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In this paper, we discuss the theoretical foundation and implementation of two alternative instructional courses that aimed to support the development of elementary school students' early algebraic thinking. Both courses approached three basic algebra content strands: generalized arithmetic, functional thinking and modelling languages. The courses differed according to the characteristics of the tasks that were used. The first course involved 'pure mathematical guided investigations' emphasizing scaffolding steps in pure mathematics contexts. The second course focused on 'applied open explorations' underlining more open questions in applied everyday contexts. The courses were compared in respect to students' learning outcomes. The findings, yielded from the analysis of pre-test and post-test data, indicated that the second course had better learning outcomes compared to the first. [Translation from English by Silvia Montero.]

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The definite integral is a central concept in the applications of calculus to experimental sciences and engineering, and consequently, a relevant didactic research topic. This paper analyses the different meanings of the definite integral by applying theoretical tools of the ontosemiotic approach to mathematical knowledge and instruction, particularly, the interpretation of meaning in terms of systems of operational and discursive practices related to the resolution of types of problems and the algebraization levels model of mathematical activity. Types of problem-situations and configurations of practices, objects, and processes are identified that allow us to characterize and articulate the various partial meanings of the definite integral (geometric-intuitive, as a limit of Riemann sums and cumulative function) as well as its extensions to the case of the double integral (as a particular case of the multiple) and the line, from the most intuitive to the most formal. The analysis allows us to identify the generality degrees of the objects of integral calculus and the role of algebra in the characterization of the meanings of the definite integral, which must be considered in the planning and management of the processes of teaching and learning of integral calculus in engineering degrees. [ABSTRACT FROM AUTHOR]

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Copyright of Revista Electrónica Redes de Ingeniería is the property of Universidad Distrital Francisco Jose de Caldas, Facultad de Ingenieria and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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The goals of this paper fall into two closely related areas. First, we develop a formal framework for deterministic unital quantities in which measurement unitization is understood to be a built-in feature of quantities rather than a mere annotation of their numerical values with convenient units. We introduce this idea within the setting of certain ordered semigroups of physical-geometric states of classical physical systems. States are assumed to serve as truth makers of metrological statements about quantity values. A unital quantity is presented as an isomorphism from the target system's ordered semigroup of states to that of positive reals. This framework allows us to include various derived and variable quantities, encountered in engineering and the natural sciences. For illustration and ease of presentation, we use the classical notions of length, time, electric current and mean velocity as primordial examples. The most important application of the resulting unital quantity calculus is in dimensional analysis. Second, in evaluating measurement uncertainty due to the analog-to-digital conversion of the measured quantity's value into its measuring instrument's pointer quantity value, we employ an ordered semigroup framework of pointer states. Pointer states encode the measuring instrument's indiscernibility relation, manifested by not being able to distinguish the measured system's topologically proximal states. Once again, we focus mainly on the measurement of length and electric current quantities as our motivating examples. Our approach to quantities and their measurement is strictly state-based and algebraic in flavor, rather than that of a representationalist-style structure-preserving numerical assignment. [ABSTRACT FROM AUTHOR]

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In this paper we propose a tableaux method for the intermediate syllogistic of Peterson and Thompson by using the algebra of Sommers and Englebretsen. The result is an analytic tableaux method capable of modeling inference in basic, relational, and intermediate syllogistic. [ABSTRACT FROM AUTHOR]

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Copyright of Revista Integración is the property of Universidad Industrial de Santander and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents the partial results of a research on the professional knowledge of mathematics olympiad evaluators teachers put into action when analyzing errors relating to algebra. By means of two tests on errors interpretation and by using analysis inspired by the grounded theory, we obtained dimensions for the characterization of knowledge in understanding about errors. In the results section, we describe a teacher's knowledge related to practice and knowledge about students' learning. [ABSTRACT FROM AUTHOR]

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The article discusses concept of a prime number is no longer the same as before. It mentions about considering only the positive integers; and the consideration or not of 1 as a prime number. It mentions the connection of the theory of premises with mathematics constructive; and highlighting its important algebraic facet.

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article offers information on the mathematics and computing including calculation of the number of real roots, geometry and informal description of the concepts, problems and methods. Topics include geometric theorems, incorporation of computational algebra techniques and algebraic geometry theorems.

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