Abstract Our study analyses the general method for solving polynomial equations that the Valencian mathematician José Zaragoza exposed in his book Arithmetica Universal, published for the first time in 1669. This method is based on the one developed by Vieta, which was published in his book De numerosa potestatum (1600), and it is an evolution of the ancient Babylonian method for calculating roots. Specifically, this resolution method is based on the binomial expansion of the powers involved in the equation, and it has two key points: the selection of the number of digits in the solution and the selection of the appropriate divisor for estimating the successive digits. The configuration used by Zaragoza includes tables and detailed explanations of the different ramifications of the process and these didactic aspects allow us to highlight Zaragoza’s work, when we compare it with other European mathematicians who used this method during the 17th century. Universal 1669 Vieta 1600, 1600 , (1600) roots Specifically equation points Zaragozas s work th century 166 160 (1600 16 (160 1 (16 (1 (

Resumen En el presente trabajo se estudia el método general de resolución de ecuaciones polinómicas que expuso el matemático valenciano José Zaragoza en su libro Arithmetica Universal, publicado por primera vez en 1669. Este método está basado en el desarrollado por Viète y publicado en su libro De numerosa potestatum, de 1600, y es una evolución del antigüo método babilonio de cálculo de raices. En concreto, este método de resolución se basa en la expansión binomial de las potencias implicadas en la ecuación, detectando dos puntos clave: uno es la selección del número de dígitos de la solución y otro es la selección del divisor adecuado para la estimación de los sucesivos dígitos. El uso de tablas y la explicación detallada de las diferentes ramificaciones del proceso hacen que la configuración empleada por Zaragoza sea muy didáctica, incluso más que la de algunos de los diferentes matemáticos europeos que emplearon este método durante el siglo XVII. Universal 1669 potestatum 1600 raices concreto ecuación clave didáctica XVII 166 160 16 1

This study presents the perceptions of trainee teachers regarding the realisation of practical mathematical sessions to expand on the concepts that are taught in primary education using manipulatives. For a 4-month period, a practical session with the mentioned characteristics was carried out weekly with Year 1 students of the Primary Education Teaching Degree. After their completion of the module the students were requested to comment in writing on the utility of such practical sessions. The resulting information was analysed qualitatively through content analysis using ATLAS.ti software (Version 7.5.4). Six broad categories grouping the utilities considered by the students were found.

Abstract This paper shows a study about some mathematics books written in Spanish and published during the 16th century. All the examples included in these books and their relations with daily situations from that time have been identified and categorized. In order to do that, we made an historical-mathematical analysis supported by the content analysis technique of textbooks, widely used by authors in researches related to the history of mathematics and mathematics education. In general, all the books included in this study present many similarities. The analysis has highlighted the large number of examples included in each book even though most of them are related to trade and to common situations of accountants and businessmen of that century.

Resumen Este trabajo presenta un estudio sobre algunos libros de matemáticas publicados en castellano durante el siglo XVI. A lo largo de él, se han identificado y categorizado los ejemplos utilizados en estos manuales y su relación con las situaciones cotidianas de la época. Para ello se ha realizado un análisis histórico-matemático apoyado en la técnica de investigación del análisis de contenido de libros de texto, ampliamente utilizado por diversos autores en investigaciones relativas a la Historia de las Matemáticas y la Educación Matemática. Todas las obras analizadas presentan, en general, bastantes similitudes. En ellas se incluyen un elevado número de ejemplos aunque la gran mayoría de ellos están relacionados con asuntos comerciales y otras situaciones cotidianas de mercaderes y contadores.