In this text we discuss how power, mathematics and cryptography establish dialogues that are considered critical for the present, but which have influence from the past and concerns for the future. ...We contextualize our reflections from a historical perspective, especially in the Brazilian context, and advance the debates about how cryptography, based on mathematical theories, influenced and dynamized wars. Going a little beyond this historical context, we present some reflections concerning the role of cryptography as a means of data security, one of the main discussions in contemporary society. In this reflection, we point out the position of power that the holders of this knowledge occupy, and that, in the scope of basic school, lacks important discussions for both teachers and students.
COMMUNITY SERVICE INNOVATION OF THE SCHOOL MATHEMATICS HEALTH CENTER (PUSKESMAS) IN LEARNING MATHEMATICS BASED ON THE TOWN SQUARE. The purpose of this study was to develop an innovation in the ...school’s mathematics health center in mathematics learning through city square-based mathematics learning. Descriptive method is used with subjects in early childhood and elementary school students who are in the location of the school mathematics health center. The instrument used by the researcher itself, data collection techniques using structured interviews, observation and documentation. The data analysis technique used triangulation, data reduction, data presentation and conclusion drawing. The results showed that the media presented at the Puskesmas were all new and they had not yet gotten them in their respective schools. The attitude of students who become happy, like, cheerful in learning mathematics and easy to understand mathematical concepts, and bring out the creativity of early age and elementary school students in learning mathematics. Student concentration also increases because the learning model used uses an individual approach, so that they can focus more on seeing the student learning process. Parents who accompany their children generally feel happy because their children enjoy learning mathematics. Puskesmas activities have an impact on early age and elementary school students to be happy learning mathematics, like learning with mathematics media, cheerful in following math tutoring and enjoy learning mathematics. This program is also highly supported by parents because it is very helpful in the learning process of their children and eases the family’s economic burden in education.
•Problem solving and reasoning are facilitated by a particular lesson structure.•This report offers insights into the use of prompts that differentiate tasks and posing variations on the initial task ...to consolidate the learning.•Activating thinking through an initial challenge is a feasible way of initiating a sequence of learning.•Teachers who taught lessons structured in this way reported that the lesson elements were feasible and effective.•The ways that some teachers used students’ responses to the initial challenge to plan subsequent experiences seemed critical in enhancing transfer to other situations.
While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks intended to prompt problem solving and reasoning to students, not only to activate their thinking but also to develop an orientation to persistence. Data were sought from teachers and students in middle primary classes (students aged 8–10 years) via online surveys. One lesson focusing on the concept of equivalence is described in detail although mention is made of other lessons. The research questions focused on the teachers’ reactions to the lesson structure and the specifics of the implementation in a particular school. The results indicate that student learning is facilitated by the particular lesson structure. This article reports on the implementation of this lesson structure and also on the finding that students’ responses to the lessons can be used to inform subsequent learning experiences.
The use of student drawings to assess their experiences and beliefs about teaching and learning of mathematics has become almost a regular research method - especially when working with young ...students who may not express themselves well, for example, in self-report questionnaires. These methods, nevertheless, need to be improved regarding their objectivity and validity. By building on the existing research, in this study, we focus on objectivity and validity issues in drawing-based methods. We use a drawing-based instrument:
(DAMC) and present 104 fourth-grade students to draw a picture of their regular mathematics lessons. We especially aim to develop and validate a data coding manual with low-inferent categories; that is, well-operationalizable categories that can be used with high interrater-reliability like the presence of teachers, the arrangement of student desks, and teacher-student interactions. The results reveal that almost half of the participating students perceive their lessons as teacher-centered. The results also confirm the reliability and validity of the methodological approach. For example, in pictures where the teacher is depicted larger than the students, the teacher is also depicted in the center, and students are pictured working alone. Classroom observations support students' perceptions, and all these show that the manual used in this study is useful to getting insights into young students' perceptions of their mathematics classroom.
In this text we discuss how power, mathematics and cryptography establish dialogues that are considered critical for the present, but which have influence from the past and concerns for the future. ...We contextualize our reflections from a historical perspective, especially in the Brazilian context, and advance the debates about how cryptography, based on mathematical theories, influenced and dynamized wars. Going a little beyond this historical context, we present some reflections concerning the role of cryptography as a means of data security, one of the main discussions in contemporary society. In this reflection, we point out the position of power that the holders of this knowledge occupy, and that, in the scope of basic school, lacks important discussions for both teachers and students.
In our society, which is based on the division of labor, the ability to communicate with experts is a core competence. Reflection plays a central role for non-experts/laypersons in classifying and ...evaluating expert statements, and in the closely related decision-making process. Reflection is seen as a cognitive ability as well as an attitude. Mathematical concepts and models are applied in many socially relevant areas. For a (better) understanding of these, their fit, effects, limitations as well as their role and meaning, they should be dealt with and reflected on different levels. In the paper, the following levels of reflection are considered in more detail from this social perspective: mathematics-oriented, model-oriented, context-oriented, and subject-oriented reflection. The fact that such reflections can also be integrated into mathematics lessons is demonstrated by means of concrete tasks.
Classroom dialogue is widely used in mathematics teaching and learning, and if managed strategically, it will have productive benefits for mathematics achievement. However, dialogic participants ...often lack awareness of how dialogue could be constructed, and few studies show the characteristics of dialogic patterns in different stages of education. Drawing on the data from the Chinese National Cloud Platform, this study therefore comparatively examined the dialogic patterns of mathematics lessons captured in primary, secondary and high schools in China, using 300 video-recorded mathematics lessons, with 100 lessons for each stage of education. Classroom dialogue was transcribed and systematically coded, after which a lag sequential pattern mining technique was used to examine the collective process of dialogic contributions. Findings indicated that there were both similarities and differences in terms of the dialogue pattern throughout the three stages. Dialogue concerning previously-learnt knowledge, subjective expressions and analysis appeared frequently in mathematics lessons in the three education stages, while speculative talk and querying were less often observed. There were commonalities between dialogic patterns captured in mathematics lessons in secondary and high schools, which were significantly different from those in primary schools. The variation was most obvious in dialogue showing high-level cognition, namely, analysis, coordination and speculation. Prominent sequences captured in secondary and high school lessons were able to involve dialogue at both low and high cognitive levels, which demonstrated the characteristics of exploratory talk. This knowledge could help create productive classroom dialogue, and benefit mathematics teaching and learning.
Specific data mining methods were developed, drawing on computer science to achieve an understanding of dialogue patterns.
A lag sequential mining technique was applied to capture the collective and constructive process of classroom dialogue.
Similar dialogic patterns in terms of low-cognitive dialogues were recognized in primary, secondary and high schools.
A skewed high-cognitive dialogues among three education stages was suggested as possible reasons which lead to transitional difficulties in mathematics learning.
Researchers have recently queried whether musical activities that express mathematical concepts enhance young students' math skills. The use of abstract notations for math learning is also debated. ...The current study examined the effect of a music intervention program on pattern and symmetry knowledge. Simple graphical notation-writing was used for clarifying the abstractness of the music form and its relation to mathematical concepts. Four third-grade classes attended ten lessons on patterns and symmetry: two music classes (n
= 48), and two comparison classes (n = 48). The students in the music classes were taught to write symbolic representations of musical properties and to recognize patterns and symmetry via the symbols they wrote. Pre- to post-intervention analyses indicated that the integrated music/math intervention groups had higher pre-to-post gains on math tests scores that were retained 6-months post-intervention. Students in the music groups also showed effective learning of notation-writing and transfer of note writing knowledge to a different musical piece. The music-math intervention enabled students to acquire knowledge about patterns and symmetry through repeated experiences, particularly through music-related notation-writing, suggesting that multiple representations facilitated deeper understanding and learning outcomes.
Teacher–student interactions are critical for effective mathematics teaching and learning. Certain technologies, especially dynamic geometry software (DGS), can have a great impact on interactions ...between teachers and students. In Chinese mathematics educational environments, we selected three mathematics teachers as examples to analyze how DGS impacts their method of teaching and feedback and what role it plays in their interactions with students. Based on the data, we found mathematics to be the main focus for Chinese teachers, even though DGS was widely used in their lessons. DGS was mainly used as a projector to present geometric properties. This implies that the interactivity of the DGS was simply used for pressing buttons on the screen during lessons. Although teachers may have used DGS for many years, they still lack sufficient skills to integrate this software into mathematics teaching.
This anthology presents successful examples of "research work" by teacher education students. Seminar concepts from the fields of natural sciences, music, educational science, mathematics and art, ...applied social psychology and the subject of German are presented. The volume is framed by a comprehensive theoretical introduction to the concept of research-based learning and its implementation at Leuphana University Lüneburg.
In diesem Sammelband werden gelungene Beispiele von „Forschungsarbeiten“ von Studierenden der Lehrkräftebildung dargestellt. Dazu werden Seminarkonzepte aus den Bereichen Naturwissenschaften, Musik, Bildungswissenschaft, Mathematik und Kunst, der angewandten Sozialpsychologie sowie dem Unterrichtsfach Deutsch vorgestellt. Gerahmt wird der Band durch eine umfangreiche theoretische Einführung in das Konzept des forschenden Lernens und seiner Umsetzung an der Leuphana Universität Lüneburg
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