The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to…

Teachers' understanding of the concepts they teach affects the quality of instruction and students' learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers' knowledge of key concepts underlying fraction arithmetic. Teachers' explanations were coded based on the accuracy of their…

This paper focuses on the mathematical sensemaking by women of color in the USA as part of the global effort of dismantling deficit narratives about historically marginalized groups of students. Following Adiredja's anti-deficit framework for sensemaking, this cognitive study invited a group of women of color to share their understanding of basis…

Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits…

This paper presents findings from a larger research project that provides insight into the attitudes of high-school students who were taught using different types of mathematics curricula when they were in middle school. A total of 44 12th-grade students from 10 high schools in the same urban school district were interviewed. Eighteen (41%) of…

The teaching objectives and curriculum content of the secondary school mathematics program in China are discussed. Public examination papers and classroom teaching methods are described, with specific examples. (MNS)