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Mathematics is one of the most important subjects which is connected to all sciences. It belongs to the subjects that are taught from the beginning till the end of compulsory education, in elementary, primary and secondary school years – in the majority of education systems worldwide. Therefore, studies on mathematics education are widespread (Adler, 2017; Yesildere & Turnuklu, 2007; Arslan & Yildiz, 2010; Gibney, 2014; Herlina, 2015; Saragih & Napitupulu, 2015; Hudson, Henderson, & Hudson, 2015; Ramaley, 2007). The researchers emphasize the importance to develop mathematical thinking in education since mathematics is an important branch of science that involves developing thinking (Onal, Inan, & Bozkurt, 2017). According to studies, thinking skills can be developed in two different ways (see Chapter 2.3.): separately (Lipman, 1985) or embedded into school subjects (Swartz, 2001; McGuinness et al., 2003; Rajendran, 2010). Mathematics is one of the school subjects that can develop and enhance thinking skills (Rajendran, 2010; Aizikovitsh & Amit, 2010). In addition, mathematical thinking skill is considered as a cognitive skill (Onal, Inan, & Bozkurt, 2017) since both skills are connected to each other. Onal et al. (2017) explained in their study on mathematical thinking skills that the weaker the cognitive skill abilities, the weaker the mathematical skills are. They reached this result when they noticed that the failure of some participants in the mathematical thinking skills in their study was related to the weakness of cognitive skills of the participants.

Pupils need to have the minimum mathematical skills to be able to handle any mathematical tasks. The general rule says, the earlier the better, this can be applied to the development of numeracy for pupils. The earlier the child learns numeracy, the advanced the child becomes in mathematics as studies emphasize the importance of the development of early numeracy and the success that can be achieved afterwards with mathematics knowledge (Pásztor, Molnár, & Csapó, 2015). Early numeracy consists of several basic skills and concepts (Jordan, Kaplan, Locuniak, & Ramineni, 2007). Early mathematical skills have important skills that can be considered as the number word

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sequence skills (Rausch & Pásztor, 2017). Enumeration skills can be developed by the knowledge of the correct order of number words either forward or backward, it is also related to other things like solving basic additions and subtractions (Aunio & Rasanen, 2015). Many international assessment studies use mathematical content as a main component in the process of their data collection such as the assessment programmes PISA (OECD, 2013) or TIMSS (Mullis & Martin, 2013), it is also used in the national assessment systems around the globe (Pásztor, Molnár, & Csapó, 2015).

The connected skills and abilities to mathematics has been studied carefully for about two decades ago focusing on the assessment or the development (Csapó & Csíkos, 2011). Csapó and Csíkos (2011) added that these skills and abilities are necessary to access to mathematics, for example, a pupil should have a proper level of reading comprehension to be able to go into mathematics, at the same time, the skills of reading comprehension of texts is improved by learning mathematics since the logic between both of them (mathematics and language) influences and improves each other. Some of these studies focused on the relations between mathematical skills and the ability of intelligence and the findings concluded that mathematical achievements are significantly connected to several components of fluid intelligence like general sequential reasoning, quantitative reasoning and the Piagetian reasoning (Carroll, 1993).

It is commonly assumed that the development of reasoning skills is embedded in ordinary school material (de Konig, 2000), which focuses mainly on reading, writing, and mathematics (Molnár, 2011). However, according to Molnár and Csapó (2019a), no appreciable development could be noticed in pupils’ reasoning skills in reading and science between grades 2 and 6, and “there was a steady increase detectable in mathematics, especially in the first four years of schooling…. Overall, these results highlighted the importance, sensitivity and potential of the development of thinking skills in the early years of schooling”. Therefore, enhancing thinking skills should become a real goal in education (Vainikainen et al., 2015).

According to Csapó and Csíkos (2011) linguistic development is highly correlated with mathematical achievement since people tend to count in a particular language. Counting skills are influenced by the designation of numbers in various languages. They added that mathematical word problems can be understood by oral and written comprehension skills, they also stated that reasoning skills and mathematical thinking are highly relevant. Thinking skills and mathematics are closely connected to each other and

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the skills can be assessed and developed using mathematical contents by many diagnostic assessment programs which have used thinking abilities in that context including inductive (Csapó, 2002). Molnár and Csapó (2019c) supported the previous point by saying that generic objects and domain specific objects are there in mathematics. They added that the generic covers operational reasoning like seriation, class inclusion, classification, combinatorial reasoning, probabilistic reasoning, proportional reasoning as well as some higher-order thinking skills like inductive reasoning and problem solving, and all of them can be assessed by mathematics. They added in literature, that there are very few studies that focus on the cognitive processes like reasoning skills and its connection with understanding mathematics, and the main focus of these studies was on the most hidden aspects of learning.

In their study on the psychological dimension of learning (cognitive development and reasoning), Molnár and Csapó (2019c) reported thinking and reasoning can be assessed separately from the other dimensions (application and disciplinary knowledge) (see Csapó & Szendrei, 2011; Csapó & Csépe, 2012; Csapó & Szabó, 2012) with a good validity. They also noted that the psychological dimension of learning can be measured in early years in the context of mathematics as one of the most important domains of learning. They added that the cognitive development of pupils can be effectively enhanced if it is taught intensively (see also de Koning et al., 2002; Klauer & Phye, 2008; Perret, 2015) and that enhancement can be seen mainly in the first years of schooling, in the domain of mathematics. In other words, the findings indicate that the development of the psychological dimension of learning can be achieved in school knowledge in mathematics.

Pásztor (2014) presented in his study on fostering inductive reasoning through mathematical content using technology environment that integrating mathematical content and reasoning strategies through learning tasks is possible even in computer- based settings. The findings of the study showed that even with the current form of the training program in mathematical content, the development of the pupils’ IR thinking skills are possible and achievable at early age and for all types of pupils regarding their achievement, whether they are weak, average or high achievers.

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