Rimas Norvaiša

Critical thinking in school mathematics

  Critical thinking in school mathematics

Rimas Norvaiša

Vilnius University, The Center for Mathematics Education, Lithuania

Critical thinking is a part of the cognitive competence included in the latest version of the Lithuanian curriculum framework. According to D.T. Willingham, thinking is defined as critical if it is novel, self-directed, and effective. In any school subject matter, the person’s thinking is self-directed if they are not merely executing instructions given by someone else. Additionally, their thinking is effective if they respect certain conventions that make thinking more likely to yield useful conclusions. The meaning of effective thinking depends on the subject matter of study. We discuss critical thinking in the context of school mathematics.

Thinking in school mathematics is effective if it follows habits of mathematical reasoning similar to those used in academic mathematics. Specifically, mathematical reasoning in a school context involves looking for patterns among mathematical objects, making, testing, proving or disproving conjectures, refining them, and, finally, communicating the results. The implementation of mathematical reasoning and critical thinking in schools depends on the alignment of the three dimensions of the curriculum. Aligning with these dimensions ensures that the educational goals set forth in the intended curriculum are what gets taught in the enacted curriculum and ultimately what students actually learn. Finally, all this depends on teacher preparedness to teach mathematical reasoning effectively.

Rimas Norvaiša is a professor with a habilitation degree in mathematics and serves as the Head of the Center for Mathematics Education at Vilnius University. He graduated from Vilnius University in 1980 and has been a researcher at the Institute of Data Science and Digital Technologies (formerly known by different names until 2018) at Vilnius University since 1991. From 1994 to 2006, he was a Visiting Scholar at the Massachusetts Institute of Technology. Between 2003 and 2018, he was a professor at the Faculty of Mathematics and Informatics at Vilnius University. Since 2018, he has been a Chief Researcher and Professor at the Institute of Applied Informatics at Vilnius University. He also served as the President of the Lithuanian Union of Scientists from 2010 to 2012.     Professor Norvaiša's research interests include probability theory, mathematical statistics, and function theory. He has published more than 50 scientific papers.