Plenary talks for the different themes will be given by the following colleagues.

Inspiring learning and teaching

Jürgen Roth (Universität Koblenz-Landau, Germany)

Title: Inspiring learning and teaching of functional thinking by experiments with real and digital materials

Inspiring learning means to aim on promoting skills, knowledge and interest. In a pre-post-test intervention study (N = 282, two experimental groups: real material vs. digital material, control group) we investigated whether experiments with real materials or digital materials based on GeoGebra are an appropriate measure to promote the functional thinking of sixth graders. Even though both types of material led to a significant increase in functional thinking, the increase of the digital material group was significantly higher. Digging deeper into data we found, that the use of different material has different impact on the learning of functional thinking.

To inspire teaching we use a concept of long-term in-service teacher training, were the analysis of video vignettes from student work processes within our online learning environment ViviAn is one measure among several others.

Lynda Ball (University of Melbourne, Australia)

Title: An online resource to inspire learning and reflection on teaching: The potential of the SER

This presentation will outline a new STEM education resource (SER) which was initially targeted for use with year 9 and 10 students. Through use of the SER the hope is to ‘inspire’ learning by developing students’ independence and their capacity to plan and conduct real life investigations. The challenge to ensure that there is adequate focus on ‘M’ in a STEM investigation and this is going to be evidenced through students’ analysis, interpretation and presentation of evidence to support conclusions. The design of the resource can prompt teachers to consider ways to develop the investigative skills of their students, thus there is the potential to ‘inspire’ teachers to reflect on their teaching through use of the resource. Results from the initial trials of the SER will be presented, including implications for teaching and learning.

Networking of theories

Angelika Bikner-Ahsbahs (Universität Bremen, Germany)

Arthur Bakker (Universiteit Utrecht, Netherlands)

Title: Networking theories when designing for mathematics education with technology

Designing for mathematics education is not an easy task. It requires insights from multiple resources including different theoretical perspectives. Rather than as a problem, the networking theories group conceptualizes this diversity as having learning potential. Over the past decade more insight has been gained into how theories can work together.

Bikner-Ahsbahs provides an overview on research where the networking of theories has been used. By examples she highlights networking strategies and cross-methodologies as ways to link theoretical perspectives systematically. Reflecting on two design studies which include technology as part of a multimodal perspective, she outlines the potential of a networking theory approach to designing for teaching and learning mathematics with technology.

Bakker conceptualizes networking strategies as boundary-crossing learning mechanisms for both design of educational materials and analysis of data. He illustrates such mechanisms as a deliberate attempt to integrate embodied design and instrumental genesis so as to take advantage of embodied interaction with digital technology to help students develop understanding of proportion and trigonometry.

Enhancing Assessment

Michal Yerushalmy (The Mathematics Education department and the MERI center, University of Haifa, Israel)

Title: Seeing The [Entire] Picture with STEP: Studying Example-Eliciting approach to online formative assessment

Many attempts to reform mathematics teaching over the past decades have shifted views of instruction to emphasize mathematical reasoning and strategic competence to be the central learning goals. The affordances of technology for creating learning environments that nurture mathematical reasoning have been developed and investigated over the past few decades. Recent efforts bring diagnostic tools from cognitive research into technological platforms that automatically assess students’ work to provide immediate feedback. Such feedback is used for assessment, to support conceptual adaptive learning and to support teachers with classroom formative assessment. Yet, the automatic feedback has usually been limited to tasks that require procedural interactions which do not necessarily offer teachers opportunities to assess various dimensions of mathematical conceptual understanding. Over the past few years we developed and experimented an innovative online assessment platform (STEP) that provide meaningful feedback online, study the affordances of Example-Eliciting tasks and articulate design-principles for online example-based formative assessment environment. I will focus on the rational and principles of the development and the design based research. I will analyze cognitive aspects of the conceptual online feedback and our attempts to articulate the potential of technology for making example eliciting tasks less demanding for teachers to manage.

NEW: Bastiaan Heeren (Open University of the Netherlands, Heerlen, Netherlands)

Title:  Automated feedback for mathematical learning environments

Digital learning environments that offer well-designed feedback have the potential to enhance mathematics education. Building such a system is typically a huge and complex undertaking. Generating informative feedback at the level of steps a student takes requires the encoding of expert knowledge about the problem domain in software. The software component that processes this knowledge is traditionally called a domain reasoner. Such a reasoner can produce various types of feedback, for example about the correctness of a step, common errors, hints about how to proceed, or complete worked-out solutions.

In this presentation I will highlight the main components of a domain reasoner that is responsible for generating feedback: rules, problem-solving procedures, normal forms, buggy rules, and constraints. Examples are drawn from the Digital Mathematics Environment (DME), which uses feedback generated by specialized domain reasoners for solving equations and structuring hypothesis tests. Similar techniques have also been used in the Advise-Me project for assessing free-form input for math story problems.

Cancelled:Chris Sangwin (Centre for Technology Enhanced Science Education, School of Mathematics, University of Edinburgh, Great Britain)