Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics education which is struggling through a crisis of its own, socio-economic and political by its nature. The mathematical community faces Pandora's box of problems, which, surprisingly, are not usually discussed in any connected form. The present paper attempts to address this issue in a bit more joint and cohesive way.
In this paper the context of the 1940 mathematical paper by Kolmogorov on Mendel's laws of genetics is considered, also thanks to a recent study by Stark and Seneta (2011). Kolmogorov's vision of the relationship between mathematics and science in the understanding of the natural world appears to have encouraged him in tacking part in the discussions around Mendelism in while Lysenko's position against it was becoming the only permissible for Soviet Union biologists.
We consider the mathematical theory of geographical maps, with an emphasis on the eighteenth century works of Euler, Lagrange and Delisle. This period is characterized by the frequent use of maps that are no more obtained by the stereographic projection or its variations, but by much more general maps from the sphere to the plane. More especially, the characteristics of the desired geographical maps were formulated in terms of an appropriate choice of the images of the parallels and meridians, and the mathematical properties required by the map concern the distortion of the maps restricted to …
This paper is an introduction to our ongoing more comprehensive work on a critically important period in the history of Russian mathematics education; it provides a glimpse into the socio-political environment in which the famous Soviet tradition of mathematics education was born. The authors are practitioners of mathematics education in two very different countries, England and Russia. We have a chance to see that too many trends and debates in current education policy resemble battles around mathematics education in the 1920s and 1930s Soviet Russia. This is why this period should be revisit…
In the last decade, major efforts have been made to promote inquiry-based mathematics learning at the tertiary level. The Inquiry-Based Mathematics Education (IBME) movement has gained strong momentum among some mathematicians, attracting substantial funding, including from some US government agencies. This resulted in the successful mobilization of regional consortia in many states, uniting over 800 mathematics education practitioners working to reform undergraduate education. Inquiry-based learning is characterized by the fundamental premise that learners should be allowed to learn 'new to t…
Exploring Gender Differences in Graduation Proficiency in Mathematics Education Using a Markov Chain Model: Implications for Economic Growth in Nigeria
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics courses. These activities are, in some important ways, natural precursors to the use of Artificial Intelligence in Mathematics Education. This paper reflects on some of our course designs and experiences and is therefore a mix of theory and practice. Underlying both is a clear recognition of the value of computer programming for mathematics education. We use th…
In the Soviet Union a reform movement in mathematics education was triggered by Andrey Kolmogorov in the 1970s, and followed by a counter-reform. This movement was rooted in the very different socioeconomic conditions of that time and place, and followed a strategy with very significant contrasts to similar programs in the USA, England, or France. This provides an interesting case study which may illuminate the way such movements arise and succeed or fail, and, at the social level, certain fundamental commonalities of constraints as well as significant differences according to local conditions…
Why Do Students (Not) Choose Second-Cycle Mathematics Studies? Questionnaire and Graduate-Tracking Evidence from Poland
Institute of Mathematics, Lodz University of Technology（罗兹理工大学数学研究所）；Institute of Theoretical and Applied Informatics, Polish Academy of Sciences（波兰科学院理论与应用信息学研究所）；Center of Mathematics and Physics, Lodz University of Technology（罗兹理工大学数理中心）；Faculty of Mathematics, Informatics and Mechanics, University of Warsaw（华沙大学数学、信息学与力学系）
Graduate school admission committees consider many factors for admission into a mathematics PhD program, and aspiring applicants often wonder which factors are more important. Applicants discerning where to best dedicate their time may ask questions such as, "should I take graduate level courses or participate in research?" This paper seeks to answer such questions by constructing an ordinal ranking of admission criteria and provide insight on why some factors are more valued. Using a conjoint analysis method called Analytic Hierarchy Process from mathematician Thomas Saaty, this paper evaluat…
If we want mathematics education to be valuable to everybody, including those who do not pursue mathematics-related careers, we need to use mathematics as a training ground for certain ways of thinking. This dissertation focuses on one aspect of mathematical thinking, namely theory building. It has three parts - unpacking what constitutes theory building, the development of a course aimed at theory building, and a qualitative description of an implementation of that course with 12 to 15-year-old students in two schools in Pune, India. The description aims to understand some of how students eng…
Overlapping Circles Grid Drawn with Compass and Straightedge on an Egyptian Artifact of 14th Century BC
研究古代文明的数学和几何学似乎是一项非常困难的任务，甚至是不可能完成的，如果很少有书面文件，或者根本没有，从过去幸存下来。然而，除了我们可以从书面文件中获得的直接信息外，我们还可以从对人工制品上发现的装饰的分析中获得一些关于数学和几何的间接证据。例如，在这里，我们将展示古埃及人能够使用指南针和直尺制作尺规作图法，这比生活在公元前450年左右的希腊人乔伊斯的奥诺皮德斯（Oenopides of Chois）宣布几何作图法的一些基本原理要早得多。事实上，在为第18王朝（公元前1400-1350年）的三位国王服务的建筑师Kha的坟墓中发现的一块覆盖着重叠圆圈网格图案的木板，证明了在Oenopides时代之前大约九个世纪，古埃及使用了一些简单的指南针和直尺。
The flipped classroom technique has recently been a focus of attention for many math instructors and pedagogical researchers. Although research on the subject has greatly increased in recent years, it is still debated whether the flipped classroom technique can significantly increase the overall success of students in undergraduate math courses. While there have been meta-analyses that consider the efficacy of the technique across university disciplines and within other STEM fields, there has not yet been a systematic review within undergraduate math education. By analyzing the existing resear…
This survey paper is an expanded version of an invited keynote at the ThEdu'22 workshop, August 2022, in Haifa (Israel). After a short introduction on the developments of CAS, DGS and other useful technologies, we show implications in Mathematics Education, and in the broader frame of STEAM Education. In particular, we discuss the transformation of Mathematics Education into exploration-discovery-conjecture-proof scheme, avoiding usage as a black box . This scheme fits well into the so-called 4 C's of 21st Century Education. Communication and Collaboration are emphasized not only between human…
A stochastic approach in physics exercises of mathematics education
HUN-REN–SZTE Analysis and Applications Research Group, Bolyai Institute, University of Szeged（塞格德大学博莱伊研究所匈牙利研究与创新网络-塞格德大学分析与应用研究组）；Department of Basic Technical Studies, Faculty of Engineering, University of Debrecen（德布勒森大学工程学院基础技术研究系）
