Eleventh-Grade High School Students’ Accounts of Mathematical Metacognitive Knowledge: Explicitness and Systematicity

  • Joke H. van VelzenEmail author


Theoretically, it has been argued that a conscious understanding of metacognitive knowledge requires that this knowledge is explicit and systematic. The purpose of this descriptive study was to obtain a better understanding of explicitness and systematicity in knowledge of the mathematical problem-solving process. Eighteen 11th-grade pre-university students solved two kinds of complex mathematical thinking problems that included the finding of a solution and the writing of mathematical texts and arguments. They also answered open-ended questions to obtain reasoned and reflective accounts regarding their metacognitive knowledge. Content analysis indicated 4 levels of explicitness and 5 levels of systematicity. Quantitizing of the accounts provided for a strong positive correlation with mathematical performance. It is concluded that explicitness and systematicity appeared to be potential indicators of the participants’ understanding of effective problem-solving strategies.


Mathematical writing Metacognition Planning Problem solving Secondary education 


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Copyright information

© Ministry of Science and Technology, Taiwan 2015

Authors and Affiliations

  1. 1.Research Institute of Child Development and EducationUniversity of AmsterdamAmsterdamThe Netherlands

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