Background: The post-colonial and anti-colonial theories in mathematics education, difference and inclusion led Souza and Skovsmose to create the term deficiencialism. Objective: To present the potential of Jurgen Habermas’s theory of the inclusion of the other to contribute to concepts of inclusive mathematics education. Design: Considering that Habermas is a German philosopher who defends ethical communication to solve social problems, we believe that his concepts can help understand the idea of inclusion in teaching to guide the academic community towards a better understanding and positioning about who the Other is. Setting and participants: Jurgen Habermas (2018, 2019) and Ole Skovsmose (2014). Data collection and analysis: Bibliographical and theoretical study. Results: We found possible similarities between Habermasian theories and the critical mathematics education by Ole Skovsmose, each concept with its particularities converging on ethical communication that can favour a more inclusive mathematics education.

Background : Several investigations have shown the difficulties that pre-service mathematics teachers present in articulating the elements of a function, in particular, its different representations. Objective : To analyse pre-service mathematics teachers’ articulation of semiotic representations and partial meanings of the notion of function. Design: This research uses qualitative design. Setting and participants : The respondents’ sample comprised 37 pre-service mathematics teachers from a Chilean university. Data collection and analysis : To collect the information, interviews were applied based on the answers given by the pre-service teachers when solving problem situations that involve functional relationships, of which they had to produce and connect their representations, both with conceptual elements and with the sociocultural context. The information was processed using the content analysis technique. Results: The results show a good state of development of the mathematical dimension of the participants’ didactic-mathematical knowledge. Regarding didactic knowledge, while some managed to articulate the partial meanings of function and the representations produced adequately, others show limitations, by not putting at the service of mathematical knowledge the knowledge with which they can potentially carry out teaching situations, establishing few connections between the elements of the representations produced, with corresponding conceptual and sociocultural elements. Conclusions: There is a need for implementing strategies that allow pre-service teachers to articulate partial meanings and representations of a function with conceptual and sociocultural elements that leads them to envision potential teaching activities of this concept.

Background: Math teacher training in Brazil has been the subject of numerous studies under the most diverse approaches. From a historiographical perspective, we can highlight the performance of the Oral History and Mathematics Education Group and the History of Mathematics Education in the Research Group, both acting more directly with the narratives. Disciplines with the content of Geometric Constructions have historically been part of the training of Mathematics teachers. At issue in this text is the contribution of these disciplines to the formation of future teachers. Objective: This paper adds elements to mapping Mat teacher training and performance in the state of Mato Grosso do Sul and in Brazil, expanding discussions about the state and the possible role of geometric disciplines in undergraduate courses. Design: We present the normative documents of such courses and disciplines and the narratives, in the end, comparing the relevant literature for their analysis based on the researchers' questions. Environment and participants: Courses of Math Teacher Training at the Federal University of Mato Grosso do Sul – Brazil. The time frame of the research ranged from 2004 to 2019, the period in which the seven interviewees taught the subjects mentioned earlier. Data collection and analysis: The narratives of the interviewees, the teaching materials presented by them, and the normative documents are analyzed. Results: The narratives and pertinent literature allowed us a dispersive look, which turned outside the narratives themselves, having in them the triggering movement of reflections. Thus, we could produce questions and possible answers to such inquiries. Conclusions: Among the final notes, the following stand out: the importance of these disciplines, identified as “basic” in the course, to recover Geometry contents that students should have studied in Basic Education; the relevance of failure as a stimulus for the study; and the choice of materials that focus on other aspects of geometry. Such subjects are often intended for the substitute teacher, and there is no prior training to work in this discipline with a specific focus on teacher training.

Background: Research in initial education and professional performance of pedagogues in mathematics is increasing, but they are still few compared to other topics in mathematics education and point to the need for more studies. Objectives: To present a reading of the speeches of beginning mathematics teachers in early childhood education and the early years of elementary school about teaching mathematics, addressing its difficulties and facilities and how they work in classrooms, establishing relationships with the school modules involving mathematics in the degree in pedagogy courses they attended. Design: Qualitative research. Setting and Participants: Six teachers from the municipal schools of São José do Rio Pardo, who agreed to participate in the research through a questionnaire sent to schools in this municipality, the environment being stipulated by them. Data collection and analysis: Data were produced through semi-structured interviews and analysed based on the assumptions of the model of semantic fields. Results: the main result was that the pedagogues had many difficulties in how to teach mathematics, even though their training was more focused on the methodological aspects of the modules that involved mathematics. Conclusions: Although the pedagogues had doubts about how to teach mathematics, we observed that the mathematical contents, practically not addressed in initial education, do not concern them in professional practice, as most of them work in early childhood education; this suggests research on what mathematics are necessary for the initial and even continuing education of pedagogues who teach mathematics.

Background: Research in educational mathematics has shown that elementary school students poorly understand the concept of ratio due to the difficulties that emerge from its interpretation as a fraction. Objective: Therefore, based on the Pirie-Kieren theoretical model, we intend to analyse the comprehension process that appears when students solve tasks on ratio. Design: The approach is qualitative, and the research design was a case study. We used the field observation technique. Context and participants: The study was done in a primary school in the state of Guerrero, Mexico. The cases involved four students (11-12 years old) enrolled in the 6th grade. Data collection and analysis: The data was collected through a questionnaire (task) and an interview. For data analysis, the eight levels of understanding of the theoretical model were used. Results: The results indicate that the students do not manage to formalise their comprehension of the concept of ratio because of difficulties in applying mathematical strategies correctly when solving the proposed tasks. Conclusion: The results indicate that for students to reach higher levels of comprehension, it is necessary to carry out the dynamic process of repeating between levels as it makes one reflect on what is required to advance comprehension.

Background: Natural sciences is considered a markedly masculine field of study. Despite the criticisms and changes observed in recent years, the effects on society of male science are still observed in school performance. Objectives: This study proposes to compare the performance inequality based on students’ gender in the contents of natural sciences in Brazil at the end of two learning cycles, lower secondary education (LSE) and upper secondary education or high school (USE). Design: The research was designed to identify the size of the effect on the performance of male and female groups in the International Student Assessment Program (PISA) and in the National High School Exam (ENEM) between 2009 and 2018. Setting and Participants: Public school students who, in the year in which the exam was taken, were in their final year of LSE or USE. Data collection and analysis: PISA performance data were collected from the PISA Data Explorer. From ENEM, they came directly from the database made available by INEP. We applied statistical significance tests to identify differences in performance in the natural sciences test of the two exams. Results: The PISA results indicate that there is no difference in the students’ performance based on gender. In contrast, the ENEM results indicate a difference of 0.3 standard deviations in favour of boys. Conclusions: The results point to an expansion of the gender-based differences in the contents of natural sciences during the EM.

Background: Several countries and organisations highlight creativity when advocating an education connected to the current moment of scientific and technological progress we live, especially in the mathematics field. Objectives: We aim to answer the following questions: (a) Is senior high school students’ creativity, motivation, and mathematics performance triad positively influenced by extracurricular mathematics classes based on creativity techniques? And (b) What are the different students’ perceptions of mathematics based on the type of classes they received throughout the course (conventional classes and classes based on creativity techniques)? Design: To this end, we structured an experimental study to compare the results obtained from conventional classes to a control group and from classes based on creativity techniques to an experimental group. Settings and participants: The sample consisted of 41 senior high school students of a public school in the Federal District, Brazil, randomly selected after wide dissemination. Data collection and analysis: Initially, students underwent pre-tests (creativity in mathematics, motivation in mathematics, and performance in mathematics). Then, they participated in mathematics classes (conventional to the control group and based on creativity techniques to the experimental group). At the end of each class, they completed one step of the logbook. Finally, they were submitted to post-tests for direct comparison with the tests initially performed and participated in a conversation roundtable. Thus, the analysis included quantitative aspects of the results of the tests; and qualitative aspects of the study of the material written in the diaries and oral speeches during the conversation roundtable. Results: Although both groups increased their scores for the three variables investigated, statistically significant results were perceived only with the experimental group, which had all variables increased. We also found that the students recognised the classes based on creativity techniques as being good. Conclusions: This suggests that the class model investigated in this research may favour students’ creative thinking ability and motivation, consequently increasing their performance in mathematics.