Dialogical interaction or teaching in teaching-learning processes can be understood as the action of sharing something to assign collective meaning to it in order to understand and establish communicative relationships between subjects and give communal meaning to the message conveyed. However, most of the interactions are ‘question-answer-follow-up’ three-part sequences   where relatively shared interaction patterns prevail. They are characterised by closed questions, little student participation and follow-ups with low metacognitive potential.

Research is needed on interactive processes to improve them and overcome the limitations of the lecture method, as using it means that teachers do not know what their students are learning or what their actual level is until their performance is assessed. Dialogue and interaction in teaching-learning processes promote student participation and the development of cognitive, motivation and linguistic skills, while also improving classroom atmosphere.

Mathematics is an important discipline, but it is too often seen as being especially difficult at Compulsory and Post-compulsory Secondary Education levels. The subject can be unattractive if classroom work involves repeatedly solving problems and completing activities, avoiding real-life applications and teaching only how to apply procedures mechanically, for example. An inadequate introduction to Mathematics causes students to become frustrated, dissatisfied, demotivated and discouraged. Factors such as attitudes towards the subject, academic motivation, beliefs, stereotypes and achievement expectations seem to have a direct relationship to achievement in Mathematics. It would therefore be extremely useful to enquire about what interactive teaching-learning processes are like in Mathematics, how they could be used and what their effects would be on students, with a view to seeking improvement.

The successive regulations regulating the teaching of Mathematics have called for the use of both active and interactive methods, including reviewing procedures to find solutions, clarifying ideas and procedures, valuing the contributions made by others, establishing hypotheses and comparing them, giving presentations and making arguments, among others.

Research has shown that interaction has an academic impact. Through the exchange of meanings, contributions, questions, arguments and opinions about a topic, students directly and closely engage with the subject in question, are sure to ask questions about aspects they do not understand and raise points of interest to both their classmates and the teacher. This participation allows knowledge to be better internalised and leads to the generation of deeper, more meaningful, and longer-lasting learning.

Interaction also has effects on an emotional level. In interactive classes both teachers and students can communicate, propose, and negotiate meanings, ask questions about points they do not understand, etc., thus achieving greater satisfaction and becoming more emotionally involved with the subject. Students who have had interactive experiences have reported that they pay more attention in class, become more involved with the subject and the teacher, and have enjoyed the classes more.

Interaction also has effects in terms of communicative performance, as it helps develop the linguistic skills necessary for communication and argumentation. Asking open-ended questions provides scope for students to answer and for further questions to be asked, calling for answers to be restated in different ways, building and expanding knowledge, and providing integrative summaries, among other things. 

However, although some earlier studies have shown that teacher-pupil interaction in Secondary Education is highly important in the teaching-learning processes involved in Mathematics, more research is need as this is still a budding field of research. What effects do the communicative exchanges that take place in the Mathematics classroom produce in students academically, emotionally and/or communicatively? Do these different effects occur to the same extent? Are there any other effects involved? This paper takes a close look at examples of communicative exchanges in class to answer these research questions.

This study is an exploratory investigation aimed to help guide further, larger studies. Its objective is to examine the different effects of interactive teaching-learning processes on pupils' learning of Mathematics and class dynamics looking at the academic, emotional and/or communicative impact involved. Following careful analysis of different transcripts of interactive processes, some suggestions will be made for improved interactive teaching. The observational research method was chosen, following in the wake of some previous studies in the field of Mathematics teaching methods to find out more about the actual classroom practice and analyse it. A state Secondary School located in the main town in a rural area was contacted to request their collaboration in carrying out this study. The location was chosen due to its proximity to the research team's homes, given the need to travel to the school over a month to participate as ethnographers in different classes taught by experienced Mathematics teachers. The necessary steps were taken to be able to visit both large and small class groups of all educational levels of Compulsory Secondary Education and Baccalaureate. Five teachers and 11 different groups of pupils took part in the study, resulting in 50 interactive processes being compiled. All the lessons were audio-recorded and the interactive situations were listened to in full and transcribed for further examination. At content analysis was then carried out with Microsoft Excel being used to organise and categorise the data. Calculations were performed to answer the research questions: What effects did the communicative exchanges that took place in the Mathematics classroom produce in pupils academically, emotionally and/or communicatively? Did these effects occur to the same extent? Were there any other effects observed? The data analysis identified the expected three types of effects plus a fourth type that had not been initially considered, axiological effects. There were also notable differences in the length of time involved in the various effect types, as will be shown below. Ethical guidelines were followed throughout the study, including Anonymous collaboration, impartiality and data protection. The participants in the study signed an informed consent which explained the nature of the study and stated that it had been approved by the Ethics Committee of the University of Cantabria.

It was found that the communicative exchanges that occurred in the Mathematics lessons had academic, emotional and/or communicative effects on pupils. However, it was also observed that they did not take place to the same extent, and that some impact was also seen at the axiological level. It should be noted that there were very frequent interactive processes that had academic effects, which had a direct impact on improving learning. They occurred in 39 of the 50 processes examined. Most of the exchanges of messages took place during the completion of exercises and while discussing results. The most frequent affective impact of interactive processes was related to participation, motivation and involvement, which occurred in 47 of the 50 processes examined. Both positive and negative affective interactions were observed. While the majority were positive (such as laughing in the classroom, showing interest in having their questions answered, celebrating that they had understood certain mathematical points and showing a desire to pass their exams), the negative ones should not be ignored. These interactive processes highlighted that the subject is difficult for pupils and that it is necessary to make it attractive, practical, non-repetitive and non-mechanical. There were frequent linguistic effects of interactive processes, which were related to corrections in oral communication (in 24 of the 50 processes examined). Both positive and negative interactive situations were identified related to the affective sphere. The cases in which pupils used the specific vocabulary appropriately in the classroom predominated (9 situations compared to 4). However, some situations could have been improved. Although the axiological effects of interactive processes (relating to values education) had not been initially included in the analysis, they were also frequent, as they occurred in 23 of the 50 processes examined. They were organised around three themes: advice, warnings and participation in class.

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