Number sense is defined as individuals’ ability to understand the meaning of numbers and perform calculations flexibly and effectively (McIntosh et al., 1992). It is a fundamental component of mathematics education and plays a significant role in developing students’ mathematical thinking skills (Yang, 2005). Consequently, number sense is regarded as an important research topic in mathematics education.

A review of the literature suggests that number sense has been examined from various psychological perspectives, has established theoretical frameworks, and has defined key characteristics and essential components (McIntosh et al., 1997; Howden, 1989). Yang (2009) analysed relevant studies and reports to identify the core components of number sense:

1) Understanding the meaning of numbers: This entails comprehending the base ten number system, including whole numbers, fractions, and decimals. It also involves grasping place value, recognizing number patterns, and representing numbers in multiple ways (McIntosh et al., 1992).

2) Recognizing the magnitude of numbers: This refers to an individual’s ability to comprehend numerical size relationships. For example, when comparing fractions, students should employ meaningful strategies such as same numerator, same denominator, transitivity, and residual reasoning rather than relying solely on standard written methods like finding the least common denominator (Cramer et al., 2002).

3) Using benchmarks appropriately: Individuals should be able to use reference points such as 1, 1/2, and 100 flexibly in different situations (McIntosh et al., 1992). For instance, when estimating 21/32 × 7/16, students should recognize that 21/32 is less than 1 and 7/16 is less than 1/2, leading to the conclusion that the result is less than 1/2.

4) Knowing the relative effect of operations on numbers: This involves recognizing how the four basic operations affect numerical results (McIntosh et al., 1992). For example, when estimating 391 × 0.95 or 128 ÷ 7/16, students should use their understanding of operations instead of relying on standard algorithms. They should realize that multiplication does not always increase a number and that division does not always yield a smaller value (Graeber & Tirosh, 1990).

5) Developing estimation strategies and judging the reasonableness of results: This entails applying mental estimation without written computation (McIntosh et al., 1992). For example, when determining where to place the decimal in 638.5 × 0.254 = 162179, students should recognize that 600 multiplied by approximately 1/4 is about 150, making 16.2179 an unreasonable result.

Yang’s (2009) framework provides a strong foundation for understanding how number sense is shaped by teachers. This study employs the five components outlined above as a framework to support research design and data analysis.

Research on how pre-service teachers use number sense strategies suggests that their knowledge levels and strategy preferences vary. Reys and Yang (1998) explored how number sense skills develop during teacher education. Their findings indicate that pre-service elementary mathematics teachers tend to focus more on number sense strategies, whereas pre-service primary school teachers often rely on standard algorithm-based approaches. Similarly, Verschaffel et al. (2010) emphasized that training programs designed to enhance pre-service teachers’ number sense skills and flexible strategy use significantly impact their pedagogical approaches. Such programs are particularly crucial for improving number sense skills among pre-service primary school teachers.

Teacher knowledge is a key factor in developing number sense (Alsawaie, 2011). However, research suggests that both in-service and pre-service teachers possess limited number sense skills (Tsao, 2004). Given these findings, this study aims to compare how pre-service primary school teachers and pre-service elementary mathematics teachers use number sense strategies. To achieve this objective, the study seeks to answer the following research question: “What are the differences in number sense strategies between pre-service elementary mathematics teachers and pre-service primary school teachers?”

This study aims to compare the number sense strategies used by pre-service elementary mathematics teachers and pre-service primary school teachers. A Comparative Descriptive Research model was adopted to achieve this objective. The sample consists of 37 pre-service teachers enrolled in the "Teaching Numbers" course within an elementary mathematics teacher education program and 55 pre-service teachers enrolled in the "Teaching Mathematics" course within a classroom teacher education program at a public university in Turkey. Both groups receive training in their respective courses to develop students' number sense. Since the sample consists of pre-service teachers in Turkey, all data were collected in Turkish. The "Number Sense" test developed by Yang et al. (2009) was used as a data collection tool. Since the original test included only five items, only these were used for comparison. No further information was available regarding other items. During adaptation, the test was translated into Turkish and reviewed by two mathematics education experts. Based on their feedback, unclear sentences were revised, and necessary formal adjustments were made. The test was administered on separate sheets, and both groups received the following instructions: "Solve the problems without performing exact calculations. Justify your answer and explain how you arrived at the solution. You will have three minutes for each question." The data were analysed using descriptive analysis, which summarizes and interprets data under predefined themes, categories, or codes. Such analyses aim to describe individuals, events, or situations and require extensive background knowledge (Robson, 2001). Responses were coded as 1 for correct and 0 otherwise. The reasoning strategies were categorized as follows: Number Sense-Based (NS): Using one or more number sense components. Rule-Based (RB): Relying only on algorithms or memorized rules. Partially Number Sense-Based (PNS): Combining number sense with memorized rules and/or algorithms. Higher-Level Mathematical Reasoning (HM): Using reasoning beyond the required level, such as generalization or sequences. Wrong Reasoning (WR): Using mathematically incorrect arguments. Unclear or No Explanation (Unclear): Providing insufficient or no justification. Blank (B): Leaving the question unanswered. The test was analyzed based on the categories used by Yang et al. (2009), but two additional categories—Blank (B) and Higher-Level Mathematical Reasoning (HM)—were added during coding. To ensure reliability, three researchers independently coded the responses. In cases of discrepancies, a common agreement was reached. This triangulation process enhances the validity of the study.

As a result of the study, it was observed that the differentiation in teacher candidates' number sense strategies varied according to their level of education. It was found that pre-service elementary mathematics teachers used number sense-based and higher-order mathematical reasoning strategies more frequently when solving problems. This finding is consistent with previous studies indicating that number sense is used more effectively by individuals with advanced mathematics education (Yang, 2009). On the other hand, pre-service primary school teachers were found to prefer rule-based strategies more often, although some of them partially adopted number sense strategies. This finding suggests that number sense education in primary teacher training programs may not be at a sufficient level and that teacher candidates tend to rely more on memorized algorithms (Alsawaie, 2011; Verschaffel et al., 2010). However, it was also observed that five pre-service primary school teachers solved problems using higher-order mathematical reasoning strategies. This indicates that with appropriate guidance and education, teacher candidates can develop their number sense skills. In this regard, it can be argued that teacher training programs should incorporate more instructional strategies that support number sense. Encouraging teacher candidates to think flexibly during problem-solving and facilitating their transition from rule-based strategies to number sense-based approaches is crucial for effective mathematics instruction. This, in turn, can help teacher candidates teach different number sense strategies to their future students. Ultimately, comparing the number sense strategies of teacher candidates at different levels of education has helped us understand the number sense components emphasized in the instructional process for both groups. In this context, examining the differences between pre-service primary school teachers and pre-service elementary mathematics teachers in their number sense strategies can contribute to the development of teacher education programs.

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