Developing the skills of critical and creative thinking by probability teaching

AbstractThe study reported here described a small step in the direction of developing additional learning units within the traditional curriculum. It is apparent that if a teacher makes a decision to focus on improving higher order thinking and perseveres over time, the chances are good that the teacher will succeed. The purpose of this study was to explore whether teaching our specially designed learning unit would enhance the students’ critical and or creativity thinking. The unit “Probability in Daily Life” was taught to a group of tenth-grade students, with the purpose of encouraging critical thinking dispositions such as open-mindedness, truth-seeking, self-confidence and maturity. The teacher encouraged class discussion and planned investigative lessons. The students completed a pre and post CCTDI test. The findings of the present research are likely to help composing new study programs and methods that can be based on the connection between critical thinking, creative thinking and the study of mathematics, which this research brings

Tareas híbridas: promover el pensamiento estadístico y el pensamiento crítico por medio de las mismas actividades matemáticas

Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should be possible to stimulate both forms of thinking through the one task. This paper explores the implications of an exploratory qualitative study into processes when working on tasks encompassing both these areas for the design of tasks that simultaneously stimulate critical thinking and domain-specific thinking.Aunque desde un punto de vista teórico, el pensamiento estadístico y el pensamiento crítico parecen tener fuertes conexiones, la investigación empírica sobre la intersección y la potencial interrelación entre estos aspectos de competencia es escasa. Nuestra investigación sugiere que las habilidades de pensamiento en ambas áreas pueden ser interdependientes. Dada esta interconexión, debería ser posible estimular ambas formas de pensamiento mediante una tarea. Este artículo explora las implicaciones de un estudio cualitativo exploratorio sobre los procesos de pensamiento en tareas que abordan ambas áreas para el diseño de tareas que simultáneamente estimulan el pensamiento crítico y pensamiento específico de un dominio

Hybrid tasks: Promoting statistical thinking and critical thinking through the same mathematical activities

Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should be possible to stimulate both forms of thinking through the one task. This paper explores the implications of an exploratory qualitative study into processes when working on tasks encompassing both these areas for the design of tasks that simultaneously stimulate critical thinking and domain-specific thinking

International comparisons of mathematics classrooms and curricula: the validity-comparability compromise

The pursuit of commensurability in international comparative research by imposing general classificatory frameworks can misrepresent valued performances, school knowledge and classroom practice as these are actually conceived by each community and sacrifice validity in the interest of comparability. The “validity-comparability compromise” is proposed as a theoretical concern with significant implications for international cross-cultural research. We draw on current international research to illustrate a variety of aspects of the issue and its consequences for the manner in which international research is conducted and its results interpreted. The effects extend to data generation and analysis and constitute essential contingencies on the interpretation and application of international comparative research

Construction of Critical Thinking Skills by the infusion approach in “Probability and Statistics in Daily Life”

International audienceThis paper presents a teaching experiment that combined the explicit teaching of critical thinking with the content of an existing mathematics unit called “Probability and Statistics in Daily Life”. The original unit was designed to teach probability and statistics through real-life scenarios at the high-school level. I took the original mathematical content and “infused” it with a progression of critical thinking skills, so that both the mathematics and the critical thinking competencies developed hierarchically, growing more and more complex as the unit progressed. This paper illustrates the mutual benefits of this “infusion” to both the teaching of statistics and of critical thinking. The paper discusses the problem of transfer of critical thinking skills and shows some promising elements in that sense, deriving from the analysis. Finally, it also discusses some educational implications of the work done, the limitations of the unit’s first run and the improvements that may yet be made

Construction of Critical Thinking Skills by the infusion approach in “Probability and Statistics in Daily Life”

International audienceThis paper presents a teaching experiment that combined the explicit teaching of critical thinking with the content of an existing mathematics unit called “Probability and Statistics in Daily Life”. The original unit was designed to teach probability and statistics through real-life scenarios at the high-school level. I took the original mathematical content and “infused” it with a progression of critical thinking skills, so that both the mathematics and the critical thinking competencies developed hierarchically, growing more and more complex as the unit progressed. This paper illustrates the mutual benefits of this “infusion” to both the teaching of statistics and of critical thinking. The paper discusses the problem of transfer of critical thinking skills and shows some promising elements in that sense, deriving from the analysis. Finally, it also discusses some educational implications of the work done, the limitations of the unit’s first run and the improvements that may yet be made

PNA

Resumen basado en el de la publicaciónEl pensamiento estadístico y el pensamiento crítico parecen tener fuertes conexiones en su aspecto teórico, la investigación empírica sobre la intersección y la potencial interrelación entre estos aspectos de competencia es escasa. La investigación sugiere que las habilidades de pensamiento en ambas áreas pueden ser interdependientes. Se exploran las implicaciones de un estudio cualitativo sobre los procesos de pensamiento en tareas que abordan ambas áreas, para el diseño de tareas que simultáneamente estimulan el pensamiento crítico y el pensamiento específico de un dominio.ES

Hybrid tasks: Promoting statistical thinking and critical thinking through the same mathematical activities (Tareas híbridas: promover el pensamiento estadístico y el pensamiento crítico por medio de las mismas actividades matemáticas)

Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should be possible to stimulate both forms of thinking through the one task. This paper explores the implications of an exploratory qualitative study into processes when working on tasks encompassing both these areas for the design of tasks that simultaneously stimulate critical thinking and domain-specific thinking. Resumen Aunque desde un punto de vista teórico, el pensamiento estadístico y el pensamiento crítico parecen tener fuertes conexiones, la investigación empírica sobre la intersección y la potencial interrelación entre estos aspectos de competencia es escasa. Nuestra investigación sugiere que las habilidades de pensamiento en ambas áreas pueden ser interdependientes. Dada esta interconexión, debería ser posible estimular ambas formas de pensamiento mediante una tarea. Este artículo explora las implicaciones de un estudio cualitativo exploratorio sobre los procesos de pensamiento en tareas que abordan ambas áreas para el diseño de tareas que simultáneamente estimulan el pensamiento crítico y pensamiento específico de un dominio