Accordingly, the improvements are likely to be domain-specific. All this means that good subject-specific teach-ing makes the connection between specific knowledge, e.g. the use of specific concepts, with the general use of concepts,rules and their application. This gradually leads to gains also in the functioning of the general mechanisms (Demetriou et al.,2011; Gustafsson, 2008).
One of the most studied constructs in the development of general thinking skills and the functioning of the generalmechanisms (cf., Demetriou et al., 2011) is the control of variables strategy (CV), which is also often referred to as thevary-one-thing-at-a-time (VOTAT) strategy. It was first introduced by Inhelder and Piaget (1958) as part of the formaloperational thinking construct (see Shayer, 1979). Regardless of criticisms concerning explicitness of Inhelder and Piaget’swork it still provides overarching illustration how adolescents’ cognitive competences develop during the second decade oftheir life (Kuhn, 2008). The emergence of formal operations at around age 12–15 involves reasoning based on hypotheses,independent of concrete objects, which means “the real is subordinated to the realm of the possible” (Piaget, 2006). Agevariation is seen to be ingrained in the differing intellectual stimuli in children’s environments and to depend on personalinterests and experiences. However, formal thinking is not necessarily applied all the time or across all domains (Piaget, 1972,2006). Even if individual differences in formal operational thinking are related to intelligence, verbal ability and executivefunctions, these are considered to be partly culturally bound (Emick & Welsh, 2005). It has been shown that that the controlof variables strategy is central to science and an essential skill attainable and trainable by the time children are cognitivelyadvancing from a concrete toward a formal operational level (Neimark, 1975; Shayer, 2008).
Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparingthe mind to new learning. Thinking Skills and Creativity (2015), http://dx.doi.org/10.1016/j.tsc.2015.04.006
In this study, we use the CV-schema as the apex of our interpretation of the cognitive component of learning to learn.In psychometric studies, the apex is general (g) or fluid (gf) intelligence (Carroll, 1989; Gustafsson, 2008), but it seemsthat there are also other possibilities for the apex due to the law of positive correlations amongst reliable cognitive tasks.In the psychologically oriented approach to education, g is mainly used as an explanatory factor (Deary, Strand, Smith, &
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ernandes, 2007; Rohde & Thomson, 2007; Sternberg, 1999). General cognition is expressed or invested in various waysn different learning situations and school achievements (Gustafsson & Carlstedt, 2006). But the developmentally orientednterpretation of general cognition as an expression of growth of logical thinking opens up an option for intervention (Adey,sapó, Demetriou, Hautamäki, & Shayer, 2007; Shayer, 2008). This integrated understanding, educating the developing mind,
s well represented in the work of Demetriou (2014) and Demetriou et al. (2011).According to Demetriou’s theory, we expect the thinking skills measured within the Finnish LTL context to be structured
n a way that in addition to the core of formal thinking, residual factors of all the specialised reasoning systems are to beound. In practice, only the verbal and quantitative factors can be identified here as the sixth grade version of the Finnish LTLcale used in the present study does not have sufficient number of items on the areas of spatial, causal or social reasoning.ven though ninth grade data with a larger scope of cognitive tasks would have been available, 12-year-olds were selecteds the target group of the present study due to the sensitiveness of this age group in regard to both the development oformal thinking (Piaget, 2006), and to the enhancement of thinking skills in general (Csapó, 1997).
.2. Enhancing the development of thinking skills
Many researchers see that induction processes, such as performing mental comparisons form a basis for knowledge-uilding. This, in turn, has been shown to have a transfer effect on learning in school subjects (Adey & Shayer, 1994; Adhami
Yates 2008; Bloom, Engelhart, Furst, Hill, & Krathwohl, 1956; Klauer & Phye, 2008; Tomic & Klauer, 1996). Thus, byromoting the development of thinking skills, e.g. how to put things in order, classify or perform mental rotations, weimultaneously enhance fundamental learning skills, which have transfer effects across the school curriculum. This alsoacilitates the attainment of higher order thinking skills (Anderson & Krathwohl, 2001; Shayer, 2008).
It could be argued that there are two main ways to promote thinking skills in school. The first approach can be calledxplicit with specific educational programmes, which are expected to promote thinking skills if the programme guidelinesre appropriately followed. These programmes can be further divided into two categories according to how the trainingf thinking skills is arranged (McGuinness & Nisbett, 1991). The first category, the content-based method, consists of pro-rammes which ensure that thinking skills are taught within conventional curriculum areas (e.g. mathematics or science).
well-studied programme representing this method is the Cognitive Acceleration (CA) Programme (Adey & Shayer, 1994)ased on Piagetian cognitive stages. Programmes belonging to the second category share the idea that thinking skills cane taught as such (e.g. Feuerstein, Rand, Hoffman, & Miller, 1980; Klauer, 1989; Klauer, 1991). The promotion of generickills has been criticised for developing thinking skills a-contextually and inhibiting the transfer of the developed skills toew contexts. Yet, programmes based on Klauer’s theory have recently shown strong evidence for transfer effect on bothuid intelligence and various academic subjects (Klauer & Phye, 2008; Molnár, 2011; Molnár, Greiff, & Csapó, 2013). Regard-
ess of strong evidence by now that specific programs can promote 21st century skills, their large-scale use has not beenidely spread to the educational field due to both short-sighted educational policy-decision making and limited resources
f stakeholders (Pellegrino & Hilton, 2012).The second approach can be described as an implicit one. In this approach, curricula do not per se emphasise systematic
ultivation of thinking skills but such development is expected to result as a side-effect (Kuhn, 2005; Molnár, 2011). Especiallyn the Nordic countries, approaches, practices, and initiatives towards enhancing thinking skills are very limited. For example,n the Finnish national core curriculum, thinking skills are regarded to belong into each conventional curriculum area. Thus,t is expected that the implemented curriculum with annually more demanding content complexity (spiral curriculum;f. Bruner, 1960) raises implicitly the level of thinking skills, as well. However, research has shown that the promotionf thinking skills needs to be either integrated purposefully in the curriculum or they have to be explicitly taught to gainffective results (Adey & Shayer, 1994; Kuhn, 2005; Nisbett, 1993).
As in Finland explicit methods for teaching general thinking skills are not pointed out in the core curriculum and the samelass teacher typically teaches their class from third to sixth grade, the Finnish school system allows us to study teacher- andlass-related variation in the development of general thinking skills. The expected class-level variation in the developmentf thinking skills could provide evidence for that even implicit teaching of thinking skills can be beneficial. It can also givestimates about how much or alternatively how little teachers can influence the developing general thinking skills.
.3. Educational assessment and thinking skills
To assesses the effectiveness of formal schooling also with regard to 21st century skills, programmes have been launchedoth internationally, such as the OECD’s Programme for International Student Assessment (PISA, OECD, 2013a) or the Euro-ean Commission’s pilot study for learning to learn (Kupiainen, Hautamäki, & Rantanen, 2008), and nationally (e.g. the FinnishTL assessments, see Vainikainen, 2014). In PISA, which mainly measure subject matter-related knowledge and skills andheir application, Finnish students have recurrently performed at a high level whereas between-school variation has beenow, indicating the Finnish education system’s high level of equity (OECD, 2013b). The same applied to creative problem
Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparingthe mind to new learning. Thinking Skills and Creativity (2015), http://dx.doi.org/10.1016/j.tsc.2015.04.006
olving measured as a 21st century skill in PISA 2012 (OECD, 2014). However, recent studies have shown that differencesetween classes in the same school can be relatively large in Finland (ICCs ranging from 10 to 20% depending on measuredompetence; Hautamäki & Kupiainen, 2014; Hautamäki, Kupiainen, Marjanen, Vainikainen, & Hotulainen, 2013; Thuneberg,autamäki, & Hotulainen, 2015), also compared with other Nordic countries (Yang Hansen, Gustafsson, & Rosén, 2014). The
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found between-class differences call for further research to gain a more comprehensive picture regarding the developmentof 21st century skills in relation to subject-specific learning and to re-evaluate the equity of the Finnish education system(cf., Sahlberg, 2007). In the present study, a first step towards this direction is taken by analysing class-level variation in thethinking skills measured by the Finnish LTL scale. The longitudinal data of the present study allows controlling for initialdifferences between classes, revealing some of the possible effects schooling has produced as compared to cross-sectionalstudies, which might just indicate the non-random allocation of pupils in classes (cf., Vainikainen, 2014).
1.4. Research questions and hypotheses
As described above, the structure of thinking skills, their development in educational settings, and educational equityhave all been extensively studied independent from each other. However, there is very little research, which combines theseperspectives and evaluates to what extent thinking skills really develop as a result of formal schooling if they are not taughtexplicitly. Therefore, the research questions and the hypotheses of the present study are
Q1: Do the thinking skills measured by the Finnish LTL scales have a nested higher-order structure as the theories abovesuggest?
H1: There is a nested higher-order structure: the higher-order general thinking skills factor is determined by formalthinking but there are separable factors for verbal and quantitative reasoning skills (Demetriou et al., 2011; Gustafsson,2008; Piaget, 2006; Shayer, 1979).
Q2: Is there between-class variation in formal thinking and the residual factors of verbal and quantitative reasoning?H2: There is between-class variation in all these factors, and it explains between 10% and 20% of the variance (Hautamäki
et al., 2013; Yang Hansen et al., 2014).Q3: Is the between-class variation explained by initial differences between classes, which has in earlier studies been
shown to explain about 5% of the variance already at the starting point (Vainikainen, 2014), or does it tell about differenttrajectories of development in different classes? That is, have the differences at the end of sixth grade been partially causedby schooling as thinking skills can be emphasised differently in teaching when explicit methods are not specified in theFinnish curriculum?
H3: The class-level variation in thinking skills does not only reflect initial differences between classes: it has been shownearlier that towards the end of primary school, between-class differences explain 10–20% of the variance of performance ondifferent domains, which is much more than initial differences between classes (Vainikainen, 2014 Yang Hansen et al., 2014).To our knowledge, there are no prior multilevel longitudinal studies explaining the possible schooling effects on thinkingskills.
2. Methods
The data were drawn from the Vantaa panel study, in which four full age cohorts (the first, third, sixth and ninth graders)of the municipality were followed from 2010 to 2013. The present study utilises the sixth grade data from 2013 which,regarding the measures used here were first reported by Krkovic, Greiff, Kupiainen, Vainikainen, and Hautamäki (2014)and Vainikainen (2014). None of these studies was about the nested structure of thinking skills. More recently, we usedthe nested model in another article accepted for publication in a Finnish special education journal (Vainikainen, Hienonen,Hautamäki and Hotulainen, in press). In the article, we applied only individual-level modelling and showed that class sizedid not explain the development of formal thinking of pupils with special education needs. Regarding the nested model, wereferred to the current study as the original publication and did not repeat any of the results presented here.
2.1. Participants
The studied cohort originally consisted of 2113 sixth graders in 118 classes in 37 schools. Due to the pre-defined exclusioncriteria, 8 small special education classes did not participate, and about 5% of pupils were absent due to sickness or otherreasons. 20% of the pupils were randomly assigned to a paper-based assessment group whereas 80% completed the computer-based version (CBA) of the LTL test. Only the data of the CBA group (N = 1543, 49.2% girls) were used in the present study,and the final number of classes with sufficient data for multilevel modelling was 102. The age of the pupils was M = 12.67,SD = .43. Longitudinal data comprising also pupils’ third grade results in analogical reasoning, which was utilised for testingthe last hypothesis, were available for 1303 pupils. Parents were informed through the City Education Department, and 77%of the parents also filled out a background questionnaire, which is not reported here.
2.2. Measures
The measures used in the study were the cognitive subtests of the sixth grade version of the Finnish LTL scale. Verbal
Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparingthe mind to new learning. Thinking Skills and Creativity (2015), http://dx.doi.org/10.1016/j.tsc.2015.04.006
proportional reasoning (see Inhelder & Piaget, 1958) was assessed by five items from the Bond’s Logical Operations Test(Bond, 1995, 1976), and five items from the Missing Premises task of the Ross Test of Higher Cognitive Processes (Ross & Ross,1979). In the first, each multiple-choice item comprised of two to four short sentences followed by a set of four or fivealternative responses (e.g. A prospector has found that some rich metals are sometimes found together. In his life he has
ometimes found gold and silver together, sometimes he has found silver by itself, every other time he has found neitherilver nor gold. Which of the following rules has been true for the prospector? Gold and silver are found together, neverpart.; if he found silver then he found gold with it.; if he found gold then he found silver with it.; if he found gold then heid not find silver; see Bond, 2010 for more details). In the latter, the pupils were given one premise and the conclusion (e.g.onclusion: Lake Saimaa is too cold for swimming. First fact: the temperature of Lake Saimaa is 5 centigrades), and they hado choose from amongst five alternatives the second premise which would make the conclusion valid (e.g. Most lakes are tooold for swimming.; it is wintertime.; five degree water is too cold for swimming.; Lake Saimaa is always cold.; swimmingn cold water is no fun.). The items were scored dichotomously as correct or incorrect.
Quantitative reasoning was assessed by seven items adapted from the Hidden Arithmetical Operators task by Demetriou,latsidou, Efklides, Metallidou, and Shayer (1991) and eight items based on the Invented Mathematical Concepts task ofternberg, Castejon, Prieto, Hautamäki, & Grigorenko (2001). In the first seven items there were one to four hidden operatorse.g. Which operator do the a and b stand for in (5 a 3) b 4 = 6?). In the latter items, two invented arithmetical operators wereonditionally defined (e.g. if a > b, lag stands for subtraction, but if a ≤ b, it stands for multiplication). After the definition, theupils had to select the correct answer from amongst four multiple choice alternatives to eight items (e.g. How much is 7
ag 5?). The items were coded dichotomously for the whole equation.Formal thinking was measured by the Control of Variables task, which is a modified version (Hautamäki, 1984 see also
otulainen, Thuneberg, Hautamäki, & Vainikainen, 2014, for a detailed description of the task) of Shayer’s Science Reasoningask ‘Pendulum’ (1979). It is based on one of the formal schemata identified by Inhelder and Piaget (1958). The pupils wereresented with four items in the form of comparisons set in the world of Formula 1 races with four variables: driver, car,ires, and track, with two alternatives for each. The pupils had to judge whether the single effect of the driver, car, tires, andrack could be concluded from the comparison (e.g. Round 1: driver Räikkönen, car Ferrari, tires Michelin, track Hockenheim;ound 2: driver Hamilton, car Ferrari, tires Michelin, track Monaco; can you conclude the effects of driver/car/tires/trackn the result?) There were two comparisons with 3 or 4 Yes/No-choices for the variables and two comparison-sets to beomplemented. The four items were coded dichotomously for a correct answer to all of the variables in the item.
For testing the last hypothesis, pupils’ analogical reasoning scores from three years earlier were merged in the otherwiseross-sectional data. The task was adapted from the geometric analogies test of Hosenfeld, van den Boom, and Resing (1997).he pupils were presented a pair of geometric figures, that is, a small square on the left and a big square on the right. Theask was to apply the same rule when choosing a pair from five options for another figure, that is, a small circle, between 5nswer options. The transformations included adding an element, changing sizes and positions, halving and doubling. Theaximum number of simultaneous transformations was five. The eight items were coded dichotomously, and the number
f correct items was converted to percentage.The reliabilities of the measures are presented in Table 1. Even though some of the reliabilities were somewhat low due
o the small number of items, the reliabilities were concluded acceptable for population-level studies.
.3. Statistical analyses
Descriptive statistics were calculated with SPSS22. Single- and multi-level nested factorial models were tested in Mplus.2 (Muthén & Muthén, 2012) using the MLR estimator without imputation of missing values. To reduce the number ofarameters to be estimated, the items of the subtests were parcelled into four verbal reasoning, four quantitative reasoning,nd two formal thinking parcels, which were treated as continuous variables. According to the recommendation of Marsh,üdtke, Nagenkast, Morin, and Von Davier (2013), we used a homogeneous parcelling strategy, in which items from differentheoretical origins were not mixed in the same parcels and the items in one parcel were as similar as possible. Beforearcelling, we calculated IRT item discrimination estimates for the three scales, ensuring the sufficient unidimensionalityf the scales (see Marsh et al., 2013). The models were considered as having a good fit with CFI & TLI > .95 and RMSEA < .05,nd an acceptable fit with CFI & TLI > .90 and RMSEA < .08. Also reported are �2 values, but due to the large sample size andhe number of parameters to be estimated significant p-values were to be expected. Accordingly, models with significant-values were not discarded if all the other indices were acceptable.
. Results
Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparingthe mind to new learning. Thinking Skills and Creativity (2015), http://dx.doi.org/10.1016/j.tsc.2015.04.006
.1. Descriptive statistics
The descriptive statistics of the item parcels and the analogical reasoning test are presented in Table 2. The descriptivesf the original items are presented in Appendix A.
N = Number of responses, Min = minimum value, Max = maximum value, M = Mean, SD = Standard deviation, ICC = Intraclass correlation.
Fig. 1. The expected nested structure of thinking skills. The error terms of the factor indicators are not presented in the figure.
3.2. Hypothesis 1
In the first hypothesis we expected that the measured thinking skills would have a nested factorial structure. That is, thehigher-order general thinking skills factor would be determined by Piagetian formal thinking but there would neverthelessbe separable factors for verbal proportional and quantitative reasoning skills. To test this hypothesis, the model presentedin Fig. 1 was first tested on individual-level data without modelling between-level variance.
The nested model of Fig. 1 fitted the data well (CFI = .978, TLI = .962, RMSEA = .034, �2 = 73.411, df = 26, p < .001) andshowed a better fit than an alternative model with three non-nested correlated factors (CFI = .954, TLI = .935, RMSEA = .045,�2 = 131.972, df = 32, p < .001) or a model without correlations between the secondary factors of verbal proportional andquantitative reasoning. The standardised factor loadings for the nested model are presented in Table 3.
Table 3 shows that as expected, the factor loadings of the formal thinking parcels were the strongest for the formal factor,
Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparingthe mind to new learning. Thinking Skills and Creativity (2015), http://dx.doi.org/10.1016/j.tsc.2015.04.006
which, however, had moderate loadings of the other parcels too. Even though the verbal proportional reasoning parcelshad also statistically significant loadings on a separable verbal proportional factor, these loadings were almost equal to orweaker than the loadings of the same parcels on the formal thinking factor. Moreover, the latent verbal proportional factordid not have statistically significant own variance (s2 = 0.001, p = .23). The quantitative reasoning factor, in contrast, had
M.-P. Vainikainen et al. / Thinking Skills and Creativity xxx (2015) xxx–xxx 7
Table 3Standardised factor loadings in the individual-level model.
Parcel Formal Verbal proportional Quantitative
Verbal proportional 1 .48*** .12*
Verbal proportional 2 .46*** .39***
Verbal proportional 3 .36*** .33***
Verbal proportional 4 .24*** .27***
Quantitative 1 .45*** .21***
Quantitative 2 .31*** .17***
Quantitative 3 .35*** .54***
Quantitative 4 .42*** .57***
Formal 1 .59***
***
stw
3
bfp(rot
m
lf
3
fogl
TS
Formal 2 .73
* p < .05.*** p < .001.
lightly higher factor loadings and statistically significant own variance (s2 = 0.004, p < .010). These results together indicatehat quantitative reasoning skills were clearly separable from the more general formal thinking skills, whereas the sameas not true for the measured verbal thinking skills. Thus, the results gave only partial support to the first hypothesis.
.3. Hypothesis 2
In the next hypothesis we assumed that there would be between-class effects that would explain 15–20% of the varianceoth in formal thinking and in the more specific verbal proportional and quantitative reasoning skills. The between-levelactors were specified for formal thinking containing all parcels and for quantitative reasoning. A between-level verbalroportional reasoning factor caused problems with the fit indices and had to be removed. The model fit the data wellCFI = .968, TLI = .949, RMSEA = .030, �2 = 135.548, df = 57, p < .001). Unlike in the single-level model of H1, the quantitativeeasoning factor was not statistically significant at the class level and in this model it did not have statistically significantwn variance at any level regardless of its statistically significant factor loadings at the individual level. Thus, the formalhinking factor captured all pupil-level and class-level variation (ICC = .18) in this model.
Adding the class level in the model changed slightly the factor loadings at the individual level compared to the single-levelodel. The within and between-level factor loadings without any constraints across the two levels are reported in Table 4.
Table 4 shows that at the class level, all the parcels except the last parcel for verbal proportional reasoning had strongoadings on the formal thinking factor. It was concluded that H2 was partially supported regarding the class-level effects onormal thinking.
.4. Hypothesis 3
In the last hypothesis it was assumed that the class-level variation in thinking skills would not only reflect initial dif-
Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparingthe mind to new learning. Thinking Skills and Creativity (2015), http://dx.doi.org/10.1016/j.tsc.2015.04.006
erences between classes but would be partially caused by schooling. To test this hypothesis, longitudinal data in the formf analogical reasoning test scores from the third grade were used, which were available for about 85% of the pupils. Thirdrade analogical reasoning skills were added in the two-level model specified in H2 as both within-level and between-evel predictors of formal thinking. The model fit was acceptable also for this model (CFI = .958, TLI = .939, RMSEA = .034,
able 4tandardised factor loadings in the two-level model.
8 M.-P. Vainikainen et al. / Thinking Skills and Creativity xxx (2015) xxx–xxx
Fig. 2. The final two-level model. The parcel names and the error terms are not presented in the figure. ***p < .001, ns. = non-significant.
�2 = 185.772, df = 75, p < .001). As expected, third grade analogical reasoning skills predicted sixth grade formal thinking atthe individual level ( ̌ = .57, SE = .03, p < .001) and at the class-level ( ̌ = .58, SE = .14, p < .001), explaining 32% and 34% of itsvariance, respectively. As the verbal proportional and quantitative factors turned out to be non-significant in the two-levelmodel, it was also tested whether they could be completely omitted from the model. However, this decreased the predictivepower of third grade analogical reasoning skills, indicating that these non-significant factors nevertheless removed someirrelevant variance from the formal thinking factor. The final two-level model is presented in Fig. 2.
As only a third of the between-level variance of formal thinking demonstrated in the sixth grade could be explained byinitial differences between the classes when measured by the analogical reasoning test, it was concluded that there was truevariance left after controlling for initial differences and that schooling during the interim years can have produced an effecton formal thinking. Thus, H3 was supported.
4. Discussion
Enhancing thinking skills can be seen as one of the many tasks of schooling (Olson, 2003), and it can be argued that inthe 21st century this task has become increasingly important due to the changes in working life (Deakin Crick et al., 2014).In Finland, thinking skills are embedded in the core-curriculum for basic education but there is only limited informationavailable about how schools succeed in this task. Moreover, it has not been studied in any larger scale, whether the teachingof thinking skills is limited to subject-specific areas or if schooling manages to target the more general thinking skills as well.Therefore, the present study had two goals: on the one hand, the aim was to find support for the theoretical assumptionderiving from Piaget (2001) and Shayer (2008), and more recently from Demetriou et al. (2011), about thinking skills havinga nested structure with its core in logical or formal thinking but with additional specialised structures. On the other hand,the educability of these skills in a context where thinking skills are embedded in the curriculum was tested by studyingclass-level variation in formal thinking at grade six when initial differences between classes had been taken into account.The data were drawn from a learning to learn panel study in one of the major cities in Finland, where a full cohort (N ≈ 2000)of pupils were assessed at grade three and six by the Finnish LTL scale (Hautamäki et al., 2002). The cognitive subtasks ofthe scale covered formal thinking, verbal proportional reasoning, and quantitative reasoning, which can all be consideredcritical 21st century skills (Adey & Csapó, 2014).
The first hypothesis regarded the nested structure of thinking skills. More specifically, it was assumed that verbal propor-tional and quantitative reasoning skills would not be independent from the core factor of formal thinking but the structurewould be nested (see Härnqvist et al., 1994). Single-level confirmatory factor analysis indeed supported this assumption: thenested higher-order model fitted the data better than a normal three-factor model, and in the nested model the higher-orderfactor was dominated by the formal thinking items even though the verbal proportional and quantitative items had moder-
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ate loadings on it as well. It was also possible to identify separate factors for verbal proportional and quantitative items withstatistically significant factor loadings, and of these the quantitative factor had own statistically significant variance. That is,quantitative reasoning differs from formal thinking also in the numeric context, whereas the measured verbal proportionalskills were not easily separable from it. The results support the theoretical assumptions based on the work of Piaget (2001),
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hayer (1979, 2008) and Demetriou (2014), who claim that there are the core operators, which are needed in every task. Theesults also fit together with the findings of Härnqvist et al. (1994), even though their terminology differs somewhat fromhe concepts used in this study. Also, the residual verbal factor was in their study of a greater importance, most likely dueo the nature of the tasks used.
As the first results supported the higher-order structure of the measured skills, we proceeded to test the class-levelariation of both the general formal and the quantitative thinking skills. Somewhat unexpectedly, in the two-level model,he variance of the quantitative factor was no longer statistically significant at the individual level, in addition to not having
uch relevance at the class level. However, as it clearly removed some of the irrelevant variance in the formal thinkingactor, it was kept in the model. The results showed that just as in the study of Härnqvist et al. (1994), there was class-levelariation that accounted for 18% of the variance in the general factor of formal thinking. The testing of the third hypothesishowed that this variation was only partially explained by initial between-class differences as measured by an analogicaleasoning test at grade three. As earlier analogical reasoning skills are indicators of the functioning of the same general
echanisms that at the later stage of development can be measured by formal thinking tasks (Demetriou et al., 2011), it wasoncluded that pupils’ formal thinking skills had clearly developed differently in different classes. Even though there may bether factors explaining the development, which accounted for approximately 12% of the total variance, for instance socio-conomic background and selective classes (Härnqvist et al., 1994), the results support the possibility that formal thinkingkills can have been enhanced differently by different teachers. Here, it is important to remember that any specific trainingrogrammes for thinking skills were not applied. Thus, the main contribution of this study is not that the higher-order factortructure was found, but that the general factor – here formal thinking – could be given an interpretation, which can be tiedo educational interventions, even if just embedded in everyday teaching. Also the residual factors, even if their independentariances were different at individual and class-levels, open windows for teaching-related interventions.
.1. Limitations of the study
The data set some limits to the possible research questions and the analyses to be performed. The multilevel analysesould be conducted only at the class-level even though it would have been interesting to look at between-school effects asell – especially when the differences between schools have traditionally been very small in Finland also in the learning
o learn assessments (see Hautamäki et al., 2013). This, however, was not possible with the present data due to the smallumber of schools. Therefore, it would be important to replicate this study with a sample consisting of sufficient number ofchools for school-level MFA.
There are also limitations regarding the measures: The verbal tasks measured proportional logical thinking and deductiveeasoning but did not cover the full scope of verbal reasoning skills. This may be the reason for the non-significant variancef the verbal proportional factor. Regarding the longitudinal data, the initial third grade initial differences were measurednly by the analogical reasoning task, which only accounts for some of the possible sources of initial variation between thelasses. If other measures had been used in addition to analogical reasoning, the share of unexplained variance of sixth gradeormal thinking might have been somewhat smaller. However, as the unexplained share was as high as two thirds of theariance, the results point strongly to the direction that there is true variation produced by classes. The remaining class-levelariance was not related to pupils’ initial cognitive competence that often explains about a third of the variance (cf., Duncant al., 2007), just as in the present study, or the very usual non-random allocation of pupils in classes in Finnish schools (seeainikainen, 2014).
.2. Conclusions and practical implications
The goal of this paper was to look at the structure and development of thinking skills in the context of regular curricularearning. First, a distinction was made between general and specific thinking skills. Second general thinking skills werenterpreted as the general factor in a nested factorial solution and specific skills as secondary-level constructs (Gustafsson,002). Third, the general and the specific thinking skills were regarded from a point-of-view of educational intervention,odelling the class-level variance in the development of them. There is ample evidence of the use of developmentally
riented interventions for the advancement of thinking (Adey & Shayer, 1994; Higgins, Hall, Baumfield, & Mosely, 2005;uusela, 2000), but the results of the present study indicate that schooling enhances thinking skills even without specific
nterventions. However, if the 21st century demands on learning will be is as unpredictable and fast changing as it has beenlaimed (Rocard et al., 2007), there is a risk that traditional subject knowledge-centred education will not suffice for the fullevelopment of the skills needed for leading a successful life. Work and social life will constantly afford novel tasks whichannot be solved by just applying earlier acquired knowledge. A new habit-of-mind is needed, to be built at school with anctive agenda for nurturing the development of general cognitive competence and the attitudes and emotions supportingts use (Pellegrino & Hilton, 2012). This will allow seeing new cognitive requirements as chances to be used for new learning.
Seen from the perspective of this paper, the Finnish LTL is related to 21st skills through its connection to the concept
Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparingthe mind to new learning. Thinking Skills and Creativity (2015), http://dx.doi.org/10.1016/j.tsc.2015.04.006
f scientific thinking (Kuhn, 2005; Kuhn 2008), and is closely aligned with the concept of thinking abilities (Adey et al.,007; Adey & Csapó, 2014). Accordingly, 21st century skills can be seen to get advanced through teaching which is basedn analysing the curricular content of each subject from the point-of view of thinking patterns like conservation, seriation,lassification, combinatorial reasoning, analogical reasoning, proportional reasoning, probabilistic reasoning, correlational
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reasoning, and separation and control of variables. Accordingly, the LTL framework can be used to guide the advancement ofthinking skills, be it through intervention or their conscious imbedding in the curriculum, and the success of this advancementcan be assessed using the LTL scale, described in this paper. By combining this to the assessment of subject-specific outcomeswill allow further analysing the actual or potential role of the various subjects in its advancement (see Adey & Shayer, 2002;Titcombe, 2015).
Pupils need to be prepared to see new options instead of obstacles, but as Christina Howe (Howe, McWilliam, & Cross,2005) expresses: “Chance favours only the prepared mind.” The well-prepared mind is, at least, a person with a goodcommand of formal, logical and scientific thinking, and a willingness to apply that skill for solving open problems. However,as Kuhn and Holman (2011, p. 65) remark: “. . .most of the empirical evidence related to adolescent cognitive skills doesnot present a picture of strong and secure competence, making the question of how to support cognitive developmentin adolescence a pressing one”. They also express the need to extend research on cognitive development from control-of-variables strategy studies to studies regarding multiple causality and evidence-based predictions to reach the level ofmeasuring students’ readiness to enter the world of intellectual discourse to participate in communities of intellectualdiscourse Also the Finnish LTL assessment is lacking in this respect. Yet the findings of the study show that LTL can be usedto measure the development of primary school pupils’ thinking skills to a sufficient degree to evaluate the success of theirfostering at school
Appendix A.
Descriptives of the original dichotomous variables.N Min Max M SD
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