I propose that attending how symbolizing activity functions for teachers and students helps to characterize student-teacher communication, and allows for an investigation of how symbolizing activity contributes to learning. I begin this discussion by articulating four ideas-schemes, symbolizing activity, communication, and learning. Then I propose…

Mathematics may be inconceivable without its diagrams and symbols--its representations. Mathematical representations help individuals organize their thinking; they bring a visual component to abstract ideas and serve as templates for computation with understanding. But the inevitability of representations is no guarantee that they are used…

A Latin square of order "n" is an "n" x "n" array using n symbols, such that each symbol appears exactly once in each row and column. A set of Latin squares is c ordered pairs of symbols appearing in the cells of the array are distinct. The popular puzzle Sudoku involves Latin squares with n = 9, along with the added condition that each of the 9…

The goal of the current research was to explore whether monkeys possess conceptual precursors necessary for understanding zero. We trained rhesus monkeys on a nonsymbolic numerical matching-to-sample task, and on a numerical ordering task. We then introduced nondifferentially reinforced trials that contained empty sets to determine whether monkeys…

Data suggests that a significant loss of African American students from STEM majors occur between their freshmen and sophomore year. This attrition corresponds to the time period when students encounter the calculus sequence. For this reason, calculus persists as a serious barrier preventing African American students from entering STEM fields.…

The algebraic expertise that mathematics education is aiming for includes both procedural skills and conceptual understanding. To capture the latter, notions such as symbol sense, gestalt view and visual salience have been developed. We wonder if digital activities can be designed that not only require procedural algebraic skills, but also invite…

When teachers provide students with every opportunity to visually understand a mathematical concept, process, definition, or notation, they allow them to construct and manipulate relevant and useful images in their minds. Visual understanding has a dynamic character that they do not easily develop with alphanumeric symbols alone despite the…

This paper describes the use of diagrams as self-explanatory tools. It considers the use of diagrams, in general, and more specifically, examines research that is currently being undertaken in the broad field of visualisation. The research participants referred to in this article were Advanced Certificate of Education students and the paper…

Research documents an income-based achievement gap in mathematics, yet children from lower-income backgrounds do not lag behind their more advantaged peers in high-level social reasoning tasks. The purpose here was to investigate whether modifying mathematics word problems to make them more socially based would impact the mathematics performance…

The purpose of this study was to extend existing research relative to the predictors of early mathematics skills. Using Vygotskian theory as a framework, our primary goal was to determine whether social skills or letter awareness skills served as better mediators between receptive language and early mathematics concepts. The secondary goal was to…

The author has worked for three days on a range of mathematical tasks in order to gain a deeper understanding of the role of notation in mathematics education. The general conclusions were that while mathematical notation can be powerful it can also be obstructive. In this article, the author explores the importance on notation in supporting…

Although it is often assumed that abilities that reflect basic numerical understanding, such as numerical comparison, are related to children's mathematical abilities, this relationship has not been tested rigorously. In addition, the extent to which symbolic and nonsymbolic number processing play differential roles in this relationship is not yet…

Children take years to learn symbolic arithmetic. Nevertheless, non-human animals, human adults with no formal education, and human infants represent approximate number in arrays of objects and sequences of events, and they use these capacities to perform approximate addition and subtraction. Do children harness these abilities when they begin to…

An elusive probability paradox is analysed. The fallacy is traced back to improper use of a symbol that denotes at the same time a random variable and two different values that it may assume.

This study investigated how a teacher in a multilingual classroom attempted to support learners who are struggling to translate written/verbal mathematics into a symbolic form. Thirty-six Grade ten learners in one multilingual classroom in South Africa were given a written test involving one algebraic question and then a discussion on the solution…