Exploring pre-service middle school matmematics teachers' number sense in teaching contexts

This research aims to examine how prospective middle school mathematics teachers utilize their number sense skills in instructional contexts. To achieve this goal, a survey design, one of the quantitative research methods, was employed in the study. The research was conducted with 174 prospective middle school mathematics teachers enrolled in five state and private universities during the 2023-2024 academic year. Data were collected using the "Number Sense Test in Instructional Contexts," developed by the researcher. Responses to open-ended questions on the test were coded, and percentage and frequency tables were generated for these responses. It was observed that prospective teachers were able to generate multiple solution methods in mathematical tasks involving mental arithmetic and estimation. However, they faced difficulties in generating different solution methods in tasks involving division operations. It was found that number sense-based approaches were predominantly used in the solution methods produced for these tasks. Prospective teachers preferred number sense based approaches in instructional tasks related to understanding numbers by associating them with different contexts and representations, interpreting operation results in different ways, and evaluating the accuracy and validity of student responses. However, the use of these approaches was not at the expected level. Furthermore, when explaining rules and algorithms, prospective teachers generally preferred rule-based approaches, while the majority chose number sense-based approaches when making generalizations about the impact of operations on numbers. The ability of prospective teachers to use number sence in instructional tasks involving natural numbers was found to be an average of 19.67 out of 35 points. This indicates that the use of number sense in instructional contexts by prospective teachers is at a moderate level.