📖 原文
(1) People appear to be born to compute. The numerical skills of children develop so early (2) and so inexorably that it is easy to imagine an internal clock of mathematical maturity (3) guiding their growth. Not long after learning to walk and talk, they can set the table with (4) impressive accuracy — one plate, one knife, one spoon, one fork, for each of the five (5) chairs. Soon they are capable of noting that they have placed five knives, spoons, and (6) forks on the table and, a bit later, that this amounts to fifteen pieces of silverware. (7) Having thus mastered addition, they move on to subtraction. It seems almost reasonable (8) to expect that if a child were secluded on a desert island at birth and retrieved seven (9) years later, he or she could enter a second-grade mathematics class without any serious (10) problems of intellectual adjustment. (11) Of course, the truth is not so simple. This century, the work of cognitive psychologists (12) has illuminated the subtle forms of daily learning on which intellectual progress (13) depends. Children were observed as they slowly grasped — or, as the case might be, (14) bumped into — concepts that adults take for granted, as they refused, for instance, to (15) concede that quantity is unchanged as water pours from a short stout glass into a tall (16) thin one. Psychologists have since demonstrated that young children, asked to count the (17) pencils in a pile, readily report the number of blue or red pencils, but must be coaxed (18) into finding the total. Such studies have suggested that the rudiments of mathematics are (19) mastered gradually, and with effort. They have also suggested that the very concept of (20) abstract numbers — the idea of a oneness, a twoness, a threeness that applies to any class (21) of objects and is a prerequisite for doing anything more mathematically demanding than (22) setting a table — is itself far from innate.
❓ 试题解析
问题 31： What does the passage mainly discuss?
A. Trends in teaching mathematics to children
B. The use of mathematics in child psychology
C. The development of mathematical ability in children
D. The fundamental concepts of mathematics that children must learn
✅ 正确答案： C）The development of mathematical ability in children
📝 解析： 全文讨论儿童数学能力的发展：早期数数、加减法能力，以及认知心理学揭示的逐步掌握过程。
💡 解题技巧： 主旨题看首段提出的内在数学成熟时钟及后文的修正。
问题 32： It can be inferred from the passage that children normally learn simple counting
A. soon after they learn to talk
B. by looking at the clock
C. when they begin to be mathematically mature
D. after they reach second grade in school
✅ 正确答案： A）soon after they learn to talk
📝 解析： "Not long after learning to walk and talk, they can set the table with impressive accuracy" — 学会走路说话后不久就能数数摆餐具。
💡 解题技巧： 推理题定位时间顺序（walk and talk → set the table）。
问题 33： The word "illuminated" in line 12 is closest in meaning to
A. illustrated
B. accepted
C. clarified
D. lighted
✅ 正确答案： C）clarified
📝 解析： "cognitive psychologists have illuminated the subtle forms of daily learning" — illuminated = 阐明/揭示。
💡 解题技巧： 词汇题：illuminate = clarify = shed light on。
问题 34： The author implies that most small children believe that the quantity of water changes when it is transferred to a container of a different
A. color
B. quality
C. weight
D. shape
✅ 正确答案： D）shape
📝 解析： "they refused to concede that quantity is unchanged as water pours from a short stout glass into a tall thin one" — 不同形状（short stout vs. tall thin）。
💡 解题技巧： 推理题定位形状对比。
问题 35： According to the passage, when small children were asked to count a pile of red and blue pencils they
A. counted the number of pencils of each color
B. guessed at the total number of pencils
C. counted only the pencils of their favorite color
D. subtracted the number of red pencils from the number of blue pencils
✅ 正确答案： A）counted the number of pencils of each color
📝 解析： "readily report the number of blue or red pencils, but must be coaxed into finding the total" — 能数每种颜色各多少，但需要引导才能找到总数。
💡 解题技巧： 细节题定位"readily report"。
问题 36： The word "They" in line 19 refers to
A. mathematicians
B. children
C. pencils
D. studies
✅ 正确答案： D）studies
📝 解析： "Such studies have suggested ... They have also suggested" — They 指 studies。
💡 解题技巧： 代词题找前一个句子的主语（Such studies）。
问题 37： The word "prerequisite" in line 21 is closest in meaning to
A. reason
B. theory
C. requirement
D. technique
✅ 正确答案： C）requirement
📝 解析： "a prerequisite for doing anything more mathematically demanding" — prerequisite = 先决条件/必要条件。
💡 解题技巧： 词汇题：prerequisite = requirement = necessary condition。
问题 3838： The word "itself" in line 22 refers to
A. the total
B. the concept of abstract numbers
C. any class of objects
D. setting a table
✅ 正确答案： B）the concept of abstract numbers
📝 解析： "the very concept of abstract numbers ... is itself far from innate" — itself 强调 this concept。
💡 解题技巧： 代词题找被强调的名词短语。
问题 39： With which of the following statements would the author be LEAST likely to agree?
A. Children naturally and easily learn mathematics.
B. Children learn to add before they learn to subtract.
C. Most people follow the same pattern of mathematical development.
D. Mathematical development is subtle and gradual.
✅ 正确答案： A）Children naturally and easily learn mathematics.
📝 解析： 作者说"the truth is not so simple"，数学基础是 gradually, with effort 掌握的，抽象数字概念 far from innate。
💡 解题技巧： "LEAST likely"题找与作者观点相悖的选项。
问题 40： Where in the passage does the author give an example of a hypothetical experiment?
A. Lines 3-6
B. Lines 7-10
C. Lines 13-15
D. Lines 19-22
✅ 正确答案： B）Lines 7-10
📝 解析： "if a child were secluded on a desert island at birth and retrieved seven years later" — 假想实验。
💡 解题技巧： 定位题找"if"引导的假设情景。
🌐 中文翻译
人似乎生来就会计算。儿童的数学技能发展得如此之早、如此不可阻挡，以至于很容易想象有一个内在的数学成熟时钟在指导他们的成长。学会走路和说话后不久，他们就能以惊人的准确性摆好桌子——五个椅子中的每一个配一个盘子、一把刀、一个勺子、一把叉子。很快他们就能注意到他们在桌子上放了五把刀、五个勺子和五把叉子，再稍晚一点，他们会意识到这只是十五件餐具。掌握了加法之后，他们又转向减法。似乎几乎有理由期望，如果一个孩子出生时就被隔离在一个荒岛上，七年后被接回，他或她可以进入二年级的数学课而没有任何严重的智力适应问题。 当然，事实并非如此简单。本世纪，认知心理学家的研究阐明了智力进步所依赖的日常学习的微妙形式。观察到儿童慢慢地掌握——或者，在某些情况下，磕磕绊绊地遇到——成年人认为理所当然的概念，例如，他们拒绝承认当水从一个短粗的杯子倒进一个细长的杯子时水量是不变的。后来的心理学家证明，幼儿在被要求数一堆铅笔中的数量时，很容易说出蓝色或红色铅笔的数量，但必须被引导才能找出总数。这些研究表明数学的基础是逐步掌握的，并且需要付出努力。它们还表明，抽象数字的概念——适用于任何一类物体的"一"、"二"、"三"的概念，并且是做任何比摆桌子更具数学挑战性的事情的先决条件——本身远非天生。
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