Peter Boon
Utrecht University

Bio:
Peter Boon (1960) works as a senior software developer, educational designer and researcher at Utrecht University’s Freudenthal Institute for Science and Mathematics Education.  He combines his technology expertise and his mathematics teacher background for developing rich learning content. He has not only designed many online resources that have had much impact on education in the Netherlands and outside, he is also the architect of the Digital Mathematics Environment DME, a tool for designing and delivering interactive online curricula, that used by many schools and publishers. 

Title of talk:
Numworx, a platform for formative and summative assessment of Mathematics

Abstract:
The Freudenthal Institute for Science and Mathematics education (Utrecht University, Netherlands) has been working on the design of a digital platform for mathematics education for more than 15 years. It was called “The Digital Mathematics Environment” (DME). Recently it has got the name “Numworx”.

 This software is the result of a several design challenges.

• What item types do we need for learning mathematics in a digital environment?
• How can we automatically grade mathematics assignments.
• How can we generate feedback to help students.
• How can we support and evaluate intermediate steps in mathematics assignments.
• How can we assess higher order skills in a digital environment.
• How can we support the use of mathematical language in a user-friendly way.
• How can we use domain models to track students learning.

In this presentation I will show how we worked on these challenges and how we struggled. I will present the resulting software and I will be happy to discuss the choices we have made.

George Kinnear
University of Edinburgh

Bio:
George Kinnear is a Reader in mathematics education in the School of Mathematics at the University of Edinburgh. He completed both his undergraduate degree and Ph.D. in pure mathematics at the University of Edinburgh. His research interests are in effective uses of technology to support undergraduate mathematics teaching and learning, with a particular focus on the use of e-assessment.

Title of talk: 
Student approaches to generating mathematical examples: comparing e-assessment and paper-based tasks

Abstract:
(by George Kinnear, University of Edinburgh, Paola Iannone, Loughborough University and Ben Davies, University of Southampton)

Asking students to generate examples of mathematical objects has been suggested as an effective way to develop their understanding of mathematical concepts. Using e-assessment makes it possible to give students feedback on their examples, in a way that might be infeasible for paper-based tasks due to the effort involved in checking examples from large numbers of students. However, translating paper-based tasks to e-assessment may change their nature, and the way that students approach them. We will report on data from two cohorts of students completing the same sequence of tasks on paper (N=333) and through e-assessment (N=322). We found that the students completing the e-assessment version of the tasks scored significantly lower than students completing the tasks on paper, and gave different types of answers. Task-based interviews with 19 further students completing the same task sequence (11 on paper and 8 through e-assessment) reflected a similar pattern. Our analysis of the students' solution strategies offers a possible explanation: the students completing the e-assessment tasks used less sophisticated example-generation strategies than the students completing the tasks on paper. We will discuss the implications of these results for the use of e-assessment.

Bärbel Barzel
University of Duisburg-Essen

Bio:
Bärbel Barzel is as professor at the University of Duisburg-Essen in Germany. She worked twelve years as a math teacher in Germany before she started working as a researcher. Her interest is the integration of technology in mathematics teaching and learning. Currently, her research focus is the conceptualization of technology based formative assessment and specifically she adapts with her group the Australian SMART-tests (Specific mathematics assessment that reveals thinking) for Germany.

Title of talk:
The Challenge of realizing an elaborated Online-Diagnostic which is more than pure skill training

Abstract:
Formative assessment as individual, diagnosis-guided support for learners is one of the most important factors for understanding and learning mathematics. Online-Diagnostic can help here by offering fast individual evaluation and supportive steps. However, most digital diagnostic tests often only assess on a rather superficial level, in the sense of correct and incorrect answers following a pure skill training. The challenge of realizing a more elaborated Online-Diagnostic which fosters understanding will be described from a theoretical point of view and possible ways of meeting this challenge are presented using different examples of (self-) assessment tools.

Christopher J. Sangwin
University of Edinburgh

Bio:
Chris Sangwin joined the University of Edinburgh in 2015 as Professor of Technology Enhanced Science Education. His learning and teaching interests include (i) automatic assessment of mathematics using computer algebra, in particular the development of the STACK system, and (ii) problem solving using student-centred approaches. Chris Sangwin is the author of a number of books, including "Computer Aided Assessment of Mathematics" and the popular science book "How Round is Your Circle", which illustrates and investigates many links between mathematics and engineering using physical models. He's also co-authored textbooks for the International Baccalaureate published by Haese Mathematics.

Title of talk:
Assessing algebraic form automatically

Abstract:
In this talk will start with a mathematical discussion of algebraic form.  For example, what is "factored form" or "partial fraction" form and how do we recognise these forms in everyday work?  Noticing, and pattern recognition, is fundamental to mathematical work.  I argue there is a continuum between recognising simple forms through to the outright obscure.  E.g. starting with quadratic expressions as ax^2+bx+c, through the difference of two squares as e.g. cos^2(x)-1, or (x-|x|)(x+|x|), to the outright obscure when Ramanujan "noticed" 1729=1^3 + 12^3 = 9^3 + 10^3. The "principal of permanence of form" has often guides how we introduce and use mathematical notation, allowing familiarity in one field, and analogy, to shape the development and expression of results in another. I will then discuss online assessment, and how appreciation of form plays a central role in all assessment of mathematics. I will call for a better vocabulary for talking about forms for mathematical expressions and parts of expressions: lack of agreed vocabulary hampers effective communication, including feedback to students. I will illustrate the talk with examples in STACK which show current capabilities, and how these can be used to give effective feedback to students.

Guido Pinkernell 
University of Education Heidelberg 

Bio:
Guido Pinkernell is Professor of Mathematics and its Didactics at the University of Education Heidelberg, Germany. After studying mathematics and music at the Universities of Hannover (DE) and Cardiff (UK), he worked as a secondary school teacher for eight years before returning to research in mathematics education at the Universities of Münster and Darmstadt. His main research interest is the teaching and learning of mathematics with digital media and tools.

Title of talk:
Activating Feedback in Formative Assessment: From Receptive to Active Learning with Automated Feedback

Abstract:
Feedback is one of the teacher's most important contributions to a successful learning process. Especially in formative contexts, a teacher can choose from a variety of feedback content, ranging from detailed explanations for low-performing students to well-placed cues for the high-performing.

Ideally, automated feedback should be as adaptable to the student's response as feedback from an experienced teacher. Whereas in analogue teaching feedback is usually situational and intuitive, for "a priori" programming of feedback in assessment software it is helpful to know of the different types, forms and structures from which to choose.

This talk will give an overview of what we currently know about successful automatic feedback. It will also propose some feedback models for adaptive feedback programming that are intended to foster active rather than receptive learning.

Andrey Chesnokov, Norwegian University of Science and Technology
andrey.chesnokov@ntnu.no
+4746420404

Niclas Larson, University of Agder
niclas.larson@uia.no
+4738142404