Objectives

Objectives (of the project)

The project SAiL-M (“semiautomatic analysis of individual learning processes in mathematics”) develops models to improve the quality of teaching mathematics in early semesters. It will

• formulate, implement, and publish pedagogical design patterns of activating learning environments for mathematics at university,

• adapt tools for the assessment of learning processes - i.e. tools for the documentation and analysis of processes - and use and evaluate them in learning environments, and

• evaluate the effectiveness of process-orientated feedback with various diagnostic methods.

Detailed description

esides students who study mathematics as a major, also students of other disciplines have to pass a large number of mathematics courses, e.g. engineering science, economic science, and computer science. Latest pedagogic approaches highlight the development of mathematical competences, such as problem solving, arguing, and communicating, besides the training of mathematical techniques. Traditional mathematics education at university level is usually more focused on teaching techniques and standard solutions than on the promotion of general mathematical processes. Often only products are focused and not the learning process itself. The reason for that may be that someone who tries to activate and support processes in mathematics courses at university faces numerous problems:

• There are often little interests in mathematics on beginners of study, except diploma or bachelor students, in particular there are required courses. Beyond that the active and interesting learning in mathematics is handicapped by the students beliefs in mathematics.

• Courses in mathematics in early stages of study often have a large number of participants. An individual feedback of learning processes, e.g. the evaluation of learning diary in math, can ill afford to manage even if there is more personal.

• There is a need of documentation for a feedback on processes (mathematical or universal). This is very complex and hard to implement in general. The autonomous supervision and illustration of such processes isn’t achievable for novices on study. There have to be more methods of recording, which support the processes as well as generate a basement of information for the teacher to give feedbacks.

• The analysis of documentation of learning processes as a basement of giving feedback and assessment/benchmark is time-consuming. For a regular feedback in courses with huge participants the analysis via computer is indispensable. The analysis of processes is highly individual and depends on the style of illustration. Methods based on computer have to be tailored to the concrete instants.

SAiL-M wants to:

1. phrase, implement and make didactic design patterns available for others for activating, expertise environments for learning mathematics on university, 2. adapted tools for the documentation and analysis of learning processes and initialise in learning environments and 3. evaluate the usability and efficiency of process-orientated feedback. Unto 1. Design patterns are used as a central approach in different levels of describing learning processes. At the macroscopic level there will be formal principles developed for activation learning processes to improve mathematic expertise. These principles include curricular standards and base on the former work of Vogel and Wippermann (2003, 2004). At this the findings of teaching psychology are very important. Inter alia there have to be self-determined formats of motivation stimulated, the improvement of mathematical self-assessment supported and the skill of cooperative learning trained. At the microscopic level the pattern based approach should be used to detect details of learning math. There should be “anti-patterns” documented and phrased based on work of the analysis of mistakes in a learning process. The shaping has to reach a granularity which affords to describe complete processes of learning based on patterns. Furthermore this should offer the assignment of computer based tools to push and automatically log learning processes for later analysis (see 2. + 3.). Unto 2. There will be developed tools, which log the subject specific learning processes of students and procure semi-automatic examination methods. In doing so standard solutions and standard mistakes should be detected and rated, while nonstandard solutions and mistakes have to be handed over to the instructor for an assessment. Hereby the instructor gets disburden of the analysis of many learning processes, on the other hand interesting processes are culled, which can be used (anonymous) in apprenticeship. These developed subject specified mechanism of analysis should be able to transfer on other subjects. Unto 3. The developed principles of designing and the tools will be tested in courses at different universities empirically. Therefore the content specific and mathematic expertise in general of the students will be evaluated. Beyond that motivational data like the level of self-determined motivation and the mathematical self-efficiency of the learners will be collected. Among the specific progress of the learners the methods of computer based semi-automatic analysis of the learning processes will be evaluated. For this the quality of the examination results will be correlated with results of various traditional methods for the analysis of learning processes (e.g. loud thinking analysis) The research questions of the project are:

1. How have learning environments be designed, which/those who assist the development of mathematic expertise within studies at university with a large number of participants? 2. Which computerized methods support the documentation and analysis of individual, content specific learning processes and how can efficient feedbacks be prepared semi-automatically? 3. Do the developed learning environments, methods and tools stand the test in practice and which elements can be carried to other contexts? This project is hold by three Universities of Education in Baden-Wuerttemberg for subject and academic didactic expertise and by RWTH Aachen for fields of research in/for computerized learning.

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