ive abilities in their intervention (or instruction), and relating them to general and specific achievement.

Besides the existence of the three models to explain the relation between intelligence, metacognitionand academic achievement (Veenman & Elshout, 1991; Veenman & Spans, 2005; Veenman et al., 1995, 2005), the results show that none of these are precise or complete to explain the data. In the intelligence model, general cognitive ability should explain school performance by itself (Veenman et al., 1997). However, that is not the case. The independent model, argues that metacognition is not related to intelligence accordingly (Veenman et al., 2005). This is also not assumed in this study, since Gf is directly explained by General Metacognitive Ability, and indirectly by the Monitoring Indicator and the Appraisal Ability on Mathematical Expressions. Furthermore, the mixed model could be the key to interpret the data of the study, whereas it postulates that both intelligence and metacognition explain school performance (Veenman & Spans, 2005). However, this could still be insufficient in explaining the results, as it points to the need of extending the traditional mixed model by adding two points. Usually the mixed and the other two models verify the metacognitive incremental validity using a general intelligence trait.

Modern intelligence models in the psychometrics area recognize that intelligence is much more than General Intelligence (Carroll, 1993; Floyd et al., 2009; McGrew, 2009; McGrew & Wendling, 2010; Newton & McGrew, 2010), being a broad set of abilities distributed in different strata or levels. So, the first proposal is to incorporate tasks and tests that measure abilities in different cognitive strata to investigate the incremental validity of metacognition rather than intelligence. The second proposal involves the incorporation of the aforementioned metacognitive architecture proposition, which defines the metacognitive abilities in a stratum-like organization. This proposal could bring new evidence on the relationship between cognition, metacognition and school achievement, investigating the role of different cognitive and metacognitive strata in the prediction of specific and general academic achievement.

Different limitations of this study can be highlighted. First of all, students from only one school composed the sample. The administration of extensive instruments and items in the sample was unfeasible because it would affect the schedule of the school, since a larger amount of tests to be administered would demand more time. Likewise, the collection of a larger sample seemed to be inconvenient to the school, which restricted a broader data collection. Secondly, the measure of academic achievement took into account exclusively Mathematics, Brazilian Portuguese, History and Geography grades. These four subjects are currently considered by the Brazilian Ministry of Education as representative of the overall academic achievement, regardless subjects like Biological Sciences and Writing. Unfortunately, this situation does not occur exclusively in Brazil, also happening in developed countries, like Germany (Steinmayr & Spinath, 2009). Thirdly, since Fluid Intelligence (Gf) can be regarded as the best predictor of intelligence (Carroll, 1993), this study follows the premise that a Gf indicator is sufficient to test the hypotheses we formulated. So we did not consider other intelligence factors, such as Crystalized Intelligence, Visual-Spatial Ability, Memory, along with others. Future studies could benefit from broadening the number of intelligence factors, seeking to replicate our results in face of a set of different broad cognitive abilities. Finally, metacognitive abilities were assessed only by two perspectives (self-appraisal and selfmonitoring) given that Schraw (1998) considers these are relevant metacognitive components. These limitations have economical and logistical reasons.

Despite these limitations, the incremental validity of psychological variables other than intelligence seems to be a valuable research agenda as it can be regarded as an important way of predicting future students’ academic achievement and learning performance.

5. Conclusion

The findings of this study provide new evidence that a General Metacognitive Ability can explain General Academic Achievement rather than intelligence, and a specific metacognitive ability explains specific academic achievement, rather than intelligence and specific knowledge. On the strength of these results, we could come to a conclusion that: 1) metacognition has incremental validity upon intelligence when predicting school performance, 2) metacognition can be either domain-general (e.g. General Metacognitive Ability) or domain-specific or both (e.g. Specific Metacognitive Ability); and 3) different metacognitive abilities, in distinct strata, can explain different school performances.

The current study is based upon some theoretical and methodological issues concerning the metacognitive research field: the necessity to distinguish cognitive components from metacognitive ones and using objective items, as well as to employ larger sample sizes. Moreover, this study suggests the development of a future research agenda concerned with: 1) the construction of a large set of metacognitive skills tests; 2) the selection of a large set of cognitive tests to assess both specific and broad abilities rather than the general cognitive ability; 3) the investigation of whether metacognitive abilities have incremental validity rather than specific, broad and general cognitive abilities; and 4) the examination of whether specific metacognitive and cognitive traits explain specific academic performances, as well as whether broad metacognitive and cognitive traits explain broad academic achievement.

Acknowledgements

The current research was financially supported by a grant provided by the Fundação de Amparo à Pesquisa de Minas Gerais (FAPEMIG) to the first two authors.

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