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Assessment of open-ended geometry problems in dynamic geometry environments

Summary form only given. Assessment of student learning requires the use of techniques for measuring student achievement. Assessment is more than a collection of techniques, however. It is a systematic process that plays a significant role in effective teaching. It begins with the identification of learning goals, monitors the progress students make toward those goals, and ends with a judgment concerning the extent to which those goals have been attained [1]. Assessment can be classified in terms of their functional role in classroom instruction as follows: placement, formative, diagnostic and summative assessment [2]. In the literature, the integration of technological tools into the assessment process is expressed by the "e-assessment" concept [3,4,5]. Assessment using ICT has come to be known as e-assessment, which includes the entire assessment process, from designing assignments to storing the results with the help of ICT [5]. The most of the researches related to the e-assessment focused on how to transfer the examinations in paper-pencil environment to the electronic environment [4,5]. In addition to those studies, in the research about the integration of computer assisted assessment tools to the mathematics instruction, the participant pre-service teachers use these tools in favor of the formative assessment [6]. In a similar study, pre-service teachers prepared lessons and home works using technological tools such as dynamic geometry software and thus it is shown that those tools can be used in the process of assessment [7]. In the literature, there is numerous studies concerning technology supported mathematics instruction [8,9, I 0, 11]. But none of them is related to the assessment dimension of the mathematics teaching. In particular, it is highly recommended to conduct researches about the use of technology in that dimension [6,12,13]. The aim of this study is to determine some necessary points of assessment of computer based mathematics instruction. As this aim is related to a very large domain of research, this study focuses on only three open-ended geometry problems that can be solved in dynamic geometry environments. Case study is considered as the methodology of the research. The reason is that a case study investigates a contemporary phenomenon in depth and within its real-life context when the boundaries between phenomenon and context are not clearly evident [14]. 30 pre-service mathematics teachers have participated to the study and have divided randomly into three groups. In each group, every pre-service teacher worked individually on one of the three problems during 30 minutes. At the same time, they explained their approaches to solve problems by filling out a paper. In addition, a screen capture program is used to grab the video of what is seen on the computer screen. Meanwhile the researchers observed pre-service teachers' work on computers. The findings of the study are revealed via the analysis of each video, of their comparison with the written explanations and of the researchers' observations. Based on the findings, the most significant result of the study is that the screen captures should be definitely used for the assessment in dynamic geometry environments; because all of pre-service teachers' work can only be seen in those videos. The final version of the saved file doesn't represent the whole tries that one pre-service teacher does while dealing with problems. Furthermore a rubric that depends on the time, the number of tools, the relation between the drawing and the construction must be absolutely used to give a score.