In a virtual learning environment with contents that follow textual and graphic (image) formats the correct reading of formulas and mathematical expressions is not feasible. The students of such non face-to-face simply do not “hear” how the formulas are read and therefore they can not access that important competence. Making use of the technological possibilities to digitalize the human voice and later to enclose the files of sound to web texts, a team formed by professors and technicians of have designed and implemented a first prototype of an open, collaborative and multilingual repository of locutions of mathematical formulas. The repository and a study case of its use will be presented.

The number of students studying sciences in Europe has steadily declined to such an extent that this is seen as a threat to the competitiveness of Europe. In France the decline has been about 5% each year during the past several years. Inquiry Based Study, IBS, is the paradigm that is generally seen as a possible way to increase students’ interest in sciences. In mathematics this approach has lead to the TERC reform in the US and to a new curriculum, which uses the book “Everyday Mathematics.” It has been deemed necessary to “relearn to teach arithmetic.” In this talk I will discuss the pitfalls of relearning to teach arithmetic, and other school mathematics topics. It seems that the need to revise mathematics curriculum comes up every now and then, like bubbles in economy. When the bubble bursts, we return back to basics until a new generation, which does not know that there was a burst, comes up with their own revisions.

This fall, we are introducing two new features of the elearning platform "physik multimedial".
http://www.physik-multimedial.de

First, this is LiLi 2.0, a totally new version of LiLi, our catalogue and search engine of physic's learning material.
LiLi provides links with descriptions, comments and ratings of learning material on the web.
Everyone may search, comment, insert or rate the links.
We have checked and updated every link and description in our database and enhanced the handling of our service.

Second, we start our authoring tools, a service for authors of elearning objects. We invite every author to join and
share her or his experience with tools and programs, didactics and more.

By exploiting synergies between available multi-purpose office machines and electronic document readers (with annotation capabilities), we can provide teachers with a mobile platform for exam reviewing. I will tell my experience on developing and using a system at my school for exams of about ninety students. As a bonus, we obtain automatic collection of grades and the possibility for the students to view their corrected exercises online.

I like to review exercises while commuting but until recently, I found it cumbersome since one has to carry a heap of sheets and manage to write on them in the narrow space of a train seat. Then, I bought an e-ink reader to carry my papers and I began to wonder if I could use the device to review my students exams too.

The procedure I'm currently using is:
1. On a pile of blank sheets I print a header displaying the name of the student, a datamatrix image encoding the same information, and a frame for the student grade.
2. At the examination room, I distribute these sheets to the corresponding students to be filled with the exercise solution.
3. After the exam, I use an office machine (which is provided with a batch sheet feeder) to scan the pile of exercises to a big PDF file that I load into my reader.
4. I review the exercises on the e-ink reader adding comments with the provided stylus and writing the awarded grade into the aforementioned frame.
5. A computer application reads the annotated exercises, identifies the student from the datamatrix code and recognises the handwritten grade from each digital page and finally collects this information in comma-separated file.

The purpose of the study that I'll describe at JEM was to evaluate the efficacy of an assessment for learning system named ACED (Adaptive Content with Evidence-based Diagnosis). We used an evidence centered design approach (Mislevy, Steinberg, & Almond, 2003) to create an adaptive, diagnostic assessment system in relation to the pre-Algebra topic of "sequences" (e.g., geometric and arithmetic sequences). ACED includes five main models: competency, evidence, task, presentation, and assembly (Shute, Graf, & Hansen, 2005). We also included instructional support in the form of elaborated feedback. The key issue we examined was whether the inclusion of the feedback into the system (a) impairs the quality of the assessment (relative to validity, reliability, and efficiency), and (b) does, in fact, enhance student learning. Results from a controlled evaluation testing 268 high-school students showed that the quality of the assessment was unimpaired by the provision of feedback. Moreover, students using the ACED system showed significantly greater learning of the content compared with a control group. These findings suggest that assessments in other settings (e.g. large-scale, mandated tests) might be augmented to support student learning with instructional feedback without jeopardizing the primary purpose of the assessment. Time permitting, I'll also describe a version of the program for use by individuals with low vision and blindness--a talking tactile tablet version of ACED.

This paper will be published shortly. The citation of the full paper is:
Shute, V. J., Hansen, E. G., & Almond, R. G. (2008). You can’t fatten a hog by weighing it—Or can you? Evaluating an assessment for learning system called ACED. International Journal of Artificial Intelligence and Education, 18(4).

The generalized availability, and the abundance, of digital resources for mathematics teachers entail a complete metamorphosis of the curriculum material, still in progress. They also yield a deep change in teachers’ professional knowledge and development. This statement leads to study mathematics teachers’ documentation work: looking for resources, selecting/designing mathematical tasks, planning their succession, managing available artifacts, sharing recombined resources etc. This documentation work is at the core of teachers’ professional activity and professional development.
Building on previous and ongoing research projects (about secondary school mathematics), I will display an approach of individual and collective aspects of this documentation work, enlightening changes brought by digital resources.

References
Gueudet, G., Trouche, L. (online) Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics.
Gueudet, G., Trouche, L. (2008) Collective documentational activity as a mode of teachers’ training : which methodological assistants ? ECER Conference, Göteborg.
Bueno-Ravel, L., Gueudet, G (2007) Online resources in mathematics: teachers’ genesis of use, in Pitta-Pantazi, D. and Philippou, G. Proceedings of the fifth congress of the European Society for Research in Mathematics Education, CERME 5, Larnaca, Chypre, http://ermeweb.free.fr/CERME5b/.

Applications such as GeoGebra and TERC together with other technology-based innovations for instructional delivery, such as mobile delivery systems, provide exciting new ways of supporting the teaching and learning of mathematics. However, as with any dramatic new innovation that stimulates people who are “early adopters,” there can be challenges in the process of integrating the innovation systemically into the mainstream of established ways of doing things. The new approaches that can be integrated into mathematics instruction might awaken interest and feelings of competence among some students who were not previously excited by the study of mathematics, but I believe it safe to assume that there remain vast numbers of students who still struggle with math and these struggles are due in part to motivational obstacles that they face, especially when the novelty effect of the innovation wears off. Furthermore, many instructors resist the implementation of new technologies because of conservative attitudes, fear, and lack of perceived value. Thus, it is important to consider a variety of change management, motivational, and instructional strategy issues when trying to creatively integrate these innovations into the mathematics curriculum and into ways of designing lessons. This presentation will address these issues and describe a validated theory and model that can be applied to designing the motivational aspects of learner attitudes and to the process of technology integration. Known by its acronym, the ARCS model refers to four categories (attention, relevance, confidence, and satisfaction) resulting from a synthesis of motivational literature. It provides a rational basis for a holistic understanding of motivation, for analyzing learners to determine what kind of motivational obstacles exist in a given situation, and for designing motivational strategies that are targeted to the needs of the learners. In addition, the issue of persistence is addressed by means of concepts of volition and self-regulation. These concepts help explain what is necessary for learners to maintain their goal-oriented behavior when faced with distractions and goal conflicts. Similarly, the successful adoption and integration of new technologies requires that certain motivational issues be addressed, such as the relative advantage and feasibility of the new technology. In summary, there are specific motivational and volitional factors to consider when implementing the exciting new technological innovations that are available and on the horizon with respect to the mathematics curriculum and methods of instruction.

Engineering students have traditionally had a lot of difficulty in reaching the objectives they have to cover, laid out in the different Mathematics courses. In a distance learning environment, both the learning methodology and the students’ profile (adults with family and professional responsibilities and with usually insufficient previous knowledge levels) are elements which aggravate these difficulties. In particular, it is mathematical notation which is necessary and ubiquitous in this kind of learning that presents a problem for the expression of content: verbalization is not a simple task and it is not easy to write using common digital resources. This second factor is especially significant in distance learning.

Mathematical expression verbalization tools have been developed with the goal of improving teaching quality in courses requiring scientific and technical notation unknown to many students. These tools have been integrated in web-based learning material, written in MathML, pertaining to a basic mathematics course for engineering at the UOC (Universitat Oberta de Catalunya). A first test with a group of students has been carried out with very satisfactory results.

Because of this initial success, we believe that this application improves the communication competences of students in courses with high mathematical content, reducing semantic confusion and so easing communication between students and teachers. From a technological point of view, it means including a new functionality to a formulae editor based on the MathML standard.

A demo can be seen in:
http://www.jem-thematic.net/en/node/1221

For some time WIRIS suite has offered tools to support education in mathematics and science topics in Moodle, the Open Source LMS. So far these solutions offered a formula editor based on icons and pallets, plus a powerful platform for mathematical calculation called WIRIS CAS. We want to present the new WIRIS family member, called Quizzes, that integrates the powerful WIRIS mathematical calculation engine of with Moodle quizzes system.

WIRIS Quizzes allows users to incorporate to all Moodle questions mathematical elements generated at random. In addition, the response can be assessed automatically by the engine of mathematical calculation no matter it has open answer or multiple-choice answers.

The WebALT project created a translator of mathematical teaching material from OpenMath formulas to seven European languages. This translator has recently become open-source, which opens new ways to develop and extend it. One of the main ambitions is to extend the system to cover all of the 23 official languages of the European Union. This goal requires organized collaboration of voluntary work. The main part of the work is the implementation of the GF Resource Grammar Library to new languages. This work is applicable not only in the WebALT grammars but also in other projects that use the library. In addition, WebALT requires a lexicon of mathematical terms to be built for each language. The talk will explain the main scientific issues of the task, as well as what skills and how much work is required, and how we intend to boost the development by organizing a Resource Grammar Summer School in 2009.

More on the summer school: http://www.cs.chalmers.se/Cs/Research/Language-technology/GF/doc/gf-summ...

Developing and experimenting a Dynamic Geometry and Computer Algebra environment for the upper-secondary algebra and calculus curriculum.

In France, at at upper secondary level, students have to consolidate their algebraic proficiencies in order to tackle pre-calculus.
The curriculum recommends non formal approaches of calculus concepts, but also that students should be introduced to abstraction and demonstration. It is then not easy to think of the role of algebraic techniques with regard to conceptualization. Rehearsing “rote” techniques certainly does not help, but it is important that students understand the equivalence of expressions and the benefit of algebraic transformations. They should also be able to perform basic transformations without too much difficulty in order to handle problems with inventiveness, intelligence and rigour.

My research group is developing and experimenting a Dynamic Geometry and Computer Algebra tool (Casyopée). This tool can be described as a symbolic calculator of functions and it is also designed to help students deal mathematically with problems of geometrical dependencies (for instance the area of a figure against a length of a segment). We experimented on a series of lessons with at 11th grade and gained some knowledge on how students can take advantage of Casyopée use.We are currently experimenting a transfer of this knowledge to a group of teachers.

In this talk, we will discuss three main issues: (a) the importance of ICT in the Portuguese Education System (PES), including new national initiatives and their impact in the New Curriculum for the Portuguese Basic Education; (b) the initiatives EECM, PmatE, TextMat, and IntBooks; and (c) our point of view regarding the current PES, the TERC reform in the US, and how the AA model may help to clarify some questions in Education.

Recently, the Portuguese State started several initiatives that in the whole aim to give “One Computer to Each Student”. This includes children in Primary Schools, where the Portuguese made computer “Magalhães” is being distributed. An outstanding idea that still misses several important issues in the educational scenario. Teachers are now less reluctant in using technology, but still do not used it conveniently, e.g., although widely spread among Basic and Secondary Schools, e-learning systems are not properly used. It is clear that, in the future, the teaching tools will change and push an increasing demand of good digital tools and quality content, which is now lacking behind. In fact, the New Curriculum for the Portuguese Basic Education (NCPBE) has already considered such changes.
As stated in the NCPBE, the learning goals in Mathematics involve the knowledge of mathematical concepts, mathematical representation, connection between distinct concepts, mastering procedures, problem solving, reasoning and communication. The use of technology (computers and calculators) is one of the resources recommended mainly in investigational tasks as, for instance, in the exploration of geometrical and numerical patterns. The NCPBE gives special emphasis to Euclidean transformations (isometries and similarities) and the use of dynamic geometrical software (Geogebra, Cabri, Geometer's Sketchpad) is highly recommended since, as it is well established, it enriches the knowledge of geometry. Through the three cycles of Basic Education the students must use calculators and computers to perform difficult calculations, representing information and geometrical objects. They should take advantage of the possibilities of experiencing a hand full of cases in real time. It is a real resource power in domains like geometry, algebra and data analysis.

There are several academic and private initiatives following such guidelines. Here we will describe, and exemplify with living examples, the initiatives EECM, PmatE, TexMat, and IntBooks of the University of Aveiro. The EECM initiative, based on the Russian model of the St. Petersburg school for young education, aims to develop mathematical qualities in children (from 4 years old) to students of all grades of the compulsory school. They run several events, e.g., involving parents in the process of how to teach “advanced” concepts to children, summer schools, and other events at local schools.

Since 1990, PmatE has been developing a platform only available in the Internet that develops contents either in the way of competition (e.g., Equamat’2008 which involved 4.000 students from 160 schools), or in the formative mode (evaluation, diagnosis and practice). PmatE has currently three main pillars: the communication and diffusion of science; school intervention; and cooperation with countries who share the same Official Language – the Portuguese (e.g., Mozambique). The platform is mainly based on an innovative system of questions randomly generated by models that has been used, not only as aforementioned, but also as complementary material in college courses in areas ranging from Mathematics, Biology, Physics and Portuguese Language.

The TexMat initiative has developed a highly interactive digital book covering the new curricula in mathematics for the 5th and 6th grades of the Portuguese Education System. Its design includes several features and capabilities as multilingual, modularity, the ability of been easily extendable by teachers (e.g., adding Geogebra constructions), model generated exercises, open questions, and centralized gathering of students statistics and assessments.

The IntBooks initiative aims to develop a platform to improve and make much easier the production of interactive digital content from any text editor. It addresses some of the common technical issues as: (a) how should mathematics be delivered and displayed in a large set of devices (PCs, PDAs, etc.); (b) how users interaction should be made and statistics collected; and (c) how authors may reuse and mesh up content from different web repositories.

Finally, and depending on time, we will discuss our point of view concerning some general issues of education, connected with the current Portuguese Education System and the TERC reform in the US. In particular, we will present the Abstract Abilities model (AA model) and how we believe it may improve Education.

A hallmark of the traditional approach to teaching is the importance of practice. Computer aided assessment provides one mechanism to automate this, providing immediate feedback to students and relieving teachers from repetitive marking. This paper is a follow-up to the JEM presentation given in Lisbon in Feb 2007 in which we asked "what is a mathematical question?". In this talk we will provide our answer. In particular we shall demonstrate the concept of mathematical question which has been implemented as part of the STACK computer aided assessment system. This include multiple "parts" which may involve interactions of a number of kinds. These may be independent or linked, and may implement "follow through marking", where appropriate. STACK questions are used by students through the Moodle content management system.

In the time period from April 2001 to December 2004, the development of the web-based learning and teaching environment EMILeA-stat has been funded by the German Federal Ministry of Education and Research (bmb+f). During this period, a consortium of several German universities was involved in the design and programming of the environment as well as the creation of its contents. EMILeA-stat contains a wide variety of introductory texts, examples, exercises and interactive visualizations for different topics in statistics and probability. Since 2005, EMILeA-stat is maintained and extended at RWTH Aachen University. The talk will focus on the concepts underlying EMILeA-stat and the new features of version 2.0 (http://emilea-stat.stochastik.rwth-aachen.de) which is released this year.

This paper reports experiences in constructing web-based questions and assignments and delivering weekly exercises and formative tests in mathematics at upper secondary level in the Helsinki School of Natural Sciences.

During the WebALT project 2006-2007 and after it we have been constructing over 1000 algorithmic and interactive web-based questions for upper secondary level. The software we have used is MapleTA.

The new version of MapleTA has given possibilities to construct step-by-step questions and we have combined this feature also for constructing “find from the graph”-questions.

The assignments can be graded automatically. We can also ask questions where students write an essay as the answer. This type of questions cannot be graded automatically. Including “essay”-parts in questions the teacher is able to study the ways the students are thinking. At the end of an assignment one can also request feedback from the students and their self evaluation.

During spring 2009 we are going to test groups of last year high school students using WebALT assignments. We will study the correlation between students’ results for these tests and their results at the matriculation examination.

We also report about experiences of using these exercises in lower secondary school mathematics and at the schools for practical nurses in drug calculation.

The study of Mathematics has always been particularly difficult for blind individuals. Indeed we can observe that a large majority of blind pupils do not succeed in maths studies, while the average mainstream pupil succeeds more easily. As maths is crucial in most science disciplines, this limits study options and future job opportunities for blind people. We assert that there is no reason that mathematical semantics can not be understood because of blindness; rather the biggest barrier is access to mathematical content, which can only be through speech or Braille.
During the last 2 decades a number of research projects have proposed partial solutions to this problem: projects focusing on access to mathematical literature and preparation of mathematical information, as well as projects trying to improve the presentation of content to the reader.
Today, we need new software tools that support the work of blind users, facilitating their understanding and helping them to carry out calculations, while facilitating inclusion in the mainstream environment. Indeed more and more such pupils attend mainstream schools, so it is important that these tools are usable with teachers who are not particularly familiar with Braille.

Curricula changes in the Finnish school system have happened in ten year intervals. In mathematics they have followed the international trends. The most obvious changes are the following:

1. Mathematics at school became descriptive - exact definitions and proofs were largely omitted.
2. Geometry and trigonometry were neglected.
3. Computations were performed by calculators and numbers and not on a more advanced level.

The effects of these changes have now penetrated the whole educational system. There are few studies on long range effects but a study of L. Naveri deserves special attention. This is compared to the PISA 2003 and TIMMS 1999 surveys. Also the feedback of the changes from professional schools and colleges is discussed.

This short presentation is devoted to briefly introduce the InterGeo project and to present their most recent news, specially the search of country representatives and curricula decoders.

Teachers and students at universities today are surrounded by diverse technologies, but the average profit got from them is not very high, and in addition it presents great variability too. The effects of technology on the curriculum seem to be rather peripheral, even for the new Bologna degrees, and for most people it is not clear, at least in the case of Mathematics, how curricula could be modified to optimize learning with the help of the available technologies. In this talk these issues will be analyzed by first presenting the current situation and then advancing possible ways forward.