幼儿园的数学往往太基础了。这就是为什么这是一个问题

幼儿园可能是数学最重要的一年——它为理解数字和数量之间的关系奠定了基础，并有助于培养“数感”

Kindergarten math is often too basic. Here’s why that’s a problem

幼儿园的数学往往太基础了。这就是为什么这是一个问题

By Holly Korbey for The Hechinger Report

作者：Holly Korbey，《赫金格报告》

On a recent morning, the children used plastic red and yellow dots for a counting exercise: One student tossed the coin-sized dots onto a cookie sheet while another hid her eyes. The second student then opened her eyes, counted up the dots and picked the corresponding number from a stack of cards.

最近的一个早晨，孩子们用塑料红点和黄点进行计数练习：一名学生将硬币大小的点扔到饼干片上，而另一名学生则遮住眼睛。然后第二个学生睁开眼睛，数出点数并从一堆卡片中选出相应的数字。

The dots showed up again a few minutes later in a more complex task. Murphy set a two-minute timer, and students counted as many dot arrays as they could, adding or taking away dots to match a corresponding written number. Four dots next to a printed number 6, for example, meant that students had to draw in two extra dots — an important precursor to learning addition.

几分钟后，在一项更复杂的任务中，这些点再次出现。墨菲设置了一个两分钟的计时器，学生们尽可能多地数出点阵列，添加或删除点以匹配相应的书面数字。例如，印刷数字 6 旁边的四个点意味着学生必须额外画两个点——这是学习加法的重要前提。

Kindergarten may be math’s most important year — it lays the groundwork for understanding the relationship between number and quantity and helps develop “number sense,” or how numbers relate to each other, experts and researchers say.

专家和研究人员表示，幼儿园可能是数学最重要的一年——它为理解数字和数量之间的关系奠定了基础，并有助于培养“数字感”，或者说数字之间的相互关系。

But, as detailed in The Hechinger Report, too often teachers spend that crucial year reinforcing basic information students may already know. Research shows that many kindergarteners learn early on how to count and recognize basic shapes — two areas that make up the majority of kindergarten math content. Though basic math content is crucial for students who begin school with little math knowledge, a growing body of research argues more comprehensive kindergarten math instruction that moves beyond counting could help more students become successful in math later on.

但是，正如《赫金格报告》中所详述的那样，教师常常在关键的一年里强化学生可能已经知道的基本信息。研究表明，许多幼儿园的孩子很早就学会了如何计算和识别基本形状——这两个领域构成了幼儿园数学内容的大部分。尽管基础数学内容对于刚开始上学时数学知识很少的学生来说至关重要，但越来越多的研究认为，更全面的幼儿园数学教学（超越计数）可以帮助更多的学生日后在数学上取得成功。

Because so many students nationally are struggling in math — a longstanding challenge made worse by remote schooling during the pandemic — experts and educators say more emphasis needs to be put on foundational, early childhood math. But for a variety of reasons, kindergarten often misses the mark: Math takes a backseat to literacy, teachers are often unprepared to teach it, and appropriate curriculum, if it exists at all, can be scattershot, overly repetitive — or both.

由于全国范围内有很多学生在数学方面遇到困难——这一长期存在的挑战因疫情期间的远程教育而变得更加严峻——专家和教育工作者表示，需要更加重视基础的幼儿数学。但由于各种原因，幼儿园常常未能达到目标：数学落后于识字，教师往往没有准备好教授数学，而适当的课程（如果有的话）可能是分散的、过度重复的——或者两者兼而有之。

Manipulating numbers in different ways, part of a supplemental math curriculum for Murphy’s whole class at Hilltop Elementary in this suburb of Philadelphia, is an attempt to address those problems. In an effort to improve math achievement district-wide, all elementary students in the Chichester School District get an extra 30-minute daily dose of math. In kindergarten, the extra time is spent on foundational skills like understanding numbers and quantity, but also the basics of addition and subtraction, said Diana Hanobeck, the district’s director of curriculum and instruction.

以不同的方式处理数字是墨菲在费城郊区山顶小学全班数学补充课程的一部分，旨在解决这些问题。为了提高全学区的数学成绩，奇切斯特学区的所有小学生每天都会额外学习 30 分钟的数学知识。该学区课程和教学主任戴安娜·哈诺贝克 (Diana Hanobeck) 表示，在幼儿园，额外的时间花在理解数字和数量等基本技能上，也花在加法和减法的基础知识上。

Chichester district leaders say implementing the intervention, called SpringMath, along with other steps that include hiring a math specialist for each school, has brought urgent attention to students’ math achievement by bringing more students to mastery — and a lot of that has to do with how much students are learning in kindergarten. Student math achievement, which dropped to a low of 13.5 percent of students proficient or advanced during the pandemic, has more than doubled across grades since the intervention began, although still below the state average. Last spring, 47 percent of the district’s fourth graders were proficient or advanced in math on the Pennsylvania System of School Assessment test.

奇切斯特地区领导人表示，实施名为 SpringMath 的干预措施，以及包括为每所学校聘请一名数学专家在内的其他措施，通过让更多学生掌握数学知识，引起了对学生数学成绩的紧急关注——而这在很大程度上与有多少学生在幼儿园学习。在疫情期间，学生数学成绩下降至 13.5% 的水平，自干预开始以来，各年级学生的数学成绩翻了一番多，但仍低于州平均水平。去年春天，该学区 47% 的四年级学生在宾夕法尼亚州学校评估系统测试中的数学成绩达到了精通或高级。

“The intervention is very targeted by skill and gives teachers data for each student,” said Hanobeck. “We are seeing it close gaps for students, and they are more able to access elementary school math.”

“干预措施非常有针对性地针对技能，并为教师提供了每个学生的数据，”哈诺贝克说。 “我们看到它缩小了学生的差距，他们更有能力学习小学数学。”

Murphy, the kindergarten teacher, said that while some students arrive at school able to do “rote counting,” others arrive with no prior knowledge or a very limited understanding of numbers and counting. The interventions have improved all students’ accuracy and fluency in more complex tasks, such as being able to count up or down from a number like 16 or 20, and adding and subtracting numbers up to 5.

幼儿园老师墨菲说，虽然有些学生到达学校时能够进行“死记硬背”，但其他学生则没有任何先验知识或对数字和计数的理解非常有限。这些干预措施提高了所有学生完成更复杂任务的准确性和流畅性，例如能够从 16 或 20 等数字进行加减数，以及 5 以内的数字加减法。

“It used to take all year for some students to count on from different starting points, that’s actually really hard for kids to do,” Murphy said. “Students are meeting their goals far faster now. We are moving on, but also moving deeper.”

“过去，一些学生需要花一整年的时间才能从不同的起点开始学习，这对孩子们来说实际上很难做到，”墨菲说。 “学生们现在实现目标的速度要快得多。我们正在继续前进，但也在更深入地前进。”

That deep thought is important, even in the earliest grades. Kindergarten math proficiency is especially predictive of future academic success in all subjects including reading, research has shown. In one study, students’ number competence in kindergarten — which includes the ability to understand number quantities, their relationships to each other, and the ability to join and separate sets of numbers, like 4 and 2 making 6 — presaged mathematical achievement in third grade, with greater number competence leading to higher math achievement.

即使在最低年级，这种深刻的思考也很重要。研究表明，幼儿园数学能力尤其可以预测未来所有科目（包括阅读）的学业成功。在一项研究中，学生在幼儿园的数字能力——包括理解数字数量、数字之间相互关系的能力，以及连接和分离数字组的能力，比如 4 和 2 等于 6——预示着三年级的数学成绩，具有更高的数字能力，从而获得更高的数学成绩。

It’s also the time when learning gaps between students are at their smallest, and it’s easier to put all students on equal footing. “Kindergarten is crucial,” said University of Oregon math education researcher Ben Clarke. “It’s well-documented in the research literature that gaps start early, grow over time and essentially become codified and very hard to remediate.”

这也是学生之间学习差距最小的时候，更容易让所有学生处于平等地位。 “幼儿园至关重要，”俄勒冈大学数学教育研究员本·克拉克说。 “研究文献中有充分记载，差距很早就开始，随着时间的推移而扩大，基本上已经被编入法典，很难弥补。”

But the math content commonly found in kindergarten — such as counting the days on a calendar — is often embedded within a curriculum “in which

但幼儿园常见的数学内容——例如计算日历上的天数——通常嵌入到课程中，“其中