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Classroom communication has been recognized as a process in which ideas become objects of reflection, discussion, and amendments affording the construction of private mathematical meanings that in the process become public and exposed to justification and validation. This paper describes an explanatory model named “interpreting games”, based on the semiotics of Charles Sanders Peirce, that accounts for the interdependence between thought and communication and the interpretation of signs in which teacher and students engage in mathematics classrooms. Interpreting games account both for the process of transformation (in the mind of the learner) of written marks into mathematical signs that stand for mathematical concepts and for the continuous and converging private construction of mathematical concepts. Teacher–student and student–student collaborative interactions establish a mathematical communication that shapes and is also shaped by the conceptual domains and the domains of intentions and interpretations of the participants. A teaching episode with third graders is analyzed as an example of a classroom interpreting game. [ABSTRACT FROM AUTHOR]

This study aims to determine how prospective middle school mathematics teachers respond to students' errors in the questions about the equal sign. This study utilizes case study method. In this case study, hypothetical scenarios, involving three common error types related to the equal sign, have been prepared by using the possible examples of student work. Through these scenarios, one-to-one interviews were conducted with seven prospective middle school mathematics teachers. In line with the data obtained in these interviews, it was seen that the prospective teachers used seven different ways to respond to students' errors related to the equal sign: showing the error, showing the right solution, guiding to find the right answer, guiding to find the error, re-explaining the concept, in-depth research, and false intervention. In addition, it was determined that two prospective teachers intervened incorrectly by taking an approach that could support the thought that led to the error. In the light of the findings, it was seen that the prospective teachers had a limited understanding of the equal sign. This study suggests that mathematics educators should create appropriate learning opportunities to improve prospective teachers' understanding of the equal sign and their ability to respond to students' errors. [ABSTRACT FROM AUTHOR]

This paper attempts to analyse how the concept of the equal sign is introduced to learners in Grade 1 textbooks in use in South Africa. In doing this, three Grade 1 textbooks (learner’s book and their accompanying teacher’s guide) were analysed in terms of the first appearance of the equal sign. Analysis reveals that the equal sign is introduced operationally and its introduction is subsumed in the introduction of the addition and subtraction signs. The author argues for the equal sign to be accorded equal status and attention as the addition and subtraction symbols by both the curriculum and Grade 1 textbooks and also makes an argument for the introduction of the equal sign first (using appropriate pictorial representations and artefacts) before the introduction of the plus and minus signs.