The Representation Strategies of Preschool Children When Solving Numeracy Task

Identifying and addressing the knowledge gap in early numeracy is crucial, given the strong associations between early numeracy skills and later school success. The purpose of this study is to establish current viewpoints and ideas on children’s numeracy development via three forms of representation: manipulative, symbolic, and static. The Children’s Numeracy Task was used to assess eleven preschool children’s numeracy knowledge via a semi-structured interview. The task was also designed to be presented in the three mathematical representations: concrete, static, and symbolic. The findings indicate that preschool children are more likely to use symbolic representation in solving a given task. This study highlights perspectives on how to apply various representations as pedagogical and assessment strategies to address the children’s readiness for a mathematics lesson at the primary school level.

Features of the formation and development of mathematical representations in preschool children

The article deals with the actual problems of the formation of elementary mathematical representations in children. The paper shows that this approach in mathematics education based on action learning in conjunction with the natural motivation stemming from common sense is effective. Also, stimulating questions and classical famous problems are important motivating tools in mathematics, which are particularly beneficial in the framework of action learning. The analysis of psychological, pedagogical and methodological literature on the topic of research the author provides an experimental methodology for studying elementary mathematical representations, characterizes their features in young children. Key words: preschool children, mathematical representations, intellectual development of preschool children, mental education, features of development, elementary mathematical representations

A comparison among three maximal mathematical models of the glucose-insulin system

The most well-known and widely used mathematical representations of the physiology of a diabetic individual are the Sorensen and Hovorka models as well as the UVAPadova Simulator. While the Hovorka model and the UVAPadova Simulator only describe the glucose metabolism of a subject with type 1 diabetes, the Sorensen model was formulated to simulate the behaviour of both normal and diabetic individuals. The UVAPadova model is the most known model, accepted by the FDA, with a high level of complexity. The Hovorka model is the simplest of the three models, well documented and used primarily for the development of control algorithms. The Sorensen model is the most complete, even though some modifications were required both to the model equations (adding useful compartments for modelling subcutaneous insulin delivery) and to the parameter values. In the present work several simulated experiments, such as IVGTTs and OGTTs, were used as tools to compare the three formulations in order to establish to what extent increasing complexity translates into richer and more correct physiological behaviour. All the equations and parameters used for carrying out the simulations are provided.

An Analysis of Pre-service Teachers’ Understanding of the Knowledge Needed for Teaching Mathematics

In contexts of adversity, there is a need to educate pre-service teachers with specialized content knowledge so they can carry out the work of teaching effectively. This article draws upon a study with three pre-service teachers in Malawi that examines the understanding they develop of the knowledge needed to carry out mathematics teaching tasks, in particular, the knowledge needed sequence instructional tasks sequence and use mathematical representations in classrooms. The research was conducted in one teacher education college where the curriculum is under development and has an emergent demand for qualifying teachers in mathematics. The research methodology was based on a questionnaire, interviews, teaching observations, and group discussions. The data were thematically analyzed through two themes reflecting the knowledge pre-service teachers considered necessary for teaching mathematics. While the first theme reveals how pre-service teachers understand this knowledge as a reference for meeting curricular standards and students’ needs, the second captures a form of understanding that attempts to go beyond conceptual knowledge. The findings can help better understand the pre-service teachers’ learning and experience during teacher education and how theoretical constructs are conceived in challenging contexts of teacher education.

Analysis of Mathematical Representation Ability Based on Level of Reading Interest in Geometry Course

Reading literacy activities are currently being held by all levels of education. Literacy activities have a positive effect on students in understanding information. The ability to understand information can be realized through mathematical representation, which is one of the main elements in mathematical understanding. This research can help educators in mapping the mathematical representation ability based on the reading interest of students. The purpose of this research is to identify which indicators can be mastered by students who have reading interests at high, medium, and low levels. This research is qualitative. The research subjects were students of the Mathematics Education Department of Ivet University. The data collection procedures used were scale, test, and interview. The instruments of this study were the reading interest scale, mathematical representation ability test, and interview sheets. The data analysis technique of this study adopted data analysis techniques from Miles and Huberman. The conclusions of this study are (1) students with high and medium reading levels have the ability to represent mathematical representations to model and interpret physical, social, and mathematical phenomena; have the ability of mathematical representations to create and use representations to communicate mathematical ideas or concepts; have the ability of mathematical representations in selecting, applying, and translating mathematical representations to solve problems, (2) students with a low reading level have lacked on the ability of mathematical representations to use representations to model and interpret physical, social, and mathematical phenomena, thus it caused them couldn’t mastering the ability of mathematical representations to create and use representations to communicate mathematical ideas or concepts and the ability of mathematical representations to select, apply, and translate mathematical representations to solve problems. Keywords: mathematical representation ability, reading interest, geometry.

KEMAMPUAN REPRESENTASI MATEMATIS SISWA PADA MATERI SEGITIGA

The mathematical representation ability referred to in this study is the ability to express mathematical ideas or ideas to solve a problem with various mathematical representations of visual forms (pictures) and verbal forms (writing).This type of research is descriptive with a qualitative approach which aims to describe systematically the ability of visual mathematical representations and the ability of verbal mathematical representations.The data collection technique in this study was carried out using essay. Test questions were given to student an grade VIII A at SMP Negeri 1 Mandor, where there were three groups, namely the upper, middle, and lower group. Students who will be interviewed are selected based on the representation ability test scores where only two students will represent for each group.The results showed that the ability of visual mathematical representation when given verbal form questions to answer indicators using pictures was in the percentage of students' average score 66.67% and the ability of verbal mathematical representation if given visual questions, for the answer indicator using words is in the percentage of the student's average score of 33.33%. Students still have difficulty with verbal representation if given a visual form. Keywords: visual representation, verbal representation and trangle material

Improve the Ability to Use Mathematical Representation for Junior High School Students in Vietnam

The world's tendency to develop competence in secondary education and the need to reform secondary education in Vietnam today aim to reach UNESCO's four pillars of learning in the 21st century learning to know, learning to do, learning to be, and learning to live together. This article aims to create opportunities for students to form and develop their mathematical representation competencies through teaching Mathematics in junior high schools in Vietnam. By surveying 1390 students in 15 secondary schools about the actual situation of learning mathematical representations, to analyze, compare and propose solutions to improve mathematical representation competence for students. The results showed many opportunities for students to observe and compare, help students understand and use different mathematical representations when expressing similar relationships, and flexibility in mathematical operations in the learning process.

Coordination in theory extension: how Reichenbach can help us understand endogenization in evolutionary biology

Reichenbach’s early solution to the scientific problem of how abstract mathematical representations can successfully express real phenomena is rooted in his view of coordination. In this paper, I claim that a Reichenbach-inspired, ‘layered’ view of coordination provides us with an effective tool to systematically analyse some epistemic and conceptual intricacies resulting from a widespread theorising strategy in evolutionary biology, recently discussed by Okasha (2018) as ‘endogenization’. First, I argue that endogenization is a form of extension of natural selection theory that comprises three stages: quasi-axiomatisation, functional extension, and semantic extension. Then, I argue that the functional extension of one core principle of natural selection theory, namely, the principle of heritability, requires the semantic extension of the concept of inheritance. This is because the semantic extension of ‘inheritance’ is necessary to establish a novel form of coordination between the principle of heritability and the extended domain of phenomena that it is supposed to represent. Finally, I suggest that—despite the current lack of consensus on the right semantic extension of ‘inheritance’—we can fruitfully understand the reconceptualization of ‘inheritance’ provided by niche construction theorists as the result of a novel form of coordination.