A sociological analysis of the pictures used in the South African foundation phase numeracy workbooks and their mathematical implications

About half of South Africa’s Department of Basic Education foundation phase numeracy workbooks’ content consist of pictures (Pausigere, 2016), yet the implications of these pictures to the different lower grades is not clear. To analyse the types of pictures, and the inferences to be drawn upon learners’ mathematical understanding this article is theoretically informed by Dowling’s (1996; 1998) sociology of mathematics education, specifically drawing from his textual description concepts. A sociological qualitative content analysis of the numeracy workbook pictures led to the development of a model capable of classifying key mathematical pictures used in mathematical workbooks and applicable to conventional maths textbooks. The analytical framework’s pictorial categories show abstract and concrete-abstract mathematical pictures as being effective in translating generalising, context-independent mathematical principles. On the other hand concrete and abstract-concrete mathematical pictures through situational activities exhibit context-dependent numerical strategies. Given the analytical framework the study discusses the mathematical implications of its findings across the foundation phase

An Inquiry into the Practice of Proving in Low-Dimensional Topology

The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology

MATHEMATICAL COMMUNICATION ABILITY OF CLASS V SD STUDENTS ON FLAT BUILDING MATERIALS VIEWED FROM GENDER

This study aims to describe the mathematical communication abilities of fifth grade students on the material of flat shapes in terms of the gender of students at SDN 84 Singkawang. The research used is descriptive quantitative research. The population of this study was the fifth grade students at SDN 84 Singkawang consisting of VA and VB classes, which consisted of 44 students. The data collection technique used was the test technique and the data analysis technique used was quantitative descriptive analysis with percentages. The results showed that mathematical communication skills in terms of gender where the mathematical communication skills of fifth grade male students in solving problems, subjects with high abilities were able to fulfill all indicators of students' mathematical communication abilities. Subjects with moderate ability are less able to explain ideas, everyday situations and mathematical relationships in writing with pictures. While the mathematical communication abilities of fifth grade female students in solving questions on subjects with high abilities were able to fulfill all indicators of students' mathematical communication abilities. Subjects with moderate ability are less able to explain ideas, everyday situations and mathematical relationships in writing with pictures. Meanwhile, subjects with low abilities are less able to explain ideas, everyday situations and mathematical relations in writing with pictures and communicate the conclusions of answers to problems according to the results of the questions. Thus it can be concluded that students' mathematical communication abilities in terms of gender in this study averaged 74% in the moderate category

Dark Energy: the equation of state description versus scalar-tensor or modified gravity

Dark energy dynamics of the universe can be achieved by equivalent mathematical descriptions taking into account generalized fluid equations of state in General Relativity, scalar-tensor theories or modified F(R) gravity in Einstein or Jordan frames. The corresponding technique transforming equation of state description to scalar-tensor or modified gravity is explicitly presented. We show that such equivalent pictures can be discriminated by matching solutions with data capable of selecting the true physical frame.Comment: LaTeX file, 10 pages, 3 figures, the fit of two equivalent models with observational data is added, new reference

Schwinger's Picture of Quantum Mechanics I: Groupoids

A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual applications. In this first paper, the kinematical background is described using elementary notions from category theory, in particular the notion of 2-groupoids as well as their representations. Some basic results are presented, and the relation with the standard Dirac-Schr\"odinger and Born-Jordan-Heisenberg pictures are succinctly discussed.Comment: 32 pages. Comments are welcome

A descriptive and evaluative bibliography of mathematics films

Thesis (M.A.)--Boston UniversityAs the title indicates, this thesis is concerned with describing and evaluating motion pictures which are being used to supplement teaching in a mathematics classroom. We are attempting to describe and evaluate mathematics films. Specifically, we may state the purposes as: 1. To give a brief history of techniques used in evaluating educational motion pictures. 2. To describe fully the mathematical content, the presentation of the mathematical content, and physical aspect of each film. 3. To evaluate each film as to technical makeup, mathematical content, the presentation of the mathematical content, and educational purpose and use. 4. To give an over-all outlook of a large number of mathematics films with regard to the evaluative items in purpose number three above