Acta Scientiae

Background : Student numeracy reflects their interaction with the environment, especially with their teacher. Therefore, the formation of teacher numeracy must start from their education when in college. Objectives : This study explores the numeracy, which parts become limited or lacking, and what hinders and supports those skills. Design : This study employs an exploratory descriptive method and involves case studies to achieve the objectives. Setting and Participants : The research participant is 84 students of the department of elementary school education at one of the public universities in Indonesia, consisting of 3 classes: undergraduate, postgraduate, and postgraduate cooperation class. Data collection and analysis : Numeracy tests and semi-structured cognitive interviews are used to collect data. The test results were analyzed using descriptive statistics to see the numeracy profile, and essential parts were clarified in the discussion. Results : Our findings show that for all classes, statistics and probability became the content with the lowest achievement on this test. We also highlight that the undergraduate class become the best class based on the test results, followed by the regular postgraduate class and the postgraduate cooperation class. In other words, this study's teaching experience and level of education are not enough to help students solve numeracy problems. Conclusions : Data and uncertainly (quantitative) literacy must emphasize improvements and potential studies for subsequent researchers. The implications of our research are also focused on teacher education; numeracy provision should not only be noted on in-service teachers but also target their education in college.

Suci Dewi Asmara

Yoppy Wahyu Purnomo

Context of Data and Uncertainty: One of the Challenges for Numeracy Provision in Elementary School Teacher Education

数据与不确定性的情境：小学教师教育中数育素养供给的挑战之一

Background: After mathematics curricular reform in 2012 in Costa Rica, which accentuate the functional vision of mathematics, it is worth inquiring if teachers designed tasks respond to established curricular guidelines and what mathematical and didactic characteristics that these tasks exhibit. Objectives: The aim of the study was to describe and analyze the mathematical and didactic elements, linked to the curricular proposal for Secondary Education in Costa Rica, used by in-service mathematics teachers for designing or selecting school tasks oriented to the development of mathematics skills on the subject of functions. Design: It corresponds to a descriptive-qualitative research, based on an intrinsic study of cases. Setting and Participants: Participants were five mathematics teachers from different educational institutions in Costa Rica during the year 2022 were studied, all teachers participated in a training program to promote teacher reflection competence regarding the design and analysis of school mathematics. Data collection and analysis: Data was collected from school mathematical tasks designed by the participants. The analysis of the information was carried out by defining categories and units of analysis based on the curricular provisions established for the teaching and learning of mathematics in Costa Rica, and the components of didactic analysis, as a methodology for the design of school mathematics tasks. Results: The analyzed tasks exhibit strengths in the curricular component, as well as in the didactic component. However, they lack elements that allow understanding how and when to put the designed tasks into practice, among other aspects. Conclusions: The training of in-service teachers takes a significant enhancement to strengthen knowledge and capacities oriented to the design, selection, and analysis of school mathematics tasks, associated with the functional vision of mathematics that articulates the curricular plan regarding student learning in Secondary Education in Costa Rica.

José Romilio Loría Fernández

Miguel Evelio Picado Alfaro

Tareas matemáticas escolares diseñadas por docentes de educación secundaria: un análisis desde la visión funcional de las matemáticas

中学教师设计的数学作业：从数学功能视角的分析

Background: The pastel de arroz [rice pie] is part of the traditional foods of the Colombian coast. Its preparation and sale encompass various unconventional mathematical processes. At this point, ethnomathematics allows the study of such processes without separating them from the social and cultural environment where they are employed. Objective: To study the mathematical processes involved in preparing and selling rice pies from an ethnomathematical perspective. Design: A qualitative methodology was applied for this purpose through an ethnographic approach. Setting and participants: Two cooks who are experts in making rice pies and are recognised for their work participated in the study. Data collection and analysis: Semi-structured interviews and participant observation were used as data collection methods, and electronic devices were also used to collect audiovisual material. The analysis of the information was categorical. Results: Among the main results, measurement processes, the use of non-conventional measurement units, and the use of mathematical processes, such as groping and the simple rule of three, for determining the quantities of ingredients and the price of the pies are identified. Conclusions: The stages of the preparation of the rice pies and the mathematical processes that are implicitly developed in them are exposed, and the importance of the connections of the results with topics related to school mathematics education and its potential contribution to this field is raised.

Armando Alex Aroca Araújo

Andrea Paola Cervantes Wilches

María Ofelia Silva Carreño

Mathematics in the Preparation and Sale of Colombian Rice Pies and Its Potential Contribution to Mathematics Education

哥伦比亚米饼的制作与销售中的数学及其对数学教育的潜在贡献

Background: Given the oversight of specific topics in the history of mathematics books, this research was motivated by the extensive coverage of the Fibonacci sequence. In addition, the existence of the Padovan sequence, which is considered a Fibonacci cousin, stands out. Objectives: Investigating the Padovan sequence, building its definition through a combinatorial model using manipulative materials based on the theory of didactical situations in the initial mathematics teacher education course context. Design: The research methodological design follows didactic engineering, and a didactic teaching situation is created to investigate the Padovan sequence. Thus, manipulative material was developed to facilitate the teaching process and the construction of the sequence definition. Settings and participants: The interventions were done in the mathematics degree course of a higher education institution in Fortaleza. Five students enrolled in the component of History of Mathematics participated in the study. Data collection and analysis: Data were collected during classes, recorded through photos and audio recordings, based on didactic engineering and the theory of didactical situations. Results: The most relevant result of this study is constructing the definition of the Padovan sequence through the manipulative material. Conclusions: We concluded that the research allowed an investigation of the Padovan sequence, enabling the visualisation of its terms and their integration with other mathematical contents, contributing to teaching these numbers.

Renata Passos Machado Vieira

Francisco Regis Vieira Alves

Paula Maria Machado Cruz Catarino

The Construction of Definitions Through Padovan’s Combinatorial Model: An Investigation With Didactic Engineering in an Initial Education Course for Mathematics Teachers

通过Padovan组合模型构建定义：对数学教师初始教育课程中的教学工程的探究

Background : Currently, statistical graphics are an interdisciplinary resource for the development of various activities, such as mathematics, natural sciences and history, geography, and social sciences, being essential for the teaching process. Objective : To analyse activities related to statistical graphs in natural sciences and history, geography, and social sciences textbooks in Chilean primary education. Design : Qualitative methodology, descriptive level, using the content analysis method. Setting and participants : The sample consisted of two textbook collections for both subjects (n=24), covering elementary school courses from grades 1 to 6. Data collection and analysis : Through content analysis, types of graphs, reading levels, levels of semiotic complexity, and types of tasks and activities with statistical graphs. Results : The results show a total of 105 activities. In natural sciences, reading level 4, semiotic level 3, and the explaining task predominated. In the case of history, geography and social sciences, level 1, semiotic level 2, and the example task predominate. Conclusions : More activities must be included in the HGSSci in the first years of schooling, as they only appear in the 5th and 6th grades, especially if analysis work is encouraged. NSci textbooks include some graphs to be addressed in mathematics in later subjects, so we suggested working the graphs systematically within the subjects.

Matías Bustamante-Valdés

José Pardo-Cañete

Danilo Díaz-Levicoy

Statistical Graphs in Natural and Social Sciences Textbooks in Chile

智利自然与社会科学教科书中的统计图表

Background: The beliefs from the area of mathematics teacher training allow us to understand the function that future education professionals assign to mathematical activities, including problem solving, and how in this type of activities it is possible to incorporate the cultural knowledge of the students, when the teaching process takes place in culturally diverse classrooms. Objective: To analyze the beliefs of mathematics undergraduate students from a university in the department of Nariño about problem solving and cultural knowledge in culturally diverse classrooms. Design: A descriptive methodological complementarity research design was used, since this gives the possibility of understanding and contrasting the quantitative and qualitative information. Scenario and participants: The sample consisted of 60 undergraduate students in mathematics. Data collection and analysis: The information was collected through a Likert-type questionnaire with 35 statements and 3 open questions, which were analyzed in the SPPS 25.0 and Atlas TI 9.0 software. Results: Favorable beliefs are evidenced in the participants to work on solving problems in culturally diverse classrooms and during the development of this activity to integrate the cultural knowledge of students. Conclusions: The need to improve mathematics teacher training curricula to develop the teaching process in culturally diverse classrooms is exposed.

Renán Adolfo Concha-Zelada

Miguel Friz Carrillo

Hilbert Blanco-Álvarez

Preservice Mathematics Teachers' Beliefs about Problem-Solving in Culturally Diverse Classrooms

职前数学教师对文化多样性课堂中问题解决的信念

Background: A concept that exists in students' minds and is used to describe and explain a phenomenon is called a mental model. Objective: This study aims to describe the transition-apprehending mental model of students in understanding the concept of integers. Design: This study used a qualitative approach and the type of research conducted was descriptive. Setting and participants: The subjects of this study were 35 students in grade VII Junior High School. Subjects were given a test to determine their understanding of the concept of integers. Data collection and analysis: data collection in this study, using test questions and interviews. Data analysis used five steps, namely 1) data transcoding; 2) reviewing data; 3) data reduction; 4) presenting data; 5) analyze the process of forming mental models; and 6) verify the findings. Results: showed that grade VII students were at the transition-Apprehending level, as evidenced by students being able to compare negative integers and positive integers with the same magnitude symbol. Conclusion: based on the results of research that has been found, that students already understand positive integers and negative integers using a number line .

Sukiyanto Sukiyanto

Toto Nusantara

Sudirman Sudirman

I Made Sulandra

Transitional-Apprehending Mental Model for Junior High School Students in Understanding the Concept of Integers

初中生理解整数概念的过渡性认知模型

Background: There are, in the school context, especially in mathematics education, different historical and cultural meanings that are being produced and impregnated in the term Problem, as well as different understandings regarding the roles of Problems in teaching practices, which justifies studies focused on to the analysis of the implications of such conceptual meanings in the training of teachers who teach mathematics. Objectives: The aim is to answer the question: What are the meanings of Problem present in research and publications that dialogue with training for teaching mathematics? What would be, specifically, the meaning of Problem from a cultural-historical perspective? Design: The research was carried out with students of the degree course in mathematics of a Brazilian public institution, in which they participated in a training movement that had Problems as mediators. In the context of that research, theoretical and bibliographical studies were developed to understand ideas impregnated in didactic-pedagogical proposals that exalt the importance of Problems in teaching practices. We recognise these ideas as meanings based on the analysis that considers the theoretical and methodological assumptions of the cultural-historical theory. Setting and participants: Publications that circulated in the context of the training course for mathematics teachers were analysed, which contextualised the research that gave rise to this clipping about the understandings of the authors of those texts regarding their understanding of the possible relationships between the Problem and the teaching of mathematics. Data collection and analysis: The texts were selected from the bibliographies present in the teaching plans of the subjects of that degree course or that were used as a textual reference during the formative experiment carried out to produce research data and were analysed according to the assumptions of the cultural-historical theory to the concept of meaning. Results: The results point to the constitution of meanings according to which the Problems are usually adopted, in teaching practices, as lessons already presented or as opportunities to apply concepts in supposedly everyday situations. There is also a process of meaning from which the Problems are understood, from a cultural-historical perspective, as triggers of mathematics learning. Conclusions: The main conclusion points to the understanding that the Problems play, historically and culturally, some roles in mathematics teaching practices, among which, three stand out: they are opportunities to practice lessons already taught; they are opportunities to apply techniques, algorithms, or definitions in simulated situations (problem solving); or they are learning-triggering problems.

Wellington Pereira das Virgens

Vanessa Dias Moretti

Meaning of Problem in School Mathematics: From Exercise and Application to the Learning-Triggering Problem

学校数学中问题的意义：从练习和应用到学习触发问题

Background : Given its nature guided by inquiry, collaboration, communication and reflection, Exploratory Mathematics Teaching (EMT) practices are considered challenging to the teacher, particularly due to the characteristics and role given to the action of anticipating . Objectives : Investigating learnings arising from teachers' reflections based on the anticipation of EMT practices . Design : It is a qualitative study, of interpretive nature, about collective reflections of Mathematics teachers who developed EMT practices raised in a focus group. Setting and Participants : Five teacher participated in the study after accepting a voluntary invitation, sent by email, for a focus group conducted remotely through the Google Meet platform. When conducting EMT practices, two of them were already working on Basic Education and three others performed them in actions of supervised internship, research projects, or extension ones during their undergraduate course, which justifies referring to them as future teachers in this study. Data collection and analysis : The data were produced from a focus group, guided by a script that focused on teachers’ reflections about EMT practices, whose video recording was transcribed; and, in this study, the aspects related to the action of anticipating were focused. The analyses problematize, in an interpretative way, actions, reflections, dilemmas, possibilities of referrals and considerations about the EMT, in reference to a framework that guides practices of this nature. Results : The results point out some demanding actions for the teacher anticipating and learnings raised by reflection on these aspects highlight changes in understanding planning and the mathematical task, as well as about the roles played by the students and teachers. Conclusions : While the study highlights the potential investigations located in practices to emphasize specific ways of appropriating demanding teaching perspectives – such as Exploratory Teaching – it highlights the effectiveness of said practices and reflects on them as potentially enrichening for professional learning and for expanding theoretical frameworks for guidance.

Eduardo Pereira de Oliveira Rossa

Everton José Goldoni Estevam

Learnings and Reflections by (Future) Teachers on Anticipation in Exploratory Mathematics Teaching

(未来)教师在探索性数学教学中对预期的学习和反思

Context: The implementation of curricular extension in Brazilian higher education, driven by the National Education Plan 2014-2024, led to curricular re-adjustment at ULBRA, emphasizing the integration of theory and practice in teacher training. Objectives: Promote extension activities that envision the formation of the researcher and the production of knowledge as an academic dimension necessary for future teachers. Design: Meetings between the coordinators of the teaching courses at the ULBRA/RS units, the coordinators of the Postgraduate Stricto Sensu programs with the assistance of the Academic Vice-Chancellor's Office and the Community Affairs Directorate. Environment and participants: Development of activities in a face-to-face class composed of 26 students who developed 05 projects based on the needs of the investigated communities. Data Collection and Analysis: The data was collected throughout the activities carried out in online classrooms and compiled in the final report of the extension project, registered in the virtual environment of the University, enabling the analysis of the projects carried out by the teams. Results: Two Interdisciplinary Extension Programs (IEPs) for undergraduate degrees have been defined, consisting of two courses in each IEP, totalling four courses from the curriculum. The described projects were carried out in the Educational Practices course, which is part of the 1st IEP - Educational Practices in Diversity. These guide the extension experiences of the students in the teaching degrees at the university, thus leading to the adjustment of the curriculum matrices of the courses according to the guidelines of the Institutional Development Plan (PDI). Conclusions: The strategies used by the project teams proved to be effective for involvement in all stages of the project, as well as commitment to extension actions and activities for responsible and ethical citizenship formation, providing the opportunity to combine theoretical education with practical activities in the training of the teaching students.

Marlene Fernandes

Interdisciplinary Extension Program in Teaching: Challenges, Possibilities, and Unexpected Situations

跨学科教学拓展计划：挑战、可能性与意外情况

Publication Information	Publisher: Lutheran University of Brazil，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2018，Proportion of original research papers: 0.00%，Self Citation Rate:N.A.， Gold OA Rate: 0.00%

Acta Scientiae

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