Abstracts - Earli

goal is to help students to develop deeper and higher-order understanding of mathematical ideas.All sessions make wide use of activities that employ contexts in which students can use theirsense-making abilities to solve complex problems in a collaborative atmosphere. Moreover, theactivities are designed so that students produce models for constructing, describing, manipulating,predicting, and controlling complex systems. Student solutions are not simply answers to specificquestions; rather, they reveal many aspects of the thought process that goes into the final solution.In this way, pre and in service teachers, researchers, etc. can focus on the work that the studentsproduce in an effort to deepen their own understanding of the mathematical content, and the waysin which students learn the content, develop and use representations, and formulate justificationsand solutions of the content. When the participants examine students’ work, the initial or earlymodels that they use to make sense of the situations (e.g., to make predictions or provideexplanations that guide actions such as instructional practices) may be shallow or lesssophisticated versions of later models. This research will provide an analysis of the ways in whichteachers revise, refine, extend, test and share their evolving models for understanding themathematical ideas that are produced over extended periods of time, and the implications this hasfor classroom practice.Multimodal aspects of assessment — Analysis of national diagnostic materials in swedenAstrid Pettersson, Stockholm Institute of Education, SwedenLisa Björklund Boistrup, Stockholm Institute of Education, SwedenThis presentation addresses the use of a multimodal framework for analyzing assessment materialsin general and diagnostic materials in particular. What is assessed and how an assessment iscarried out influence students’ learning and teachers’ teaching (see for example Gipps, 1994).Consequently, an analysis of the different assessment materials in mathematics that are offered bya government is important. In our study we analyze the Swedish national diagnostic materialsdeveloped for the compulsory school. The framework for the study consists of (1) research ofassessment and its influences on teaching and learning, mainly the importance of qualitativefeedback (Black & Wiliam 1998); (2) the "goals to aim for" in the national mathematicscurriculum (Swedish National Agency for Education, 2001); and (3) the multimodal approach. Weuse the multimodal approach as it is described by Kress et al. (2001). In short, this multimodalapproach emphasizes that learning can be seen in a semiotic frame and that communication isconsidered not only from a linguistic perspective. Instead all modes of communication arerecognized. Modes can be speech, writing, gestures and pictures. Each mode has its "affordances"for a person engaged in a communication (Kress et al., 2001). In our study we analyze what kindof feedback interaction the teacher and student will become engaged in when using the material.We also investigate which areas of mathematics are focused on in the material and what roledifferent communicational modes play in the materials. In our results we will describe thedifferences and similarities between the various materials provided by the government. We alsodiscuss the opportunities for the materials to be useful tools for teaching and learning.Getting access to students’ understanding of function — considering assessment in mathematicsfrom the perspective of multiple representationsIliada Elia, University of Cyprus, CyprusAthanasios Gagatsis, University of Cyprus, CyprusThe use of multiple representations has been strongly connected with the complex process oflearning in mathematics, and more particularly, with the seeking of students’ understanding ofimportant mathematical concepts. Learning to use multiple representations requires students to– 165 –