数学与ATL：解锁终身学习的“超能力” I Math and ATL

国际文凭教育（IB）通过四大阶段（小学PYP、中学MYP、预科DP、职业CP），系统培养学生的核心学习能力。ATL技能贯穿全程，是学生成长的“黄金法则”。

ATL技能的五大核心能力：

• 思考技能：批判性思维、创造力

• 研究技能：信息搜集、分析与验证

• 交流技能：有效表达、合作沟通

• 自我管理：时间规划、情绪调节

• 社交技能：团队协作、同理心

这些能力让学生在课堂内外游刃有余，无论是完成小组项目、规划学习时间，还是解决实际问题，都能看到ATL技能的作用。

在一年级《100以内数的认识》单元中，学生通过摆弄小棒、分解数字（如将28拆分为“2个十和8个一”），实践数据收集与整理；在百数表中发现“每行10个数字”的规律，锻炼模式识别能力；而讨论“49后面为什么是50”时，则体现了假设验证的过程。这些活动不仅帮助学生建立数感，更培养了研究技能的子能力：

• 数据采集：通过实物操作收集信息

• 组织信息：分类整理数字

• 推理能力：解决“缺失数字”问题

• 呈现成果：用语言描述发现

数学课，就这样成为了学生的“研究方法启蒙课”！

在二年级《认识轴对称》课程中，教师设计了多层级互动场景：

• 观察与表达：学生用“我发现……”句式分享生活实例（如蝴蝶、球拍）。

• 验证与归纳：通过“对折验证”活动，学生用“我的方法是……”“我同意/补充……”等语言合作探究，最终用“我们认为……因为……”总结轴对称图形的特征。

• 小组任务：分工寻找图形的对称轴，轮流分享发现，锻炼逻辑表达与倾听能力。这样的设计，让学生在交流中学习，从碎片化描述进阶到逻辑表达。

在六年级的数学探究课程中，学生通过小组合作完成数据收集、扇形统计图设计等活动：

• 团队协作：协商扇区划分、颜色选择，培养审美共识与尊重多样性。

• 展示与反馈：轮流汇报成果，面对提问时清晰表达观点，学会倾听与反思。

• 问题解决：共同探讨AI对职业的影响，锻炼批判性思维与同理心。

这些活动不仅提升了数学能力，更培养了学生的社交技能，为未来成为全球化公民奠定基础。

五年级《折线统计图》单元中，学生们参与职业的探究，自我管理技能涵盖时间管理、组织能力、情绪调节和自我激励等方面。在数学课上，这些能力通过真实的任务情境得到自然培养。学生以AI和科技发展对社会职业的影响为主题，展开数学探究：

• 时间管理与组织能力：学生需自主规划时间，完成数据收集、绘制折线统计图并分析趋势，每一步都考验着他们的计划性和条理性。

• 自我激励与情绪调节：面对数据处理的困难或团队合作中的分歧，学生学会调整心态，通过自我激励克服挑战，同时适应团队角色，保持积极协作。

• 目标导向的学习：学生基于未来职业需求反推当前的学习重点，将数学知识与个人发展紧密结合，赋予学习更深的意义。

这一过程不仅提升了学生的数学能力，更让自我管理技能在实践中生根发芽。

三年级《认识小数》单元，通过课堂活动的设计，学生们的思考技能得到进一步提升。我们知道，思考技能是数学学习的核心驱动力，包括逻辑推理、知识迁移、问题解决等能力。数学课堂中的每一个问题，都是培养学生思考技能的契机。

• 知识迁移：学生借助T图，将已学的整数、分数知识与小数类比，预判学习内容，实现知识的无缝衔接。

• 推理与归纳：通过对比整数加减法，学生推理出“小数点对齐”的原理，理解“相同计数单位对齐”的数学本质。

• 生活应用与建模：在解决购物问题时，学生圈画关键词、画图梳理数量关系，将抽象数学与生活场景紧密结合。

• 验证与反思：在探究“数的产生史”任务中，学生提出“分数早于小数”的假设，并通过制作时间轴验证观点，锻炼了逻辑思维与实证能力。

这些活动让学生从被动接受知识变为主动思考者，逐步构建起坚实的思维基础。

IB教师常引导学生反思：

• “今天我用什么新方法解决了问题？”

• “小组讨论时，我是否倾听了同伴的意见？”

• “下次如何更有效地规划时间？”

通过反思，学生不断优化学习方法，让成长清晰可见。

掌握ATL技能的学生将拥有：

• 学习内驱力：从被动接受变为主动探索。

• 问题解决力：面对挑战时能拆解步骤、寻找资源。

• 情绪调节力：在挫折中自我激励，保持积极心态。

• 社会适应力：快速建立协作关系，融入新环境。

The International Baccalaureate (IB) systematically develops students' core learning competencies through the four phases (Primary PYP, Secondary MYP, Foundation DP, and Vocational CP), and ATL skills are used throughout the entire program, which is the “Golden Rule” for student growth.

The five core competencies of ATL skills：

• Thinking skills: critical thinking, creativity

• Research skills: information gathering, analysis and validation

• Communication skills: effective expression, cooperative communication

• Self-management: time planning, emotional regulation

• Social skills: teamwork, empathy

These abilities allow students to navigate in and out of the classroom, whether it's completing a group project, planning study time, or solving a real-world problem, ATL skills can be seen shining through.

In the first grade unit “Knowing Numbers up to 100”, students practice data collection and organization by fiddling with sticks and decomposing numbers (e.g., splitting 28 into “2 tens and 8 ones”); they discover the pattern of “10 numbers in each row” in the hundreds table and practice pattern recognition; and they discuss why “49 is followed by 50”, which reflects the process of hypothesis verification. Discovering the pattern of “10 numbers in each row” in the table of hundreds exercises pattern recognition; and discussing why “49 is followed by 50” embodies the process of hypothesis verification.

These activities not only help students develop a sense of number, but also cultivate research skills:

• Data collection: collecting information through physical manipulation.

• Organizing information: sorting numbers.

• Reasoning: solving 'missing number' problems.

• Presenting results: describing findings in words.

Math class thus becomes an “introduction to research methods” for students!

In the second grade lesson “Recognizing Axial Symmetry,” the teacher designed a multi-level interactive scenario:

• Observation and Expression: Students share life examples (e.g., butterflies, racquets) using “I found ......” sentences.

• Verification and generalization: Through the activity of “Folding and verifying”, students use language such as “My method is ......”, “I agree/add ......” and so on. /add ......” and other language to explore cooperatively and finally use “We think ...... because ......” to summarize the characteristics of axisymmetric figures.

• Group task: divide the work to find the axis of symmetry of a figure and take turns to share the findings, practicing logical expression and listening skills. This design allows students to learn through communication, progressing from fragmented descriptions to logical expressions.

In the sixth grade Math Explorations program, students work in small groups to complete activities such as data collection and fan chart design:

• Teamwork: Negotiate the division of sectors and the choice of colours to develop aesthetic consensus and respect for diversity.

• Presentation and Feedback: Take turns to report results, express opinions clearly when facing questions, and learn to listen and reflect.

• Problem Solving: Explore the impact of AI on careers, practice critical thinking and empathy.

These activities not only enhance math skills, but also develop students' social skills, laying the foundation for future global citizenship.

In the fifth grade unit (line charts), students engage in career exploration with self-management skills covering time management, organizational skills, emotional regulation, and self-motivation. In math class, these skills are naturally developed through authentic task situations. Students engage in mathematical inquiry on the topic of the impact of AI and technological advances on careers in society:

• Time Management and Organizational Skills: Students need to plan their own time, complete data collection, draw line graphs and analyze trends, testing their planning and organization at every step.

• Self-Motivation and Emotional Regulation: When faced with difficulties in data processing or disagreements in teamwork, students learn to adjust their mindsets and overcome challenges through self-motivation while adapting to their team roles and maintaining positive collaboration.

• Goal-directed learning: Students give deeper meaning to their learning by backcasting their current learning priorities based on future career needs, and by integrating math knowledge closely with their personal development.

This process not only improves students' math skills, but also allows self-management skills to take root in practice.

In the third grade unit “Recognizing Decimals”,students' thinking skills are further enhanced through the design of classroom activities. As we know, thinking skills are the core drivers of math learning, including logical reasoning, knowledge transfer, problem solving and other abilities. Every problem in the math classroom is an opportunity to develop students' thinking skills.

Knowledge transfer: Students use the T-chart to compare what they have learned about whole numbers and fractions with decimals, to anticipate what they will learn, and to realize a seamless transition of knowledge.

• Reasoning and generalization: By comparing the addition and subtraction of whole numbers, students reason out the principle of “aligning decimal points” and understand the mathematical essence of “aligning the same counting units”.

• Life application and modeling: In solving shopping problems, students circle key words and draw diagrams to sort out quantitative relationships, closely integrating abstract mathematics with life scenarios.

• Verification and Reflection: In the task of investigating the “History of Numbers”, students put forward the hypothesis that “fractions predate decimals” and verified their viewpoints by making a timeline, thus practicing logical thinking and empirical skills.

These activities allow students to change from passive recipients of knowledge to active thinkers, gradually building a solid foundation for thinking.

IB teachers often guide students to reflect:

• “What new ways did I use to solve problems today?”

• “Did I listen to my peers during the group discussion?”

• “How can I plan my time more effectively next time?”

Through reflection, students continue to optimize their approach to learning, making growth clearly visible.

Students who master ATL skills will have:

• Internal drive to learn: move from passive acceptance to active exploration.

• Problem Solving Power: the ability to unpack steps and find resources when faced with a challenge.

• Emotional Regulation: self-motivation to maintain a positive mindset in the face of setbacks.

Social Adaptability: quickly builds collaborative relationships and integrates into new environments.