人工智能在数学教育中的应用 | 现状、探索与实践

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International Electronic Journal of Mathematics Education

国际数学教育电子期刊

2022, 17(3), em0694

2022 年，第 17 卷第 3 期，em0694 号

e-ISSN: 1306-3030 https://www.iejme.com

电子国际标准连续出版物编号：1306-3030，网址：https://www.iejme.com

Artificial intelligence in mathematics education: A systematic literature review

人工智能在数学教育中的应用：系统文献综述

Mohamed Zulhilmi bin Mohamed Norhafiza binti Mat Sabri ¹, Muhamad Khairul Hakim bin Mahmud ¹, Siti Nurshafikah binti Baharuddin ¹, Riyan Hidayat ¹*, Nurain Nabilah binti Suhaizi ¹

穆罕默德·祖尔希米·本·穆罕默德·诺哈菲扎·本提·马特·萨布里¹、穆罕默德·海尔·哈基姆·本·马哈茂德¹、西蒂·努尔沙菲卡·本提·巴哈鲁丁¹、里扬·希达亚特¹*、努拉因·纳比拉·本提·苏海兹¹

¹ Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Perak, MALAYSIA

¹ 马来西亚霹雳州苏丹伊德里斯教育大学科学与数学学院数学系

*Corresponding Author: riyanhidayat@fsmt.upsi.edu.my

*通讯作者：riyanhidayat@fsmt.upsi.edu.my

Citation: Mohamed, M. Z. b., Hidayat, R., Suhaizi, N. N. b., Sabri, N. b. M., Mahmud, M. K. H. b., & Baharuddin, S. N. b. (2022). Artificial intelligence in mathematics education: A systematic literature review. International Electronic Journal of Mathematics Education, 17(3), em0694. https://doi.org/10.29333/iejme/12132

引文格式：穆罕默德、M. Z. 本、希达亚特、R.、苏海兹、N. N. 本提、萨布里、N. 本提·M.、马哈茂德、M. K. H. 本、巴哈鲁丁、S. N. 本提（2022）。《人工智能在数学教育中的应用：系统文献综述》，《国际数学教育电子期刊》，第 17 卷第 3 期，em0694 号。网址：https://doi.org/10.29333/iejme/12132

ARTICLE INFO

文章信息

Received: 14 Mar. 2022

ABSTRACT

摘要

The advancement of technology like artificial intelligence (AI) provides a chance to help teachers and students solve and improve teaching and learning performances. The goal of this review is to add to the conversation by offering a complete overview of AI in mathematics teaching and learning for students at all levels of education. A systematic literature review (SLR) was conducted using established and robust guidelines. We follow the preferred reporting items for systematic reviews and meta-analyses (PRISMA). We searched ScienceDirect, Scopus, Springer Link, ProQuest, and EBSCO Host for 20 AI studies published between 2017 and 2021. The findings of the SLR indicate that AI approach used in mathematics education for the samples studied were through robotics, systems, tools, teachable agent, autonomous agent, and a comprehensive approach. Then, it can be shown that the majority of the collected studies were carried out in the USA and Mexico. The analysis revealed that most of the reviewed studies used quantitative research methods. The types of themes for AI in mathematics education were categorized into advantages and disadvantages, conceptual understanding, factors, role, idea suggestion, strategies and effectiveness.

人工智能（AI）等技术的发展为师生解决教学问题、提升教与学成效提供了契机。本综述旨在通过全面梳理人工智能在各教育阶段数学教与学中的应用，为相关研究对话补充内容。研究采用成熟且严谨的规范开展系统文献综述（SLR），遵循系统综述与元分析优先报告条目（PRISMA）。研究人员在 ScienceDirect、Scopus、Springer Link、ProQuest 和 EBSCO Host 等数据库中检索了 2017-2021 年间发表的 20 项关于人工智能的研究。系统文献综述结果显示，在研究样本中，人工智能应用于数学教育的方式包括机器人技术、系统、工具、可教智能体、自主智能体及综合方法。此外，多数纳入研究在美国和墨西哥开展。分析表明，大部分综述研究采用定量研究方法。人工智能在数学教育中的研究主题可分为优势与劣势、概念理解、影响因素、作用、建议、策略及有效性等类别。

Keywords: artificial intelligence, mathematics education, PRISMA, robotics, systematic literature review

关键词：人工智能、数学教育、系统综述与元分析优先报告条目（PRISMA）、机器人技术、系统文献综述

INTRODUCTION

引言

Artificial intelligence (AI) applications in education are becoming more popular and have gotten a lot of press in recent years. AI is a leap across creative and innovative thinking in various fields, including mathematics education. The current study indicates various research of AI in different context (Chen et al., 2020a; Cope et al., 2020; He et al., 2019; Schiff, 2021; Vaishya et al., 2020). The use of AI can enhance our abilities in living a life covered in increasingly sophisticated technology. According to Gao (2020), based on the development of computer technology, AI continues to expand and innovate. AI enables students to develop and enhance more mathematical skills and cognitive skills in learning. Popenici and Kerr (2017) the role of technology in higher learning is to enhance human thinking and augment the educational process. AI helps students in finding answers faster and easier. All information about the lesson can be easily accessed by students using this innovative intelligence software. In this generation, students are more inclined to learn and explore new knowledge on their own, so this powerful tool of AI can help students to explore more without waiting for an educator. Cope et al. (2020) indicate, however, the role of AI will never 'take over' the duty of educator in any way. Furthermore, the deployment of these technologies for teaching, learning, student assistance, and administration faces various hurdles (Popenici & Kerr, 2017).

近年来，人工智能（AI）在教育领域的应用日益普及，且受到广泛关注。在包括数学教育在内的多个领域，人工智能都是创造性与创新性思维的一次飞跃。现有研究显示，人工智能在不同场景下的研究已有诸多成果（Chen 等，2020a；Cope 等，2020；He 等，2019；Schiff，2021；Vaishya 等，2020）。人工智能的应用能够提升我们在日益复杂的技术环境中的生活能力。Gao（2020）指出，依托计算机技术的发展，人工智能持续拓展与创新。在学习过程中，人工智能能帮助学生培养并提升更多数学技能与认知能力。Popenici 与 Kerr（2017）认为，技术在高等教育中的作用是增强人类思维、辅助教育过程。人工智能可帮助学生更快速、更便捷地找到答案，学生通过这款创新性智能软件能轻松获取所有课程相关信息。当下，学生更倾向于自主学习和探索新知识，因此人工智能这一强大工具能让学生无需等待教师指导，自主开展更多探索。但 Cope 等（2020）指出，人工智能在任何情况下都不会"取代"教师的职责。此外，将这些技术应用于教学、学习、学生辅助及管理工作仍面临诸多障碍（Popenici & Kerr，2017）。

AI is a process that produces human intelligence through machines, especially computer systems. Specific applications of AI include expert systems, natural language processing, speech recognition and machine vision. With the advanced system, AI can perform human-like functions or duties through the level of difficulties that have been set up. A pedagogical agent (teachable agent) is a type of educational software that has human characteristics and/or appearances and are designed to support learners in online learning environments (Song, 2017). Besides, AI machines or systems can perform complex tasks that the human brain cannot do. AI has various perceptions in society. They felt that this AI was wrong because these machines were believed to take over human tasks. A portion of this public awareness refers to the anticipation of likely negative consequences related to the variety of applications of AI as a technology, known as the public perception of risk of AI or merely the risk perception of AI (Neri & Cozman, 2020). Recently, Voskoglou and Salem (2020) summarized the benefits of using AI or machine in teaching and learning. The current finding of studies discussed the use of robotics in learning and teaching mathematics (Casler-Failing, 2018; Harper et al., 2021; Lopez-Caudana et al., 2020). Learning programming and problem-solving (PS) at a young age is very challenging for them. Francis and Davis (2018), for example, also indicate that the learning process has become more interactive using the AI approach.

人工智能是通过机器（尤其是计算机系统）模拟人类智能的过程。其具体应用包括专家系统、自然语言处理、语音识别及机器视觉等。借助先进的系统，人工智能能够在预设难度范围内执行类人功能或任务。教学智能体（可教智能体）是一类具备人类特征和/或外观的教育软件，旨在为在线学习环境中的学习者提供支持（Song，2017）。此外，人工智能机器或系统还能完成人类大脑无法完成的复杂任务。社会各界对人工智能的看法不一，部分人认为人工智能存在问题，因为他们担心这些机器会取代人类的工作。公众对人工智能的认知中，有一部分是对该技术各类应用可能引发的负面后果的预期，这一认知被称为"人工智能公众风险感知"或简称为"人工智能风险感知"（Neri & Cozman，2020）。近期，Voskoglou 与 Salem（2020）总结了人工智能或机器在教与学中的应用优势。现有研究成果探讨了机器人技术在数学教与学中的应用（Casler-Failing，2018；Harper 等，2021；Lopez-Caudana 等，2020）。对青少年而言，学习编程与问题解决（PS）难度较大。例如，Francis 与 Davis（2018）也指出，采用人工智能方法后，学习过程的互动性更强。

Concerning existing systematic literature review (SLR) about exploring the potential of educational robotics in education settings, there are few SLR has been conducted (Chen et al., 2020a; Guan et al., 2020; Zawacki-Richter et al., 2019; Zhong & Xia, 2020), including mathematics education. Zhong and Xia (2020), for example, provides an exciting learning experience with robotics in mathematics learning. It focuses on empirical evidence towards the application of robotic in mathematics education. However, there are some limitations of a SLR conducted about AI in mathematics education. It is because previous studies have only focused on the use of AI in the fields of engineering, computer science and STEM. Therefore, using this opportunity, lots of research about the maximum use of AI in mathematics education can be done. The goal of this review is to add to the conversation by offering a complete overview of AI in mathematics teaching and learning for students at all levels of education. This SLR contributes on the impact of AI and the use of robotics or software as well as machines from AI in the teaching and learning of mathematics to students at all levels of education.

关于教育机器人在教育场景（包括数学教育）中应用潜力的现有系统文献综述（SLR）数量较少（Chen 等，2020a；Guan 等，2020；Zawacki-Richter 等，2019；Zhong & Xia，2020）。例如，Zhong 与 Xia（2020）的研究指出，机器人技术能为数学学习带来丰富的学习体验，且该研究聚焦于机器人在数学教育中应用的实证证据。然而，现有关于人工智能在数学教育中应用的系统文献综述存在一定局限性：以往研究仅关注人工智能在工程、计算机科学及 STEM（科学、技术、工程、数学）领域的应用。因此，借助此次研究契机，可开展大量关于人工智能在数学教育中最大化应用的研究。本综述旨在通过全面梳理人工智能在各教育阶段数学教与学中的应用，为相关研究对话补充内容。本系统文献综述的贡献在于，分析了人工智能对各教育阶段学生数学教与学的影响，以及人工智能领域的机器人技术、软件及机器在数学教与学中的应用情况。

Research Questions

研究问题

  1. What AI approach used in mathematics education for the samples studied?

    在所研究的样本中，人工智能应用于数学教育的方式有哪些？

  2. How is AI in education distributed in terms of the country?

    人工智能在教育领域的研究按国家/地区分布情况如何？

  3. How is AI in education distributed in terms of the research methodology?

    人工智能在教育领域的研究按研究方法分布情况如何？

  4. How are the AI in mathematics education distributed in terms of publication year?

    人工智能在数学教育领域的研究按发表年份分布情况如何？

  5. What themes are currently instigated?

    目前人工智能在数学教育领域的研究主题有哪些？

Theoretical Foundation

理论基础

Six years later, in 1956, Marvin Minsky and John McCarthy (a Stanford computer scientist) convened the eight-week-long Dartmouth Summer Research Project on Artificial Intelligence (DSRPAI), which formally originated the term AI. To date, there are diverse concept of AI in the current literature. The problem in defining AI, known as machine intelligence (Poole et al., 1998), is to define artificiality's parameters, or the manners in which computers differ from human intelligence (Cope et al., 2020). AI is clearly the confluence of computer, computer-related technology, machine, and information communication technology advancements and developments, allowing computers to perform activities that are close to or identical to those performed by humans (Chen et al., 2020b). Baker and Smith (2019) defined AI as computers that do cognitive functions, such as learning and PS, that are often associated with human brains. Data mining, natural language processing, machine learning, neural networks, and algorithms are some examples of technologies and methodologies in AI. However, AI in educational contexts may help with teaching, learning, and decision-making (Hwang et al., 2020).

六年后的 1956 年，马文·明斯基与约翰·麦卡锡（斯坦福大学计算机科学家）发起了为期八周的"达特茅斯人工智能夏季研究项目"（DSRPAI），"人工智能（AI）"这一术语也由此正式诞生。迄今为止，现有文献中对人工智能的定义各不相同。Poole 等（1998）指出，人工智能（即机器智能）的定义难题在于确定"人工性"的参数，或明确计算机与人类智能的差异之处（Cope 等，2020）。显然，人工智能是计算机、计算机相关技术、机器及信息通信技术发展与进步的融合产物，它能使计算机执行与人类相近或完全相同的任务（Chen 等，2020b）。Baker 与 Smith（2019）将人工智能定义为具备人类大脑常有的认知功能（如学习、问题解决（PS））的计算机。人工智能领域的技术与方法包括数据挖掘、自然语言处理、机器学习、神经网络及算法等。在教育场景中，人工智能可对教学、学习及决策提供支持（Hwang 等，2020）。

The basic mathematics teaching based on AI adapts and pays attention to the cultivation of students' personality development under the existing education conditions (Wu, 2021). In mathematics education in particular, the animation of figure and of mathematical representations, obtained by using the proper software, increases the student imagination and PS skills (Voskoglou & Salem, 2020). The incorporation of AI technologies into education settings enables computer-based learning system to play roles of intelligent tutor, tools or tutees as well as policy-making facilitators (Basel, 2021). Since its origin, the holy grail of AI has been to understand the nature of intelligence and to engineer systems that exhibit such intelligence through vision, language, emotion, motion, and reasoning. In such context, AI researchers have always looked for challenges to push forward the limit of what computers can do autonomously and to measure the level of "intelligence" achieved (Chesani et al., 2017). The concept of ICT has emerged as a technological convergence of electronics, software, and telecommunications infrastructure. Robotics is one of the expressions of technology whose application has extended to various life contexts. The importance of showing how technology allows for significant improvements in attention and motivation towards mathematics, which, in turn, allows for an improvement in training programs and teaching practices; thus, achieving a positive impact on student learning (Basel, 2020).

基于人工智能的基础数学教学能在现有教育条件下适应并关注学生个性发展的培养（Wu，2021）。尤其在数学教育中，通过合适的软件制作图形与数学表征动画，可提升学生的想象力与问题解决（PS）能力（Voskoglou & Salem，2020）。将人工智能技术融入教育场景，能使计算机学习系统扮演智能导师、工具、学习对象及决策辅助者等角色（Basel，2021）。自诞生以来，人工智能的核心目标便是理解智能的本质，并构建能通过视觉、语言、情感、动作及推理展现智能的系统。在此背景下，人工智能研究者始终在寻找挑战，以突破计算机自主任务处理的极限，并衡量其已达到的"智能"水平（Chesani 等，2017）。信息通信技术（ICT）是电子技术、软件技术与通信基础设施技术融合的产物。机器人技术是技术的一种表现形式，其应用已延伸至生活的多个领域。研究技术如何显著提升学生对数学的关注度与学习动机至关重要，这进而有助于完善培训方案与教学实践，最终对学生学习产生积极影响（Basel，2020）。

AI has promoted the social development, and has gradually been applied to the education and teaching with its innovation and epochal characters. Mathematics teacher educators and teachers should consider using innovative tools not typically seen in classrooms, such as robotics, in mathematics instruction as they work to support a focus on reasoning and sense making and make connections to children's community and cultural funds of knowledge (Harper et al., 2021). There is a positive predisposition towards the addition of robots in the learning and teaching of mathematic processes during the first years of school, even though teachers claim there is a struggle to incorporate robots in their lessons due to the high number of students and the reduced space in their classrooms (Seckel et al., 2021). One form of technology that has been shown to be beneficial to the learning of mathematics is LEGO robotics, namely EV3 Mindstorms. Select children and educators have had access to LEGO robotics for the past 20 years however, robotics has not experienced widespread use in the mathematics classroom, in a middle-school mathematics classroom working with LEGO robotics demonstrated that robotics could provide richer learning and engagement than traditional 'I do, we do, you do' instruction (Casler-Failing, 2021). Therefore, in the current work, we follow the idea of Ouyang and Jiao (2021) as conceptual framework namely AI-directed (learner-as-recipient), AI-supported (learner-as-collaborator), and AI-empowered (learner-as-leader). Figure 1 indicates conceptual framework in the current SLR.

人工智能凭借其创新性与时代性，推动了社会发展，并逐渐应用于教育教学领域。数学师范教育者与一线教师在开展数学教学时，应考虑使用课堂中不常见的创新工具（如机器人技术），以培养学生的推理与意义建构能力，并将教学内容与学生所在社区及文化知识体系相联系（Harper 等，2021）。尽管教师们表示，由于班级人数多、教室空间有限，难以将机器人融入课堂，但在小学低年级数学教与学过程中引入机器人的意愿仍较为积极（Seckel 等，2021）。乐高机器人（即 EV3 Mindstorms）是已被证实对数学学习有益的技术形式之一。过去 20 年间，部分儿童与教育工作者已接触过乐高机器人，但该技术尚未在数学课堂中广泛应用。一项在中学数学课堂中应用乐高机器人的研究表明，相较于传统的"教师演示---师生共同练习---学生独立练习"（I do, we do, you do）教学模式，机器人技术能提供更丰富的学习体验，提升学生参与度（Casler-Failing，2021）。因此，本研究采用 Ouyang 与 Jiao（2021）提出的概念框架，将人工智能在教育中的应用模式分为三类：人工智能主导型（学习者为接受者）、人工智能支持型（学习者为合作者）及人工智能赋能型（学习者为主导者）。图 1 展示了本系统文献综述的概念框架。

According to recent studies, AI has a positive impact on student accomplishment (Min et al., 2021), creative PS skills and computing thinking (Kim & Han, 2021), and learning attitude (Liao & Gu, 2022) from kindergarten to higher education settings (Ma & Siau, 2018). For example, the role and importance of wisdom classroom instruction can be understood by early childhood via AI context. Other possibilities in higher education settings involve the usage of AI assistants and AI instructors in the classroom. Chen et al. (2020b) also found the impact of AI toward education such as environments in the classroom, conceptual understanding, advanced deep learning algorithms' adoption and the integration of AI technologies with educational philosophies. However, applying AI to education appears to be a new challenge (Hwang et al., 2020; Pedro et al., 2019). Zawacki-Richter et al. (2019) found the low connection between AI and theoretical pedagogical views. Moreover, for educational scholars, not only computer programming abilities, but also ways for replicating the intellect of human specialists are hurdles in designing intelligent tutoring and adaptive learning education systems (Hwang et al., 2020). In brief, although AI has the potential to improve students' learning outcomes, it remains a problem for most educational academics, educators and practitioners.

近期研究表明，从幼儿园到高等教育阶段，人工智能对学生的学业成绩（Min 等，2021）、创造性问题解决能力与计算思维（Kim & Han，2021）及学习态度（Liao & Gu，2022）均有积极影响（Ma & Siau，2018）。例如，在人工智能场景下，幼儿能更好地理解智慧课堂教学的作用与重要性。在高等教育场景中，人工智能还可用于课堂中的智能助手与智能教师。Chen 等（2020b）还发现，人工智能对教育的影响体现在课堂环境、概念理解、先进深度学习算法的应用及人工智能技术与教育理念的融合等方面。然而，将人工智能应用于教育仍是一项新挑战（Hwang 等，2020；Pedro 等，2019）。Zawacki-Richter 等（2019）发现，人工智能与教学理论观点之间的关联性较弱。此外，对教育学者而言，设计智能辅导与自适应学习系统时，不仅需要具备计算机编程能力，还需掌握模拟人类专家智能的方法，而这两方面均为研究难点（Hwang 等，2020）。简言之，尽管人工智能具有提升学生学习成效的潜力，但对多数教育学者、教育工作者及实践者而言，其应用仍存在诸多问题。

METHODOLOGY

研究方法

Research Design

研究设计

We conducted a comprehensive SLR to answer our research questions. SLR is a method of gathering appropriate data on a certain topic that meets pre-determined eligibility criteria (Mengist et al., 2020). This study only looked at journal publications published between 2017 and 2021; no older articles were included. The preferred reporting items for systematic reviews and meta-analyses (PRISMA) approach analyzed the collected journal articles. PRISMA establishes a standardized, peer-reviewed methodology that employs guideline checklists to contribute to the revision process's quality assurance and replicability (Conde et al., 2020; Moher et al., 2015). PRISMA is based on four steps: identification, screening, eligibility, and inclusion. Identification is the first phase. These steps are detailed in the sub-sections that follow. This technique was chosen because it can assist us in synthesizing important journal publications. By following PRISMA guidelines, we could conduct an accurate search for best practices in AI in mathematics education. Figure 2 displays the PRISMA flow chart in this study adapted and modified from Moher et al. (2009).

为解答研究问题，本研究开展了全面的系统文献综述（SLR）。系统文献综述是一种针对特定主题，收集符合预设纳入标准的数据的研究方法（Mengist 等，2020）。本研究仅纳入 2017-2021 年间发表的期刊文章，不包含更早的文献。研究采用系统综述与元分析优先报告条目（PRISMA）对收集的期刊文章进行分析。PRISMA 构建了标准化、经同行评审的方法体系，通过指南清单保障综述过程的质量与可重复性（Conde 等，2020；Moher 等，2015）。PRISMA 包含四个步骤：文献识别、文献筛选、文献合格性判定及文献纳入。其中，文献识别是第一步。下文将详细阐述各步骤内容。选择该方法是因为它有助于整合重要的期刊文献；遵循 PRISMA 指南，可精准检索人工智能在数学教育中应用的最佳实践案例。图 2 展示了本研究的 PRISMA 流程图，该图改编自 Moher 等（2009）的研究并进行了调整。

Systematic Review Process

系统综述过程

Identification
文献识别

The search took place on ScienceDirect, Scopus, Springer Link, ProQuest, and EBSCO Host. We came up with two main search terms based on our fundamental research topics: AI and mathematics education. We compiled a list of synonyms and alternate terms based on the most popular search terms (Table 1 ).

文献检索在 ScienceDirect、Scopus、Springer Link、ProQuest 和 EBSCO Host 数据库中进行。基于核心研究主题，确定了两个主要检索词：人工智能（AI）与数学教育（mathematics education）。研究人员根据常用检索词整理了同义词及替代词列表（表 1）。

Table 1. Synonyms and alternatives terms for main search terms
表 1 主要检索词的同义词及替代词

Therefore, we expanded our search terms and strategies in exploring as many potentially relevant studies as possible. To search, we used a key search term that was created by combining the words discovered from (Table 1 ), as follows: TITLE-ABS-KEY. Through ProQuest, EBSCOHost, ScienceDirect, Springer, Scopus, 864 results were identified using search strategies, while additional papers (n=20) were identified from other sources. As a result, a total of 884 journal articles had been classified at this stage in the process.

因此，为尽可能检索到更多潜在相关研究，研究人员扩展了检索词与检索策略。检索时，采用"标题-摘要-关键词"（TITLE-ABS-KEY）检索方式，将表 1 中的词汇组合形成核心检索式。通过 ProQuest、EBSCOHost、ScienceDirect、Springer、Scopus 数据库的检索策略，共获得 864 条结果；从其他来源补充检索到 20 篇文献。至此，本阶段共筛选出 884 篇期刊文章。

Table 2. Inclusion and exclusion criteria
表 2 纳入与排除标准

Screening
文献筛选

As displayed in Figure 2 , the selection process followed the PRISMA principles (Moher et al., 2009). We used a variety of inclusion and exclusion criteria in this approach. There were no systematic review articles or books, book chapters, or conference proceedings included in the selection of literature. And, we were only concentrating on English-language journal articles made it less likely that complex or uncertain translations would be required. Then, we looked at articles published within the previous five years (between 2017 and 2021). There were no exclusions for specific countries or regions. In the final stage of the screening process, we focused their attention on publications that contained at least one reference to mathematics. Following the screening phase, 909 papers were identified as not meeting the study's criteria, while 55 articles were identified as duplicates. Additionally, there are just 845 articles remaining.

如图 2 所示，文献筛选过程遵循 PRISMA 原则（Moher 等，2009），并采用多种纳入与排除标准。筛选过程中，不纳入系统综述文章、书籍、书籍章节及会议论文集；仅关注英文期刊文章，以减少复杂或不确定翻译带来的影响；纳入近五年（2017-2021 年）发表的文献，且不限制特定国家或地区；筛选最终阶段，仅保留至少提及数学领域的文献。筛选后，共判定 909 篇文献不符合研究标准，55 篇为重复文献，剩余 845 篇文献进入下一阶段。

Eligibility
文献合格性判定

As illustrated in Figure 2 , the eligibility phase resulted from incomplete articles. First, journal articles that did not meet the criteria for best practices in AI in mathematics were rejected. Then, to ensure that all 845 articles fit the study's selection criteria and objectives, each article's title, abstract, methodology, results, and discussion were thoroughly reviewed. At this point, 834 articles have been rejected because they do not fully explain AI in mathematics education or do not clearly explain and review the findings data in the study findings section. As a result, 20 articles were selected for publication in the final stage of the review process (see Figure 2).

如图 2 所示，文献合格性判定阶段需排除内容不完整的文献。首先，剔除不符合人工智能在数学领域最佳实践标准的期刊文章；随后，为确保 845 篇文献均符合研究的筛选标准与目标，对每篇文献的标题、摘要、研究方法、研究结果及讨论部分进行全面审查。此阶段共剔除 834 篇文献，原因包括未充分阐述人工智能在数学教育中的应用，或未在研究结果部分清晰解释与分析研究数据。最终，20 篇文献被纳入综述的最终分析阶段（见图 2）。

Inclusion and exclusion criteria
纳入与排除标准

After gathering all of the results from all identified sources, we used the selection criteria such as timeline, document type, language, and subject area to filter out the articles that were not relevant to our research. When selecting pieces for inclusion and exclusion, the inclusion and exclusion criteria must be clearly defined to ensure that the studies selected are relevant to the primary research purpose. Table 2 shows the inclusion and exclusion criteria for this review study and the findings of the research. It was determined that 20 articles were relevant, and the full-text articles of these publications were obtained.

从所有已识别来源收集文献后，研究人员根据时间范围、文献类型、语言及主题领域等筛选标准，剔除与研究无关的文献。为确保纳入的研究符合核心研究目的，需明确定义纳入与排除标准。表 2 列出了本综述的纳入与排除标准及研究结果。最终确定 20 篇相关文献，并获取了这些文献的全文。

FINDINGS

研究结果

A total number of AI studies (n=20) are analyzed, published between 2017 and 2021. This section discusses the following research questions:

本研究共分析了 2017-2021 年间发表的 20 项人工智能相关研究（n=20）。本节将围绕以下研究问题展开讨论：

  1. What AI approach used in mathematics education for the samples studied?

    在所研究的样本中，人工智能应用于数学教育的方式有哪些？

  2. How is AI in education distributed in terms of the country?

    人工智能在教育领域的研究按国家/地区分布情况如何？

  3. How is AI in education distributed in terms of the research methodology?

    人工智能在教育领域的研究按研究方法分布情况如何？

  4. How are the AI in mathematics education distributed in terms of publication year?

    人工智能在数学教育领域的研究按发表年份分布情况如何？

  5. What themes are currently instigated?

    目前人工智能在数学教育领域的研究主题有哪些？

AI Approach Used in Mathematics Education for the Samples Studied

所研究样本中人工智能应用于数学教育的方式

The first research question was concerned with the AI approach used in mathematics education for the samples studied. The AI approach used in mathematics education for the samples studied were through robotics, systems, tools, teachable agent, autonomous agent, and a comprehensive approach. As seen in Figure 3 , the majority of AI approach used for the samples studied were through robotics (45%, n=9) (Casler-Failing, 2018, 2021; Forsstrom & Afdal, 2019; Francis & Davis, 2018; Harper et al, 2021; Lopez-Caudana et al., 2020; Rico-Bautista et al, 2019; Saez-Lopez, 2019; Seckel et al., 2021) and followed by systems (15%, n=5) (Moreno-Esteva et al., 2018; Mills, 2021; Rojano & Garcia-Campos, 2017; Saha et al., 2020; Zakaria et al., 2021). There were two researches that practiced teachable agent's (Gulz et al., 2020; Song, 2017) and also two research mathematical tools' (Dunzhin & Gustafsson, 2018; Salas-Rueda et al., 2020) approach of AI in mathematics education. The AI approach through an autonomous agent (Chesani et al., 2017) and comprehensive approach (Wu, 2021) each only have one research discussion. In addition, programming also was introduced alongside robotics with the aim of gaining the advantages that arise from manipulation and experimentation in these types of activities; such benefits include developing logical thinking in algorithms, sequences and different computational concepts (Sáez‐López et al., 2019) because computer programming aligns closely with concepts and structures in mathematics (Francis & Davis, 2018).

第一个研究问题聚焦于所研究样本中人工智能应用于数学教育的方式。结果显示，这些方式包括机器人技术、系统、工具、可教智能体、自主智能体及综合方法。由图 3 可知，样本中最主要的人工智能应用方式是机器人技术（45%，n=9）（Casler-Failing，2018，2021；Forsstrom & Afdal，2019；Francis & Davis，2018；Harper 等，2021；Lopez-Caudana 等，2020；Rico-Bautista 等，2019；Saez-Lopez，2019；Seckel 等，2021）；其次是系统（15%，n=5）（Moreno-Esteva 等，2018；Mills，2021；Rojano & Garcia-Campos，2017；Saha 等，2020；Zakaria 等，2021）。采用可教智能体方式的研究有 2 项（Gulz 等，2020；Song，2017），采用数学工具方式的研究也有 2 项（Dunzhin & Gustafsson，2018；Salas-Rueda 等，2020）；采用自主智能体（Chesani 等，2017）与综合方法（Wu，2021）的研究各 1 项。此外，研究中还将编程与机器人技术结合应用，目的是利用这类活动中操作与实验带来的优势------包括培养算法、序列及各类计算概念的逻辑思维（Sáez‐López 等，2019），因为计算机编程与数学中的概念及结构高度契合（Francis & Davis，2018）。

The Distribution of Research Studies in Term of Country

人工智能教育研究的国家/地区分布

The geographic distribution of the authors was the subject of the second research question. Figure 4 shows the categorization of the selected studies according to the countries they were carried out. Even though our systematic review only included publications published in English, the research was carried out in various cultural contexts throughout the world. It can be shown that the majority of the collected studies (n=3) were carried out in the USA (Casler-Failing, 2018; Harper et al, 2021; Mills, 2021) and Mexico (Lopez-Caudana et al., 2020; Rojano & Garcia-Campos, 2017; Salas-Rueda et al., 2020). There are two articles in each of the following categories: studies conducted Spain (Sáez‐López et al., 2019; Seckel et al., 2021) and Canada (Chesani et al., 2017; Francis & Davis, 2018).

第二个研究问题关注研究作者的地理分布。图 4 按研究开展的国家/地区对纳入研究进行了分类。尽管本系统综述仅纳入英文文献，但这些研究来自全球不同文化背景的国家/地区。结果显示，多数纳入研究（n=3）在美国（Casler-Failing，2018；Harper 等，2021；Mills，2021）和墨西哥（Lopez-Caudana 等，2020；Rojano & Garcia-Campos，2017；Salas-Rueda 等，2020）开展。西班牙（Sáez‐López 等，2019；Seckel 等，2021）和加拿大（Chesani 等，2017；Francis & Davis，2018）各有 2 项研究。

In contrast, AI in mathematics education is the least frequently discussed among scholars in various countries, such as United Kingdom (Casler-Failing, 2021), Turkey (Song, 2017), Sweden (Gulz et al., 2020), Singapore (Duzhin & Gustafsson, 2018), Norway (Forsström & Afdal, 2019), Malaysia (Zakaria et al., 2021), Colombia (Rico-Bautista et al., 2019), China (Wu, 2021), Bangladesh (Saha et al., 2020), and Australia (Moreno-Esteva et al., 2018). As a result of this finding, it is possible that scholars in the USA and Mexico are becoming increasingly interested in exploring the topic of AI in mathematics teaching. Therefore, additional research into this topic is still required in other countries, among other things.

相比之下，英国（Casler-Failing，2021）、土耳其（Song，2017）、瑞典（Gulz 等，2020）、新加坡（Duzhin & Gustafsson，2018）、挪威（Forsström & Afdal，2019）、马来西亚（Zakaria 等，2021）、哥伦比亚（Rico-Bautista 等，2019）、中国（Wu，2021）、孟加拉国（Saha 等，2020）和澳大利亚（Moreno-Esteva 等，2018）等国家的学者对"人工智能在数学教育中应用"这一主题的探讨较少。这一结果表明，美国和墨西哥的学者可能对人工智能在数学教学中的应用这一主题的探索兴趣日益浓厚。因此，其他国家仍需针对该主题开展更多研究。

The Distribution of AI in Term of Research Methodology

人工智能教育研究的研究方法分布

The third research question was about research methodologies. Figure 5 illustrates the distribution of research methodologies used in the reviewed studies. According to the study's findings, only three research method approaches were used in this reviewed study: qualitative, quantitative, and mixed methods. The analysis revealed that most of the studies reviewed (40%, n=8) used quantitative research methods (Duzhin & Gustafsson, 2017; Gulz et al., 2020; Mills, 2021; Moreno-Esteva et al., 2018; Rico-Bautista et al., 2019; Rojano & Garcia-Campos, 2017; Saez-Lopez et al., 2019; Zakaria et al, 2021). Subsequently (35%, n=7) of the reviewed studies used the qualitative research method approach in the study (Casler-Failing, 2018, 2021; Francis & Davis, 2018; Forsstrom & Afdal, 2019; Harper et al, 2021; Song, 2017; Wu, 2021), while the remaining (25%, n=5) used the mixed method approach (Caudana et al., 2020; Chesani et al., 2017; Saha et al., 2020; Salas-Rueda et al., 2020; Seckel et al., 2021). However, there are multiple of data collection method has been used in certain reviewed studies. The various data collection methods in the findings of this study show that the researchers use a variety of data collection methods to ensure that the study does not have high errors on the data obtained and the information obtained is appropriate according to the topic of study.

第三个研究问题聚焦于研究方法。图 5 展示了纳入综述研究的方法分布情况。结果显示，纳入研究仅采用三种研究方法：定性研究法、定量研究法及混合研究法。分析表明，大部分纳入研究（40%，n=8）采用定量研究法（Duzhin & Gustafsson，2017；Gulz 等，2020；Mills，2021；Moreno-Esteva 等，2018；Rico-Bautista 等，2019；Rojano & Garcia-Campos，2017；Saez-Lopez 等，2019；Zakaria 等，2021）；35%（n=7）的研究采用定性研究法（Casler-Failing，2018，2021；Francis & Davis，2018；Forsstrom & Afdal，2019；Harper 等，2021；Song，2017；Wu，2021）；剩余 25%（n=5）的研究采用混合研究法（Caudana 等，2020；Chesani 等，2017；Saha 等，2020；Salas-Rueda 等，2020；Seckel 等，2021）。部分纳入研究采用了多种数据收集方法，这表明研究人员通过多样化的数据收集方式，确保研究数据误差较低，且获取的信息与研究主题高度相关。

The Distribution of AI in Term of Publication Year

人工智能数学教育研究的发表年份分布

The fourth research question was concerned with distribution AI in term of publication year (Figure 6 ). In 2021 the percentage number of articles published on AI is the highest compared to other years (30%) (Casler-Failing, 2021; Harper et al., 2021; Mills, 2021; Seckel et al., 2021; Wu, 2021; Zakaria et al., 2021). This was followed by percentage in 2020 (20%) (Gulz et al., 2020; Lopez-Caudana et al., 2020; Saha et al., 2020; Salas-Rueda et al., 2020), while in 2019 has the same number of percentage of articles published as in 2020 (20%) (Forsström & Afdal, 2019; Rico-Bautista et. al., 2019; Sáez‐López et al., 2019). The percentage of articles published in 2018 began to decline (15%) (Duzhin & Gustafsson, 2018; Francis & Davis, 2018; Moreno-Esteva et al., 2018) and the percentage remained in 2017 (15%) (Chesani et al., 2017; Rojano & Garcia-Campos, 2017; Song, 2017).

第四个研究问题关注人工智能研究按发表年份的分布（图 6）。2021 年发表的人工智能相关文章占比最高（30%）（Casler-Failing，2021；Harper 等，2021；Mills，2021；Seckel 等，2021；Wu，2021；Zakaria 等，2021）；其次是 2020 年（20%）（Gulz 等，2020；Lopez-Caudana 等，2020；Saha 等，2020；Salas-Rueda 等，2020）；2019 年发表文章占比与 2020 年相同（20%）（Forsström & Afdal，2019；Rico-Bautista 等，2019；Sáez‐López 等，2019）；2018 年发表文章占比开始下降（15%）（Duzhin & Gustafsson，2018；Francis & Davis，2018；Moreno-Esteva 等，2018）；2017 年发表文章占比同样为 15%（Chesani 等，2017；Rojano & Garcia-Campos，2017；Song，2017）。

The Distribution of Themes Instigated in the Research

人工智能数学教育研究的主题分布

The fifth research question was concerned with the themes are instigated in the previous studies. The types of themes for AI in mathematics education were categorized into advantages and disadvantages, conceptual understanding, factors, role, idea suggestion, strategies, and effectiveness. The data of the themes are collected in order to explore how AI can impact and enhance the performance of mathematics students along their teaching and learning process. As seen in Figure 7 , the most studied theme (60%, n=12) was about effectiveness (Casler-Failing, 2018, 2021; Duzhin & Gustafsson, 2018; Francis & Davis, 2018; Gulz et al, 2020; Lopez-Caudana et al., 2020; Moreno-Esteva et al., 2018; Rico-Bautista, et al., 2019; Sáez-López et al., 2019; Saha et al., 2020; Wu, 2021; Zakaria et al., 2021). Two of the research subjects (10%) were about strategies (Forsström & Afdal, 2019; Harper et al., 2021) and three of the research subjects (15%) were about idea suggestion (Chesani et al., 2017; Salas-Rueda et al., 2020; Song, 2017). Meanwhile, factor (Mills, 2021), role (Rojano & Garcia-Campos, 2017), and conceptual understanding (Seckel et al., 2021) have one for each of them (5% for each). Additional research of AI other than effectiveness should be done more.

第五个研究问题关注以往研究中涉及的主题。人工智能在数学教育中的研究主题可分为优势与劣势、概念理解、影响因素、作用、建议、策略及有效性。收集这些主题相关数据的目的是探索人工智能如何在教与学过程中影响并提升数学专业学生的学习成效。由图 7 可知，研究最多的主题是"有效性"（60%，n=12）（Casler-Failing，2018，2021；Duzhin & Gustafsson，2018；Francis & Davis，2018；Gulz 等，2020；Lopez-Caudana 等，2020；Moreno-Esteva 等，2018；Rico-Bautista 等，2019；Sáez-López 等，2019；Saha 等，2020；Wu，2021；Zakaria 等，2021）；2 项研究（10%）聚焦"策略"主题（Forsström & Afdal，2019；Harper 等，2021）；3 项研究（15%）聚焦"建议"主题（Chesani 等，2017；Salas-Rueda 等，2020；Song，2017）；"影响因素"（Mills，2021）、"作用"（Rojano & Garcia-Campos，2017）及"概念理解"（Seckel 等，2021）主题各有 1 项研究（各占 5%）。未来需更多开展除"有效性"之外的其他人工智能相关主题研究。

DISCUSSION

讨论

Our finding indicated that robotics was the most popular approach of AI in mathematics education among other approaches which were systems, tools, teachable agent, autonomous agent and a comprehensive approach. The result was in line with Zhong and Xia (2020) who conducted a systematic review that stated that there is a potential for future research and the rapid development of evidence-based research on teaching and learning mathematical content knowledge through robotics. With nine papers discussing robotics in mathematics education, it happened to give more of a positive impact than the other way around just like Seckel et. al (2021) concluded from their research that primary school teachers have conceptions that entail positive dispositions about the introduction of robots for teaching mathematics.

研究结果表明，在系统、工具、可教智能体、自主智能体及综合方法等人工智能应用方式中，机器人技术是数学教育中最常用的方式。这一结果与 Zhong 和 Xia（2020）的系统综述结论一致，该综述指出，通过机器人技术开展数学学科知识教与学的实证研究具有快速发展潜力，未来仍有研究空间。9 篇文献探讨了机器人技术在数学教育中的应用，且均表明其带来的积极影响大于消极影响------正如 Seckel 等（2021）的研究结论所示，小学教师对将机器人引入数学教学持积极态度。

Based on our findings, systems and tools were the second approaches of AI in mathematics education. There are many systems of AI used in mathematics education but Duzhin and Gustafsson (2018) used R and MATLAB software on their research. Based on our finding, tutoring system and integrated system (micro-intelligence support) were also one of the systems that has been implemented in mathematics education. An intelligent tutoring system (Hasanein & Abu-Naser, 2018) is a computer program designed to simulate the behavior and guidance of a human teacher while an integrated system here refers to the integration of a microworld system with the intelligent support system. This integrated system was still a new approach of AI and has limitations. As seen in Rojano and Garcia-Campos (2017) research, the integrated system responds differently to different learner approaches (algebra-like (formulae) or numerical) and also that the system has limitations in light of the fact that at times the answers given by students are not included in the system's repertoire.

研究结果显示，系统与工具是数学教育中第二常用的人工智能应用方式。数学教育中应用的人工智能系统种类较多，例如 Duzhin 与 Gustafsson（2018）的研究采用了 R 软件与 MATLAB 软件。此外，辅导系统与集成系统（微智能支持）也是数学教育中已应用的人工智能系统类型。智能辅导系统（Hasanein & Abu-Naser，2018）是一种模拟人类教师行为与指导过程的计算机程序；而本文中的"集成系统"指微世界系统与智能支持系统的融合。这种集成系统仍是人工智能领域的新型应用方式，且存在局限性。如 Rojano 与 Garcia-Campos（2017）的研究所示，集成系统对不同学习方式（代数式（公式）或数值式）的学习者会做出不同反应，且该系统存在局限性------有时无法识别学生给出的答案（即学生答案未纳入系统预设答案库）。

On the other hand, the comprehensive approach of AI in mathematics education is believed to affect the learning process positively just like the result of Wu (2021) research which concludes that the introduction of AI-assisted teaching has an extremely effective effect on basic mathematics education and teaching. This statement is in line with Zawacki-Richter et al. (2019) on their systematic review which concludes that even though AI has the potential to advance the capabilities of learning analytics, but on other hand, such systems require huge amounts of data, including confidential information about students and faculty, which raises serious issues of privacy and data protection. Therefore, researchers found out that robotics was the most used approach of AI in mathematics education. Hence, future research should consider focusing on the implementation of robotics in mathematics education.

另一方面，人工智能在数学教育中的综合应用方式被认为对学习过程具有积极影响------正如 Wu（2021）的研究结论所示，引入人工智能辅助教学对基础数学教育教学具有显著成效。这一观点与 Zawacki-Richter 等（2019）的系统综述结论一致，该综述指出，尽管人工智能具有提升学习分析能力的潜力，但这类系统需要大量数据支持（包括师生的机密信息），这引发了严重的隐私与数据保护问题。因此，研究人员发现机器人技术是数学教育中最常用的人工智能应用方式，未来研究应重点关注机器人技术在数学教育中的应用实践。

The majority of researchers in evaluated studies were from the USA and Mexico; and only one author came from as United Kingdom, Turkey, Sweden, Singapore, Norway, Malaysia, Colombia, China, Bangladesh, and Australia (see Casler-Failing, 2018; Harper et al., 2021; Mills, 2021). Several countries integrate programming into their mathematics curricula, thereby making robotics an interesting aspect of mathematics education (Forsström & Afdal, 2019). On the one hand, we must analyze the cultural contexts of studies examining AI concerning mathematics education, and there are several prospects for future intercultural study on AI concerning mathematics education. This research may help to explain why researchers in the USA and Mexico were eager to improve mathematics students' performance throughout the teaching and learning process.

纳入研究的作者主要来自美国和墨西哥；英国、土耳其、瑞典、新加坡、挪威、马来西亚、哥伦比亚、中国、孟加拉国和澳大利亚各有 1 位作者参与相关研究（参见 Casler-Failing，2018；Harper 等，2021；Mills，2021）。部分国家将编程纳入数学课程，这使得机器人技术成为数学教育中一个值得关注的方向（Forsström & Afdal，2019）。一方面，我们需分析人工智能在数学教育中应用研究的文化背景，未来在该领域开展跨文化研究具有较大前景；这类研究或有助于解释为何美国和墨西哥的研究人员迫切希望通过教与学过程提升数学专业学生的学习成效。

Students can reach this goal with the help of AI, which can improve the educational process. AI can have a substantial impact on students' educational experiences by making relevant courses more accessible, boosting teacher-student communication, and allowing students more time to pursue interests outside of school. According to Wu (2021), the research structure found that through the teaching of AI, students' mathematics scores are about 30% higher than the traditional teaching methods, the sense of cooperation between students' reaches. As countries build national AI strategies, the importance of mathematics education becomes apparent. According to Forsström and Afdal (2019), education systems in various countries are integrating the teaching of programming into their curricula in various ways, both by including general information and communication technology courses and by integrating programming into individual subjects. In addition, the results indicated a lack of variation among countries, particularly in the Asian perspective, about how AI might affect and increase mathematics students' performance, particularly in the teaching and learning processes. As a result, this problem has to be researched further in different countries, emphasizing studies exploring AI in mathematics education.

在人工智能的帮助下，学生能够实现这一目标（提升学习成效），同时人工智能还能优化教育过程。通过增加相关课程的可及性、促进师生沟通、为学生提供更多课外兴趣探索时间，人工智能可对学生的教育体验产生重大影响。Wu（2021）的研究结构显示，采用人工智能辅助教学后，学生的数学成绩比传统教学方法高出约 30%，且学生间的合作意识有所提升。随着各国制定国家人工智能战略，数学教育的重要性日益凸显。Forsström 与 Afdal（2019）指出，各国教育体系正通过多种方式将编程教学融入课程------既包括开设通用信息通信技术课程，也包括将编程融入各学科教学。此外，研究结果表明，各国（尤其是亚洲国家）在"人工智能如何影响并提升数学专业学生（尤其是在教与学过程中）的学习成效"这一问题上的研究存在不足。因此，不同国家需进一步开展相关研究，重点探索人工智能在数学教育中的应用。

A research methodology is a specific process or approach for identifying, selecting, processing, and analyzing information about a specific topic. This study employs three research methods: quantitative, qualitative, and mixed methods. Our results indicate that the use of quantitative and qualitative research methods is approximately equal when the difference between the number of uses of quantitative research methods is eight compared to the number of uses of qualitative research methods is seven and the use of mixed methods is the least which is five. Most researcher in reviewed study choose to used quantitative method approach as it places an emphasis on the objective measurement and analysis of statistical, mathematical, or numerical data gathered through questionnaires and surveys for the used AI in mathematics education (Duzhin & Gustafsson, 2017; Gulz et al., 2020; Mills, 2021; Moreno-Esteva et al., 2018; Rico-Bautista et al., 2019; Rojano & Garcia-Campos, 2017; Sáez‐López et al., 2019; Zakaria et al., 2021). Next, qualitative research entails gathering and analyzing non-numerical data in order to better understand concepts, opinions, or experiences. It is providing flexible approach as its suitable for the data collected in the study about the observation and behavior. For example, to see the instruction of LEGO robotics technology (Casler-Failing, 2021), the effects of incorporating LEGO robotics into a seventh-grade mathematics curriculum (Casler-Failing, 2018), and etc.

研究方法是用于识别、选择、处理和分析特定主题相关信息的特定流程或方式。本研究涉及三种研究方法：定量研究法、定性研究法和混合研究法。结果显示，定量研究法（n=8）与定性研究法（n=7）的使用频率相近，混合研究法使用频率最低（n=5）。纳入综述的研究中，多数研究者选择定量研究法，原因是该方法强调通过问卷和调查收集统计、数学或数值数据，并对其进行客观测量与分析，适用于研究人工智能在数学教育中的应用（Duzhin & Gustafsson，2017；Gulz 等，2020；Mills，2021；Moreno-Esteva 等，2018；Rico-Bautista 等，2019；Rojano & Garcia-Campos，2017；Sáez‐López 等，2019；Zakaria 等，2021）。其次，定性研究法通过收集和分析非数值数据，帮助研究者更好地理解概念、观点或经验；该方法灵活性强，适用于收集观察与行为相关数据。例如，研究乐高机器人技术的教学应用（Casler-Failing，2021）、将乐高机器人融入七年级数学课程的效果（Casler-Failing，2018）等。

When researchers conduct a mixed method study, they collect and analyze both quantitative and qualitative data in the same study. The methods are useful for understanding conflicts between quantitative and qualitative results, and they enhance the problem by comparing data results, such as WGODS, which improves the learning system on quantitative and qualitative data through a pleasant, attractive, simple, easy, and useful web interface (Salas-Rueda et al., 2020). Not only that, mixed method research will foster scholarly interaction and flexibility as the researcher can expand the distribution of data on AI in education. The reviewed studies used a variety of data collection methods, and some of them utilized more than one data collection approach, which aided in the growth of a reliable data collection system which are analysis, questionnaires, behavior observation, survey, case study and etc. For example a correlational predictive design was applied to assess the data of a purposive sample of 265 struggling students at the study site and multiple regression analysis to investigate the predictability of these variables (Mills, 2021), a quasi-experimental design, descriptive analysis and participant observation were applied across various dimensions to 93 sixth-grade students in four primary education schools (Sáez‐López et al., 2019) and comparing the control and treatment groups for all scenarios through examinations, direct observations, and testimonials (Caudana et al., 2020). Hence, the data collection for AI become diverged.

采用混合研究法时，研究者需在同一项研究中同时收集和分析定量数据与定性数据。该方法有助于理解定量结果与定性结果之间的矛盾，并通过对比数据结果深化对问题的认识。例如，WGODS（网络游戏式描述性统计学习系统）通过友好、有吸引力、简洁易用且实用的网页界面，结合定量与定性数据优化学习系统（Salas-Rueda 等，2020）。此外，混合研究法能促进学术交流并提升灵活性，研究者可通过该方法扩大人工智能教育相关数据的分布范围。纳入综述的研究采用了多种数据收集方法，部分研究甚至采用多种数据收集方式，这有助于构建可靠的数据收集体系（包括文献分析、问卷调查、行为观察、调查研究、案例研究等）。例如，Mills（2021）采用相关预测设计评估研究站点中 265 名学习困难学生的样本数据，并通过多元回归分析探究变量的预测性；Sáez‐López 等（2019）采用准实验设计、描述性分析和参与式观察，从多个维度对 4 所小学的 93 名六年级学生进行研究；Caudana 等（2020）通过考试、直接观察和访谈，对比所有场景下控制组与实验组的差异。因此，人工智能相关研究的数据收集方式呈现多样化特征。

Our findings on AI in education in terms of years of publication indicate that 2021 have the highest percentage of publications on AI over other years. In 2021, most articles are published by authors from Europe. Most authors state about AI in assisting students and teachers in further improving the quality and effectiveness in learning and teaching. According to Lopez-Caudana et al. (2020), which focused the use of robots in mathematics learning which studies evaluated how much attention the students paid to the class, if they retained more information with the help of the robot, and results were compared with a class without robotic help. The more prepared and comfortable to use the robot, the better they can plan and adapt their strategy, based on the feedback and outcomes that were provided by the students. This allows for the flexibility needed to customize learning strategies to each student and makes them responsible for their own learning. Most authors will publish articles on AI in areas of learning other than mathematics learning, which is why the number of articles published per year is not so much per year.

关于人工智能教育研究的发表年份分布，结果显示 2021 年的相关文献占比高于其他年份。2021 年发表的多数文章作者来自欧洲，且大部分作者关注人工智能在辅助师生提升教与学质量及成效方面的作用。Lopez-Caudana 等（2020）的研究聚焦机器人在数学学习中的应用，评估了学生的课堂注意力、借助机器人是否能记住更多知识，并将结果与未使用机器人的班级进行对比。研究显示，教师对机器人的准备越充分、使用越熟练，就越能根据学生的反馈和学习结果制定与调整教学策略；这使得教师能够灵活地为每位学生定制学习策略，并培养学生的自主学习责任感。多数作者会发表人工智能在非数学学习领域应用的文章，这也是每年人工智能数学教育相关发表文章数量不多的原因之一。

Our findings indicated that 12 reviewed papers used the themes of effectiveness. These findings show that most of the previous studies were interested to find out how AI can affect mathematics educations. AI is a sophisticated system that has many beneficial effects on our life especially mathematics education. Using Robotics to teach mathematics to seventh graders or as a way to go deeper into mathematics topics, it is possible to identify many interesting situations such as; The use of LEGO® education prototypes opened an interaction of the students and a way to develop creativity and problem solving and mathematical thinking (Rico-Bautista et al., 2019). The importance of showing how technology allows for significant improvements in attention and motivation towards mathematics, which, in turn, allows for an improvement in training programs and teaching practices; thus, achieving a positive impact on student learning (Lopez-Caudana et al., 2020).

研究结果显示，12 篇纳入综述的文献以"有效性"为研究主题。这表明以往多数研究关注人工智能对数学教育的影响。人工智能是一个复杂的系统，对我们的生活（尤其是数学教育）具有诸多积极作用。例如，在七年级数学教学中使用机器人技术，或通过机器人技术深入讲解数学主题，可发现许多有意义的现象：使用乐高教育原型产品能促进学生互动，培养学生的创造力、问题解决能力和数学思维（Rico-Bautista 等，2019）；研究技术如何显著提升学生对数学的关注度与学习动机至关重要，这进而有助于完善培训方案与教学实践，最终对学生学习产生积极影响（Lopez-Caudana 等，2020）。

Studies on the effectiveness are very important to be conducted. If the majority of studies show unsatisfactory results, then the use of AI may not be fully effective. So, it is a good way to do more research on effectiveness. Using AI in mathematics education will enhance creative and critical thinking skills for students as well as educators. The positive effects of incorporating robotics in mathematics classes as a means to promote student understanding and skill development (Casler-Failing, 2018). However, the strategies at the beginning to use AI need to be emphasized. The robotic solution will never result in significant learning improvement unless accompanied by the right strategy (Lopez-Caudana et al., 2020).

开展"有效性"相关研究具有重要意义：若多数研究显示人工智能应用效果不佳，则表明其应用可能尚未充分发挥作用。因此，进一步开展"有效性"研究十分必要。在数学教育中应用人工智能，能提升学生与教育工作者的创造性思维和批判性思维能力。例如，将机器人技术融入数学课堂对促进学生理解知识和发展技能具有积极作用（Casler-Failing，2018）。然而，需重视人工智能应用初期的策略制定------Lopez-Caudana 等（2020）指出，若缺乏合理策略，仅依靠机器人技术无法显著提升学习效果。

Our findings also indicated that two of reviewed papers were focused on the strategies of using AI, followed by three of reviewed papers that used the theme of idea suggestion. The good effectiveness of AI can be observed through the use of good and appropriate strategies. Mathematics educators and teachers should consider using innovative tools not typically seen in classrooms, such as robotics, in mathematics instruction as they work to support a focus on reasoning and sense-making and make connections to children's community and cultural funds of knowledge (Harper et al., 2021). Mathematics educators need to explore more about AI to apply technologies during the classes. Teachers' programming skill is what needs to be considered in mathematics teacher education and teachers' further education (Forsström & Afdal, 2020). Therefore, teachers need to know the strategies to use AI during the teaching and learning process.

研究结果还显示，2 篇纳入综述的文献聚焦"人工智能应用策略"，3 篇文献聚焦"建议"主题。合理且恰当的策略是人工智能发挥良好效果的关键。Harper 等（2021）指出，数学师范教育者与一线教师在开展数学教学时，应考虑使用课堂中不常见的创新工具（如机器人技术），以培养学生的推理与意义建构能力，并将教学内容与学生所在社区及文化知识体系相联系。数学教育工作者需深入探索人工智能，以便在课堂中应用相关技术；在数学教师培养与继续教育中，需重视教师编程技能的提升（Forsström & Afdal，2020）。因此，教师需掌握在教与学过程中应用人工智能的策略。

Other than that, our findings also indicated the factors, role, and conceptual understanding of AI. AI has its own role in mathematics education. Traditional teaching and learning method such as inductive learning and discussion is important to enhance one's knowledge and skills. However, the use of AI during the teaching and learning process will make the learning journey more interactive. Therefore, students will be more understanding and enjoy the class. The factor of using AI during the class is to make educators and students more creative and innovative. These skills very useful in the future because life is now heading towards a sophisticated technological life. Educators need to have a good conceptual understanding of AI. So that, it will be easy to deliver the knowledge to the students. Among the global results, it can be concluded that the participants have conceptions that entails positive dispositions about the introduction of robots for teaching mathematics (Seckel et al., 2021).

此外，研究结果还涉及人工智能的"影响因素""作用"及"概念理解"主题。人工智能在数学教育中具有独特作用：归纳学习 and discussion, as traditional teaching and learning methods, are crucial for enhancing knowledge and skills. However, integrating AI into the teaching and learning process makes the learning experience more interactive, helping students better understand content and enjoy classes. The key factor driving AI adoption in classrooms is to foster greater creativity and innovation among both educators and students---skills that will be invaluable in the future, as society moves toward an increasingly technology-driven lifestyle. Educators must first develop a solid conceptual understanding of AI to effectively impart related knowledge to students. From a global perspective, Seckel et al. (2021) concluded that participants (e.g., teachers) generally hold positive attitudes toward introducing robotics into mathematics teaching.

CONCLUSION

结论

AI is a simulation of humans' intelligence modelled in a machine and programmed to think like humans. In other words, AI is a computer system that can do jobs that generally require human resources or human intelligence to complete the job. AI needs experience and data so that its intelligence can run smoothly. Humans do not always order the process of learning AI, but AI will learn by itself based on the experience of AI when used by humans. There are several advantages in the use of AI in mathematics learning, among which is that students become more critical and responsible in facing daily solutions and a better understanding of fundamental problems of geometry, mathematics, and statistics. In addition, students also learn about and improve interpersonal abilities and better social interaction; it also allows effective learning to create a better environment to enhance the acquisition of mathematical concepts. Throughout this paper, we provide the findings of an analysis of 20 research publications published between 2017 and 2021, which explored how AI might impact and enhance the performance of mathematics students throughout the teaching and learning process. AI can be implemented in mathematics education through various approaches: systems, teachable agents, autonomous agents, machine learning models, digital technology devices, and comprehensive approaches. However, it seems that robotics was the most often used for mathematics students, teachers, and educational researchers from all those approaches.

人工智能是在机器中模拟人类智能的模型，通过编程使其具备类人思维能力。换言之，人工智能是一种计算机系统，能够完成通常需要人力或人类智能才能完成的工作。人工智能的顺畅运行需要经验与数据支持：人类无需全程指令人工智能的学习过程，其会在被人类使用的过程中，基于自身积累的经验自主学习。在数学学习中应用人工智能具有诸多优势，例如能帮助学生在解决日常问题时更具批判性思维与责任感，更深入理解几何、数学及统计学的基础问题；此外，还能培养并提升学生的人际交往能力与社会互动能力，营造高效的学习环境，助力学生更好地掌握数学概念。本文分析了 2017-2021 年间发表的 20 项研究成果，探索了人工智能在教与学过程中对数学专业学生学习成效的影响与提升作用。人工智能可通过多种方式应用于数学教育，包括系统、可教智能体、自主智能体、机器学习模型、数字技术设备及综合方法等。然而，在这些方式中，机器人技术是数学专业学生、教师及教育研究者最常用的方式。

AI in teaching and learning mathematics has spread throughout the country. Most countries use AI to help improve the quality of learning. Compared to other nations such as Mexico, Canada, and others, the United States has published the most significant number of publications on the application of AI in the last five years. Most aspects of AI, such as advantages, limitations, strategies to use it and others, the most observed aspect is its effectiveness in teaching and learning process, especially mathematics education. Compared to other aspects, it is still observed but not as widespread as the observation on effectiveness. It is crucial to know the extent of the effectiveness of AI in education. So, AI can be applied more widely in the future if it brings positive effectiveness. We should not expect robotics to be the primary influence on mathematical learning, but rather if educators and students can fully explore the educational potentials of robotics to focus and enhance mathematical knowledge. As a result, students' workload in math classes could be worsened by adding "seductive details" introduced by robots. In summary, with the help of AI, teaching and learning are more effective because it is exciting and creative has made it easier for students to understand a subject.

人工智能在数学教与学中的应用已在全球范围内展开，多数国家借助人工智能提升学习质量。过去五年间，美国在人工智能应用领域的发表文献数量远超墨西哥、加拿大等其他国家。在人工智能的诸多研究方向（如优势、局限性、应用策略等）中，"教与学过程中的有效性"（尤其是在数学教育领域）是最受关注的方向；其他方向虽有研究，但关注度远低于"有效性"。了解人工智能在教育中的有效程度至关重要：若其能产生积极效果，未来或可得到更广泛的应用。我们不应期望机器人技术成为影响数学学习的主要因素，而应关注教育工作者与学生能否充分挖掘机器人技术的教育潜力，以聚焦并深化数学知识学习。需注意的是，机器人引入的"吸引性细节"可能会增加学生的数学课堂负担。综上，在人工智能的助力下，教与学过程更具趣味性与创新性，不仅提升了教学成效，也帮助学生更轻松地理解学科知识。

Limitation

研究局限性

Each study is limited in some way. There may be limitations to your study due to limitations on the research design or technique, which may affect the study's findings. While this analysis identifies numerous significant trends and future research objectives for AI in mathematics education, it has several limitations. The first limitation is that only a limited number of articles are available for research. Because AI is a topic that is rarely investigated in mathematics education, the results gained are limited, making it difficult to draw broad conclusions from the findings. A small number of studies, on the other hand, only scratch the surface of what is being learned about how AI is being used in the teaching and learning of mathematics education in their research without providing in-depth explanations. Therefore, the conclusions of this review were confined to a small number of other researches that provided explicit explication of their findings. As previously stated, AI topics have a limited number of studies; therefore, eliminating duplicate articles amongst search engines decreases the acquisition of relevant research studies. Lastly, each of the papers under consideration in this review contains a significant variety of examples to choose from. Because research is carried out in large variations, the results are skewed due to bias.

所有研究均存在一定局限性。研究设计或技术层面的限制可能会影响研究结果，进而导致研究存在局限性。尽管本研究分析了人工智能在数学教育领域的诸多重要趋势与未来研究方向，但仍存在以下局限性：首先，纳入研究的文献数量有限。由于"人工智能在数学教育中的应用"是一个较少被研究的主题，研究结果的覆盖面较窄，难以得出具有普遍性的结论。其次，部分研究仅浅层次探讨了人工智能在数学教与学中的应用，未深入阐释相关内容；因此，本综述的结论仅基于少数对研究结果有明确阐释的文献。再者，如前所述，人工智能相关研究本身数量较少，剔除不同数据库中的重复文献后，获取的相关研究进一步减少。最后，纳入综述的各文献所包含的案例差异较大，研究设计与实施的多样性可能导致结果存在偏差。

Implication

研究启示

Several implications resulted from this study. According to Wu (2021), the application of AI technology has penetrated all aspects of people's daily life and has had a profound impact on the development of society. Mathematics education is one of the aspects that is well developing with AI. People have been implementing AI in mathematics education for many years now, either by teachers or students. From the study, the robotic approach was widely used among them and positively impacted their mathematics knowledge. Meanwhile, AI is also difficult to apply comprehensively due to relatively high maintenance costs. Therefore, it is believed that this was why many studies were only conducted in developed countries such as the United States, China, and Australia while zero studies in Southeast Asia, especially in Malaysia. Moreover, the AI approach in mathematics education did enhance students' learning experience since the method used was unlike the conventional teaching and learning process, which involves pen and paper. Students' and teachers' creativity will also improve when they practice AI, such as robotics, in teaching and learning. The suitable approach used by the teachers will significantly maximize their students' potential to apply and understand what they are learning. Hence, teachers should implement AI in the teaching and learning process to attract students to understand better besides enjoying learning.

本研究具有多方面启示。Wu（2021）指出，人工智能技术已渗透到人们日常生活的方方面面，对社会发展产生了深远影响，数学教育便是在人工智能助力下蓬勃发展的领域之一。多年来，教师与学生一直在数学教育中应用人工智能技术。本研究发现，机器人技术是其中应用最广泛的方式，且对学生数学知识的掌握具有积极影响。与此同时，由于维护成本较高，人工智能难以在数学教育中全面推广------这被认为是多数相关研究仅在美國、中国、澳大利亚等发达国家开展，而在东南亚地区（尤其是马来西亚）尚未有相关研究的原因之一。此外，人工智能在数学教育中的应用不同于传统的"纸笔式"教与学过程，显著提升了学生的学习体验；师生在教与学中应用机器人技术等人工智能手段时，创造力也会得到提升。教师采用合适的人工智能应用方式，能最大限度地激发学生应用与理解所学知识的潜力。因此，教师应在教与学过程中引入人工智能，以吸引学生更深入地理解知识，同时享受学习的乐趣。

Future Direction

未来研究方向

To further advance our understanding and application of AI in education, future researchers must conduct additional research on the implications and benefits of AI in education, particularly regarding the development of students' cognitive skills. If further studies demonstrate the success of AI in learning with low capacity and diverse student populations, it will serve as a positive incentive for teachers to incorporate AI into their classroom instruction. Teachers must be confident in their students' ability to benefit from AI instruction. Once they see student success in their classrooms, teachers will convince them to continue implementing machine intelligence learning. Additionally, researchers should conduct additional research on AI, mainly in the field of mathematics education, so that the findings from this SLR can be supported by more robust evidence, as the study of AI in mathematics education has limitations. Due to limitations, this review could not assess the effectiveness of AI use on students' cognitive abilities. Additional research could address this gap by examining the effect of AI on students' memory and thinking in this study. The study's scope was also limited to the impact of AI on teaching and learning and its distribution. Future trials will examine additional aspects of AI, particularly the relationship between machine learning and teaching theory. Since the studies included in the analysis focused exclusively on journal articles, future research should consider using conference proceedings and books to enhance the findings and analysis. Additionally, these studies represent high-quality publications, and future efforts may include examining other types of publications, such as books and book chapters.

为进一步深化对人工智能在教育中应用的理解与实践，未来研究者需更多探索人工智能在教育中的启示与优势，尤其是在学生认知能力培养方面的作用。若后续研究能证明人工智能对学习能力较弱及背景多样的学生群体具有积极效果，将极大激励教师在课堂教学中引入人工智能技术。教师需对学生从人工智能教学中获益抱有信心------一旦在课堂中观察到学生的学习成效，他们便会更愿意持续开展机器智能教学。此外，鉴于人工智能在数学教育领域的研究存在局限性，研究者应进一步聚焦该领域开展研究，为本次系统文献综述的结论提供更充分的证据支持。例如，本次综述未能评估人工智能应用对学生认知能力的影响，未来研究可通过考察人工智能对学生记忆与思维的作用填补这一空白。同时，本次研究范围仅局限于人工智能对教与学的影响及其分布情况，未来研究可拓展至人工智能的其他方面，尤其是机器学习与教学理论之间的关系。由于本次分析仅纳入期刊文章，未来研究可考虑纳入会议论文集与书籍等文献，以完善研究结果与分析过程；此外，当前研究主要聚焦高质量出版物，未来也可将书籍、书籍章节等其他类型出版物纳入研究范围。

Author contributions: All authors have sufficiently contributed to the study, and agreed with the results and conclusions.

作者贡献：所有作者均对本研究做出了充分贡献，并认可研究结果与结论。

Funding: No funding source is reported for this study.

资金支持：本研究未获得任何资金支持。

Declaration of interest: No conflict of interest is declared by authors.

利益声明：所有作者均声明不存在利益冲突。

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