Hasil untuk "Mathematics"

David Weintrop, Elham Beheshti, Michael S. Horn et al.

N. Else-Quest, J. Hyde, M. Linn

D. Bernstein

A. Dowker, Amar Sarkar, C. Looi

The construct of mathematics anxiety has been an important topic of study at least since the concept of “number anxiety” was introduced by Dreger and Aiken (1957), and has received increasing attention in recent years. This paper focuses on what research has revealed about mathematics anxiety in the last 60 years, and what still remains to be learned. We discuss what mathematics anxiety is; how distinct it is from other forms of anxiety; and how it relates to attitudes to mathematics. We discuss the relationships between mathematics anxiety and mathematics performance. We describe ways in which mathematics anxiety is measured, both by questionnaires, and by physiological measures. We discuss some possible factors in mathematics anxiety, including genetics, gender, age, and culture. Finally, we describe some research on treatment. We conclude with a brief discussion of what still needs to be learned.

A. Davies, Petar Velickovic, L. Buesing et al.

The practice of mathematics involves discovering patterns and using these to formulate and prove conjectures, resulting in theorems. Since the 1960s, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures1, most famously in the Birch and Swinnerton-Dyer conjecture2, a Millennium Prize Problem3. Here we provide examples of new fundamental results in pure mathematics that have been discovered with the assistance of machine learning—demonstrating a method by which machine learning can aid mathematicians in discovering new conjectures and theorems. We propose a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these observations to guide intuition and propose conjectures. We outline this machine-learning-guided framework and demonstrate its successful application to current research questions in distinct areas of pure mathematics, in each case showing how it led to meaningful mathematical contributions on important open problems: a new connection between the algebraic and geometric structure of knots, and a candidate algorithm predicted by the combinatorial invariance conjecture for symmetric groups4. Our work may serve as a model for collaboration between the fields of mathematics and artificial intelligence (AI) that can achieve surprising results by leveraging the respective strengths of mathematicians and machine learning. A framework through which machine learning can guide mathematicians in discovering new conjectures and theorems is presented and shown to yield mathematical insight on important open problems in different areas of pure mathematics.

R. Hersh, S. Dehaene

Angie Su

W. B. Jones, W. J. Thron

R. Hembree

D. Grouws

R. Battin

G. Lakoff, R. Núñez

R. Mistretta, J. Porzio

R. Barnes, E. Kreyszig

G. Brousseau

Gaurav Kumar, R. Banerjee, Deepak Kr Singh et al.

Machine learning is a way to study the algorithm and statistical model that is used by computer to perform a specific task through pattern and deduction [1]. It builds a mathematical model from a sample data which may come under either supervised or unsupervised learning. It is closely related to computational statistics which is an interface between statistics and computer science. Also, linear algebra and probability theory are two tools of mathematics which form the basis of machine learning. In general, statistics is a science concerned with collecting, analysing, interpreting the data. Data are the facts and figure that can be classified as either quantitative or qualitative. From the given set of data, we can predict the expected observation, difference between the outcome of two observations and how data look like which can help in better decision making process [2]. Descriptive and inferential statistics are the two methods of data analysis. Descriptive statistics summarize the raw data into information through which common expectation and variation of data can be taken. It also provides graphical methods that can be used to visualize the sample of data and qualitative understanding of observation whereas inferential statistics refers to drawing conclusions from data. Inferences are made under the framework of probability theory. So, understanding of data and interpretation of result are two important aspects of machine learning. In this paper, we have reviewed the different methods of ML, mathematics behind ML, its application in day to day life and future aspects.

Guillaume Lample, François Charton

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing these mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.

A. Goriely

Gwo-jen Hwang, Y. Tu

Learning mathematics has been considered as a great challenge for many students. The advancement of computer technologies, in particular, artificial intelligence (AI), provides an opportunity to cope with this problem by diagnosing individual students’ learning problems and providing personalized supports to maximize their learning performances in mathematics courses. However, there is a lack of reviews from diverse perspectives to help researchers, especially novices, gain a whole picture of the research of AI in mathematics education. To this end, this research aims to conduct a bibliometric mapping analysis and systematic review to explore the role and research trends of AI in mathematics education by searching for the relevant articles published in the quality journals indexed by the Social Sciences Citation Index (SSCI) from the Web of Science (WOS) database. Moreover, by referring to the technology-based learning model, several dimensions of AI in mathematics education research, such as the application domains, participants, research methods, adopted technologies, research issues and the roles of AI as well as the citation and co-citation relationships, are taken into account. Accordingly, the advancements of AI in mathematics education research are reported, and potential research topics for future research are recommended.

Jessica M. Namkung, Peng Peng, Xin Lin

The purpose of this meta-analysis was to examine the relation between mathematics anxiety (MA) and mathematics performance among school-aged students, and to identify potential moderators and underlying mechanisms of such relation, including grade level, temporal relations, difficulty of mathematical tasks, dimensions of MA measures, effects on student grades, and working memory. A meta-analysis of 131 studies with 478 effect sizes was conducted. The results indicated that a significant negative correlation exist between MA and mathematics performance, r = −.34. Moderation analyses indicated that dimensions of MA, difficulty of mathematical tasks, and effects on student grades differentially affected the relation between MA and mathematics performance. MA assessed with both cognitive and affective dimensions showed a stronger negative correlation with mathematics performance compared to MA assessed with either an affective dimension only or mixed/unspecified dimensions. Advanced mathematical tasks that require multistep processes showed a stronger negative correlation to MA compared to foundational mathematical tasks. Mathematics measures that affected/reflected student grades (e.g., final exam, students’ course grade, GPA) had a stronger negative correlation to MA than did other measures of mathematics performance that did not affect student grades (e.g., mathematics measures administered as part of research). Theoretical and practical implications of the findings are discussed.