Errors in algebraic statements translation during the creation of an algebraic domino

We present a research study which main objective is to inquire into secondary school students´ ability to translate and relate algebraic statements which are presented in the symbolic and verbal representation systems. Data collection was performed with 26 14-15 years old students to whom we proposed the creation of an algebraic domino, designed for this research, and its subsequent use in a tournament. Here we present an analysis of the errors made in such translations. Among the obtained results, we note that the students found easier to translate statements from the symbolic to the verbal representation and that most errors in translating from verbal to symbolic expressions where derived from the particular characteristics of algebraic language. Other types of errors are also identified. KEYWORDS: Algebraic language, domino, errors, translation between representation systems, verbal representation

The Emergence of Symbolic Algebra as a Shift in Predominant Models

Historians of science find it difficult to pinpoint to an exact period in which symbolic algebra came into existence. This can be explained partly because the historical process leading to this breakthrough in mathematics has been a complex and diffuse one. On the other hand, it might also be the case that in the early twentieth century, historians of mathematics over emphasized the achievements in algebraic procedures and underestimated the conceptual changes leading to symbolic algebra. This paper attempts to provide a more precise setting for the historical context in which this decisive step to symbolic reasoning took place. For that purpose we will consider algebraic problem solving as model-based reasoning and symbolic representation as a model. This allows us to characterize the emergence of symbolic algebra as a shift from a geometrical to a symbolic mode of representation. The use of the symbolic as a model will be situated in the context of mercantilism where merchant activity of exchange has led to reciprocal relations between money and wealth

Symbolic Representation in Native American Lumbee Art

The purpose of this thesis was to examine the art and craft products of the Lumbee to determine the extent to which their symbolic representations and artistic responses reflected the influences of their past heritage and existing culture. The descriptive nature of this study entailed personal interviews of Lumbee artists, photography of data, examination and comparison of other Native American arts and crafts, examination of pertinent literature, the maintenance of field notes for verification of data and the investigator’s personal observations and interpretations. With more than a hundred years of pursuing recognition, it was important to examine the symbolic representations of the Lumbee. These symbols and icons could also be considered a contributing component of their physical and cultural environment. The findings from this study indicated that the pinecone-quilting motif is recognized as a Lumbee symbol and has been used by the Lumbee for more than a century. The findings also include some shared imagery and craft productions of other Native American tribes with the Lumbee. However, first-hand interviews lead the researcher to understand that some symbolic representations vary in meaning from tribe to tribe. Pine needle baskets are another product unique to the Lumbee because of the materials (long leaf pine needles and tobacco twine) used for production, even though other cultures produce similar baskets using different materials. One concludes that the study gave evidence of a symbolic image produced and used by the Lumbee as their representative icon

On a representation of time space-harmonic polynomials via symbolic L\'evy processes

In this paper, we review the theory of time space-harmonic polynomials developed by using a symbolic device known in the literature as the classical umbral calculus. The advantage of this symbolic tool is twofold. First a moment representation is allowed for a wide class of polynomial stochastic involving the L\'evy processes in respect to which they are martingales. This representation includes some well-known examples such as Hermite polynomials in connection with Brownian motion. As a consequence, characterizations of many other families of polynomials having the time space-harmonic property can be recovered via the symbolic moment representation. New relations with Kailath-Segall polynomials are stated. Secondly the generalization to the multivariable framework is straightforward. Connections with cumulants and Bell polynomials are highlighted both in the univariate case and in the multivariate one. Open problems are addressed at the end of the paper

Music to measure: symbolic representation in children's composition.

Eisner maintains that the arts education community needs "empirically grounded examples of artistic thinking related to the nature of the tasks students engage in, the material with which they work, the context's norms and the cues the teachers provide to advance their students' thinking" (2000, p. 217). This paper reflects on the results of collaborative action research between teachers and university researchers in New Zealand who have been investigating how children develop and refine their ideas and related skills in music. The paper focuses specifically on the results of action research in which the impact of symbolic representation on idea development and refinement in music is examined. It raises some issues and points of tension for generalist and specialist teachers when fostering creative idea development in music