Search

Visual imagery has been an effective tool to communicate ideas connected with basic mathematics concepts since the dawn of mankind. The development of educational visualisation technology allows these ideas to be demonstrated with the help of some educational software. In this paper, we specifically consider the use of GeoGebra, a free, open-source educational application developed by an international consortium of mathematics and statistics educators, but other educational software could also be used for the same visualisation tasks. In this study, we present Torricelli's method for measuring the area under arc of cycloid as an example of using GeoGebra to visualise he area of planar figures. This kind of introduction is suitable for secondary schools and for training pre-service teachers. We will also show how GeoGebra can be used to develop students' understanding of representing data (i.e. the topic from statistics education). While students explore the visualisation of data, GeoGebra allows them to create and explore representations while building the understanding that is required for analysing data and drawing figural conclusions from graphical representations.

Official documents in several educational systems reflect the importance of integrating Science, Technology, Engineering, Arts, and Mathematics (STEAM) and consider project-based learning (PBL) as a way of integrating such disciplines in the classroom. Although STEAM-PBL has been characterized and evaluated in different ways, its impact on school mathematics teaching remains unclear. Mathematics is recognized as the fundamental basis of other disciplines; however, many students still perceive it as a difficult subject and abandon it. To analyze STEAM-PBL classroom implementation from a school mathematics standpoint, we examined 41 classroom experiences from 11 Spanish secondary education teachers (five in-field mathematics teachers), who participated in a STEAM training program for more than 4 years. To frame this study, Thibaut et al.'s (J STEM Educ 3(1):02, 2018) and Schoenfeld's (Educ Res 43(8):404-412, 2014) characterizations of well-designed and implemented projects, respectively, were employed. The results showed that in-field mathematics teachers avoided transdisciplinary projects in which school mathematics is difficult to address, while out-of-field teachers tended to overlook the mathematics in interdisciplinary projects. Unlike out-of-field teachers, mathematics teachers often eluded design-based learning processes for deeply exploiting school mathematics. The latter teachers promoted high cognitive demands and positive perceptions about mathematics in projects where formative environments were generated through discussion and a meaningful feedback loop.

Meaning Equivalence Reusable Learning Objects (MERLO) items are a new kind of didactical tool that can be designed by teachers and used in classes, in tasks aimed at engaging students in deep reasoning, exploring and arguing about mathematical concepts. The interactions across communities of mathematics teachers and educators in on-line professional development were studied with attention to the phenomenon of boundary crossing of MERLO items, viewed as boundary objects in this article. The study analysed a first (international) crossing of the object that passed institutional boundaries (between Australian and Italian school systems), and a second crossing of the same object --inside the Australian institutional community -- that passed boundaries (from static to dynamic representations) that we interpret in terms of method both for teachers and for researchers. This passage is possible due to the use of dynamic geometry software (GeoGebra) that supported a modification in the design of the item. The analysis shows boundary crossing as a process of transformation that can influence a modification (more or less stable) in the practices of the teachers involved and provides a deep research insight in relation to existing theoretical frameworks.

This paper outlines the growing phenomenon and need to integrate technologies into mathematics and science teaching and learning. There are a number of successful projects for valuable integration of technologies around the world, however, these successes are often limited reaching a relatively small number of teachers and students. In this paper, we aim to offer examples of large-scale technology projects that could create a critical mass of users that could further drive innovation and sustainability for educational technology integration. We outline how GeoGebra became one of the most widely used dynamic mathematics software with a user base of more than 100 million; highlight directions of research for technology development and integration; and describe the Geomatech project that aimed to train 2500 teachers in 950 schools in Hungary. We hope that such examples, the developed technology, resources and pedagogies could contribute to further valuable integrations of technologies in mathematics and science education.

This article reviews Education for Sustainability (EfS) in the secondary sector across a range of countries. Drawing on journal articles, book chapters and official reports, it identifies some of the more successful approaches to implementing EfS within the secondary sector. The authors first discuss the importance of educating for sustainability at the secondary level and then explore barriers to effective EfS in secondary schools. They go on to share their insights into contextual factors that influence EfS practices which are reported in the case studies. In particular, they discuss the influence of (a) politics and curriculum renewal, (b) alignment of curriculum, resources and teaching, (c) the perceived state of EfS and (d) teachers' professional development as determinants of EfS implementation and success.

This paper outlines results of the first cycle of a mathematics education project in Kuwait aimed to integrate technology into teaching and learning 11 Kuwaiti schools. The project design and methods are based on two previous studies carried out in Cambridge, UK and the Geomatech project in Hungary. Studies showed that adequate preparation of teachers is necessary to have impact on students learning with technology. In the first cycle of this project we carried out an extensive teacher training to introduce practices and resources with the GeoGebra application and materials developed in the Geomatech project. The research design was based on Design Experimental and Community of Practice approaches involving the close collaboration of teachers and researchers to jointly develop resources and pedagogies. In this paper, we will offer an outline of the study design and the frameworks based on previous projects as well as highlight some initial findings from interviews conducted in the first cycle of the project.

This paper reports on a study of the process of professional development for mathematics teachers. The analysis connects two theoretical frameworks: the Meta-Didactical Transposition model developed by Arzarello et al. (2014), which describes the macro level, and, at the micro level, the idea of emergence, which has been around since at least the time of Aristotle and has been defined by Mill (1843), Lewes (1875), Blitz (1992), Huxley and Huxley (1947) and many others. The meta-didactical transposition model considers the evolution of teachers' practices as part of a community process, while the notion of emergence helps us to gain better insights into the details of the practices of individual teachers. This paper focuses on secondary school teachers' learning of new digital technologies to illuminate this theoretical framework.

Integrating socioscientific issues (SSI) into education is gaining widespread adoption in classrooms due to its positive impact on student's critical thinking, environmental awareness, holistic knowledge and/or the idea of combining science and mathematics. This paper explores the idea of using comics as appropriate media for elementary school students to engage with SSI content. Because of the difficulties in integrating SSI into classrooms, SSI-based learning is more commonly applied in high school and higher education settings, with limited implementation in earlier education. To answer this gap, we developed comics that have SSI content for elementary schools. Comics are chosen as reliable tools for visualising and simplifying complex concepts and making SSI content more accessible and engaging. This paper describes our comics on earthquake-related issues in Indonesia and the principles that guided its design. SSI inherently involves multiple perspectives, so the integration brings together science, and mathematics within the one comic. In integrating different disciplines of comic content, we utilised the rule-of-five framework, widely employed to merge five representational models (experiential, verbal, numerical, visual, and symbolic) commonly used in developing content combining two or more different academic disciplines. [ABSTRACT FROM AUTHOR]

The data revolution has given citizens access to enormous large-scale open databases. In order to take into account the full complexity of data, we have to change the way we think in terms of the nature of data and its availability, the ways in which it is displayed and used, and the skills that are required for its interpretation. Substantial changes in the content and processes involved in statistics education are needed. This paper calls for the introduction of new pedagogical constructs and principles needed in the age of the data revolution. The paper deals with a new construct of statistical literacy. We describe principles and dispositions that will become the building blocks of our pedagogical model. Our model suggests that effective engagement with large-scale data, modelling and interpretation situations requires the presence of knowledge-bases as well as supporting dispositions.

This paper reports on the implementation of the dynamic STEM-teaching and learning technologies in teachers' classroom teaching practices resulting from their engagement in sustained professional development and classroom teaching of resources that embed carefully designed dynamic STEM-technologies within the Hungarian mathematics and science curriculum (K 1-12). The research investigated teachers' perceptions of the impact on students' mathematical understanding when teachers integrate the materials and the technology into their teaching. The sample comprised 773 mathematics and science teachers, who participated in Geomatech training over the entire period (2014-2015) of the project. Questionnaires were administered to match individual teachers' teaching schedules, and the resulting data were analysed to give summative statistics. The results indicate that teachers were able to plan tasks using Geomatech STEM resources for students to catch up with their learning, to cater to the learning needs of talented students, plan Geomatech tasks for project work and experimentation, and use them for homework tasks.

In the Australian mathematics curriculum, Year 12 students (aged 16-17) are asked to solve conditional probability problems that involve the representation of the problem situation with two-way tables or three-dimensional diagrams and consider sampling procedures that result in different correct answers. In a small exploratory study, we investigate three Year 12 students' conceptions and reasoning about conditional probability, samples, and sampling procedures. Through interviews with the students, supported by analysis of their work investigating probabilities using tabular representations, we investigate the ways in which these students perceive, express, and answer conditional probability questions from statistics, and also how they reason about the importance of taking into account what is being sampled and how it is being sampled. We report on insights gained about these students' reasoning with different conditional probability problems, including how they interpret, analyse, solve, and communicate problems of conditional probability.

The paper reports the main insights from a study aimed at equipping a group of pre-service teachers with the knowledge, skills, and practical experience required to effectively integrate educational games within the mathematics curriculum. An instructional intervention based on the Technological Pedagogical and Content Knowledge framework was implemented in an undergraduate mathematics methods course attended by thirteen (n = 13) prospective primary teachers. Participants experimented with different ways in which educational games could help students internalize key mathematical concepts across the primary curriculum, and were familiarized with the design principles for constructivist gaming environments. Upon completion of a unit on game-enhanced learning, they worked in small groups to develop and deliver, during their teaching placements, instructional episodes integrating the use of serious games. Findings indicate a positive impact on pre-service teachers' perceptions regarding game-based learning, and on their competence in selecting, evaluating, and productively utilizing digital games as an instructional tool.

This article reports on the main experiences gained from a 2-year study which incorporated A.L.E.X., an educational puzzle game available on iPad or Android tablet devices, within the primary school mathematics curriculum. The study took place in a public primary school, located in a rural area of Cyprus. The majority of its students come from low socioeconomic status families. Among the school community, a group of 15 pupils (eight boys and seven girls), aged 10-11 years old, was randomly selected to comprise the sample. The same group of students was visited twice within a period of 2 years, and a teaching intervention was organized. In both interventions, the application A.L.E.X. accompanied by a student worksheet constituted the main means of instruction. The worksheets were designed to integrate a technology with core mathematical ideas embedded in the national mathematics curriculum. Findings gained from the teaching intervention suggest that game apps hold a lot of promise as a tool for reforming mathematics education. While working with A.L.E.X., the children identified and processed mathematical themes that emerged spontaneously. They experienced unique emotions of surprise and enthusiasm regarding the existence of games with mathematical content that led them to acknowledge the pedagogical role that tablet devices could play. This helped them to broaden their fundamentally narrow viewpoint of mathematics as being primarily computation and arithmetic.

New technologies have completely altered the ways that citizens can access data. Indeed, emerging online data sources give citizens access to an enormous amount of numerical information that provides new sorts of evidence used to influence public opinion. In this new environment, two trends have had a significant impact on our increasingly data-driven society: 1) the increasing use of large-scale databases within the open data movement, and 2) the growing use of big data. The open data movement supports the availability of high quality data sets collected by national statistics offices and non-government organisations for a specific purpose. The open data movement has had significant success in recent years in persuading major data providers, and national statistics offices, (for example, the Australian Bureau of Statistics [ABS]) to give citizens access to huge databases in order to create new variables, and explore new relationships. This new access to data is having a profound impact on teaching statistics and modernising curricula to prepare students for a world filled with open and big data, or the so-called "data deluge". However, competent use of large-scale data predominantly requires comprehension of data tables, which are routinely used in daily life and in the workplace to communicate information about large data sets. This article discusses how to implement a framework for helping students develop better ability to interpret large-scale data tables, in particular by using strategies that make comparisons between and within the categories of data and by drawing inferences about data within its context while making any reference to the contextual factors.

The Technological Pedagogical Content Knowledge (TPACK) conceptual framework for teaching mathematics, developed by Mishra and Koehler (2006), emphasises the importance of developing integrated and interdependent understanding of three primary forms of knowledge: technology, pedagogy, and content. The TPACK conceptual framework is based upon the premise that effective technology integration for pedagogy around specific subject matter requires understanding of the dynamic relationship between all three knowledge components. The purpose of this article is to discuss the TPACK required for teaching Statistics, and to assist Australian teachers to make sense of the TPACK required for the effective integration of technology in statistics instruction.

This article aims to report on a pilot or proof of concept study with experienced Hungarian teachers who introduced mathematical concepts through a sequence of lessons utilising a pedagogical framework (Lavicza, Hohenwarter, Jones, Lu and Dawes, 2009a and Lavicza, Hohenwarter and Lu 2009b) for general technology integration. Our aim was to examine whether the results of this pilot study could be further utilised in material development and teachers training in a larger scale project GEOMATECH. Results of this study suggested that: a) even experienced teachers with extensive knowledge of technology use are challenged to transfer the control of the classroom to students, step back to become a facilitator in the classroom; b) teachers would have required already prepared worksheets that could be immediately suited to their lessons as their time for preparation was limited and needed to cover a wide range of materials; c) introducing technology through such sequencing would require more practice, experience and training.

This paper presents a case study of students (age 14-15) as they attempt to make sense of distribution, adopting a range of causal meanings for the variation observed in the animated computer display and in the graphs generated by a "BasketBall" simulation. The student activity is analysed through dimensions of complex causality. The results indicate support for our conjecture that the computer simulation can offer new ways for harnessing causality to facilitate students' meaning making for variation in distributions of data. In order to bridge the deterministic and the stochastic, the students transfer agency to active representations of distributional parameters, such as average and spread. This study finds that, whereas the stochastic is often seen as a distinct domain of knowledge, some students are able to exploit deterministic meanings to account for variation in terms of probabilistic causality.

Our primary goal is to design a micro world which aspires to research thinking-in-change about distribution. Our premise, in line with a constructivist approach and our prior research, is that thinking about distribution must develop from causal meanings already established. This study reports on a design research study of how students appear to exploit their appreciation of causal control to construct new situated meanings for the distribution of throws and success rates. We provided on-screen control mechanisms for average and spread that could be deterministic or subject to stochastic error. The students used these controls to recognise the limitations of causality in the short term but its power in making sense of the emergence of distributional patterns. We suggest that the concept of distribution lies in co-ordinating emergent data-centric and modelling perspectives for distribution and that causality may play a central role in supporting that co-ordination process. (Contains 14 figures.)