Development and implementation of measurement tools for determining 4th grade students' mathematical thinking levels

The aim of this study is to develop measurement tools to determine the mathematical thinking levels of 4th grade students and to examine the mathematical thinking levels of students with these measurement tools. At the end of four years of primary school education, it is important to determine and objectively evaluate the mathematical thinking levels of students with a measurement tool that is suitable for the purpose and includes diversity, both in monitoring the development of students and in determining the effectiveness of the education programme. The explanatory sequential design of mixed method was used in the study. In the first phase, which is the quantitative part, open-ended and multiple-choice questions were developed to measure the components of mathematical thinking (mathematical reasoning, estimating, specializing, generalizing, conjecturing and convincing). In addition, forms consisting of statements about mathematical thinking were prepared for teacher assessment and student self-assessment. Of these developed tools, MTT-1, MTT-2 and self-assessment form were applied to all 4th grade students (N=128) of a public school in Istanbul in the 2021-2022 academic year who volunteered to participate in the study and quantitative analyses were performed. In the second qualitative phase of the study, group interviews were conducted with 18 students selected from the study group by purposive sampling using MTT-3 with clinical interview technique. Descriptive analysis of the answers given by these students to MTT-1 and content analysis of the data obtained from the group interviews in which they answered MTT-3 questions were conducted. Students' class teachers also rated their students regarding the components of mathematical thinking through the prepared teacher assessment form. The measurement tools (MTT-1, MTT-2, MTT-3, teacher assessment form and student self-assessment form) developed to determine the level of mathematical thinking of 4th grade students were found to be valid and reliable tools. Students' mathematical thinking was at 'basic' level with 48.43%. It was found that 58% of the students were at 'sub-basic' and 'basic' level, 42% were at 'proficient' and 'advanced' MT level, and the highest achievement among the components was estimating with 58.24%. This was followed by generalizing (57.91%), mathematical reasoning (56.54%), conjecturing (48.14%), specializing (39.03%), and the lowest success rate was 28.94% for convincing. The MT level of the students who were clinically interviewed with MTT-3 questions was 'proficient' with 57.34%. Qualitative analysis findings support the quantitative analysis findings. Students' self-assessment scores for MT components are higher than both test scores and teacher assessment scores. Despite the limitations such as the lack of direct training on the components of mathematical thinking and the interruption of one and a half years of face-to-face education due to the pandemic, the mathematical thinking of primary school students is at a promising level. These results show that mathematical thinking of primary school students can be measured and developed. Suggestions for practitioners and researchers about the development and measurement of mathematical thinking are presented.