87个数学奖项背后，有怎样的分层教学支撑？

临近年底，接连传来孩子们参加数学竞赛取得好成绩的喜讯！

2022英国数学测评（高级SMC），11年级的敬可欣和黄宇扉捧回金奖；

2022澳大利亚数学竞赛（AMC），启明星学生共获得11个全国二等奖，24个全国三等奖，50个数学技能奖。

还有前不久举行的美国数学大联盟（AMC）的排名，也热气腾腾地正在赶来的路上……

“我们鼓励学生参加适合自己的竞赛。我们相信，合适的竞赛能够培养学生的重要素质，而许多素质又和启明星的核心价值观直接相关。比如，准备竞赛的过程就是追求卓越的过程......另外，参加比赛也帮助学生增强自信心和保持学习的动力……”

——启明星增益项目协调员 Vincent Harris

所以，尽管和前些年相比，启明星的学生正越来越多地参加到数学竞赛中，但在启明星，参与竞赛更多的是促进学习的一种路径，而非单纯追逐成绩的手段。

相应的，与其问启明星怎样支持学生在数学竞赛中获奖，不如换个问法——启明星为在数学方面学有余力的孩子提供了哪些支撑和资源？

中学部：识别学生的不同节奏

数学课堂，是孩子在校获得知识的“第一现场”。

启明星的数学教学，无论小学部还是中学部都提供差异化教学。

“中学部每个年级的数学教学分成2个层次——标准班和拓展班，为相应级别的学生提供教学和辅导。”中学数学组负责人、中学数学老师钱青华说，“拓展班的数学学习和标准级别的在知识框架上是一致的，但会辅以更大广度和深度的额外主题和技能教学。”

将学生划分到适合的级别遵循标准而严肃的程序，单是确定级别就要考虑4个方面的标准：

1. 内部评估数据，比如针对6至8年级学生要考虑MYP的4个评估标准；

2. 最终的学年年终分数；

3. 基于所有学生完成的相同评估做出决定，这些评估由启明星数学部门的老师共同设计、讨论和调整，以确保一致性；

4. 外部数据，如 MAP 分数等。

标准班的学生适应学习节奏、展示出连续而稳定上升的学术表现之后，老师们会根据这些表现数据重新讨论，来决定是否让学生进入更高级别的数学学习。这样的安排既不会太仓促、能够真正符合孩子的数学学习节奏，也有效保护了孩子的自信心和积极性。

小学部：课内差异化教学 + 增益项目

小学部在两个方面为孩子们提供差异化的教学。

“每位学生学习数学的节奏是不同的，兴趣多少也不一样。在课堂上，我们通过不同的解题活动和开放式问题让他们进行适合自身节奏和兴趣的水平上学习。”北皋小学部数学增益项目和数学老师Bita Zandieh-changizi说。

“有些孩子能力卓著，可以给其他同学讲题，那我们就可能就给他们转换任务。”三里屯小学部数学老师张玥媛补充说。

在两个校区的小学部高年级开设的数学增益项目是数学差异化教学在课后的延伸。老师按照连续的MAP成绩对学生的数学能力做出评估，选拔学有余力、对数学有兴趣的学生参加。

增益项目的学生在每周的固定时间活动，学习基于课堂、但范围更广的数学知识，这样的过程有助于他们发展更为灵活的数学思维。

“比如在学习简易方程期间，我们会将方程与学习过的坐标系结合起来，孩子们自然而然的就会探索到一些与一次函数有关的内容。” 三里屯小学部增益项目老师、数学教学指导张剑婷说。

“经过一段时间的增益项目学习，我们能明显看到孩子们的进步。比如孩子们能够为启明星数学日设计寻宝游戏，临近上学年末还设计出20几款策略性的数学游戏。设计数学游戏正是孩子们数学能力和逻辑能力进步的体现！” 她补充道。

Bita老师告诉我们，北皋小学增益项目的学生正在学习建立一个研究力和质量关系的科学模型。通过这个项目，孩子们学习了如何从自己的发现出发进行科学研究、收集和分析数据。

数学课后课：欢迎喜欢挑战的你来！

如果你学习之余还有参加竞赛的目标，那么老师欢迎你参加数学课后课，接受赛事培训经验丰富的老师的专项指导。

启明星的小学部和中学部都提供数学课后课，老师们会讲解比赛真题，或是围绕某个问题进行专题讲授，鼓励孩子们参加适合的比赛。

“建议3至11年级的学生参加数学竞赛。8至11年级学生参加竞赛如果取得优异成绩，对大学升学是有帮助的。目前有各种各样的数学竞赛，我们建议学生选择主流的竞赛，比如袋鼠数学竞赛、AMC等等。”拥有多年数学竞赛辅导经验、曾指导多名学生获得国际数学竞赛大奖的钱青华老师说，“但无论参加什么竞赛，课内知识点首先要扎实，都是大前提。”

启明星学校已经成为以下数学竞赛考点：

国际滑铁卢数学竞赛

袋鼠数学竞赛

美国数学思维挑战活动AMC8、AMC10/12

英国数学思维挑战赛UKMT

从某种意义上来讲，数学是解释世界的一种语言。我们越多鼓励和陪伴学生探索数的世界，他们越会发现世界的美丽和有趣。

It’s the end of the year again, and we have great news about Daystar students’ achievements in math contests!

Jing Kexin and Huang Yufei (Grade 11) won Gold in the 2022 UK Mathematics Trust: Senior Mathematical Challenge (SMC); and Daystar students won 11 national second-place prizes, 24 national third-place prizes, and 50 proficiency awards in the 2022 Australian Mathematics Competition (AMC).

Our achievements at American Math Contests (AMC) held recently will also be announced soon…

We encourage our students to attend these contests, because we believe appropriate competitions can help them develop qualities which are directly related to Daystar’s core values. For example, during their preparations for the contests, they are striving for excellence...Moreover, it helps build up their confidence and motivates them to keep learning…”

—Vincent Harris, Enrichment Coordinator of Daystar Academy

As a result, more and more students at Daystar volunteer to challenge themselves in math contests every year.But here at Daystar, attending competitions is seen more as a means to pursue academic excellence, not just as a way of achieving high scores.

So, instead of asking how Daystar can support them to win more awards, we should ask ourselves –what support and resources does Daystar offer for students gifted at math?

SS: Differentiated Instruction

Math class is the “first port of call” for the children to learn math at school.

At both Daystar Elementary and Secondary Schools, we provide students withdifferentiated instruction.

“Math teaching in each Secondary grade is divided into two levels — Standard Class and Extended Class — for students of different abilities,” said Linda Qian, Daystar math team instructor and secondary grade math teacher. “Extended Class adheres to the same knowledge framework as the Standard Class, but it covers themes and skills both more extensively and intensively.”

Dividing students into different levels is a serious and standardized process. Four criteria are considered for determining each level:

1. Internal assessment data (based on MYP Criteria – ABCD)

2. Final Q4 end of year (best fit) Criteria scores out of 8 (not just the final overall grade out of 7)

3. Decisions are made based on the same assessments completed by all students. These assessmentsare created, discussed and moderated collaboratively by the Mathematics Department, to ensure consistency

4. External data, such as MAP scores

When a student in the Standard Class adapts to the pace of learning and demonstrates continuous and steady growth in their academic performance, teachers will discuss the student’s performance data and decide whether to send them for higher-level math learning.In this way, we can make preparations ahead of time, find the ideal pace of learning for students, and ensure their confidence and positivity.

ES：Differentiated Instruction

+ Enrichment

Daystar Elementary School provides differentiated instruction in two ways.

“Each student is at different points on their mathematical journey and at varying levels of interest. Through different problem-solving activities and open ended tasks we engage each student at their own level of interest and learning.”said Bita Zandieh-changizi, math teacher for Math Enrichment at Beigao Elementary School.

“Some kids are good at math. They even help instruct other students. So, we give them different tasks,” added Rose Zhang, math teacher at Sanlitun Elementary School.

In the senior grades at both Beigao and Sanlitun Elementary Schools, we set Math Enrichment as an after-class extension of differentiated instruction.Students who continuously get high MAP scores are assessed by teachers who then select those with the ability and interest to participate.

Students who attend Math Enrichment carry out learning activities at fixed times each week. This learning is classroom-based and covers broad mathematical knowledge, helping students develop flexible mathematical thinking.

“For example, during the learning of simple equations, we will combine the equations with right angle coordinate system that we have learned, and the students will naturally explore some content related to primary functions,” said Cimi Zhang, Math Enrichment teacher and Math Coach at Sanlitun Elementary School.

“After some time, the kids have improved a lot,” said Cimi. “For example, they designed treasure hunt games for Daystar’s Pie Day, and even came up with over 20 strategic math games near the end of the last academic year. By designing these games, the students demonstrated their progress in math and logic.”

Ms. Bita said, at Beigao, the enrichment students are in the process of creating a scientific model to study the relationship of force and mass. Through this project they have learned about scientific investigation, collected data, analyzed thier data and drawn conclusions based on thier findings.

After-school Activity: Welcome to Attend!

If students have a clear goal to attend competitions, then our teachers will welcome them to after-school math activities. This way they can receive special instruction from teachers experienced in contest preparation.

Both Elementary and Secondary Schools at Daystar offer after-school math activities. Teachers will break down and explain past exam papers or teach specific questions in depth while encouraging students to choose to attend contests that suit them.

“We suggest all students in Grades 3-11 attend math contests. If Grades 8-11 students perform well, they will get an excellent advantage when applying for university. Nowadays, there are all sorts of math contests, so we recommend mainstream ones such as Kangaroo and AMC,” said Linda, a teacher who has years of contest preparation experience and has helped many students get awards in international contests.

“But whatever competition they choose, the major prerequisite is always consolidating what they have learned in class,” added Linda.

Daystar now holds the following contests:

Waterloo Mathematics Contest

Math Kangaroo

AMC8、AMC10/12

UKMT (UK Mathematics Trust)

Math is a language for making meaning of the world. The more we encourage and accompany our students to engage with math, the more they will discover the beauty of the world around them.

启明星发布《社会创新发展报告2021-2022》Daystar Academy of Ivy Education Group Released Social Innovation Progress Report 2021-2022

盘点夏日佳音：为孩子们的成就鼓掌！Let’s Take a Look at Our Good News and Applaud the Growth of the Students