Semantic investigation of mathematical words about numbers and operations in the secondary school mathematics curriculum

"How much are we aware of what we are saying?" or "Do we know what each word we use means?" Such questions make us question the relationship between language and thought. It can be said that the approaches that deal with the relationship between language and thought range from mind-focused approaches that prioritize thought – Descartes, Chomsky and to a certain extent Piaget – to linguistic deterministic approaches – Sapir and Whorf – who hold the view that language determines thought. Vygotsky, one of the researchers in this language-thought spectrum, claims that language and thought have separate origins, but that thought continues to develop in the individual through the mediation of language. Vygotsky attached great importance to words, which are the basic units of language. According to Vygotsky, the child builds concepts on the ready-made words he receives from adults. The child uses generalizations and extractions for concept formation. Vygotsky takes the unity of thought-sounds – that is, words – that emerged as a result of this development as inseparable wholes. However, it can be observed that words sometimes lose their connection with thoughts (concepts). This observation suggests that words and concepts are different and distinct things. This distinction seems necessary, at least for theoretical consideration. In this context, sign, signifier and signified, which are the concepts of Saussure's Structural Linguistics, can be used to separate form (acoustic image) and meaning (concept). In this research, mathematical terms are the sign, the sound image of these terms is the signifier, and the mathematical concepts are the signified. By the way, it should be remembered that Saussure claimed that the sign is arbitrary. Therefore, it seems impossible or unnecessary to question why mathematical concepts are given a particular name. However, according to researchers such as Guiraud, the sign is not arbitrary but only conventional. When considered this point of view, it can be traced to a certain point why a name is given to a concept. In this tracing, etymology, which is one of the diachronic approaches, and morphology, which can be considered as its synchronic counterpart, can be listed as suitable methods. Finally, it may be beneficial to touch on the distinction between mathematical terms and mathematical words, which has not been mentioned much in the literature. To give an example from this research, rational number is a mathematical term, but rational is a mathematical word. While terms have static meanings specific to a field, it can be said that words acquire meanings according to the contexts in which they are used. In this research, the reason why mathematical words are considered is the potential for change in their meanings. A partial causal relationship can be established between the word and the concept by looking at the meanings of mathematical words which have other than the concept meaning. Meaning is the focus of this whole process and the relationship between meaning and form can be called semantics. According to some researchers and thinkers -such as Descartes, Vinner, Kuryel-, words are used unconsciously with the hastiness of everyday language. When conceptual concerns and researcher experiences meet, the question "Is it possible to make a similar inference for mathematical words?" comes to mind. In this respect, one aim of this research is to establish a relationship between mathematical words and mathematical concepts within the framework of the literature, while another aim is to investigate how these relationships can be established by the participants (students, pre-service teachers and teachers). However, when discussion comes to the relationship between mathematical words and concepts, it can be said that the mathematical concepts formation stages are also important. Therefore, Vygotsky's Concept Formation Framework was used. There are two main reasons for this preference. First, it is thought that this theoretical framework will bring innovation to the field since it has not been used much before. Second, this conceptual framework explains concept development in the context of social interaction. The main stages in Vygotsky's Concept Development Framework can be listed as heaps, complex thinking, pseudo-concept and concept. The heaps is the stage of random trials. Complex thinking is the stage when the main concrete relationships are established and these relationships are often wrong. Although the pseudo-concept is actually a stage of complex thinking, it has been discussed separately due to its importance. This stage serves as a bridge to the concept stage. In the pseudo-concept stage, concrete, correct and functional uses are predominant. The concept stage is the stage where abstract relationships can be established. At this stage, it is possible to get correct answers including abstract relations to the "What is this?". A number of conceptual concerns have been addressed up to this point, in coming lines some practical concerns, methodology, findings and results of this research will be touched on. This study is a qualitative study and the principles of the case study design were adopted. The research is a descriptive research as it aims to determine the current situation. The sample of the research consists of 15 8th grade students, 20 secondary school mathematics teacher candidates and 10 teachers. This sample was selected among the purposive sampling types with accessible/convenient sampling. Two types of data were collected from the participants, written and verbal. Two questionnaire consisting of open-ended questions were developed to collect written data. Verbal data were collected through semi-structured interviews from selected participants by analysis of written data. In data analysis process, the content analysis method was adopted for the written data. The descriptive analysis method was used for the verbal data. Findings for the first research problem indicate that the majority of the participants are at the pseudo-concept level. In the second sub-problem, word-concept distinction is handled. Although the participants do not seem very successful in distinguishing between words and concepts, it is possible to say that they do not have a big difficulty. In addition, it seems to be a slightly more difficult task for students to distinguish between words and concepts. The rate of participants' word-concept distinction is negatively affected by the fact that the words are of foreign origin and are not used in a sense other than the mathematical context. In the third sub-problem, the methods of establishing a relationship between the word and the concept of the participants were investigated. Participants prefer methods based on their experiences rather than using linguistic elements, units and relations. In the fourth sub-problem, it was found that the participants had difficulty in establishing a relationship between mathematical words and concepts. In the fifth sub-problem, the reasons for the invalid relationships established by the participants were discussed. It was concluded that the participants get the wrong meaning of mathematical words considerably. Also a considerable amount of answers are categorized as word and concept are incompatible/no relation made. In response to the sixth sub-problem, it is determined that there is no strong correlation between the hierarchical structure of concept development levels and the ratio of valid word-concept relationships established. This may be related to the possibility that the participants have not thought much about very mathematical words before. It is recommended to think about the relationship of mathematical words with concepts and to make use of these relationships in mathematics education processes. In the literature, no Turkish books or etymological dictionaries dealing with the relationship between especially mathematical words and concepts could be found. It is thought that it is important to bring books, dictionaries, articles and similar sources focused on mathematical words to the literature. Keywords: Mathematical Words, Numbers and Operations, Semantic.