LIMITATIONS OF SECONDARY SCHOOL STUDENTS IN SOLVING A TYPE OF TASK RELATING TO THE EQUATION OF A CIRCLE: AN INVESTIGATION IN VIETNAM

In Vietnam, secondary school students learn the equation of a circle in Grade 10. Based on how to present this equation in the textbook “Geometry 10” and types of task for students, we believe that some limitations happen to students when they solve problems related to the equation of a circle. This paper reports the investigation of 845 students from the Mekong Delta-Vietnam. The results show that our prediction is correct.  Article visualizations

A SURVEY OF STUDENTS’ ABILITY OF IDENTIFYING ERRORS IN WRONG SOLUTIONS FOR THE MATHEMATICAL PROBLEMS RELATED TO THE MONOTONICITY OF FUNCTIONS

The monotonicity of a function plays an important role in the general mathematics curriculum in Vietnam, because it is considered as an effective tool for solving mathematical problems involved with the monotonic intervals of functions, their extreme, absolute maximum value and absolute minimum value. Normally, students commit errors in solving these problems because of their complexity and difficulty. In addition, specific characteristics of knowledge also make children make mistakes. The sample consisted of 362 students, and they had the task of identifying errors in false assumptions. From the results of the survey, it was found that when dealing with the monotonicity of the functions, students were still misled.  Article visualizations

Étude didactique des relations entre enseignement de la notion de limite au lycée et décimalisation des nombres réels dans un environnement ‘calculatrice'. Une étude de cas au Viêt-nam.

date de rédaction : 2 septembre 2007The study of the didactical transposition of the notions of limits and real numbers guides our research.In Vietnam, the set of real numbers is introduced in lower secondary mathematical teaching as the set of decimal writings whereas the notion of series and limits only appear in upper secondary education (Class 11, age 17). There is no issue about approximation and the institutional relation to limits is bound to algebra. However, the Ministry of Education has officially introduced the use of pocket calculators, that modifies the conditions for calculation and of its results which is obtained as a decimal value which is most of the time an approximation. The results of an epistemological investigation about the inter-relations historically built between the construction of real numbers, the notion of limit and the decimalisation of real numbers lead us to a description of Mathematical Organisations (MO), that we qualified as reference MO.From an institutional analysis (chronological evolution of curricula, instructions and textbooks) we identify mathematical organisations to be taught, interpreted as traces of reference MO in the teaching of mathematics. The distance between reference OM and OM to be taught are explained by conditions and constraints proper to each institution, lower and upper secondary mathematics education. Building, experimenting and analysing a didactical engineering is a means for us to give some elements of answer to the question of viability of a teaching aiming at introducing (under today's conditions and constraints) a topological viewpoint on the notion of limit in relation with the decimalisation of real numbers in a calculator environment.L'étude de la transposition didactique des notions de limites et de nombres guide notre recherche. Au Viêt-nam, l'ensemble des nombres réels est introduit au niveau du collège comme l'ensemble des écritures décimales alors que les notions de suite convergente et de limite n'apparaissent au lycée qu'en classe 11 (Première). Toute problématique de l'approximation est absente et le rapport institutionnel à la notion de limite est fortement algébrisé. Cependant le ministère de l'Éducation et de la Formation préconise l'introduction officielle de la calculatrice ce qui modifie les conditions du calcul - en l'instrumentant, et le résultat de ce calcul - en le décimalisant en une valeur le plus souvent approchée. Les résultats d'une enquête épistémologique sur les interrelations historiquement mises en place entre la construction des nombres réels, la notion de limite et la décimalisation des nombres réels nous conduisent à décrire des Organisations Mathématiques (OM) dites de référence.A partir d'une analyse institutionnelle (évolution chronologique des programmes et des manuels vietnamiens du collège et du lycée), nous identifions des organisations mathématiques à enseigner, interprétées comme les traces des OM de référence dans l'enseignement des mathématiques. L'écart entre les OM de référence et les OM à enseigner sont expliquées par des conditions et des contraintes propres aux institutions, collège et lycée. La conception, l'expérimentation et l'analyse d'une ingénierie didactique nous permettent d'apporter des éléments de réponse à la question de la viabilité d'un enseignement visant à introduire (dans les conditions et les contraintes actuelles) un point de vue topologique sur la notion de limite en relation avec la décimalisation des nombres réels dans un environnement « calculatrice »

Étude didactique des relations entre notion de limite et décimalisation des nombres réels dans un environnement "calculatrice". Une étude de cas dans l'enseignement mathématique secondaire au Viêt-nam.

L étude de la transposition didactique des notions de limites et de nombres guide notre recherche. Au Viêt-nam, l ensemble des nombres réels est introduit au niveau du collège comme l ensemble des écritures décimales alors que les notions de suite convergente et de limite n apparaissent au lycée qu en classe 11 (Première). Toute problématique de l approximation est absente et le rapport institutionnel à la notion de limite est fortement algébrisé. Cependant le ministère de l'Éducation et de la Formation préconise l'introduction officielle de la calculatrice ce qui modifie les conditions du calcul - en l instrumentant, et le résultat de ce calcul - en le décimalisant en une valeur le plus souvent approchée. Les résultats d une enquête épistémologique sur les interrelations historiquement mises en place entre la construction des nombres réels, la notion de limite et la décimalisation des nombres réels nous conduisent à décrire des Organisations Mathématiques (OM) dites de référence.A partir d une analyse institutionnelle (évolution chronologique des programmes et des manuels vietnamiens du collège et du lycée), nous identifions des organisations mathématiques à enseigner, interprétées comme les traces des OM de référence dans l enseignement des mathématiques. L écart entre les OM de référence et les OM à enseigner sont expliquées par des conditions et des contraintes propres aux institutions, collège et lycée. La conception, l expérimentation et l analyse d une ingénierie didactique nous permettent d apporter des éléments de réponse à la question de la viabilité d un enseignement visant à introduire (dans les conditions et les contraintes actuelles) un point de vue topologique sur la notion de limite en relation avec la décimalisation des nombres réels dans un environnement calculatrice .The study of the didactical transposition of the notions of limits and real numbers guides our research. In Vietnam, the set of real numbers is introduced in lower secondary mathematical teaching as the set of decimal writings whereas the notion of series and limits only appear in upper secondary education (Class 11, age 17). There is no issue about approximation and the institutional relation to limits is bound to algebra. However, the Ministry of Education has officially introduced the use of pocket calculators, that modifies the conditions for calculation and of its results which is obtained as a decimal value which is most of the time an approximation. The results of an epistemological investigation about the inter-relations historically built between the construction of real numbers, the notion of limit and the decimalisation of real numbers lead us to a description of Mathematical Organisations (MO), that we qualified as reference MO. From an institutional analysis (chronological evolution of curricula, instructions and textbooks) we identify mathematical organisations to be taught, interpreted as traces of reference MO in the teaching of mathematics. The distance between reference OM and OM to be taught are explained by conditions and constraints proper to each institution, lower and upper secondary mathematics education. Building, experimenting and analysing a didactical engineering is a means for us to give some elements of answer to the question of viability of a teaching aiming at introducing (under today s conditions and constraints) a topological viewpoint on the notion of limit in relation with the decimalisation of real numbers in a calculator environment.GRENOBLE1-BU Sciences (384212103) / SudocSudocFranceF

FACTORS INFLUENCING TEACHERS’ INTENTIONS TO USE REALISTIC MATHEMATICS EDUCATION IN VIETNAM: AN EXTENSION OF THE THEORY OF PLANNED BEHAVIOR

Although Realistic Mathematics Education (RME) has become familiar to many mathematics teachers, we still have little understanding of the extent to which mathematics teachers are willing to employ RME rather than traditional teaching approaches. Based on the theory of planned behavior, in conjunction with some other factors, including facilitating conditions and perceived autonomy, this study investigated a model explaining the continued intention of mathematics teachers to use Realistic Mathematics Education. A structural equation model was used to access data from an online survey involving 500 secondary school mathematics teachers in Vietnam. The results revealed that while attitude, perceived behavioral control and perceived autonomy have positive significant impacts on intention to use RME, it appears that subjective norms and facilitating conditions do not. These findings are of significance to stakeholders, including policymakers, school managers, and mathematics teachers

Multimodal analysis of methylomics and fragmentomics in plasma cell-free DNA for multi-cancer early detection and localization

Despite their promise, circulating tumor DNA (ctDNA)-based assays for multi-cancer early detection face challenges in test performance, due mostly to the limited abundance of ctDNA and its inherent variability. To address these challenges, published assays to date demanded a very high-depth sequencing, resulting in an elevated price of test. Herein, we developed a multimodal assay called SPOT-MAS (screening for the presence of tumor by methylation and size) to simultaneously profile methylomics, fragmentomics, copy number, and end motifs in a single workflow using targeted and shallow genome-wide sequencing (~0.55×) of cell-free DNA. We applied SPOT-MAS to 738 non-metastatic patients with breast, colorectal, gastric, lung, and liver cancer, and 1550 healthy controls. We then employed machine learning to extract multiple cancer and tissue-specific signatures for detecting and locating cancer. SPOT-MAS successfully detected the five cancer types with a sensitivity of 72.4% at 97.0% specificity. The sensitivities for detecting early-stage cancers were 73.9% and 62.3% for stages I and II, respectively, increasing to 88.3% for non-metastatic stage IIIA. For tumor-of-origin, our assay achieved an accuracy of 0.7. Our study demonstrates comparable performance to other ctDNA-based assays while requiring significantly lower sequencing depth, making it economically feasible for population-wide screening