1. The document discusses various myths about gifted mathematics students, including that mathematical ability is mainly genetically determined, that gifted students are only Asian or white males, and that gifted students should accelerate their mathematics classes. 2. It argues that doing mathematics requires hard work and practice, and that both biological and environmental factors contribute to ability. It also notes diversity among high-performing students internationally. 3. The document concludes that the definition of giftedness matters and should be inclusive, and that support for students should focus on raising all achievement through developing confidence, resilience, and hard work.

1. Gifted mathematics students in
international perspective
（国际视野下的数学资优生）
Dr Christian Bokhove
CCME
Panel Discussion: 性别、文化、资优教育与数学教育
时间：2018年10月27日上午，11：00-12：30
Time table: 11:00-12:30, October 27, 2018

2. Defining giftedness
资优的界定
• What is the meaning of mathematics?（数学的意义？）
• When are you a mathematician?（何时成为数学家?）
• Sawyer (1955) and Devlin (1997): study of patterns.
• Polya in How to Solve it: “Yes, mathematics has two faces; it
is the rigorous science of Euclid but it is also something
else. Mathematics presented in the Euclidean way appears
as a systematic, deductive science; but mathematics in the
making appears as an experimental, inductive science.”
(1945, p. 7)
（波利亚：数学有两面; 它是严谨的欧几里德科学，但它
也是另一回事。 以欧几里德方式呈现的数学似乎是一种系
统的演绎科学; 但数学在发展中似乎是一种实验性的归纳
科学。）

3. What is giftedness?
什么是资优
• Growth mindset: intelligence fixed?思维模型的
生长：智力的固化
– This has also been critiqued.
• OECD: stresses the plasticity of the brain and the
importance of the environment.强调大脑的可塑
性和环境的重要性
• Differences between novices and experts: role of
genes, but not deterministic, but the
environment key.新手和专家之间的差异：基因
的作用，但不是确定性的，而环境是关键。
• Measurement: IQ tests?

4. Mathematical giftedness
数学资优
“Perhaps the most widely cited is Krutetskii
where “mathematical giftedness” is the name
given to a unique aggregate of mathematical
abilities that opens up the possibility of
successful performance in mathematical activity
(Krutetskii, 1976, p. 77).”
克鲁茨基：是对一种独特的数学能力综合体
的命名，这种能力为数学活动的成功打开可
能的通道

5. These aspects beg the questions…
这些方面带来如下问题：
• What does this practically mean? 实践上意味着什
么？
• Best in the country, best in school, best in
class? 国家中的最好，学校中的最好，班级中的最好?
• If we do original and challenging tasks, doesn’t
everyone deserve them? 如果我们从事些原始的、
有挑战的任务时，不是每个人都应付这些任务？
• Olympiads, Kangaroo tests?奥林匹克竞赛，
Kangaroo 测试？

6. International
国际视野
• So if we take a broader view of giftedness
TIMSS and PISA also 以广阔的视野看待资优
• Internationally, the measures of ‘top
performing’ differ though… 国际上看，“好成绩”
的测量各有不同
• So when we look at ‘giftedness’ in
international perspective, most countries are
talking about different things….许多国家对 “资优”
的讨论各不相同

7. Black circles denote
the % of advanced
benchmark in TIMSS
grade 8.
黑点代表TIMSS中8年级
的高水平的基准
Benchmark the same
but clear that
countries differ in
achievement.
基准相同，但在成绩
上的表现有差异

9. 5 myths from Sheffield (2017)
Shefield的5个神话
Sheffield, L.J. (2017). Dangerous myths
about “gifted” mathematics students.
ZDM Mathematics Education, 49, 13-23.

10. Myth 1 神话1
Mathematics ability is mainly genetically
determined 数学能力主要由遗传基因
• Doing mathematics is hard work → deliberate
practice (Ericsson) 做数学是艰辛的-深入实践
• Resilience, grit (Duckworth) 弹性，毅力
• Growth mindset (Dweck)思维模式的生长
But…

11. Myth 1
• Fundamental number system 基本的数系
– Approximate Number System (ANS) 近似数系
• “genius emerges from an improbable confluence of
multiple factors—genetic, hormonal, familial and
educational. Biology and environment are intertwined in an
unbreakable chain of causes and effects, annihilating all
hopes of predicting talent through biology or of giving birth
to a baby Einstein by crossbreeding two Nobel Prize
winners” (Dehaene, 1997, p. 162).
• 天才来自多因素的非常态的汇合 - 遗传，荷尔蒙，家庭
和教育。 生物学和环境交织在一个牢不可破的因果链中，
消除了通过生物学预测人才的所有希望，或通过杂交两
位诺贝尔奖获得者生下爱因斯坦类的孩子

12. Myth 2
Gifted mathematics
students are Asian or
White males.
数学资优生为亚洲或
白人男性
From TIMSS 2015 →
• Role (lack) of
confidence.
信心的作用

13. Myth 3
Mathematics is not creative. 数学不是创新
• Do not agree with view that algorithms not
creative (Fan & Bokhove, 2014).不同意算法不是
创新
• But also depends on definition of creativity: big-C
vs small-C. Everyone can be creative.依据创新的
定义，每个人是能够创新的
• My view: all students deserve this, not just those
seen as “gifted”.我的观点：所有学生都应该拥
有，而不是那些被认为“资优”的学生

14. Myth 4
Gifted mathematics students develop on their
own.数学资优生的自我发展
• Support with opportunities for excellence.对
优秀生支持的机会
• Cast a wide net → inclusivity for all.构筑宽广
的网络-人人包容
• Procedural and Conceptual knowledge hand-
in-hand. 程序知识和概念知识的并进

15. Myth 5
Gifted students should accelerate their
mathematics classes as much as possible.资优生应
该尽可能加速数学课堂学习
• Do not speed up but allow depth. Learning
mathematics costs time.不需要加速但加深，学
习数学需要时间
• I disagree with Sheffield (2017) that tracking
necessarily bad → context of the Netherlands.我
不同意Sheffield ,要追踪必要的问题

16. Conclusions结论
• The definition of (mathematical) giftedness
matters.资优生的界定很重要
• I think a focus on the top-performing students
(‘gifted’), should be in a context of ‘raising the
whole boat’, so also lower performing students.
关注高成绩的学生（资优），应该“提升整艘
船”，也要关注低成绩的学生
• “Giftedness” should be inclusive“资优”应该是
包容的
• Work on confidence, resilience, hard work. 自信，
弹性，刻苦

17. References
Dehaene, S. (1997). The number sense: how the mind creates mathematics.
New York: Oxford University Press.
Devlin, K. (1997). Mathematics: the science of patterns: the search for order in
life, mind and the universe. New York: Scientific American Library.
Fan, L., & Bokhove, C. (2014). Rethinking the role of algorithms in school
mathematics: a conceptual model with focus on cognitive development.
ZDM-International Journal on Mathematics Education, 46(3),
doi:10.1007/s11858-014-0590-2
Krutetskii, V. A. (1976). The psychology of mathematical abilities in
schoolchildren. Chicago: University of Chicago Press.
Polya, G. (1945). How to solve it: a new aspect of mathematical method.
Princeton: Princeton University Press.
Sawyer, W. W. (1955). Prelude to mathematics. London: Penguin.
Sheffield, L.J. (2017). Dangerous myths about “gifted” mathematics students.
ZDM Mathematics Education, 49, 13-23.