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A classification of resources used by mathematics teachers in an English high school
Michael Umameh, John Monhagan, university of Leeds, University of Adger

This paper provides a classification of resources used by mathematics teachers in an English high school. It is based on data analysis from ongoing PhD research exploring mathematics teachers' appropriation of digital resources and the impact on classroom practices in selected schools. This paper reports a way of making sense of the myriad curricular and digital resources that are increasingly available to the teachers in planning and enacting their teaching and assessing their students' understandings in the context of their every day practices. The classification has potential to aid understandings of teachers' appropriation of resources for teaching mathematics.

Planning to teach lower secondary mathematics with dynamic mathematical technology: quality features of lesson plans
Alison Clark-Wilson, Celia Hoyles, University college, London

Set within the context of the longitudinal Cornerstone Maths project in England. we adapt Thomas and Hong's theoretical framework (mathematical) ‘pedagogic technology knowledge' (MPTK, Thomas & Hong, 2013) to explore teachers' espoused knowledge to teach with dynamic mathematical technology in lower secondary mathematics. We conclude a set of eight ‘quality features' of such plans, and highlight how each of these features can provide a dynamic insight into teachers' MPTK development over time.

Effect of GeoGebra collaborative and iterative professional development on in-service secondary mathematics teachers' TPACK
Houssam Kasti, Murad Jurdak, Lebanese University, American University of Beirut  (AUB)

Integrating technology in education is still not an easy task. Teachers' adoption of technology in their teaching is even more problematic. This study aims at understanding what critical factors affect technology adoption by in-service mathematics teachers. This article is one out of four parts of the study. The type of the study is a multiple case studying in depth the effect of a GeoGebra (a free mathematics software) intervention on the Technological Pedagogical Content Knowledge (TPACK) of in-service mathematics teachers in secondary schools who follow the Lebanese curriculum. The methodology used is Design-Based Research that focuses on working closely with practitioners in collaborative and iterative manner in the real context to add principles to theory and practice. Results showed an increase in the level of TPACK domains of teachers especially in their student-centered teaching approach.

MOOC for mathematics teacher training: design principles and assessment
Gilles Aldon, Ferdinando Arzarello, Monica Panero, Ornella Robutti, Eugenia Taranto, Jana Trgalová, École Normale Supérieure de Lyon, Università degli studi di Torino, Université Claude Bernard Lyon 1

This paper reports on an ongoing international research about MOOCs for in-service mathematics teacher training. We describe and analyse two different experiences of this kind: the Italian MOOC Geometria and the French MOOC Efan Maths. Both MOOCs aimed at supporting the teachers' professional development through a suitable mediation of technology and at triggering as much as possible the teachers' engagement so that they could develop from a non-community towards one or more communities of practice. As authors of this paper, we are members of the trainers' team of their respective MOOC and we also participated in its design. Starting from our methodological choices, we want to propose some reflections about design principles of MOOCs for mathematics teacher training in order to foster participation and collaboration among trainees and to efficiently assess this kind of engagement.

There is more than one flipped classroom
Chiara Andrà, Domenico Brunetto, Igor Kontorovich, Politecnico di Milano, The University of Auckland

The Flipped Classroom pedagogy has been developed for being responsive, student-centered and promoting self-directed learning. Three years ago, we started an international research project aimed at understanding how the FC can be implemented by secondary school math teachers through the use of a MOOC (Massive Open Online Course) developed at the Polytechnic of Milan. In particular, we focus on the teachers' use of MOOC videos. A variety of scenarios emerged from our direct classroom observations and work-in-team with the teachers. In this paper we propose a sketch of such a variety of FC implementations.

Teaching with Geogebra: resource systems of mathematics teachers
Gulay Bozkurt, Kenneth Ruthven, Eskisehir Osmangazi University, University of Cambridge

This paper reports from a study of use of the dynamic mathematics software, GeoGebra. This study used Ruthven's (2009) Structuring Features of Classroom Practice model to analyse the classroom practices of three teachers in English secondary schools. Here the particular focus is on how teachers manage their resource system with the use of GeoGebra. The main conclusion was that the stage teachers were at in terms of learning to teach with this software indicated differences in regard to establishing a functioning resource system especially in teaching the operation of the software, preparing the dynamic files and the choice of tasks. It became evident that the most experienced teacher was more fluent in managing his system of resources.

In search for standards: teaching mathematics in technological environment
Michal Tabach, Jana Trgalová, Tel Aviv University, Claude Bernard University Lyon 1

In the literature review on teacher education aimed at integrating technology to mathematics lessons we presented in the topic study group 43 at the 13th ICME conference, we brought to the fore a lack of standards for teaching mathematics with technology, which is, in our view, an issue for the actors of teacher education. In this paper, we tackle this issue by presenting existing ICT standards at the international and national levels and analyse them through the lenses of TPACK model and double instrumental genesis. We argue that the existing standards are too general, as they are neither school level, nor subject matter specific. We call the mathematics education community to take this issue in consideration.

A case study of a secondary school mathematics teacher's classroom practice with web-based dynamic mathematical software
Ali Simsek, UCL, Institute of Education

The broad purpose of this research is to gain a holistic understanding of teachers' integration of technology into classroom practices. This research examined a case of a secondary school mathematics teacher's classroom teaching in England in which a web-based dynamic mathematical tool, the Cornerstone Maths software, was used in the teaching of the subject of geometric similarity. One of the contemporary theoretical frameworks, The Structuring Features of Classroom Practices (SFCP) (Ruthven, 2014), guided my research with its five different components related to the integration of new technologies into classroom practice. Classroom observation and semi-structured post-lesson teacher interview was employed for data collection. The analyses showed how the teacher used the Cornerstone Maths software to teach geometric similarity in terms of five underlined features of classroom practice within the SFCP model.

Geogebra and numerical representations: a proposal involving fundamental theorem of arithmetic
Gerson Oliveira, Pontifícia Universidade Católica de São Paulo

This paper reports a qualitative research whose subjects were Elementary School Teachers who took part in a workshop about primality of positive integers and the Fundamental Theorem of Arithmetic (FTA). These topics was dealt with from different technological perspectives and analysed under a theoretical proposal connected to the concepts of transparency and opacity of numerical representations and to the "humans-with-media" approach. The interactions occurred in a Post Graduate Program in Mathematics Education and they consisted of two activities created to ask subjects which numbers in a random list would be prime. The analysis showed that participants had difficulties with FTA, which led them to adopt strategies with a high cognitive cost and make mistakes. Likewise, data showed that hindrances were overcome based on the educational proposal planned from a configuration of humans-with-GeoGebra.

Analysing the teacher's knowledge for teaching mathematics with technology
Helena Rocha, Universidade NOVA de Lisboa

The teacher's knowledge has long been viewed as a strong influence on the students' learning. Several authors have sought to develop procedures to assess this knowledge, but this has proved to be a complex task. In this paper I present an outline of a conceptualization to analyze the teacher's knowledge, based on the model of the Knowledge for Teaching Mathematics with Technology (KTMT) and a set of tasks. These tasks are chosen by the teacher taking into account the potential of the tasks to take advantage of the technology's potential. The analysis of the teacher's KTMT is based on the characteristics of the tasks chosen by the teacher; the balance established between the representations provided by the technology that the tasks advocate; the way how the tasks pay attention to the new issue of seeking for a suitable viewing window; and also the way how the tasks take into account the expectable difficulties of the students in the process of looking for the window.

Documentation expertise and its development with documentational experience in collectives: a French case of collective lesson preparation on algorithms
Katiane De Morales Rocha , Chongyang Wang, Luc Trouche

With a background of great changes of curriculum reform in France, there comes the new challenge for both (1) the new teaching contents such as the new content of algorithmic and (2) their working way in collective, such as inter-discipline teaching practice and three-year-cycles. In this study, we are interest to see the way the mathematics teachers react to the new challenges from a resource view. The two notions of documentational experience and documentation expertise are used through a case study of Anna and Cindy in our research.

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Surprise-driven abductions in DGEs
Anna Baccaglini-Frank, Nathalie Sinclair, University of Pisa, Simon Fraser University


Abductive inferences, which are the only types of inference that produce new ideas, are important in mathematical problem solving. Such inferences, according to Peirce, arise from surprising or unexpected situations. Therefore, one way to improve student problem solving may be to provide them with environments that are designed to evoke surprise. In this paper, we examine the potential of dynamic geometry environments (DGEs) to foster surprise. We conjecture that the ease with which students can explore configurations, along with the immediate feedback, may lead them to encounter surprising situations. We analyse three different examples of student problem solving featuring surprised-provoked abduction, and identify the specific role that the DGE played.

Exploiting potentials of dynamic representations of functions with parallel axes
Giulia Lisarelli, University of Florence

The concept of function has a central role both at school and in everyday situations. Several studies revealed that it is hard for students to think of functions and graphs in terms of covariation and this could contribute to their struggles in Calculus. The emergence of available technologies has fostered new teaching and learning approaches to overcome students' difficulties and some of them concerns the use of dynamic algebra and geometry software programs to experience the dependence relation and to explore functions as covariation. In this paper we describe a particular representation of functions with parallel axes and the analysis of a protocol in which three students work together on a problem that involves the exploration of a function represented in a dynamic interactive file. The analysis has been carried out to explore the potential of the proposed dynamic representation of functions that incorporates the semantic domain of space, time and movement.

Feedback in a computer-based learning Environment about quadratic functions: Research design and Pilot study
Elena Jedtke, University of Munster

Even though feedback is an essential part of computer-based learning environments (CBLEs), it is still not clear what effect different types of feedback have on students math achievement and on their abilities to assess their own achievement. To approach this problem we are currently planning a quasi-experimental study with grade eight or nine students using a CBLE called “Discover Quadratic Functions”. This paper gives insight both into existing research concerning the design of CBLE as well as concerning different types of feedback and into the theoretical principals that guided the CBLE design. Additionally, results of a qualitative pilot study as well as the design of the up-coming main study are presented.

Reasoning strategies for conjecture elaboration in DGE
Iman Osta, Madona Chartouny , Nawal Abou Raad, Lebanese American University, Lebanese University

The present study analyzes students' reasoning strategies for elaboration of conjectures when working in a Dynamic Geometry Environment (DGE). We observed 18 pairs of ten-graders in a private school in Lebanon, while working on open geometrical proof problems using Dynamic Geometry Software (DGS), namely GeoGebra. The analysis revealed three reasoning strategies employed by students. In the first two, the students worked on satisfying the presumed premise of the conjecture in the figure and identifying / validating the conclusion, either by observing the figure at hand (strategy 1) or by dragging the figure to validate the conclusion across different instances (strategy 2). Conversely, in the third strategy, the students worked on satisfying the conclusion of the conjecture in the figure and observing it to identify the premise that corresponds. Each strategy entails the use of different construction tools and types of constructions which affect the correctness of the resulting conjecture.

Gamifying math trails with the MathCityMap app: impact of points and leaderboard on intrinsic motivation
Iwan Gurjanow, Matthias Ludwig, Goethe-University Frankfurt am Main

Gamification in education describes the application of game elements in the design of learning processes. The MathCityMap project, which consists of a web portal and a gamified application for smartphones, combines the idea of math trails with the possibilities of mobile devices. To evaluate the impact of points and leaderboard on intrinsic motivation a pilot study has been conducted. The results suggest that there is no significant difference between these two game elements. However, gender seems to play an important role on the impact of gamification on intrinsic motivation.

Central and parallel projections of regular surfaces: geometric constructions using 3D modeling software
Petra Surynkova, Faculty of Mathematics and Physics Praha

The contribution addresses the constructions of central and parallel projections of regular surfaces which can be regarded as a subarea of descriptive geometry. My aim is to increase the interest of students in classical and descriptive geometry primarily through 3D computer modeling. I have been seeking to establish a stronger connection between descriptive geometry and its practical applications and to extend descriptive geometry with knowledge of computer graphics and computer geometry. In order to provide insight into more complex geometric problems and to increase the interest in geometry, I have integrated 3D computer modeling in my lectures and seminars. Geometry is a necessary component of many engineering processes such as the development of innovative graphics software or the design of complex industrial and architectural structures. My aim is to show that the principles and knowledge of classical and descriptive geometry are the stepping stones for solving tasks in practice.

Algebra structure sense in a web environment: design and testing of the expression machine
Teresa Rojano, Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional

The article reports on outcomes from a study that aims to investigate the role of affordances, level-up and feedback in the web environment Expression Machine in developing the algebra structure sense of tertiary education students. Algebraic substitution is the main procedure involved in the way the software works. Its design and testing methodology are based on the Human - Computer Interaction aspect of Activity Theory. From this approach, the study redefines the notion of algebra structure sense formulated in previous works. Results from the experimental sessions show that some features of the environment favor the development of sutudents structure sense, specifically when they deal with substitution and factorization tasks. At the same time, it was possible to identify aspects to be improved, for instance, adding categories of tasks with increasing structural complexity and less visually salient, which may require a greater cognitive demand from students.

Looking at compositions of reflections in a DGE from thinking modes and semiotic perspectives
Ana Donevska-Todorova, Melih Turgut, Humboldt Universität zu Berlin, Eskisehir Osmangazi University

The aim of this paper is to investigate whether and how three modes of thinking and semiotic perspectives are compatible for researching the teaching and learning of elementary geometry in a dynamic geometry environment (DGE). It first provides an epistemological analysis of compositions of reflections in a line from geometric, analytic and abstract aspects. Then, it represents a design of a task considering semiotic potential of particular tools in the DGE that was field-tested with a pair of prospective primary school teachers. Further, it discusses how has the double analyses allowed a detailed understanding of the semiotic potential of the designed artefact for the development of all three modes of thinking of the chosen geometric concept by the teachers. It finalizes with suggestions for future investigations of development of knowledge of other concepts in geometry through the modes and their support by digital tools. 

Spatial–semiotic analysis of an eighth grade student's use of 3D modelling software
Candas Uygan, Melih Turgut, Eskisehir Osmangazi University

The aim of this paper is to analyse the emergence of spatial–semiotic resources attached to an eighth-grade student's use of 3D modelling software while solving certain spatial tasks. The data comes from a task-based interview and it is analysed within a spatial-semiotic lens, including different kinds of resources not only based on the discourse, but also based on extra-linguistic expressions such as that sketches and gestures. The results of the study show that generally the student's reasoning steps explored a viewpoint for adding or removing cubes by use of the ‘orbit' and ‘select' tools, using ready-made mental pictures derived from completed steps, linking 2D and 3D representations through spatial visualisation and spatial orientation, emergence of spatial vocabulary including his strategies and generalizations.

Students' expanding of the Pythagorean theorem in a technological context
Ahlam Anabousy, Michal Tabach, Tel Aviv University, Al-Qasemi Academic College of Education

Dynamic Mathematical Software (DMS) in general and GeoGebra in particular have attracted the attention of mathematics educators because of their potential to influence student learning. The present research aims to add to the growing research efforts to study the influence of GeoGebra on processes used by dyadic learners to construct knowledge. Specifically, we study the context of three pairs of seventh graders who worked on an inquiry task to construct the relations between areas of squares built on the sides of an obtuse/acute triangle in a specially designed GeoGebra environment. The analysis used the Abstraction in Context (AiC) framework. The findings indicate that the three pairs constructed all the expected knowledge elements, and that one pair constructed unexpected construct. Generally, findings indicate the positive influence of the GeoGebra technological tool on the construction processes.

“Power of Speed” or “Discovery of Slowness”: Technology-assisted Guided Discovery to Investigate the Role of Parameters in Quadratic Functions
Lisa Göbel, Bärbel Barzel, Lynda Ball, University of Duisburg-Essen, University of Melbourne

This paper reports an intervention-study where students investigated the role of parameters in quadratic functions through technology-assisted guided discovery. The intervention had three experimental groups of students, each of which used a different type of visualisation – sliders, “drag mode” and a function plotter and one control group. The study provides insight into whether technology-assisted discovery learning supports the conceptualization and understanding of the role of parameters in quadratic functions. Qualitative analysis of students' work investigated the potential and constraints of each of the four different approaches for visualisation. Initial findings showed that technology does support the students in their learning, with the dynamic visualisation groups (drag mode and sliders) showing greater understanding than the function plotter group.

Pre-service teachers' preparation as a catalyst for the acceptance of digital tools for teaching matheamtics and science
Wajeeh Daher, Nimer Baya'a, Ahlam Anabousy, Rawan Anabousy, An-Najah National University, Al-Qasemi Academic College of Education

The present research examines whether pre-service teachers' preparation in using digital tools in their teaching in the training schools, develop their acceptance of these tools as teaching tools. Here, acceptance is measured in terms of the constructs of the technology acceptance model (TAM). It also examines the mediation of self-efficacy, anxiety of using digital tools for teaching mathematics and science and enjoyment of this use between the constructs of the pre-service teachers' acceptance of digital tools for their teaching. We used questionnaires that are part of TAM introduced by Davis. Forty eight mathematics and science pre-service teachers participated in the study. We analyzed the collected data using SPSS 21. The research results indicate that the pre-service teachers' preparation resulted in significant differences in their scores of affective and usage constructs associated with their acceptance of digital tools for mathematics and science teaching, except in the scores of anxiety.

The effect of collaborative computerized learning using Geogebra on the development of concept images of the angle among seventh graders
Nimer Baya'a, Wajeeh Daher, Samah Mahagna, Al-Qasemi Academic College of Education, An-Najah National University

This research intends to investigate the effect of collaborative computerized learning using GeoGebra on the development of the concept images of angle among seventh graders who were engaged with computerized collaborative activities that encouraged the development of five types of the angle concept images: verbal, authentic-life, graphical, numeric and dynamic. The research sample consisted of eight seventh grade students who worked collaboratively in groups of two. Two tests (a pre-test and a post-test) were administered to examine the development of students' concept images of the angle. In addition, interviews were held with the participants to study this development. The Constant Comparison Method was used to analyze the data. The results showed positive effects of the visual and dynamic use of GeoGebra, as well as of the collaborative learning on the development of participants' concept images of the angle, especially the dynamic one.

Dynamic Geometry Software in Mathematical Modelling: About the Role of Programme-related Self-Efficacy and Attitudes Towards Learning with the Software
Corinna Hertleif, Westfälische Wilhelms-Universität Münster

Mathematical modelling is a complex process consisting of several steps, which can also be carried out with the use of digital tools. This paper takes a closer look on how students perceive the DGS GeoGebra when learning mathematical modelling, how their confidence in their tool competencies changes when using the software to do modelling, and if the learning outcome concerning modelling competencies is influenced by programme-related self-efficacy or attitudes towards learning with the digital tool. Results from both qualitative and quantitative evaluations of a study with approx. 300 grade 9 students are reported.

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The transposition of counting situations in a virtual environment
Marina De Simone, Hamid Chaachoua, Université Grenoble Alpes

The mathematics education research is increasingly focused on different didactical hypotheses for constructing teaching and learning situations involving the decimal principle of the numeration system. One of these situations is, for example, counting a big collection of objects through the tangible manipulation. Within this situation, several problems at different levels arise: the time demanding, the role of the retro-actions and the class orchestration made by the teacher. This paper aims to show how a simulating device can overtake some of these problems related to the type of task “Counting a big collection” implemented in a tangible environment. 

Teaching locus at undergraduate level: a creativity approach
Mohamed El-Demerdash, Jana Trgalová, Oliver Labs, Christian Mercat, Menoufia University, Claude Bernard University Lyon 1

In this paper, we present our experience, while working in the MC Squared project, with the design of educational digital resources aiming at promoting creative mathematical thinking among undergraduate students. The resources, called “c-books” (c for creative), are produced within an innovative socio-technological environment by a community gathering together, computer scientists and researchers in mathematics and mathematics education. The paper highlights the importance of teaching loci curves at undergraduate level as an introduction to implicit equations. It presents the design choices providing the c-book with affordances to promote creativity in mathematics in terms of personalized non-linear path, constructivist approach, autonomous learning, and meta-cognition based activities, among others

Monitoring a technological based approach in mathematics in Portugal - the case of Khan academy
António Domingos, Ana Santiago, Cláudia Ventura, Conceição Costa, José Manuel Matos, Ricardo Machado and Paula Teixeira, Universidade NOVA de Lisboa

This paper intends to present a project to monitor the implementation of the Khan Academy Platform (KAP), in mathematics classrooms of 1st to 9th grade in Portugal. Based on a partnership between EDUCOM, Portugal Telecom and the Ministry of Education, a project is underway that involves the training of teachers in the use of the platform (KAP) and its implementation with students from five schools in the outskirts of Lisbon. We present here the theoretical and methodological assumptions that underlie this monitoring, with the objective of characterizing the training of the teachers involved, the students' learning and the role played by the platform in the process of teaching and learning mathematics.

Handwaver: a gesture-based virtual mathematical making environment
Justin Dimmel, and Camden Bock, University of Maine

We report on the design and development of HandWaver, a gesture-based mathematical making environment for use with immersive, room-scale virtual reality. A beta version of HandWaver was developed at the IMRE Lab at the University of Maine and released in the spring of 2017. Our goal in developing HandWaver was to harness the modes of representation and interaction available in virtual environments and use them to create experiences where learners use their hands to make and modify mathematical objects. In what follows, we describe the sandbox construction environment, an experience within HandWaver where learners construct geometric figures using a series of gesture-based operators, such as stretching figures to bring them up into higher dimensions, or revolving figures around axes that learners can position by dragging and locking. We describe plans for research and future development.

The design and use of open online modules for blended learning in STEM teacher education
Theo Van Den Bogaard, Paul Drijvers and Jos Tolboom, Utrecht University, University of Applied Sciences Utrech, Netherlands Institute for Curriculum Development

Blended learning, a teaching format in which face-to-face and online learning is integrated, nowadays is an important development in education. Little is known, however, about its affordances for teacher education, and for domain specific didactical courses in particular. To investigate this topic, we carried out a design research project in which teacher educators engaged in a co-design process of developing and field-testing open online learning units for mathematics and science didactics. The preliminary results concern descriptions of the work processes by the design teams, of design heuristics, and of typical ways of collaborating. These findings are illustrated for the case of two of the designed online units on statistics didactics and mathematical thinking, respectively.

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An interactive book on axial symmetry and the synergic use with paper and pin
Eleonora Faggiano, Antonella Montone, Michele Giuliano Fiorentino, Maria Alessandra Mariotti, Universita di Bari, Università di Siena

This work presents results from a teaching experiment concerning the construction-conceptualization of axial symmetry at Primary School through an interactive book, developed in a Dynamic Digital Environment (DGE), which embeds a set of tasks to be accomplished with selected DGE tools. The tasks are part of a teaching sequence, framed by the Theory of Semiotic Mediation (TSM), whose main characteristic is the synergic use of a “duo of artefact”. The duo is made up of a digital artefact - the interactive book - and a manipulative artefact, constituted by paper and pin. Herein, we describe the design of the interactive book and we show how a cognitive synergy arises from its use combined with the use of the manipulative artefact within the sequence, thus leading to the conceptualization of mathematical meanings.

Students' covariational reasoning: a case study using function studium software
Verônica Gitirana, UNIVERSIDADE FEDERAL DE PERNAMBUCO

This paper presents a case study on students' covariational reasoning, that used the software Function Studium to perform activities about the rate of change of linear and quadratic functions. Such software was designed by the research group (anonymous) and its development was guided by a model of software process based on Informatic-Didactic Engineering (anonymous). The results of the case study pointed out the contribution of activities designed within the software to support students' covariational reasoning, such as the dynamic and simultaneous connection of the different notations in the software and the tool "rate of change", which allowed students to infer patterns of variation of the functions addressed and the transition from average rate of change to instantaneous rate of change.

WIMS Www Interactive Multipurpose Server an interactive exercise software that has 20 years and still is at the top
Magdalena Kobylanski, Université Paris-Est Marne-la-Vallée

WIMS (Web Interactive Multipurpose Server) is a collaborative, open source e- learning platform hosting online interactive exercises in many different fields such as mathematics, chemistry, physics, biology, French and English among others. It is widely used in France mainly in maths from secondary school and up to the first university years. Using it in a proper way can bring advantage both to students and teachers.

Feedback in a computer-based learning Environment about quadratic functions: Research design and Pilot study
Elena Jedtke,  University of Munster

Even though feedback is an essential part of computer-based learning environments (CBLEs), it is still not clear what effect different types of feedback have on students math achievement and on their abilities to assess their own achievement. To approach this problem we are currently planning a quasi-experimental study with grade eight or nine students using a CBLE called “Discover Quadratic Functions”. This paper gives insight both into existing research concerning the design of CBLE as well as concerning different types of feedback and into the theoretical principals that guided the CBLE design. Additionally, results of a qualitative pilot study as well as the design of the up-coming main study are presented.

Function hero: an educational game to afford creative matheamtical thinking
Pedro Lealdino, Université Claude Bernard - Lyon I

The enhancement of educational processes at all levels of education can be achieved by implementing Game Based Learning (GBL), engaging students to the educational objectives affording the “Flow” mind state in which individuals optimize their actions scaffolded by intrinsic motivation. In mathematics, most of the games are based on arithmetical or logical thinking due the software's limitation in assessing user's inputs. Aiming to develop a game about functions affording Creative Mathematical Thinking (CMT), we used a Dynamic Cinderella Software (DCS) called Cinderella, the Game Development Environment, Unity and the Kinect Sensor from Microsoft. In this paper, we present design elements of the game Function Hero that affords CMT.

Incorporating LyX as standard tool for writing mathematics - effects on teaching and learning
Ittay Weiss, University of Portsmouth

We report on the experience of half a decade of teaching mathematics in the South Pacific region, incorporating LyX as a standard tool for the students in the preparation of their submitted assignments. LyX is a What-You-See-Is-What-You-Mean graphical frontend to LaTeX, the most widely used mathematics markup tool for publishing mathematics documents. We briefly survey the current state of affairs of software use in common practices relevant to the teaching of mathematics, and then concentrate on the advantages offered by LyX. We describe the practicalities of adopting LyX as part and parcel of the course tools and aims,and we then discuss the immediate and longer term effects thereof, and contemplate on the pedagogical efficacy and relevance of LyX as a communication tool.

(Un)intended representations in dynamic geometry software: pedagogical considerations
Samet Okumus, Recep Tayyip Erdogan University

Dynamic geometry software (DGS) has become more common in classrooms for teaching and learning mathematics. In this paper, I address some representational issues with which students and teachers may encounter while using DGS. Unintended representations may stem from the design principles for DGS, tasks that involve constructions with a limitation and representations of mathematical objects in DGS. Pedagogical considerations about using those representations as an opportunity for mathematical investigation are discussed.

CATO-ANDROID: The guided user interface for CAS on android smartphones
Hans-Dieter Janetzko , FH Lübeck

CATO is the self-explanatory user interface for several CAS on Windows, Linux/Unix and Mac/Ox. The principles of CATO are for example: packages realized as selection menus for the commands and extra windows for the input of multi-parameter commands.  The author has developed an application, CATO-Android, with the principles of CATO for smartphones with the operating system android. It is a user interface for guided input for CAS, at the moment only for Symja. In the article below, the author describes this app and how he realized the principles of guided input.