Cabri's role in the task of proving within the activity of building part of an axiomatic system

We want to show how we use the software Cabri, in a Geometry class for preservice mathematics teachers, in the process of building part of an axiomatic system of Euclidean Geometry. We will illustrate the type of tasks that engage students to discover the relationship between the steps of a geometric construction and the steps of a formal justification of the related geometric fact to understand the logical development of a proof; understand dependency relationships between properties; generate ideas that can be useful for a proof; produce conjectures that correspond to theorems of the system; and participate in the deductive organization of a set of statements obtained as solution to open-ended problems

Una propuesta para abordar el teorema de Pitágoras en clase

En este artículo se expone una propuesta de enseñanza para presentar el teorema de Pitágoras a alumnos de educación media. También se refieren algunos detalles del análisis que fundamentó la propuesta. Esta incluye trabajo de los estudiantes en torno a la desigualdad triangular, a la relación pitagórica y a expresiones algebraicas

Instrumented activity and semiotic mediation: two frames to describe the conjecture construction process as curricular organizer

We document part of the process through which conjectures produced by students, with the aid of the dynamic geometry software Cabri, when they solve proposed geometric problems, become a curriculum organizer in the classroom. We first focus on characterizing students’ instrumented activity recurring to utilization schema (Rabardel, 1995, in Bartolini Bussi and Mariotti, 2008), and then describe the teacher’s content management through which the ideas produced by the students become key elements of knowledge construction

Analyzing the proving activity of a group of three students

We present an analysis and outline an evaluation of the proving activity of a group of three university level students when solving a geometrical problem whose solution required the formulation of a conjecture and its justification within a specific theoretical system. To carry out the analysis, we used the model presented by Boero, Douek, Morselli and Pedemonte (2010) that centers on the arguments and rational behavior. Our analysis indicates that the student‘s proving activity is close to the one we used as a reference

Prefacio

Aunque los artículos que componen este libro provienen principalmen- te de nuestro más reciente trabajo investigativo, no son documentos de inves- tigación sino de divulgación. En ellos nos acercamos, mucho más de lo que es habitual para un profesor, a asuntos clave para la enseñanza y el aprendizaje de la demostración, entendido este como participación en prácticas propias de la comunidad del discurso matemático. El libro está dirigido principalmente a profesores de matemáticas en ejercicio de su profesión y a estudiantes de postgrado en el campo de la Educación Matemática

Dynamic geometry, implication and abduction: a case study

In this paper we illustrate the role of dynamic geometry as an environment that propitiates the use of empirical explorations to favor learning to prove. This is possible thanks to abductive processes, related to the establishment of implications that university students of a plane geometry course carry out when, supported by a dynamic geometry program, they solve a problem in which they must discover a geometric fact, formulate a conjecture and prove it

Use of dragging as organizer for conjecture validation

In this article, we report on a study centred on the teaching and learning of proof in which there is evidence that dragging becomes a source for significant student participation in the validation of conjectures. The findings highlight the teacher’s use of dragging as an organizer of the activity, in cases when there are conjectures that students consider acceptable but for which they do not have the theoretical elements to validate them

Learning to prove: enculturation or…?

Empirical evidence coming from a curriculum innovation experience that we have been implementing in the Universidad Pedagógica Nacional (Colombia), in a plane geometry course for secondary mathematics pre-service teachers, allows us to affirm that learning to prove, more than enculturation into mathematicians’ practices, is participation in proving activity within the community of mathematical discourse

To Hospitalize or Not to Hospitalize? Medical Care for Long-Term Care Facility Residents

Examines factors behind frequent hospitalizations of long-term care facility residents, such as limited capacity, physician preferences, and financial incentives. Suggestions include support and training, advanced care planning, and changes in thinking

The Dual Capacity Doctrine in Products Liability Cases in Pennsylvania

Worker\u27s compensation statutes limit recovery by employees, for injuries occurring in the course of employment, to the benefits of the statute. The dual capacity doctrine in products liability cases allows recovery against the employer, as a manufacturer of a defective product, beyond worker\u27s compensation recovery. This comment explores the possibility of acceptance of the dual capacity doctrine in light of the implications of a recent Pennsylvania Supreme Court decision