Metacognition demonstrates great potential to equip children to become successful learners. Metacognition’s significance for mathematical competence is especially proven (Siagian et al., 2019). Therefore, attention should be paid to metacognition throughout students’ school path.

The most prominent definition of metacognition comes from the psychologist Flavell (1979); it refers to individuals’ knowledge of their own cognitive processes and their ability to regulate these processes. Most theoretical definitions distinguish between metacognition into metacognitive knowledge (later in this paper McKnow) and metacognitive skills (later McSkil) (Desoete & De Craene, 2019). McKnow refers to individuals’ knowledge of how people learn and process information, and it is categorised into strategy, task, and person knowledge (Flavell, 1979). Instead, Conrady (2015) distinguishes knowledge to declarative, procedural, and conditional knowledge. McSkil indicates the ability to consider one's actions and, when necessary, correct them (Schraw et al., 2006). Scholars (Schraw et al., 2006) define McSkil into evaluation, debriefing, planning, information management, and monitoring.

Several studies about metacognition in mathematics learning are conducted. Studies have highlighted the significant role of metacognition in performance and supporting the selection of learning strategies and fostering the development of self-regulatory (Desoete & De Craene, 2019). In this study, metacognition is explored more detailed subcomponents of metacognition. The research questions are as follows: what subcomponents of metacognition are recognisable from students’ answers about a problem-solving task, math, and its learning? How do subcomponents differ among different age students?

In total, our sample was comprised of 225 students from one school: 71 of them are sixth-graders (about age 12), 81 are in grade seven (around age 13) and 73 are in ninth-grade (near age 15). During data collection, students solved a mathematical problem-solving task and participated in an interview. In the interview, students used a tool called Reflection Landscape, which supports to describe own cognitive processes by visual representation. The interview questions covered the problem-solving task, mathematics, and its learning. The data were examined by qualitative theory-guided content analysis (Kohlbacher, 2006). As a theoretical framework, we used metacognition taxonomies by Conrady (2015), Flavell (1979) and Schraw et al (2006). A frequency table was generated and tested based on observed metacognition using K-means cluster analysis. The Chi-square test determined whether statistically significant differences existed between groups based on cluster analysis.

We found references to all McKnow subcomponents, a total of 1646. Compared to McKnow, much fewer subcomponents of McSkil (N=288) were found and only three of five were identified in the data. Our analysis resulted in four final groups that encompassed metacognition subcomponents in the data. Group 1 (n=55) was characterised by declarative and strategy knowledge. Instead, students in group 2 (n=38) share a high degree of variation in McKnow, mentioning several times all McKnow subcomponents. One of the largest groups, group 3 (n=66) had by far the lowest number of observed metacognition subcomponents. Members of the group have two commonalities: indications only of declarative and strategy knowledge. In group 4 (n=66), the second one of the largest groups, responses were evenly spread across person, strategy, and task knowledge. Moreover, declarative, procedural, and conditional knowledge was also highly observed, although declarative information was the most plentiful. Statistically significant differences between groups and grades were found (ꭕ²(6)=33.313, p<.001, V=.27). In group 3, we found an over-representation of 6th-graders between the observed and expected number of students and an under-representation of 9th-graders. In addition, an over-representation of ninth graders in group 4 was evident. We found that students had a high number of McKnow, but McSkil often remained unlikely. However, studies (Desoete & De Craene, 2019) suggest that metacognition should be fully developed by age 12. This may refer that students’ metacognition lacks mathematics-specific concepts and needs more activating (Siagian et al., 2019). Students' metacognitive processes have a variety of components, mostly staying in the declarative level of McKnow. However, high-level components of McSkil were also recognized. Previous studies (Desoete & De Craene, 2019; Siagian et al., 2019) support that metacognition is an ongoing process, which needs to be included in mathematics learning to make learning process more aware.

Conrady, K. (2015). Modeling Metacognition: Making Thinking Visible in a Content Course for Teachers. Journal of Research in Mathematics Education, 4(2), 132–160. https://doi.org/10.17583/redimat.2015.1422 Desoete, A., & De Craene, B. (2019). Metacognition and mathematics education: An overview. ZDM, 51(4), 565–575. Flavell, J. (1979). Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry. American Psychologist, 34(10), 906–911. https://doi.org/10.1037/0003-066X.34.10.906 Kohlbacher, F. (2006). The Use of Qualitative Content Analysis in Case Study Research. Forum: Qualitative Social Research, 7(1), 1–30. https://doi.org/10.17169/fqs-7.1.75 Schraw, G., Crippen, K. J., & Hartley, K. (2006). Promoting Self-Regulation in Science Education: Metacognition as Part of a Broader Perspective on Learning. Research in Science Education, 36(1), 111–139. https://doi.org/10.1007/s11165-005-3917-8 Siagian, M. V., Saragih, S., & Sinaga, B. (2019). Development of Learning Materials Oriented on Problem-Based Learning Model to Improve Students’ Mathematical Problem Solving Ability and Metacognition Ability. International Electronic Journal of Mathematics Education, 14(2). https://doi.org/10.29333/iejme/5717