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

Abstract

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.

Aspects of self-regulated learning and their influence on the mathematics achievement of fifth graders in the context of four different proclaimed curricula

“…The tool was created by combining the two different tools tested in CERMAT (a company designing the national testing) research, MA2ACZZ506DT (test A) and M5PZD15C0T01 (test B). The renumbering of individual items and their adjustment is described in detail in Chytrý et al ( 2020 ). To verify the content validity, expert opinions were considered.…”

“…Moreover, sensitivity was solved using a point biserial sensitivity coefficient. Compared to our previous study (Chytrý et al, 2020), one item was excluded, due to the incorrect use of confidence scales by pupils. Pupils could achieve 0-20 points in the final version of the math achievement test.…”

The influence of students’ problem-solving understanding and results of students’ mathematics learning

“…Understanding the problem as a part of problem-solving steps involves students' cognitive processes to solve the problem and communicate the solution (OECD, 2003). The success of good students' mathematics performance is dependent on their ability to solve problems and understand when and how to apply knowledge and ability (Chytrý et al, 2020).…”

Effect of Blended Learning Models and Self-Efficacy on Mathematical Problem-Solving Ability

“…Self-efficacy is one of the main factors that can affect the success of blended learning. It also has an impact on students' choices, level of motivation, and resistance to adversity (Chytrý et al, 2020). Those with high self-efficacy generally tend to have certain beliefs, accurately perform assigned tasks, are determined, and tend to think clearly, and are therefore highly confident when solving a problem (Wiginton, 2013).…”