Creating Realistic Mathematics Tasks Involving Authenticity, Cognitive Domains, and Openness Characteristics: A Study with Pre-Service Teachers

Abstract

Creating mathematics tasks provide opportunities for students to develop their thinking, reasoning, communication, and creativity. This paper presents a study on teaching pre-service teachers to create realistic mathematics tasks in real contexts and amending them through an iterative process of analysis and refinement. The study was undertaken with pre-service teachers from two university training courses in Spain, undergraduate students from a primary teacher training course, and graduate students from an educational Master’s course. The students worked in groups to collaborate in the creation of the requested tasks and improvement of them based on critical thinking and creativity. The tasks were not only evaluated concerning their level of realism, but also regarding their level of authenticity, the cognitive domains involved, and their openness characteristic. These are the key characteristics related to environmental and sustainability aspects. The outcomes confirmed that the creation of realistic mathematics tasks was a challenge for future primary teachers; however, they were able to create tasks with high levels of cognitive domain, authenticity, and openness. This evidences, on the one hand, the difficulty that future teachers have in understanding the realism of a mathematics task, and, on the other, the possibilities offered by the task’s creation and the revision activity, which has educational implications and opens paths for future research.

Analysis of Teacher-Student Interaction in the Joint Solving of Non-Routine Problems in Primary Education Classrooms

“…Different types of tasks can be approached in mathematics classrooms. In order to acquire adequate mathematical competence, students should develop skills, learn different types of mathematical contents with a variety of complexity levels [45], and use different types of mathematical tasks [46]. Among these types of tasks are mathematics problems, which may be of a routine or a nonroutine nature.…”

Education for Sustainable Development in Primary Education Textbooks—An Educational Approach from Statistical and Probabilistic Literacy

“…Therefore, the more aspects that are verified, the more legitimate the lesson is, deepening the knowledge of the SDG. Thereby, the legitimacy of the lessons related to the study of statistics and probability is observed, based on an adaptation of the indicators proposed by Paredes, Cáceres, Diego-Mantecon, Blanco and Chamoso [44]:…”

“…Following this approach, a task can be considered authentic, believable or fictitious [44]. For a task to be considered plausible or authentic it must develop the indicators described in the 'event', 'question' and 'information' described in the authenticity section of the analysis instrument.…”

Social Interaction: A Crucial Means to Promote Sustainability in Initial Teacher Training

“…Generating opportunities for future teachers to identify the importance of social interaction in learning and promoting a logical and rational understanding of fundamentals may lead to reflective practice [47]. The analysis of the implications that socio-cultural assumptions of learning have on the teaching role can build on professional solutions.…”

“…The results show that 57.7% of the groups (15 out of 26) did not identify the role of socio-cognitive conflict in learning, while 42.3% of the groups (11 out of 26) identified it. When interacting with environment-related issues, the ability to overcome the conflict it entails is often a significant aspect to be taken into account in order to address said problems [47,68,69].…”