Conceptions and Misconceptions about Computational Thinking among Italian Primary School Teachers

International audienceMany advanced countries are recognizing more and more the importance of teaching computing, in some cases even as early as in primary school. "Computational thinking" is the term often used to denote the conceptual core of computer science or "the way a computer scientist thinks", as Wing put it. Such term - given also the lack of a widely accepted definition - has become a "buzzword" meaning different things to different people. We investigated the Italian primary school teachers' conceptions about computational thinking by analyzing the results of a survey (N=972) conducted in the context of "Programma il Futuro" project. Teachers have been asked to provide a definition of computational thinking and to answer three additional related closed-ended questions. The analysis shows that, while almost half of teachers (43.4%) have included in their definitions some fundamental elements of computational thinking, very few (10.8%) have been able to provide an acceptably complete definition. On a more positive note, the majority is aware that computational thinking is not characterized by coding or by the use of information technology

Educational Research Abstracts

Editors\u27 Note: As noted in previous issues of the Journal of Mathematics and Science: Collaborative Explorations, the purpose of this Educational Research Abstract section is to present current published research on issues relevant to math and science teaching at both the K-12 and college levels. Because educational research articles are published in so many different academic journals, it is a rare public school teacher or college professor who reads all the recent published reports on a particular instructional technique or curricular advancement. Indeed, the uniqueness of various pedagogical strategies has been tacitly acknowledged by the creation of individual journals dedicated to teaching in a specific discipline. Yet many of the insights gained in teaching certain physics concepts, biological principles, or computer science algorithms can have generalizability and value for those teaching in other fields or with different types of students. In this review, the focus is on background knowledge. Abstracts are presented according to a question examined in the published articles. Hopefully, such a format will trigger your reflections about the influence of students’ entering mathematical and scientific conceptions (and misconceptions,) as well as generate ideas about your own teaching situation. The abstracts presented here are not intended to be exhaustive, but rather a representative sampling of recent journal articles. Please feel free to identify other useful research articles on a particular theme or to suggest future teaching themes to be examined. You may send your comments and ideas via email to [email protected] or by regular mail to The College of William and Mary, P. O. Box 8795, Williamsburg, VA 23185-8795

Exploring Fijian high school students’ conceptions of averages

This paper focuses on part of a much larger study that explored form five (14 to 16 year-old) students’ ideas in statistics. A range of ideas was explored, including the students’ ideas about measures of centre and graphical representations. Students’ ideas about measures of centre were analysed and categories of responses identified. While students could compute mean and median, they were less competent with tasks that involved constructing meanings for averages. This could be due to an emphasis in the classroom on developing procedural knowledge or to linguistic and contextual problems. Some students used strategies based on prior school and everyday experiences. The paper concludes by suggesting some implications for mathematics education

Responsible research and innovation in science education: insights from evaluating the impact of using digital media and arts-based methods on RRI values

The European Commission policy approach of Responsible Research and Innovation (RRI) is gaining momentum in European research planning and development as a strategy to align scientific and technological progress with socially desirable and acceptable ends. One of the RRI agendas is science education, aiming to foster future generations' acquisition of skills and values needed to engage in society responsibly. To this end, it is argued that RRI-based science education can benefit from more interdisciplinary methods such as those based on arts and digital technologies. However, the evidence existing on the impact of science education activities using digital media and arts-based methods on RRI values remains underexplored. This article comparatively reviews previous evidence on the evaluation of these activities, from primary to higher education, to examine whether and how RRI-related learning outcomes are evaluated and how these activities impact on students' learning. Forty academic publications were selected and its content analysed according to five RRI values: creative and critical thinking, engagement, inclusiveness, gender equality and integration of ethical issues. When evaluating the impact of digital and arts-based methods in science education activities, creative and critical thinking, engagement and partly inclusiveness are the RRI values mainly addressed. In contrast, gender equality and ethics integration are neglected. Digital-based methods seem to be more focused on students' questioning and inquiry skills, whereas those using arts often examine imagination, curiosity and autonomy. Differences in the evaluation focus between studies on digital media and those on arts partly explain differences in their impact on RRI values, but also result in non-documented outcomes and undermine their potential. Further developments in interdisciplinary approaches to science education following the RRI policy agenda should reinforce the design of the activities as well as procedural aspects of the evaluation research

Investigations and explorations in the mathematics classroom

In Portugal, since the beginning of the 1990s, problem solving became increasingly identified with mathematical explorations and investigations. A number of research studies have been conducted, focusing on students’ learning, teachers’ classroom practices and teacher education. Currently, this line of work involves studies from primary school to university mathematics. This perspective impacted the mathematics curriculum documents that explicitly recommend teachers to propose mathematics investigations in their classrooms. On national meetings, many teachers report experiences involving students’ doing investigations and indicate to use regularly such tasks in their practice. However, this still appears to be a marginal activity in most mathematics classes, especially when there is pressure for preparation for external examinations (at grades 9 and 12). International assessments such as PISA and national assessments (at grades 4 and 6) emphasize tasks with realistic contexts. They reinforce the view that mathematics tasks must be varied beyond simple computational exercises or intricate abstract problems but they do not support the notion of extended explorations. Future developments will show what paths will emerge from these contradictions between promising research and classroom reports, curriculum orientations, professional experience, and assessment frameworks and instruments

What counts as numeracy?

The purpose of the study was to infer the Scottish HMI view of what is meant by Numeracy given the concerns that primary children's achievements in Numeracy reflect a lack of flexibility in handling number and an overemphasis on procedures at the expense of understanding (HMI, 1997). Three hundred HMI reports on primary schools in Scotland were randomly selected. Content analysis of the sections on Number, Money and Measurement revealed Numeracy to be conceived of as computational proficiency and as understanding of number. Surprisingly, there were significantly more (p<0.05) references to computational proficiency than there were to understanding of number. The results are discussed in terms of what it means to understand number. It is suggested that there needs to be much clearer delineation of what is required and meant by the idea of understanding number

Subtraction involving negative numbers: Connecting to whole number reasoning

In this article, we explore how students attempt to bridge from their whole number reasoning to integer reasoning as they solve subtraction problems involving negative numbers. Based on interviews with students ranging from first graders to preservice teachers, we identify two overarching strategies: making connections to known problem types and leveraging conceptions of subtraction. Their initial connections suggest that rather than identifying the best instructional models to teach integer concepts, we should focus on identifying integer instructional models that build on the potentially productive connections that students’ already make; we propose an example of one such form of instruction

Developing Learning Trajectory For Enhancing Students’ Relational Thinking

Algebra is part of Mathematics learning in Indonesian curriculum. It takes one half of the teaching hours in senior high school, and one third in junior high school. However, the learning trajectory of Algebra needs to be improved because teachers teach computational thinking by applying paper-and-pencil strategy combining with the concepts-operations-example-drilling approach. Mathematics textbooks do not give enough guidance for teachers to conduct good activities in the classroom to promote algebraic thinking especially in the primary schools. To reach Indonesian Mathematics teaching goals, teachers should develop learning trajectories based on pedagogical and theoretical backgrounds. Teachers need to have knowledge of student’s developmental progressions and understanding of mathematics concepts and students’ thinking. Research shows that teachers’ knowledge of student’s mathematical development is related to their students’ achievement. In fostering a greater emphasis on algebraic thinking, teachers and textbooks need to work more closely together to develop a clearer learning trajectory. Having this algebraic thinking, students developed not only their own character of learning and thinking but also their attitude, attention and discipline. Key Words: Learning Trajectory, Relational Thinkin

On the integration of digital technologies into mathematics classrooms

Trouche‘s (2003) presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing knowledge with technology; the latter concerning the problem of integrating technology into classroom practice. At the Symposium, there was considerable discussion of the idea of situated abstraction, which the current authors have been developing over the last decade. In this paper, we summarise the theory of instrumental genesis and attempt to link it with situated abstraction. We then seek to broaden Trouche‘s discussion of orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated abstraction could be used to make sense of the evolving mathematical knowledge of a community as well as an individual. We conclude by elaborating the ways in which technological artefacts can provide shared means of mathematical expression, and discuss the need to recognise the diversity of student‘s emergent meanings for mathematics, and the legitimacy of mathematical expression that may be initially divergent from institutionalised mathematics

Teacher Candidates’ Conceptions and Practices of Computational Thinking for Equity

This study documents novice science and math teachers’ developing pedagogical approaches to integrating computational thinking (CT) and data into their courses to support educational equity and social justice. The 10 novice teacher candidates (TCs) studied were part of an urban teacher residency program that empowered them with an asset-based pedagogy we describe as “CT for Equity.” Drawing on coursework and interviews as data, we asked three questions: What are teachers’ conceptions of CT? What are their CT instructional practices? And how did their students respond to those practices? To explore conceptions of CT, we used Kafai et al.’s (2020) articulation of three frames of CT – cognitive, situated, and critical approaches – and found that the TCs’ conceptions do not narrowly fit into one of the three frames, but rather they mix and match components of the perspectives to support a range of student outcomes, from transferable skills to preparing youth to explore social justice issues. We also identified a small but powerful set of core practices that the teachers used to support learning outcomes, including integrating data on locally and socially relevant issues. We present group-level trends and three classroom stories, or profiles of practice, to illustrate the generative ways TCs blended priorities from the three frames in instruction. The diversity in the TCs’ conceptions and practices deepens understandings of asset-based pedagogies in CT by shining light on the rich and varied ways that math and science teachers meet the needs of their minoritized students