Curriculum Matters: What We Teach and What Students
（continued）
Learning Progression. This section describes when topics are introduced and developed, the duration of these topics, and topics progression in the grades1 – 8.We found that topics are introduced in different grades and have different duration with in the two curricula. Many topics in Ontario curriculum are introduced earlier than within the Chinese curriculum.For example, concepts of fractions,estimating computations, polygons and circles, and patterning and algebra(simple) are introduced in grade one within Ontario curriculum, while the Chinese curriculum does not introduce these in grade one.
Most topics in grades1 – 8in the Ontario curriculum are taught over a longer span of years than many topics in the Chinese curriculum. For example, the Ontario curriculum has fractions as a topic in all eight elementary school years, while the Chinese curriculum has fractions as a topic for only 4 years.This also holds true for the ideas surrounding patterning and algebra and relations and functions that introduced in grade 1 within the Ontario curriculum and continue the next 7 years. In grade 8,there is some formal algebra and formulas within Ontario, but not to the depthfoundin China where students discuss(a b)(c d),(aplusmn;b)2,and a2minus; b2.In contrast, in the Chinese curriculum, concepts of patterning and algebra are introduced in grade 5, continue in grade 6, and then formal algebra commences in grade 7.
Over the grade1 – 8 span, each grade of the Chinese curriculum has fewer topics than those countries in the A composite group, while the Ontario curriculum has many more topics. The Ontario curriculum is spiral and repetitive, meaning students and teachers revisitthe same topic in multiple grades.In the Ontario curriculum,10 topics out of 34 are taught in every grade throughout grades1 to8, 9 topics are delivered in 5 to 7 years, 5 topics are delivered for 4 years, and 10 topics are delivered for 3 years or less(seeTable 1). In contrast, the Chinese curriculum is divided into three strands in elementary school: arithmetic, geometry,andstatistics(data).The three strands in secondary school(since grade7)are as follows:formal algebra, geometry, and statistics.The topics are taught for no more than 3 years in secondary school.Only one out of 43 topics is taught throughout the 8 years; two out of 43 topicsis taught in 5 and 6 years,respectively;five topics are taught for 4 years; and 36 topics are taught for 3years or less (seeTable 2).
Within Chinese curriculum, topic progression is faster than Ontario curriculum. An example of this is that Chinese students learn algebra at a different rate compared to Ontario students. They are exposed to one, two, and three variable systems of linear equations and linear inequalities in grade7,and learn algebra formulas such as(a b)(c d),(aplusmn;b)2,and a2minus; b2, and factors in grade 8. Chinese students also learn Euclidean geometry including proof and linearand reciprocal functions and properties in grade8.In contrast, Ontario students learn most of the linear equations and properties and algebra formulas such as(a b)(c d),(aplusmn;b)2,and a2minus; b2 when they are in grade9.
Grades 9– 12 Mathematics Curricula in Ontario and China
This section describes the topic coverage, focus, coherence, and learning progression in secondary schools.
Topic Coverage. In grade9 – 12, the two curricula cover different topics.The Ontario secondary school mathematics curriculum has 47 topics, and each grade includes 13, 10, 13,and 25 topics, respectively. In contrast, the Chinese curriculum has 35 topics, and each grade includes 10,9,11, and 8 topics, respectively.Some topics in the Chinese curriculum in this stage arranged in grades7 – 8 compare to the Ontario curriculum.The difference between the two curricula over the 4-year spanis that the Chinese students learn more topics about the concepts, equations, and properties of the circle, ellipse, hyperbola, and parabola, as well as the properties of absolute value functions, proving inequality, and complex number and operations while these topics were removed from the Ontario curriculum and integrated into post-secondary mathematics courses. At the same time, the Ontario curriculum also deemphasized formalgeometry and analytic geometry and the concept of formal proof and proving. Overall,the duration of 12 years sees Chinese students having learned more formal geometry and three more topics(absolute value, basicset theory andlogic, andconics)than their Ontario peers.
Focus. In grades9 – 11,the two compared curricula have a similar number of topics each year.However,in grade12,the Ontario curriculum has17 additional topics because there are three possible mathematics courses at this level.There are a total of 43 topics in grades 9– 12 in the Ontario curriculum;25 topics appear in grade12,and many are new topics because of these additional mathematics courses available to the Ontario secondary school
Table3 Ontario mathematics curriculum topics (grades9– 12
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Topic |
Grade： |
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11 |
12 |
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Data managementand simple probability |
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2Dgeometry: basics (shapes) |
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Polygons andcircles (shapes) |
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剩余内容已隐藏，支付完成后下载完整资料 课程事项：我们教什么以及学生收获什么（下）学习进展。本节介绍了主题在1-8年级引入和发展的时间、这些主题的持续时间以及主题的进展。我们发现在这两门课程中，主题是不同年级引入的和学习的时长也是不同的。安大略省课程中的许多主题比中国课程介绍得更早。例如，在安大略省的一年级课程中引入了分数、估计计算、多边形和圆、图形和代数（简单）等概念，而在一年级的中国课程中没有引入这些概念。 安大略省1-8年级的大部分课程都比中国课程中的许多课程的授课时间更长。例如，安大略省的课程在所有八个小学年度都有分数作为一个主题，而中国课程只有四个年度里把分数作为一个主题。这也适用于安大略省一年级课程中引入的关于模式和代数以及关系和函数的思想，并在接下来的7年里持续下去。在8年级，安大略省有一些正式的代数和公式，但没有深入到中国学生讨论，的程度。相比之下，在中国课程中，模式和代数的概念在五年级引入，在六年级继续，然后在七年级开始正式代数。 在1-8年级，中国课程的每一年级都比A 组合组中的国家有更少的主题，而安大略省的课程有更多的主题。安大略省的课程是螺旋式和重复性的，这意味着学生和教师在多个年级重温同一主题。在安大略省的课程中，34个科目中的10个科目在1至8年级的每个年级都有，9个科目在5至7年内完成，5个科目在4年内完成，10个科目在3年或3年以下完成（见表1）。相比之下，小学阶段的中国课程分为三个部分：算术，几何，以及统计数据。中学（从七年级开始）的三个方面是：形式代数、几何和统计学。这些题目在中学里教了不超过3年。43个主题中只有一个是在8年中教授的；43个主题中有两个分别在5年和6年内教授的；5个主题教授了4年；36个主题教授了3年或3年以下（见表2）。 在中国课程中，主题的发展比安大略省的课程要快。举个例子，中国学生学习代数的速度与安大略省学生不同。他们在7年级接触一、二和三个变量的线性方程组和线性不等式，学习代数公式，如，，以及8年级的因式。中国学生在八年级还学习包括证明的欧几里德几何，线性函数和反比例函数及其性质。相比之下，安大略省学生在9年级时学习大多数线性方程和性质以及代数公式，如，。 中国和安大略省9-12年级的课程本节介绍中学的主题覆盖、重点、连贯性和学习进展。 主题报道。在9-12年级，这两门课程涵盖不同的主题。安大略省中学数学课程有47个主题，每个年级分别包括13、10、13和25个主题。相比之下，中国课程有35个主题，每个年级分别有10个、9个、11个和8个主题。与安大略省的课程相比，这一阶段的中国课程中的一些主题安排在7-8年级。这两门课程在四年的时间里的不同之处在于，中国学生学习了更多关于圆、椭圆、双曲线和抛物线的概念、方程和性质，以及绝对值函数的性质、不等式的证明、复数和运算的知识，而这些知识从安大略省的课程中删除了，并纳入高中后数学课程。同时，安大略省课程也不强调形式几何和解析几何以及形式证明和证明的概念。总的来说，在12年的时间里，中国学生比安大略省的同龄人学习了更多的形式几何和更多的三个主题（绝对值、基本集合理论和逻辑、圆锥曲线）。 重点。在9-11年级，两个比较课程的主题数量相似。然而，在12年级，安大略省课程有17个额外的主题，因为在这一级别有三个可能的数学课程。安大略省课程中9-12年级共有43个主题；12年级共有25个主题，其中许多是新主题，因为这些额外的数学课程可供安大略省中学生使用（见表3）。相比之下，中国课程集中在较少的话题上，特别是在12年级，只有8个新的话题。在一年多的时间里，只有两个主题被教授（见表4）。在中国，12年级的大部分时间都是为了入学考试而学习，而在安大略省，没有入学考试，因此学生有更多的时间专注于许多新的课题。然而，在这两种教育体系中，12年级的学生必须申请高中后学习。 表3安大略省数学课程主题（9-12年级）
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