Metacognitive Knowledge and Mathematical Intelligence—Two Significant Factors Influencing School Performance

Chytrý, Vlastimil; Říčan, Jaroslav; Eisenmann, Petr; Medová, Janka

doi:10.3390/math8060969

Cited by 17 publications

(16 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…All the factors influencing the ability to solve mathematical problems can be divided into the three following groups: metacognitive, cognitive, and affective. It has been shown that higher metacognitive knowledge, i.e., the ability to monitor one's activity and regulate learning [45], may increase students' ability to solve mathematical problems [46][47][48][49][50][51][52]. In the affective area, a mutual effect is observed.…”

Section: Mathematical Problem-solvingmentioning

confidence: 99%

Relation between Pupils’ Mathematical Self-Efficacy and Mathematical Problem Solving in the Context of the Teachers’ Preferred Pedagogies

et al. 2020

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Mathematical Problem-solvingmentioning

confidence: 99%

Relation between Pupils’ Mathematical Self-Efficacy and Mathematical Problem Solving in the Context of the Teachers’ Preferred Pedagogies

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this way, affordable mathematical tools provided to students advances learning. Metacognitive knowledge and mathematical intelligence are independent [36]. Metacognitive knowledge can be understood as the ability to recognize the strengths and weaknesses of one's learning process and the subsequent ability to correct them [37], as well as possessing the mathematical intelligence to solve mathematical problems [38].…”

Section: Discussionmentioning

confidence: 99%

“…The first term corresponded to the increase in length due to Hooke's law; the second corresponded to the increase in length due to temperature; the third corresponded to the increase in cable length to be added to the straight line r ab that defined the profile of the cable, s c (see Figures 5 and 6). The negative sign of this third summand corresponded to the fact that point b, when bending the cable in Phase II, moved to the left (negative direction, Equation (36)).…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, we have obtained an expression for u(x) and sc(x). If w is substituted according to (36), then (39) can be solved as Replacing (38) with (37) and approximating for small values of ϕ results in…”

Section: Segment 2: Curved Segment-segment A-bmentioning

confidence: 99%

“…Therefore, we have obtained an expression for u(x) and s c (x). If w is substituted according to (36), then (39) can be solved as…”

Section: Segment 2: Curved Segment-segment A-bmentioning

confidence: 99%

See 2 more Smart Citations

A Didactic Procedure to Solve the Equation of Steady-Static Response in Suspended Cables

et al. 2020

View full text Add to dashboard Cite

Students in the electrical branch of the short-cycle tertiary education program acquire developmental and design skills for low voltage transmission power lines. Aerial power line design requires mathematical tools not covered well enough in the curricula. Designing suspension cables requires the use of a Taylor series and integral calculation to obtain the parabola’s arc length. Moreover, it requires iterative procedures, such as the Newton–Raphson method, to solve the third-order equation of the steady-static response. The aim of this work is to solve the steady-static response equation for suspended cables using simple calculation tools. For this purpose, the influence of the horizontal component of the cable tension on its curvature was decoupled from the cable’s self-weight, which was responsible for the tension’s vertical component. To this end, we analyzed the laying and operation of the suspended cables by defining three phases (i.e., stressing, lifting, and operation). The phenomena that occurred in each phase were analyzed, as was their manifestation in the cable model. Herein, we developed and validated the solution of the steady-static response equation in suspended cables using simple equations supported with intuitive graphics. The best results of the proposed calculation procedure were obtained in conditions of large temperature variations.

show abstract

Metacognitive strategies in solving mathematical word problems: a case of Rwandan primary school learners

Kusaka

Ndihokubwayo

2022

SN Soc Sci

View full text Add to dashboard Cite

This study aims to understand the use of metacognitive skills by Rwandan learners while solving mathematical word problems. We interviewed and assessed third-, fourth- and fifth-grade learners from a public primary school. The following three points emerged. First, the metacognitive skills of learners with correct answers were considerably higher than that of those with incorrect answers. Second, although there was no considerable difference in metacognitive skills between learners who answered correctly and those who did not at the stage of ‘understand the problem’, considerable differences were observed in the ‘search for solving methods’ and ‘execute the solving methods’ and ‘examine the answer’ stages. During the ‘search for solving methods’ and ‘execute the solving methods’ stage, learners who answered correctly mainly used three metacognitive skills to control their learning—‘writing the process by sentences’, ‘drawing tables’ and ‘drawing pictograms’. Third, when metacognitive skills were measured and scored, the average scores for fifth and third graders were similar. The interview revealed that the teachers of third graders taught them metacognitive strategies in mathematics lessons. It can be inferred that consequently, the metacognitive skills of third graders were raised to be as high as those of fifth graders. Although this is only a single empirical study in Rwanda, it is a major step towards improving the standard of mathematics education in African countries. In the future, similar research must be conducted in other African countries to accumulate relevant research results.

show abstract

Metacognitive Knowledge and Mathematical Intelligence—Two Significant Factors Influencing School Performance

Cited by 17 publications

References 65 publications

Relation between Pupils’ Mathematical Self-Efficacy and Mathematical Problem Solving in the Context of the Teachers’ Preferred Pedagogies

Relation between Pupils’ Mathematical Self-Efficacy and Mathematical Problem Solving in the Context of the Teachers’ Preferred Pedagogies

A Didactic Procedure to Solve the Equation of Steady-Static Response in Suspended Cables

Metacognitive strategies in solving mathematical word problems: a case of Rwandan primary school learners

Contact Info

Product

Resources

About