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Existing research suggests that young children can develop a partial understanding of the equal sign as an operator rather than as a relational symbol of equivalence. This partial understanding can be the result of overemphasis on canonical equation syntaxes of the type a + b = c in elementary school mathematics. This paper presents an examination of context and syntax nuances of relevant sections from the grade 1 Greek series of textbooks and workbooks. Using a conceptual framework of context variation, the analysis shows qualitative differences between equations of similar syntax and provides a nuanced determination of contextual and structural aspects of 'variation' in how the equal sign is presented in elementary mathematics. The paper proposes that since equations have context-specific meanings, context variations should constitute a separate element of analysis when investigating how the equal sign is presented. The implication for practice and future research is that nuanced considerations of equation syntax within varied contexts are needed for elaborating analyses of the equal sign presentation that move beyond dichotomized categorizations of canonical/non-canonical syntaxes. [ABSTRACT FROM AUTHOR]

The paper explores and analyzes the influences of game and mathematical symbols on the poetry of the Romanian modern poet Ion Barbu. The paper presents the analysis of the theories of game as a poetic art as well as the analysis of the links between science and poetry in the poeworks of Ion Barbu - links which led to the conclusion that his poetry is imbued with mathematical symbols. This was the reason why literary critics reviewed his work as original and a novelty in Romanian literature. Poet and mathematician Ion Barbu (Dan Barbilian) became known as one of the most significant modern poets of Romania, Barbus' lyric went not only through different phases distinct by various specific representations, but it also went through language modifications. Thus the motive of the game which we encounter in Barbu's poetry changes according to the literary phase through which the poet goes. The analysis of game as ars poetica by critics and other foreign and Romanian researchers represents the point of departure of this paper while the goal of this research is to identify those components which demonstrate that game is not only a cultural and literary topic but also a way of life. Literature itself is a game of time and space, a game of different eras and fashions. Poetry is a game of words and a creator of a fascinating imaginary and complex space. Life unfolds within the space of an intellectual game, in a world created by the mind where things are different from those in real life and linked with links other than the logical ones. Game is thus an element that belongs within the field of poetry and every poetic form seems closely tied to the structure of the game. [ABSTRACT FROM AUTHOR]

Our understanding of proportions can be both symbolic, as when doing calculations in school mathematics, or intuitive, as when folding a bed sheet in half. While an understanding of symbolic proportions is crucial for school mathematics, the cognitive foundations of this ability remain unclear. Here we implemented a computerized training game to test a causal link from intuitive (nonsymbolic) to symbolic proportional reasoning and other math abilities in 4th grade children. An experimental group was trained in nonsymbolic proportional reasoning (PR) with continuous extents, and an active control group was trained on a remarkably similar nonsymbolic magnitude comparison. We found that the experimental group improved at nonsymbolic PR across training sessions, showed near transfer to a paper-and-pencil nonsymbolic PR test, transfer to symbolic proportions, and far transfer to geometry. The active control group showed only a predicted far transfer to geometry. In a second experiment, these results were replicated with an independent cohort of children. Overall this study extends previous correlational evidence, suggesting a functional link between nonsymbolic PR on one hand and symbolic PR and geometry on the other. [ABSTRACT FROM AUTHOR]