This paper is based on the analysis of the relationship between early education, mathematical skills, and student achievement in Bosnia & Herzegovina, using data from the trends in international mathematics and science study (TIMSS) 2019. The study involves 5,628 fourth-grade students whose average age was 10.1 years. The research specifically focuses on factors such as the age of students at the beginning of schooling, attendance at preschool institutions, and their mathematical skills before starting school. Through the application of SPSS analysis, insights into the statistical relationships and trends between these factors are provided, emphasizing the importance of early educational experiences to improve the quality of education in Bosnia & Herzegovina. The analysis results show that the length of stay in preschool institutions, attendance in preschool programs, and the early acquisition of mathematical skills (counting skills, recognition of numeral representations, numeral writing, simple addition, and subtraction) impact later mathematical achievements of students.

Understanding the concepts related to real function is essential in learning mathematics. To determine how students understand these concepts, it is necessary to have an appropriate measurement tool. In this paper, we have created a web application using 32 items from conceptual understanding of real functions (CURF) item bank. We conducted a psychometric analysis using Rasch model on 207 first-year students. The analysis showed that CURF is a dependable and valid instrument for measuring students’ CURF. The test is uni-dimensional; all items are consistent with the construct and have excellent item fit statistics. The results indicate that the items are independent of each other and unbiased towards the gender and high school background of the students.

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