Mathematical thinking and understanding in learning of mathematics

The concept “mathematical thinking” can be found in several studies of mathematics education, in national curricula or in media during the decades all over the world. We searched words “mathematical thinking” from the database of international scientific articles, and we found 456 707 mentions at first time. These are the main reasons why we have chosen “mathematical thinking” as the central concept of the Special Issue. The other interesting question from our point of view is how a student can express his/her mathematical thinking? By answering this question, we have made simple model for the teacher education purposes, and we call it “languaging” (of mathematical thinking). The articles of the Special Issue gives some answers to the questions: “What is mathematical thinking and how we can express it?” and “What are the relationships between conceptual understanding and mathematical thinking?”.nonPeerReviewe