周末，海淀凯文中学数学组好消息不断传来。不仅同学们在上海举办的美国STEM大联盟杯2019赛季中国站NSL全速智能车比赛中取得优异成绩，中学数学组组长Stephen Pattenden老师也被评为“2018年度海淀区优秀外籍教师”。

荣誉是数学教学成绩的认可之一，这背后是老师们对数学课程不断的潜心研究和探索实践。对此我们邀请了Stephen Pattenden老师撰写了一篇文章，希望大家透过此篇内容，可以更深入了解凯文的数学教学。

Making Mathematics Fun in KWA / 在凯文，让数学更有趣

 Stephen Pattenden

When asked to write an article to describe what constitutes great math teaching, an avalanche of ideas and information came to mind. Of course, a comprehensive and challenging curriculum is needed, with excellent resources and effective teachers. Providing timely and focused feedback of student progress would rank highly too.

当我被要求写一篇文章来描述数学教学时，脑海中一下子涌上大量的想法和信息。当然，首先我们需要一个全面而富有挑战性的课程体系，拥有优秀的教学资源和师资队伍。同时，及时有效、科学而有针对性的学生学习过程评价体系也很重要。

Coincidently, our Head of Curriculum recently asked Kaiwen Academy teachers to choose 3 adjectives to describe a good class. My instinctive response was – engaging, interactive and goal-oriented. Words, chosen by other teachers from across the school, suggested a comprehensive and definitive set of quality lessons taking place.

碰巧，最近我们的课程负责人要求凯文的老师用三个形容词来形容一节优秀的课程。我的第一反应是：有吸引力、双向互动和目标明确。最终，由全校其他教师选择的词语，共同组成了大家认可的一节高质量课程应该具备的要素。

So, what is the over-arching goal I try to achieve with my students?

所以，我和学生努力达成的，贯穿整体的目标究竟是什么呢？

The question reminded me of a conversation I had at last year’s Berkeley mini Math Competition (BmMT) with Po-Shen Loh, Professor of Mathematics at Carnegie Mellon University and national coach to the US International Math Olympiad team (gold-medal winners, 2015, 2016 & 2018).  We had been discussing the recent success of his team, when Jianbo Chen, Head of Primary Math, here at Kaiwen, asked him how he goes about finding talented team members. Dr Loh’s solution focused less on seeking out strong mathematicians, but rather on how to make mathematics more fun in schools. His point being, that students work harder on subjects they enjoy and often choose their university major based on this and their success in the subject. That way you get more talent to choose from.

这个问题让我想起了去年伯克利迷你数学竞赛(BmMT)上，我与美国卡内基梅隆大学(Carnegie Mellon University)数学教授、美国国际数学奥林匹克队(International Math Olympiad team)国家队教练Po-Shen Loh的交流。我们在讨论他的团队最近取得的成功时，凯文小学部数学组组长陈建波问他“如何才能找到有才华的团队成员”。Loh博士的解决方案是：不要太关注寻找未来优秀的数学家，而是关注如何让数学在学校变得更有趣。他的观点是，学生在他们最喜欢的科目上才会更加努力，并且经常根据他们在这门课上的成功来选择他们的大学专业。这样你也才能有更多的选择。

Further conversations with university professors during in-school college-counselling sessions have helped reinforce my overall goal – which is to inspire my students. Through my passion for the subject, I aim to show my students the beauty of mathematics and its effectiveness as a tool to understand the world around them. To let them see that it’s a fun and creative endeavor; not just about learning facts and studying in books, but one where we can apply and explore our ideas and discuss solutions.

校内的升学指导环节中，与大学教授的进一步交流也有助于巩固我的总体目标 —— 为了激励我的学生。秉持对数学这个学科的教学热情，我的目标是向学生展示数学之美及其作为理解周围世界的工具的有效性。我希望让他们看到这是一个充满趣味性和创造性的努力。这不仅仅是对基础事实和书本内容的学习，而是我们可以应用和探索我们的想法并讨论解决方案。

For example, in my G7 class this year, students will study beyond the textbook in a variety of different ways. They will solve puzzles that practice core thinking skills in a fun way. They will enter competitions and find success in problem-solving at a high level. They will work on projects with cross-curricular connections, showing how mathematical thinking helps them to understand the world and make better choices and decisions.

例如，在今年我教学的七年课堂上，学生将学习到课本知识之外的一系列不同的问题解决方法。学生们会玩数学游戏，以更有趣的方式锻炼核心思维技能。他们将参加比赛，在一个高水平的竞争环境中寻找问题解决方案并获得成功。他们将进行跨学科的项目学习，展示数学思维是如何帮助他们了解世界并作出更好的选择和决策。

Two upcoming Grade 7 projects help illustrate connections to the real world. The first asks students to consider the question, “What if everyone had a car?” This encourages societal questions such as why we want or need cars and who gets to choose who has one. It considers technological challenges to pollution and traffic jams. It prompts students to quantify the resources and economics required and predict how transportation might work in the future.

学校即将推进的两个七年级项目将会帮助同学们了解数学与现实世界的联系。第一个项目要求同学们思考一个问题：如果每一个人都拥有一台车，会怎么样？这是一个社会问题，将鼓励同学们思考：我们为什么要拥有汽车？谁可以选择谁拥有汽车？这个问题涉及了污染和交通拥堵问题带来的技术挑战。它促使学生量化所需的资源和经济，并预测未来交通运输的可能性。

Another investigation has students look at the Olympic medal table and asks, “Which is the sportiest nation?” This challenges students to question why some nations appear to perform better that others. It encourages them to use the concepts of rate and proportion to consider population size, wealth, equality and available resources. Students are challenged to re-frame the problem, reflecting on their research, to present alternate solutions to the question.

另一项调查让学生们观察奥运会奖牌榜并回答问题 “哪个是最具运动性的国家？”这让学生们思考，为什么有些国家的表现要好于其他国家。这将鼓励他们使用比率的概念来考虑人口规模，财富，民主平等和可用资源等。学生们面临的挑战是重新构建问题，反思他们的研究，提出替代解决方案。

Such tasks aim to develop interest, providing students with the skills, strategies and desire to continue studying mathematics – both in school and beyond.

这些任务都旨在培养学生的兴趣，并为学生提供学习数学的方式技巧、策略，帮助他们达成在未来学习中进一步学习数学知识的愿望，不管在学校还是离开校园。