Metacognitive knowledge and mathematical intelligence were tested in a group of 280 pupils of grade 7 age 12–13 years in the Czech Republic. Metacognitive knowledge was tested by the tool MAESTRA5-6+. Mathematical intelligence is understood as an important criterion of a learner’s ability to solve mathematical problems and defined as the specific sensitivity to the six particular phenomena: causality, patterns, existence and uniqueness of solution, geometric imagination, functional thinking, and perception of infinity. The main objective of the research is to explore relationships and links between metacognitive knowledge and mathematical intelligence of the learners and discover the scope of impacts of their metacognitive knowledge on the school success rate. Based on the collected answers and nearly zero correlation (r = 0.016) between the researched domains, a two-dimensional model considering the correlations between metacognitive knowledge and mathematical intelligence was designed. The developed model enables to describe an impact of the domains on the learner’s school performance within the selected school subjects, and concurrently, it emphasizes their importance within the educational practice as such.
In research focused on self-efficacy it is usually teacher-related phenomena that are studied, while the main aspects related to pupils are rather neglected, although self-efficacy itself is perceived as a belief in one’s own abilities. Evidently, this strongly influences the behavior of individuals in terms of the goal and success in mathematical problem-solving. Considering that alternative teaching methods are based on the principle of belief in one’s own ability (mainly in the case of group work), higher self-efficacy can be expected in the pupils of teachers who use predominantly the well-working pupil-centered pedagogies. A total of 1133 pupils in grade 5 from 36 schools in the Czech Republic were involved in the testing of their ability to solve mathematical problems and their mathematical self-efficacy as well. Participants were divided according to the above criteria as follows: (i) 73 from Montessori primary schools, (ii) 332 pupils educated in mathematics according to the Hejný method, (iii) 510 pupils from an ordinary primary school, and (iv) 218 pupils completing the Dalton teaching plan. In the field of mathematical problem-solving the pupils from the Montessori primary schools clearly outperformed pupils from the Dalton Plan schools (p = 0.027) as well as pupils attending ordinary primary schools (p = 0.009), whereas the difference between the Montessori schools and Hejný classes was not significant (p = 0.764). There is no statistically significant difference in the level of self-efficacy of pupils with respect to the preferred strategies for managing learning activities (p = 0.781). On the other hand, correlation between mathematical problem-solving and self-efficacy was confirmed in all the examined types of schools. However, the correlation coefficient was lower in the case of the pupils from the classes applying the Hejný method in comparison with the pupils attending the Montessori schools (p = 0.073), Dalton Plan schools (p = 0.043), and ordinary primary schools (p = 0.002). Even though the results in mathematical problem-solving are not consistent across the studies, the presented results confirm better performance of pupils in some constructivist settings, particularly in the case of individual constructivism in the Montessori primary schools. The factors influencing lower correlation of self-efficacy and performance in mathematical problem-solving ought to be subject to further investigation.
Metacognition is a part of the models of self-regulated learning. The consideration of a broader context resonates with a social cognitive perspective approach to learning which dominates the educational academic field with the theory of self-regulated learning. Metacognition is considered a crucial factor influencing mathematics achievement. Furthermore, the affective field including pupils' self-efficacy, interest and motivation are the phenomena involved in mathematical problem-solving. On the other hand, metacognitive knowledge and metacognitive regulations are not a regular part of mathematics education in the Czech Republic. The main aim of this study was to investigate the relation between pupils' attitude toward mathematics; metacognitive knowledge; self-efficacy and motivation; metacognitive monitoring; and their achievement in solving mathematical problems. All together 1,133 students of Grade 5 from four types of Czech schools participated in the study. There were traditional schools; schools teaching mathematics by genetic constructivism, i.e., Hejný's method; Montessori schools; and Dalton schools were involved. The assessed variables, namely relation to mathematics; metacognitive knowledge; self-efficacy and motivation; metacognitive monitoring; and mathematical achievement were used as an input to regression analysis. Item-response theory was used for assessing the performance of the students and demands of the tasks. The metacognitive monitoring was detected as the most significant predictor of mathematics achievement for higher- and lower-performing students as well as for the item with high and low demands. The study reveals how the different mathematics curricula (un)support the metacognitive processes involved in mathematical problem-solving. The information allows teachers to spend sufficient time with particular types of mathematics problems whose solutions is determined by activation of metacognitive processes. This demonstrates the importance of including the activities for development of metacognitive monitoring in mathematics education.
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