The process of problem posing: development of a descriptive phase model of problem posing

The aim of this study is to develop a descriptive phase model for problem-posing activities based on structured situations. For this purpose, 36 task-based interviews with pre-service primary and secondary mathematics teachers working in pairs who were given two structured problem-posing situations were conducted. Through an inductive-deductive category development, five types of activities (situation analysis, variation, generation, problem-solving, evaluation) were identified. These activities were coded in so-called episodes, allowing time-covering analyses of the observed processes. Recurring transitions between these episodes were observed, through which a descriptive phase model was derived. In addition, coding of the developed episode types was validated for its interrater agreement.

TEACHERS’ CONCEPTIONS AND PROFESSIONAL KNOWLEDGE OF VARIABILITY FROM THEIR INTERPRETATION OF HISTOGRAMS: THE CASE OF VENEZUELAN IN-SERVICE SECONDARY MATHEMATICS TEACHERS

Many studies have reported on the influence of teachers’ conceptions of variability on different aspects of their professional knowledge for teaching statistics and their classroom practices. However, research on these kind of conceptions is still scarce, particularly in Latin American countries like Venezuela. In an effort to help fill this gap, a qualitative study was conducted that aimed to characterize the different ways in which Venezuelan in-service secondary school mathematics teachers conceptualize variability. For that purpose, a survey instrument was developed and administered to 27 teachers working at the metropolitan area of Caracas. This paper focuses on the participants’ answers to two items in which interpretation of histograms was necessary. It was found that about a third of the participants exhibited a sophisticated recognition of variability (e.g., gave answers connecting both middles and extremes), whereas about half of them exhibited misconceptions of variability, such as acknowledging variability from the viewpoint of idiosyncratic ideas, or the degree of symmetry (or lack thereof) of a histogram. Moreover, it was also found that about two-thirds of the participants were unable to correctly match real-life contexts to their corresponding histograms, while about two-fifths were unable to correctly determine the accuracy or inaccuracy of descriptions of the variability in a histogram. The author discusses possible reasons for the obtained results, in order to identify relevant implictions for teacher education in the area of statistics. Abstract: Spanish Diversos estudios han reportado que las concepciones de los docentes sobre variabilidad influencian tanto su conocimiento profesional para la enseñanza de la estadística, como sus prácticas en el aula. Sin embargo, investigaciones sobre este tipo de concepciones son aún escasas, particularmente en países latinoamericanos como Venezuela. Intentando satisfacer esta necesidad, se condujo un estudio cualitativo para identificar y caracterizar las diferentes maneras en que maestros venezolanos de matemáticas a nivel de secundaria conceptualizan la variabilidad. Con tal propósito, un cuestionario fue desarrollado y administrado a 27 docentes en el área metropolitana de Caracas. Este artículo se centra en las respuestas dadas por los participantes a dos ítems del cuestionario, en los que era necesaria la interpretación de histogramas. Se descubrió que aproximadamente un quinto de los participantes demostró un reconocimiento sofisticado de la variabilidad (e.g., considerar simultáneamente valores centrales y extremos de un histograma), mientras que alreadedor de la mitad exhibió concepciones erróneas, tales como el reconocimiento de la variabilidad a partir de ideas idiosincrásicas, o del grado de simetría de un histograma. Además, unos cuatro quintos de los participantes fueron incapaces de establecer una correspondencia entre contextos de la vida real y sus respectivos histogramas, mientras que unos dos quintos fueron incapaces de determinar si descripciones de la variabilidad en un histograma eran o no correctas. El autor discute las posibles razones de los resultados obtenidos, con el fin de identificar implicaciones relevantes para la formación docente en el área de la estadística.

A Rationale for the Junior-Senior Secondary Mathematics Curriculum 2.0

This paper proposes a rationale that supports a renewal of our predominantly 19th century curriculum for Grades 7–12, identified as Mathematics 1.0. It was originally established in the mid 1800s to prepare learners mostly from upper-class families to succeed in a post-industrial society. Today’s digital revolution has changed society remarkably, and the variety of learners has certainly broadened, but Mathematics 1.0 fundamentally remains the same Plato-based (Platonist) curriculum due to its social-political power, which is documented in the article. The major changes to society’s culture and the composition of learners have caused faults in Mathematics 1.0 (e.g., a relevance deficit). For the majority of learners, school mathematics has mostly become an obsolete, inequitable, and harmful rite-of-passage into adulthood, to varying degrees. A renewed curriculum, Mathematics 2.0, is rationalized and specific suggestions are offered. The minority of learners who successfully pursue mathematics to varying degrees would experience small changes in their new Mathematics 1.2. Keywords: school mathematics, humanistic, curriculum differentiation, relevance