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En este artículo se reportan los resultados de una investigación cuyo objetivo fue identificar las preconcepciones de pendiente en estudiantes de Educación Secundaria. Se empleó una entrevista basada en tareas para la recolección de datos de 30 estudiantes de 10.º grado y el método de análisis temático para su respectivo análisis. Los resultados muestran que las preconcepciones de pendiente que manifiestan los estudiantes son la pendiente como la longitud de un segmento de recta, un objeto, una propiedad física, el valor del ángulo, la intersección de la recta con los ejes asociada a una expresión algebraica y el cociente de los valores de las intersecciones en el eje x e y. Aunque algunos estudiantes declararon una primera experiencia con el concepto, este conocimiento tuvo una mínima influencia en sus procedimientos y justificaciones. This article reports an investigation whose objective was to identify Secondary Education students' preconceptions of slope. A task-based interview was used to collect data from 30 10th grade students and the thematic analysis method for their respective analysis. The results indicate that the slope's preconceptions evidenced by the students were the slope as length of the straight segment, an object, a physical property, the value of the angle, the intersection of the straight line with the axes, associated with an algebraic expression and the quotient of the values of the x and y intercepts. Although some students reported a first experience with the concept, this knowledge had minimal influence on their procedures and justifications.

Resumen Este escrito reporta las conceptualizaciones de la pendiente de 21 estudiantes universitarios. Para la recolección de datos se utilizó una entrevista basada en tareas y para su análisis se identificaron las frases y procedimientos claves relacionados con las once conceptualizaciones reportadas por investigadores en educación matemática sobre el concepto de pendiente. Los estudiantes evidenciaron de una a ocho conceptualizaciones, entre las cuales se identificaron: Propiedad Física, Razón Algebraica, Propiedad Determinante, Constante Lineal, Coeficiente Paramétrico, Razón Geométrica, Indicador de Comportamiento y Situación Mundo Real (Situación Física). Abstract This article reports an investigation that explored Slope's conceptualizations in 21 university students. The data was collected with a Task-Based Interview and for its data analysis it focused on the identification of key phrases and procedures that referred to any of the eleven conceptualizations reported on the slope concept. The students evidenced from one to eight conceptualizations, among which were identified: Physical Property, Algebraic Ratio, Determining Property, Linear Constant, Parametric Coefficient, Geometric Ratio, Behavior Indicator, and Real-World Situation (Physical situation).

International audience; Generalisation is a key element of algebraic thinking, and children's developing thinking is supported by engagement with algebraic activities when they attend primary school (Kaput, 2008). Shape patterns provide a context within which children may identify structure, and construct general terms. Within my research I presented children with shape patterns and observed their interactions as they discussed the structure of the patterns and sought to construct general terms. In this paper, I discuss the elements of the patterns to which they attended, and how their focus supported some children in constructing general terms, while other children experienced more challenge in their engagement with the patterns. Specifically I focus on children who observed both numerical and figural aspects, and I examine the varying levels of success they experienced.

The subject of this study is how pupils in math disabilities communicate and reason during calculations involving fractional numbers. The study comprises eight informants, two from eigth grade (a boy and a girl, 13 to 14 years old) and six from ninth grade (three girls and three boys, 14 to 15 years old) who all were considered to have math disabilities. They were all interviewed alone about their reasoning when solving ten tasks involving fractions to see what knowledge and misconceptions the pupils showed. The conclusion of the study is that the pupils posessed procedural abilities, but were weaker in their concepual abilities. Most pupils in the study were uncertain about the meaning of nominator and denominator. Several of the pupils preferred to think in percent rather than fractions but they had problems in converting from percent to fractions and vice versa.