看看俄罗斯小学数学都教什么？四至六年级数学大纲

众所周知，俄罗斯是个数学强国，在近代一百年间，曾涌现出多位杰出的数学家。在欧美的大学和数学研究所里，前苏联时代移民过去的大数学家也比比皆是。

那么，俄罗斯是怎么培养出这么多数学人才的？这要归功于坚实的数理基础教育。

今天，我们来看看俄罗斯在小学阶段的课程大纲。小学四至六年级。

俄罗斯四年级

Calculation-larger numbers

The numbers 100 to 999

Addition

Addition up to the number 999

Subtraction

Subtraction with borrowing

Subtraction of two-digit numbers Involving comparison.

Subtraction up to the number 999 using the renaming method

Multiplication

Multiplication – important facts.

Place value

The numbers 1000 to 9999

The multiplication sign

Strategies for division

Calculations

Multiples of 10 up to 100

Addition

Subtraction up to the number 10

Problems

Solve and record division using known facts and sharing

Division

Division with and without a remainder

Length

Using the metre as a formal unit to measure perimeter

Using the formal unit of the centimetre to measure length and perimeter

Read and calculate distances on a map using the formal unit kilometre

Compare and convert formal units of measurement

Area

Introduction to the square centimetre

Comparing and ordering areas.

Weight/mass

The kilogram

The gram and net mass

2-D shapes

Using the prefix to determine polygons

Spatial properties of quadrilaterals

Recognise and name triangles

Tessellating 2-D shapes

Use grids to enlarge/reduce 2D shapes

3-D shapes

Recognise and name pyramids according to spatial properties

Angles

Measure and classify angles

Lines and angles

Mapping and grid references

Main and intermediate compass points

Informal coordinate system

Capacity

The relationship between the common units of capacity, the litre and the millilitre

Using the cubic cm and displacement to measure volume and capacity

Using the cubic cm as a standard unit of measurement for volume and capacity

Converting between volume and capacity using kilolitres and litres

Estimate, measure and compare the capacity of containers

Converting between volume and capacity using millilitres and litres

Time

Analogue – Telling time – minutes in the hour

Comparing analogue and digital time

Units of time

Minutes to the hour

Minutes past the hour

AM and PM time

Decimals

Introduction to decimals

Comparing and ordering decimals to two decimal places

Decimals with whole numbers 10th and 100th

Adding decimals to two decimal places

Subtracting decimals to two decimal places

Using decimals – shopping problems

Using decimals to record length

Rounding decimals

Fractions

Using fractions 1/2, 1/4, 1/8 to describe part of a whole

Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection

Comparing and ordering fractions

Finding equivalent fractions

Mixed numbers (mixed numerals)

Fractions 1/5, 1/10, 1/100

Percentages

Introduction to percentages, including relating common fractions to percentages

Changing fractions and decimals to percentages using tenths and hundredths

俄罗斯五年级

Place value

The numbers 1000 to 9999

Addition

Addition up to the number 999

Subtraction

Subtraction up to the number 999 using the renaming method

Subtraction involving four digit numbers and beyond using the renaming method.

Counting and numeration

The numbers 10 000 to 99 999

Addition to 9999 and beyond

Multiplication

Multiples and factors of whole numbers

Multiplication using extended algorithms.

Division

Division with and without a remainder.

Dividing two and three digit numbers by a single digit number.

Multiplication

Multiplication by 2 and 3 digits

Multiplying 2-digit numbers by multiple of 10

Multiplying 3 and 4-digit numbers by multiples of 100

Time

AM and PM time

24 hour time

Average speed

Angles

Measure and classify angles

Lines and angles

Mapping and grid references

Main and intermediate compass points

Informal coordinate system

2-D shapes

Recognise and name triangles

3-D shapes

Recognise and name pyramids according to spatial properties

Recognise and name prisms according to spatial properties

Viewing 3-D shapes.

Tessellating 2-D shapes

Use grids to enlarge/reduce 2D shapes

Data

Line graphs.

Pie and bar graphs.

Length

Read and calculate distances on a map using the formal unit kilometre

Compare and convert formal units of measurement

Area

Introduction to the square centimetre

Comparing and ordering areas

Larger areas: square metre, hectare, square kilometre.

Volume

Using the cubic centimetre to measure volume

Capacity

The relationship between the common units of capacity, the litre and the millilitre

Using the cubic cm and displacement to measure volume and capacity

Using the cubic cm as a standard unit of measurement for volume and capacity

Converting between volume and capacity using kilolitres and litres

Estimate, measure and compare the capacity of containers

Weight/masss

The kilogram

The gram and net mass

Decimals

Introduction to decimals

Comparing and ordering decimals to two decimal places

Decimals with whole numbers 10th and 100th

Adding decimals to two decimal places

Subtracting decimals to two decimal places

Using decimals – shopping problems

Using decimals to record length

Rounding decimals

Adding decimals with a different number of decimal places

Subtracting decimals with a different number of places

Multiplying decimals by 10, 100 and 1000

Multiplying decimals by whole numbers

Dividing decimals by 10, 100 and 1000

Dividing decimal fractions by whole numbers

Fractions

Finding equivalent fractions

Mixed numbers (mixed numerals)

Fractions 1/5, 1/10, 1/100

Subtracting fractions from whole numbers

Adding and subtracting fractions with the same denominator

Percentages

Introduction to percentages, including relating common fractions to percentages

Changing fractions and decimals to percentages using tenths and hundredths

Sign word problems

Solving Word Problems by recognising Sign Words

Equations

Problem solving strategies

Number problems

Problems with numbers.

Money

Problems involving money

俄罗斯六年级

Counting and numeration

The numbers 10 000 to 99 999

Addition to 9999 and beyond

Seven digit numbers

Subtraction

Subtraction involving four digit numbers and beyond using the renaming method.

Multiplication

Multiples and factors of whole numbers

Multiplication using extended algorithms

Multiplication by 2 and 3 digits

Multiplying 2-digit numbers by multiple of 10

Multiplying 3 and 4-digit numbers by multiples of 100

Multiplying 2-digit numbers by 2-digit numbers

Multiplying 4-digit numbers by 3-digit numbers

Division

Division with and without a remainder.

Dividing two and three digit numbers by a single digit number.

Divide whole numbers by a 2 digit divisor

Division/

repeat subtraction

Repeated subtraction with divisors less than 20 with no remainders

Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders

Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders

Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders

Repeated subtraction by multiples of 10 with divisors less than 20 with remainders

Repeated subtraction with divisors greater than 20 with remainders as fractions

Repeated subtraction with divisors less than 35 with some remainders

Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders

Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders

Using divide, multiply and subtraction in the bring down method

3-D shapes

Recognise and name pyramids according to spatial properties

Recognise and name prisms according to spatial properties

Recognise nets for prisms, pyramids, cubes and cones

Area

Introducing the rules for finding the area of a rectangle and a parallelogram.

Larger areas: square metre, hectare, square kilometre.

Problems with area.

Volume

Introducing the formula for volume

Using the cubic metre to measure volume.

Solving Problems about Volume

Capacity

Converting between volume and capacity using millilitres and litres

Weight/mass

The tonne – converting units and problems

Problems with mass

Decimals

Decimals to three decimal places

Adding decimals with a different number of decimal places

Subtracting decimals with a different number of places

Multiplying decimals by 10, 100 and 1000

Multiplying decimals by whole numbers

Dividing decimals by 10, 100 and 1000

Dividing decimal fractions by whole numbers

Dividing numbers by a decimal fraction

Percentages

Introduction to percentages, including relating common fractions to percentages

Changing fractions and decimals to percentages using tenths and hundredths

Changing percentages to fractions and decimals

Fractions

Improper fractions

Subtracting fractions from whole numbers

Adding and subtracting fractions with the same denominator

Multiplying and dividing to obtain equivalent fractions

Reducing fractions to lowest equivalent form

Comparing and ordering fractions greater than (>) 1

Multiplying fractions by whole numbers

Fractions of whole numbers

Sign word problems

Solving Word Problems by recognising Sign Words

Equations

Problem solving strategies

Number problems

Problems with numbers

Money

Problems involving money

Volume/capacity

Problems with volume/capacity

对比上期的一到三年级教学内容，我们会发现量明显有所增加，但从深度上说并没有急于拉高难度，仍然给小学生足够的时间消化巩固基础知识。

再看看新加坡，我们以前发过的新加坡数学大纲，小学的内容也不难。其实，这些国家的模式是先松后紧，在数学启蒙阶段打好基础，做好从具体到抽象的反复训练，强调理解而不是硬记，或许可以给我们焦虑的家长些启发。