Role of an artefact of Dynamic algebra in the conceptualisation of the algebraic equality

In this contribution, we explore the impact of Alnuset, an artefact of dynamic algebra, on the conceptualisation of algebraic equality. Many research works report about obstacles to conceptualise this notion due to interference of the previous arithmetic knowledge. New meanings need to be assigned to the equal sign and to letters used in algebraic expressions. Based on the hypothesis that Alnuset can be effectively used to mediate the conceptual development necessary to master the algebraic equality notion, two experiments have been designed and implemented in Italy and in France. They are reported in the second part of this pape

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.

Solving a contextual problem with the spreadsheet as an environment for algebraic thinking development

In this article we report and discuss a contextual problem solving task that was proposed to a class of 8th grade (13–14-year-old) students. These students had been developing a reasonable experience in the use of the spreadsheet to model relations within contextual problems and chose to use this tool to solve the mentioned problem, engaging in the process of translating relations between variables and combining them in chained models, while working with fractions, multiples and expressions. We intend to highlight the role of the spreadsheet in students’ processes of variable identification and translation of the problem conditions, their numerical approaches to algebraic models and their experimental forms of finding solutions to equations

The design of new digital artefacts as key factor to innovate the teaching and learning of algebra: the case of Alnuset

no abstract availabl

Peirce's sign theory as an open-source R package.

Throughout Peirce’s writing, we witness his developing vision of a machine that scientists will eventually be able to create. Nadin (2010) raised the question:Why do computer scientists continue to ignore Peirce’s sign theory? A review of the literature on Peirce’s theory and the semiotics machine reveals that many authors discussed the machine;however, they donot differentiate between a physical computer machine and its software. This paper discusses the problematic issues involved in converting Peirce’s theory into a programming language, machine and software application. We demonstrate this challenge by introducing Peirce’s sign theory as a software application that runs under an open-source R environmen

Algebra Education and Digital Resources: A Long-Distance Relationship?

This chapter considers the general question of how technology impacts mathematical contents for the case of algebra and addresses it from the conceptual notion of instrumental distance. It first provides an overview of perspectives on the teaching and learning of algebra in primary and secondary education. Next, it presents the theoretical lens of instrumental distance, used to study how these algebraic contents are transformed by digital tools. Using three examples of digital resources that cover different school levels and different types of design, the chapter shows that this lens indeed reveals how digital technology may create distance with respect to the regular algebraic contents and procedures carried out in the paper-and-pencil environment. The results thus raise awareness not only of new potentialities, but also of the complexity generated by technology. They suggest that being aware of the instrumental distance would be beneficial while developing digital resources and professional development programs that aim to integrate digital technologies into the teaching and learning of algebra

TELMA Cross Experiment Guidelines

Cerulli, M., Pedemonte, B., Robotti, E. (eds.). Internal Report, R.I. 01/07, I.T.D. - C.N.R., GenovaThis document contains the guidelines developed by members of TELMA as a means for planning, conducting, and analysing a cross experiment aimed at contributing to the construction of a shared research perspective among TELMA teams . This is the product of the PhD students and young researchers that brought forward the whole activity. The actual experimental phase was proceeded by a reflective phase in which an agreement was achieved on what research questions to address during the experiment. On this basis the first version of the guidelines document was built, containing all the research questions to be addressed, but also the experimental plans for each team. This included the employed didactical functionalities of the considered ICT tools, indications of the experimental settings, and the methods of data collection and analysis. During the whole experimental phase, the document was constantly updated, and shared among the involved persons which were periodically required to compare the different activities and reflections brought forward by all the teams