Use of words and visuals in modelling context of annual plant

This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual representations such as flowcharts are used not only in the process to symbolization, but also used in the justification of symbols, (2) some of the visual representations serve as a bridge between the words in the problem context and the symbols that represent the mathematical equations of the number of annual plants and (3) words and context help to introduce visual representations and symbols. Also, once students come up with the visual representations and symbols, they show better understanding about words used in the problem context. These observations imply that the modelling and mathematization process is not just one-directional and linear from words describing real-life situations to the symbols in mathematical equations and expressions. Rather, the mathematization can be promoted through using other visuals that help make this transition smooth by organizing the given information in a way that can be used towards mathematization.     

Problem solving in the borderland between mathematics and physics

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization.     

医用高等数学教学改革与实践探索

现代医学发展的一大趋势是从定性研究走向定量研究,经历着数学化的发展进程.随着数学与医学的联系越来越紧密,医用高等数学在改善医学人才智能结构、培养学生科学思维和创新能力等方面都具有十分重要的意义.医用高等数学的教学要适应新的需要,必须要在改善教师知识结构、改变教学理念、完善教学内容、改变教学方法、培养创新意识和应用能力这些方面下功夫,才使之更好地与医学实际相结合.     

Wisdom of symbols

This is an overview of the origins and vistas of mathematics.