Efi Paparistodemou

Teachers’ Reflection on Challenges for Teaching Probability in the Early Years

The present research focuses on the early childhood teachers’ reflection on designing and implementing probability tasks. Five early childhood teachers participated in this research, which was organized in three stages: design of lesson plan, classroom implementation and reflection. The researchers analysed the design of each lesson, observed teachers implementing their lesson and interviewed them while they reflected on their instruction. Teachers discussed critical incidents that occurred through their teaching, and they reflected on challenges for teaching probability. An initial analysis of the collected data indicates that early childhood teachers appreciated the importance of using tools and real-life scenarios in their classrooms for teaching stochastics. The study also provided some useful insights into the varying levels of attention that teachers paid to different kinds of activities during their lesson implementation, and into the different types of instructional material they used. Moreover, the findings also show that early childhood teachers’ attention to different aspects of probability tasks can be developed through a reflective process on their teaching.

Integrating Games into the Early Statistics Classroom: Teachers’ Professional Development on Game-Enhanced Learning

Digital games hold a lot of promise as tools for improving statistics instruction in the early school years. The research discussed in this chapter aimed at equipping a group of in-service primary teachers with the knowledge, skills, and practical experience required to effectively integrate digital games within early statistics education. The study took place within an in-service teachers’ professional development program focused on game-enhanced mathematics teaching and learning. The program was designed based on the technological pedagogical and content knowledge (TPACK) framework and was attended by six educators teaching at the lower primary school level (Grades 1–3; ages 6–9). Participants experimented with different ways in constructivist gaming environments could get integrated into the early primary mathematics curriculum to motivate young children and to help them internalize important concepts, including key ideas related to data analysis and probability. They also developed and delivered instructional episodes integrating the use of digital games in different areas of the early mathematics curriculum. This chapter discusses the impact of the study on teachers’ perceptions regarding game-based statistical learning and on their competence in selecting, evaluating, and productively utilizing digital games as an instructional tool in the early years of schooling.

A Study on Statistical Technological and Pedagogical Content Knowledge on an Innovative Course on Quantitative Research Methods

This chapter is part of a main study, which aimed to (a) analyse the affordances of a Quantitative Research Methods course towards developing students’ Statistical Technological and Pedagogical Content Knowledge (STPACK), and (b) apply the STPACK model to investigate its effects in graduate Educational Studies. In particular, the chapter provides an example of raising teachers’ awareness of statistical content and pedagogy about models and modelling through exploiting the model building affordances provided by a technological learning environment like TinkerPlots2 ® (Konold and Miller 2011). The model was applied in a Quantitative Educational Research Methods course with nineteen (n=19) Cypriot participants with different academic backgrounds.

CERME7 Working Group 5: Stochastic thinking

We see stochastic thinking as embracing both probabilistic and statistical thinking. In WG5 there was considerable discussion about the role of context in teaching stochastics (specifically, papers by Ainley, Jarvis and McKeon; Bakker, Wijers and Akkerman; Meletiou-Mavrotheris and Paparistodemou; Verschut and Bakker; Santos). In particular, the debate was around what is a ‘real’ problem or question. Was reality located in the positioning of the activity inside or outside school, or was it related to how engaging the task was for students? Did it matter that the data were collected by students themselves? Could reality be found in the power of the statistical ideas to solve problems? This debate drew heavily on notions of engagement and focus (Ainley et al. 2006) and on ideas about boundary crossing (Tuomi-Gröhn and Engeström 2003). Innovative technological tools such as Fathom (www.fathom.com) and TinkerPlots (www.keypress.com/x5715.xml) were seen as helping students to visualise complex statistical concepts, such as distribution, variability and sampling distribution (Arteaga and Batanero; Ben-Zvi et al.; Doerr and Jacob; Astudillo and Sosa; Olande; Dierdorp et al.; Gil and Ben-Zvi). It was important to provide teachers with opportunities to engage with learning experiences similar to those encountered by their students in order to be able to anticipate students’ difficulties. These tools have changed the way in which students might engage with graphical information, placing more emphasis on interpretation and expression, but, at the same time, presenting a challenge as to how skills might be assessed. There has been considerable research in recent times on informal inferential reasoning, and this approach, often based around exploratory data analysis, has focussed attention on representing and interpreting data in the context of the sampling process. Stochastics education suffers from negative attitudes in society in the same way as mathematics does, but even mathematically-minded scholars often reject the stochastic way of thinking. We need to know more about these attitudes to see how they might be changed. In contrast, there has been considerable research about students’ concepts. For example, we heard about research aiming to identify the knowledge and thinking of students at different ages and levels of schooling, so as to