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Thinking Skills and Creativity

  j o u r n a l h o m e p a g e :

  General and specific thinking skills and schooling: Preparing the mind to new learning

  Mari-Pauliina Vainikainen Hautamäki, Risto Hotulainen, Sirkku Kupiainen

  University of Helsinki, Department of Teacher Education, Centre for Educational Assessment, Finland

  a r t i c l e i n f o a b s t r a c t

  Article history: Enhancing thinking skills is an important goal of formal education. It is often embedded

  Received

  3 October 2014 in national curricula, which, however, are seldom based on theoretical understanding of

  Received in revised form

  17 April 2015 the structure of the skills or how they should be taught. Accordingly, there is only limited

  Accepted

  23 April 2015 information available about schools’ success in this important task. The present study has

  Available online xxx two goals: firstly, to find support for the theoretical assumption of the nested structure of thinking skills with a core factor of formal thinking and specialised structures for verbal and

  Keywords: quantitative reasoning; and secondly, to test the differentiated development of these skills

  Thinking skills in school. This was done by studying class-level variation of sixth graders’ thinking skills in

  Cognitive development a multilevel factor analysis when initial between-class differences at grade three had been

  Formal thinking taken into account. The data (N ≈ 1543) were drawn from a learning to learn panel study in

  Class-effect on thinking skills one of the major cities of Finland. The results showed that the core factor for formal thinking

  Nested multilevel factorial models could be identified at both the individual and the class level, and that at the individual level there were statistically significant residual factors for verbal and quantitative reasoning.

  Initial between-class differences explained only a third of the variance of class-level formal thinking. This was interpreted to indicate the effect of schooling.

  © 2015 Published by Elsevier Ltd.

  1. General and specific thinking skills and schooling Discussions of current working environments and of the skills necessary for work call for a new approach towards learning. In the continuously changing work environments people need to make coherent decisions with access to unlim- ited information in a limited time, to think creatively, to adjust their actions and attitudes according to possible risks and problems, to learn quickly, and to trust their problem solving skills Hence, educational policy makers world-wide have lately become interested in concepts, such as learning to learn, thinking skills, and 21st century skills (

  The common core for the new or newly introduced concepts is that they all tap underlying cognitive competences and non-curricular domain-general skills that regard an individual’s overall learning preparedness. Depending on the framework, these skills are referred to as cross-curricular, learning to learn (LTL), transversal, or 21st century skills

  

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: (M.-P. Vainikainen).

   1871-1871/© 2015 Published by Elsevier Ltd.

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  12 M.-P. Vainikainen et al. / Thinking Skills and Creativity xxx (2015) xxx–xxx a basis for future learning from core processes and specialised structural systems to critical thinking Enhancing thinking skills have been considered as a central goal of education already for decades ( but it is 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 an explicit part, see Even though thinking skills are expected to improve when pupils proceed through their formal schooling, strategies for evaluating educational outcomes and effectiveness of schooling mainly centre on the measurement of subject-specific knowledge and skills or at best their application. In Finland, the assessment of general cognitive competences and the affective factors which support their effective use, together labelled LTL, were defined as one of the measurable outcomes of education already in the 1990s 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

  

In empirical assessment of LTL, the assessment tasks are seen to activate

  a complex of interrelated competences and beliefs, leading to an attempt to solve the tasks. Competence refers to the application 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 competences are related to intelligence, understood in a Piagetian framework as the active use of formal operational schemas. From this follows the hypothesis that the cognitive LTL tasks measure general thinking skills (see LTL as an educational 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 Framework and scales are one of few attempts to offer a tool to assess both the cognitive and the willingness- or commitment-related components of LTL

  The aim of the present study is on the one hand to test the theoretical assumption that the thinking skills measured with the Finnish LTL construct have a nested structure (cf., formal operational thinking (see its core and with specialised residual factors for verbal proportional and quantitative reasoning (see On the other hand, the aim is to evaluate whether schooling has an effect on these skills in the Finnish context, where thinking skills are defined as a goal embedded in all school subjects in the national core curriculum ( 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 both central and general mechanisms, and specialised capacity systems for different domains of knowledge or relations. The spatial, verbal, quantitative, categorical, causal, and social reasoning systems have been identified by methods from different theoretical origins, and they are considered as autonomous 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 processor and 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 domain specific skills especially on the early phases of the learning process

  

But when learning is based on already acquired skills, the gains are more likely to depend on earlier domain-specific

  knowledge. 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

  One of the most studied constructs in the development of general thinking skills and the functioning of the general mechanisms (cf., is the control of variables strategy (CV), which is also often referred to as the vary-one-thing-at-a-time (VOTAT) strategy. It was first introduced by Regardless of criticisms concerning explicitness of Inhelder and Piaget’s work it still provides overarching illustration how adolescents’ cognitive competences develop during the second decade of their life ( 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” ( Age variation is seen to be ingrained in the differing intellectual stimuli in children’s environments and to depend on personal interests and experiences. However, formal thinking is not necessarily applied all the time or across all domains

  

Even if individual differences in formal operational thinking are related to intelligence, verbal ability and executive

  functions, these are considered to be partly culturally bound It has been shown that that the control of variables strategy is central to science and an essential skill attainable and trainable by the time children are cognitively advancing from a concrete toward a formal operational level

  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 ( but it seems that there are also other possibilities for the apex due to the law of positive correlations amongst reliable cognitive tasks. g

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General cognition is expressed or invested in various ways

  in different learning situations and school achievements (

  

  According to Demetriou’s theory, we expect the thinking skills measured within the Finnish LTL context to be structured in a way that in addition to the core of formal thinking, residual factors of all the specialised reasoning systems are to be found. In practice, only the verbal and quantitative factors can be identified here as the sixth grade version of the Finnish LTL scale used in the present study does not have sufficient number of items on the areas of spatial, causal or social reasoning. Even though ninth grade data with a larger scope of cognitive tasks would have been available, 12-year-olds were selected as the target group of the present study due to the sensitiveness of this age group in regard to both the development of formal thinking

  1.2. Enhancing the development of thinking skills Many researchers see that induction processes, such as performing mental comparisons form a basis for knowledge- building. This, in turn, has been shown to have a transfer effect on learning in school subjects (

  

Thus, by

  promoting the development of thinking skills, e.g. how to put things in order, classify or perform mental rotations, we simultaneously enhance fundamental learning skills, which have transfer effects across the school curriculum. This also facilitates the attainment of higher order thinking skills (

  It could be argued that there are two main ways to promote thinking skills in school. The first approach can be called explicit with specific educational programmes, which are expected to promote thinking skills if the programme guidelines are appropriately followed. These programmes can be further divided into two categories according to how the training of thinking skills is arranged ( The first category, the content-based method, consists of pro- grammes which ensure that thinking skills are taught within conventional curriculum areas (e.g. mathematics or science). A well-studied programme representing this method is the Cognitive Acceleration (CA) Programme ( based on Piagetian cognitive stages. Programmes belonging to the second category share the idea that thinking skills can be taught as such (e.g. The promotion of generic skills has been criticised for developing thinking skills a-contextually and inhibiting the transfer of the developed skills to new contexts. Yet, programmes based on Klauer’s theory have recently shown strong evidence for transfer effect on both fluid intelligence and various academic subjects Regard- less of strong evidence by now that specific programs can promote 21st century skills, their large-scale use has not been widely spread to the educational field due to both short-sighted educational policy-decision making and limited resources of stakeholders (

  The second approach can be described as an implicit one. In this approach, curricula do not per se emphasise systematic cultivation of thinking skills but such development is expected to result as a side-effect ( Especially in the Nordic countries, approaches, practices, and initiatives towards enhancing thinking skills are very limited. For example, in the Finnish national core curriculum, thinking skills are regarded to belong into each conventional curriculum area. Thus, it is expected that the implemented curriculum with annually more demanding content complexity (spiral curriculum; cf. raises implicitly the level of thinking skills, as well. However, research has shown that the promotion of thinking skills needs to be either integrated purposefully in the curriculum or they have to be explicitly taught to gain effective results

  As in Finland explicit methods for teaching general thinking skills are not pointed out in the core curriculum and the same class teacher typically teaches their class from third to sixth grade, the Finnish school system allows us to study teacher- and class-related variation in the development of general thinking skills. The expected class-level variation in the development of thinking skills could provide evidence for that even implicit teaching of thinking skills can be beneficial. It can also give estimates about how much or alternatively how little teachers can influence the developing general thinking skills.

  1.3. Educational assessment and thinking skills To assesses the effectiveness of formal schooling also with regard to 21st century skills, programmes have been launched both internationally, such as the OECD’s Programme for International Student Assessment (PISA, or the Euro- pean Commission’s pilot study for learning to learn ( and nationally (e.g. the Finnish LTL assessments, see In PISA, which mainly measure subject matter-related knowledge and skills and their application, Finnish students have recurrently performed at a high level whereas between-school variation has been low, indicating the Finnish education system’s high level of equity ( However, recent studies have shown that differences between classes in the same school can be relatively large in Finland (ICCs ranging from 10 to 20% depending on measured competence;

  

The

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  12 M.-P. Vainikainen et al. / Thinking Skills and Creativity xxx (2015) xxx–xxx found between-class differences call for further research to gain a more comprehensive picture regarding the development of 21st century skills in relation to subject-specific learning and to re-evaluate the equity of the Finnish education system (cf., In the present study, a first step towards this direction is taken by analysing class-level variation in the thinking skills measured by the Finnish LTL scale. The longitudinal data of the present study allows controlling for initial differences between classes, revealing some of the possible effects schooling has produced as compared to cross-sectional studies, which might just indicate the non-random allocation of pupils in classes (cf.,

  1.4. Research questions and hypotheses As described above, the structure of thinking skills, their development in educational settings, and educational equity have all been extensively studied independent from each other. However, there is very little research, which combines these perspectives and evaluates to what extent thinking skills really develop as a result of formal schooling if they are not taught explicitly. 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 above suggest? H1: There is a nested higher-order structure: the higher-order general thinking skills factor is determined by formal thinking but there are separable factors for verbal and quantitative reasoning skills (

  

  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

  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 or does it tell about different trajectories of development in different classes? That is, have the differences at the end of sixth grade been partially caused by schooling as thinking skills can be emphasised differently in teaching when explicit methods are not specified in the Finnish curriculum?

  H3: The class-level variation in thinking skills does not only reflect initial differences between classes: it has been shown earlier that towards the end of primary school, between-class differences explain 10–20% of the variance of performance on different domains, which is much more than initial differences between classes To our knowledge, there are no prior multilevel longitudinal studies explaining the possible schooling effects on thinking skills.

  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 None of these studies was about the nested structure of thinking skills. More recently, we used the nested model in another article accepted for publication in a Finnish special education journal

  

In the article, we applied only individual-level modelling and showed that class size

  did not explain the development of formal thinking of pupils with special education needs. Regarding the nested model, we referred 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 exclusion criteria,

  8 small special education classes did not participate, and about 5% of pupils were absent due to sickness or other reasons. 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,

  M and the final number of classes with sufficient data for multilevel modelling was 102. The age of the pupils was = 12.67, SD = .43. Longitudinal data comprising also pupils’ third grade results in analogical reasoning, which was utilised for testing the 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 proportional reasoning (see was assessed by five items from the Bond’s Logical Operations Test

  Missing Premises Ross Test of Higher Cognitive Processes (

  

In the first, each multiple-choice item comprised of two to four short sentences followed by a set of four or five

  alternative responses (e.g. A prospector has found that some rich metals are sometimes found together. In his life he has Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparing

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  Table

  1 Reliabilities of the cognitive tasks and the attitude scales.

  Scale Number of items ˛ Verbal proportional reasoning 10 .55 Quantitative reasoning 15 .75 Formal thinking

  4 .62 Analogical reasoning third grade 8 .78

sometimes found gold and silver together, sometimes he has found silver by itself, every other time he has found neither

silver nor gold. Which of the following rules has been true for the prospector? Gold and silver are found together, never

apart.; 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 he

did not find silver; see more details). In the latter, the pupils were given one premise and the conclusion (e.g.

  Conclusion: Lake Saimaa is too cold for swimming. First fact: the temperature of Lake Saimaa is 5 centigrades), and they had to choose from amongst five alternatives the second premise which would make the conclusion valid (e.g. Most lakes are too cold for swimming.; it is wintertime.; five degree water is too cold for swimming.; Lake Saimaa is always cold.; swimming in 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

  

the first seven items there were one to four hidden operators

  (e.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 were ≤ a b, lag a

  b, conditionally defined (e.g. if > stands for subtraction, but if it stands for multiplication). After the definition, the pupils had to select the correct answer from amongst four multiple choice alternatives to eight items (e.g. How much is

  7 lag 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 also

  

pupils were

  presented with four items in the form of comparisons set in the world of Formula 1 races with four variables: driver, car, tires, and track, with two alternatives for each. The pupils had to judge whether the single effect of the driver, car, tires, and track could be concluded from the comparison (e.g. Round 1: driver Räikkönen, car Ferrari, tires Michelin, track Hockenheim; Round 2: driver Hamilton, car Ferrari, tires Michelin, track Monaco; can you conclude the effects of driver/car/tires/track on the result?) There were two comparisons with

  3 or

4 Yes/No-choices for the variables and two comparison-sets to be complemented. 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 otherwise cross-sectional data. The task was adapted from the geometric analogies test of The pupils were presented a pair of geometric figures, that is, a small square on the left and a big square on the right. The task was to apply the same rule when choosing a pair from five options for another figure, that is, a small circle, between

  5 answer options. The transformations included adding an element, changing sizes and positions, halving and doubling. The maximum number of simultaneous transformations was five. The eight items were coded dichotomously, and the number of correct items was converted to percentage.

  The reliabilities of the measures are presented in

   though some of the reliabilities were somewhat low due to the small number of items, the reliabilities were concluded acceptable for population-level studies.

  2.3. Statistical analyses Descriptive statistics were calculated with SPSS22. Single- and multi-level nested factorial models were tested in Mplus

  7.2 ( using the MLR estimator without imputation of missing values. To reduce the number of parameters to be estimated, the items of the subtests were parcelled into four verbal reasoning, four quantitative reasoning, and two formal thinking parcels, which were treated as continuous variables. According to the recommendation of

  

used a homogeneous parcelling strategy, in which items from different

  theoretical origins were not mixed in the same parcels and the items in one parcel were as similar as possible. Before parcelling, we calculated

  IRT item discrimination estimates for the three scales, ensuring the sufficient unidimensionality of the scales (see The models were considered as having a good fit with CFI & TLI > .95 and RMSEA < .05,

  2

  and an acceptable fit with CFI & TLI > .90 and RMSEA < .08. Also reported are values, but due to the large sample size and p-values the number of parameters to be estimated significant were to be expected. Accordingly, models with significant p-values were not discarded if all the other indices were acceptable.

  3. Results

  3.1. Descriptive statistics The descriptive statistics of the item parcels and the analogical reasoning test are presented in

  

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  1 In the first hypothesis we expected that the measured thinking skills would have a nested factorial structure. That is, the

higher-order general thinking skills factor would be determined by Piagetian formal thinking but there would nevertheless

be separable factors for verbal proportional and quantitative reasoning skills. To test this hypothesis, the model presented

in first tested on individual-level data without modelling between-level variance.

  = 0.001, p = .23). The quantitative reasoning factor, in contrast, had

  2

  which, however, had moderate loadings of the other parcels too. Even though the verbal proportional reasoning parcels had also statistically significant loadings on a separable verbal proportional factor, these loadings were almost equal to or weaker than the loadings of the same parcels on the formal thinking factor. Moreover, the latent verbal proportional factor did not have statistically significant own variance (s

   that as expected, the factor loadings of the formal thinking parcels were the strongest for the formal factor,

  = 131.972, df = 32, p < .001) or a model without correlations between the secondary factors of verbal proportional and quantitative reasoning. The standardised factor loadings for the nested model are presented in

  2

  = 73.411, df = 26, p < .001) and showed a better fit than an alternative model with three non-nested correlated factors (CFI = .954, TLI = .935, RMSEA = .045,

  2

   the data well (CFI = .978, TLI = .962, RMSEA = .034,

  The nested model of

  Fig.

  G Model

  ICC = Intraclass correlation.

  29.88 N = Number of responses, Min = minimum value, Max = maximum value, M = Mean, SD = Standard deviation,

  40.19

  0.00 100.00

  1 1495 .00 1.00 .59 .45 .07 Formal 2 1480 .00 1.00 .37 .44 .07 Analogical reasoning 1303

  1 1501 .00 1.00 .52 .28 .10 Quantitative 2 1401 .00 1.00 .10 .22 .03 Quantitative 3 1475 .00 1.00 .57 .29 .08 Quantitative 4 1471 .00 1.00 .35 .28 .07 Formal

  ICC Verbal proportional 1 1522 .00 1.00 .53 .30 .07 Verbal proportional 2 1512 .00 1.00 .54 .39 .07 Verbal proportional 3 1506 .00 1.00 .51 .30 .05 Verbal proportional 4 1504 .00 1.00 .23 .32 .02 Quantitative

  Variable Parcel N Min Max M SD

  2 Descriptive statistics of the variables used in modelling.

  Table

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1. The expected nested structure of thinking skills. The error terms of the factor indicators are not presented in the figure.

3.2. Hypothesis

  G Model

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  Parcel Formal Verbal proportional Quantitative Verbal proportional 1

  3 Standardised factor loadings in the individual-level model.

  Table

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• .12
• Verbal proportional
• .39
• Verbal proportional

• .33
• Verbal proportional
• .27
• Quantitative
• .21
• Quantitative

• .17
• Quantitative
• .54
• Quantitative

• .57
• Formal
• Formal
• p < .001.

  p < .05.

  Verbal proportional 1 .45

  Adding the class level in the model changed slightly the factor loadings at the individual level compared to the single-level model. The within and between-level factor loadings without any constraints across the two levels are reported in

   that at the class level, all the parcels except the last parcel for verbal proportional reasoning had strong

  loadings on the formal thinking factor. It was concluded that H2 was partially supported regarding the class-level effects on formal thinking.

  3.4. Hypothesis

  3 In the last hypothesis it was assumed that the class-level variation in thinking skills would not only reflect initial dif- ferences between classes but would be partially caused by schooling. To test this hypothesis, longitudinal data in the form of analogical reasoning test scores from the third grade were used, which were available for about 85% of the pupils. Third grade analogical reasoning skills were added in the two-level model specified in H2 as both within-level and between- level predictors of formal thinking. The model fit was acceptable also for this model (CFI = .958, TLI = .939, RMSEA = .034, Table

  4 Standardised factor loadings in the two-level model.

  Within-level Between-level

Parcel Formal Verbal proportional Quantitative Formal Quantitative

  Verbal proportional 3 .32

  Verbal proportional 2 .42

  2

  4 .27

  Quantitative 1 .40

  2 .30

  Quantitative 3 .32

  Quantitative 4 .40

  Formal 1 .55

  2 .71

  = 135.548, df = 57, p < .001). Unlike in the single-level model of H1, the quantitative reasoning factor was not statistically significant at the class level and in this model it did not have statistically significant own variance at any level regardless of its statistically significant factor loadings at the individual level. Thus, the formal thinking factor captured all pupil-level and class-level variation (ICC = .18) in this model.

  3.3. Hypothesis

  2 In the next hypothesis we assumed that there would be between-class effects that would explain 15–20% of the variance both in formal thinking and in the more specific verbal proportional and quantitative reasoning skills. The between-level factors were specified for formal thinking containing all parcels and for quantitative reasoning. A between-level verbal proportional reasoning factor caused problems with the fit indices and had to be removed. The model fit the data well (CFI = .968, TLI = .949, RMSEA = .030,

  3

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  2

  3

  4

  2

  1

  4

  1

  2

  slightly higher factor loadings and statistically significant own variance (s

  2

  = 0.004, p < .010). These results together indicate that quantitative reasoning skills were clearly separable from the more general formal thinking skills, whereas the same was not true for the measured verbal thinking skills. Thus, the results gave only partial support to the first hypothesis.

• .84***
• .98***

• Verbal proportional
• .58 (ns.)
• .17
• .56
• Quantitative

• .16
• .41 (ns.)
• .52
• .48 (ns.)

• .60
• .42 (ns.)
• Formal

• p < .05.

• p < .01.
• p < .00.

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  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

  p = 185.772, df = 75, < .001). As expected, third grade analogical reasoning skills predicted sixth grade formal thinking at the individual level (ˇ = .57, SE = .03, p < .001) and at the class-level (ˇ = .58, SE = .14, p < .001), explaining 32% and 34% of its variance, respectively. As the verbal proportional and quantitative factors turned out to be non-significant in the two-level model, it was also tested whether they could be completely omitted from the model. However, this decreased the predictive power of third grade analogical reasoning skills, indicating that these non-significant factors nevertheless removed some irrelevant variance from the formal thinking factor. The final two-level model is presented in

  

  As only a third of the between-level variance of formal thinking demonstrated in the sixth grade could be explained by initial differences between the classes when measured by the analogical reasoning test, it was concluded that there was true variance left after controlling for initial differences and that schooling during the interim years can have produced an effect on formal thinking. Thus, H3 was supported.

  4. Discussion Enhancing thinking skills can be seen as one of the many tasks of schooling In Finland, thinking skills are embedded in the core-curriculum for basic education but there is only limited information available about how schools succeed in this task. Moreover, it has not been studied in any larger scale, whether the teaching of 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 assumption deriving from thinking skills having a 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 studying class-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 The cognitive subtasks of the scale covered formal thinking, verbal proportional reasoning, and quantitative reasoning, which can all be considered critical 21st century skills

  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 structure would be nested (see Single-level confirmatory factor analysis indeed supported this assumption: the nested higher-order model fitted the data better than a normal three-factor model, and in the nested model the higher-order factor was dominated by the formal thinking items even though the verbal proportional and quantitative items had moder- ate loadings on it as well. It was also possible to identify separate factors for verbal proportional and quantitative items with statistically 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 proportional skills were not easily separable from it. The results support the theoretical assumptions based on the work of

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claim that there are the core operators, which are needed in every task. The

  results also fit together with the findings of though their terminology differs somewhat from the concepts used in this study. Also, the residual verbal factor was in their study of a greater importance, most likely due to 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-level variation of both the general formal and the quantitative thinking skills. Somewhat unexpectedly, in the two-level model, the variance of the quantitative factor was no longer statistically significant at the individual level, in addition to not having much relevance at the class level. However, as it clearly removed some of the irrelevant variance in the formal thinking factor, it was kept in the model. The results showed that just as in the study of was class-level variation that accounted for 18% of the variance in the general factor of formal thinking. The testing of the third hypothesis showed that this variation was only partially explained by initial between-class differences as measured by an analogical reasoning test at grade three. As earlier analogical reasoning skills are indicators of the functioning of the same general mechanisms that at the later stage of development can be measured by formal thinking tasks it was concluded that pupils’ formal thinking skills had clearly developed differently in different classes. Even though there may be other factors explaining the development, which accounted for approximately 12% of the total variance, for instance socio- economic background and selective classes the results support the possibility that formal thinking skills can have been enhanced differently by different teachers. Here, it is important to remember that any specific training programmes for thinking skills were not applied. Thus, the main contribution of this study is not that the higher-order factor structure was found, but that the general factor here formal thinking could – – be given an interpretation, which can be tied to educational interventions, even if just embedded in everyday teaching. Also the residual factors, even if their independent variances were different at individual and class-levels, open windows for teaching-related interventions.

  4.1. Limitations of the study The data set some limits to the possible research questions and the analyses to be performed. The multilevel analyses could be conducted only at the class-level even though it would have been interesting to look at between-school effects as well especially when the differences between schools have traditionally been very small in Finland also in the learning – to learn assessments (see This, however, was not possible with the present data due to the small number of schools. Therefore, it would be important to replicate this study with a sample consisting of sufficient number of schools for school-level MFA.

  There are also limitations regarding the measures: The verbal tasks measured proportional logical thinking and deductive reasoning but did not cover the full scope of verbal reasoning skills. This may be the reason for the non-significant variance of the verbal proportional factor. Regarding the longitudinal data, the initial third grade initial differences were measured only by the analogical reasoning task, which only accounts for some of the possible sources of initial variation between the classes. If other measures had been used in addition to analogical reasoning, the share of unexplained variance of sixth grade formal thinking might have been somewhat smaller. However, as the unexplained share was as high as two thirds of the variance, the results point strongly to the direction that there is true variation produced by classes. The remaining class-level variance was not related to pupils’ initial cognitive competence that often explains about a third of the variance (cf.,

  

  4.2. 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 curricular learning. First, a distinction was made between general and specific thinking skills. Second general thinking skills were interpreted as the general factor in a nested factorial solution and specific skills as secondary-level constructs (

  

Third, the general and the specific thinking skills were regarded from a point-of-view of educational intervention,

  modelling the class-level variance in the development of them. There is ample evidence of the use of developmentally oriented interventions for the advancement of thinking (

  

but the results of the present study indicate that schooling enhances thinking skills even without specific

  interventions. However, if the 21st century demands on learning will be is as unpredictable and fast changing as it has been claimed ( there is a risk that traditional subject knowledge-centred education will not suffice for the full development of the skills needed for leading a successful life. Work and social life will constantly afford novel tasks which cannot be solved by just applying earlier acquired knowledge. A new habit-of-mind is needed, to be built at school with an active agenda for nurturing the development of general cognitive competence and the attitudes and emotions supporting its use 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 of scientific thinking

  

Accordingly, 21st century skills can be seen to get advanced through teaching which is based

  on analysing the curricular content of each subject from the point-of view of thinking patterns like conservation, seriation, classification, combinatorial reasoning, analogical reasoning, proportional reasoning, probabilistic reasoning, correlational Please cite this article in press as: Vainikainen, M. -P., et al. General and specific thinking skills and schooling: Preparing

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  1

  1

  0.49 Formal 1 1491

  0.62

  1

  0.4 Quantitative 15 1452

  0.19

  1

  0.45 Quantitative 14 1401

  0.28

  1

  0.46 Quantitative 13 1454

  0.31

  0.49 Quantitative 12 1440

  0.49 Formal 2 1474

  0.38

  1

  0.5 Quantitative 11 1449

  0.51

  1

  0.47 Quantitative 10 1426

  0.66

  1

  0.45 Quantitative 9 1453

  0.72

  1

  0.17 Quantitative 8 1468

  0.58

  1

  1

  C) Verbal proportional 3 .460** .126** .177** .195** .119** .219** .273** .254**

  2 .416**

  J) Formal

  1 .430** .287**

  I) Formal

  4 .126** .184** .177**

  H) Quantitative

  3 .164** .203** .261** .251**

  G) Quantitative

  2 .296** .223** .261** .337** .305**

  F) Quantitative

  E) Quantitative 1 .276** .213** .146** .294** .335** .255**

  D) Verbal proportional 4 .220** .266** .218** .169** .230** .316** .338**