Thursday, February 14, 2008
Wednesday, February 13, 2008
This is what is wrong with so many US math curricula.
You probably know that in international comparisons,
US students don't do really well in math.
One reason for that can be found in comparing the typical math
curricula in those countries that do well, versus typical
curricula used in the USA.
The following article of mine is based on a report by William
Schmidt, Richard Houang, and Leland Cogan called A Coherent
Curriculum: The Case of Mathematics, which appeared in
Summer 2002 in American Educator.
Some differences that emerge are as follows. The US math
curricula tend to be
* not focused. No country in the world covers as many topics
as US in their mathematics textbooks. For example, in
Japan, eighth-grade textbooks have about 10 topics
whereas US books have over 30 topics.
* highly repetitive. The average duration of a topic in US is
almost 6 years (!) versus about 3 years in the best-
performing countries. Lots of spiraling and reviewing
is done. Like Schmidt says, "We introduce topics early and
then repeat them year after year. To make matters worse,
very little depth is added each time the topic is addressed
because each year we devote much of the time to reviewingthe topic."
* not very demanding by international standards, especially
in the middle-school. In the USA, students keep studying
basic arithmetic till 7th and 8th grade, whereas other
countries change to beginning concepts in algebra and
geometry.
* incoherent. The math books are like a collection of
arbitrary topics. Like Schmidt et al. say, "...in the United
States, mathematics standards are long laundry lists of
seemingly unrelated, separate topics."
What this means is that typically in the US, a math topic is
studied for a short time, and then the next one, and then the
next one, on and on. A good part of this short time is spent
reviewing previous year's knowledge. It follows that any
particular math topic is NEVER studied very deeply in any
given school year.
Also, during the school year, many topics are covered but not in
a coherent and logical order. Instead the topics tend to jump
here and there in somewhat of an arbitrary fashion.
So, the end result of following a curriculum that is like
hodgepodge and "inch deep and mile wide", by the end of eighth
grade US students are about two years behind their
counterparts in the best performing countries.
*******************************************
CHART WHICH I CAN'T SHOW IN THE EMAIL
*******************************************
I need you to click to my website to see these very revealing two
charts that show which topics are typically covered on which
grade, either in the States, or in the best performing countries.
I got a special permission from the main author of the
aforementioned report to reproduce these on my site.
You can continue reading the article there.
http://www.homeschoolmath.net/teaching/coherent-curriculum.php#chart
Sincerely,
Maria Miller
Saturday, February 9, 2008
Syllabus of Primary One
Mathematics Syllabus of Primary One 2007/2008
Month | Units | Lessons Periods(40') | Terms | ||
September & October 2007 | Unit1: Sets. | 1 2 | Classification Comparison Exercises And Activities | 5 9 | First Term |
Unit2: Numbers From 1 To 9 –Half And Quarter.
| 1 2 3 4 5 6 | Numbers1,2,And3 Numbers4,5,And6 Numbers7,8,And9 Ascending And Descending Order Ordinal Numbers Comparing Numbers From 1 To 9 | 3 3 3 3 3 2 | ||
November 2007 | Unit2: (Continued). | 7 | Half And Quarter Exercises And Activities | 5 | |
Unit3: Relative Positions. . | 1 2 3 4 5 | In Front Of/Behind Over/Under Up/Down Right/Left/Between Into/Out Of Exercises And Activities | 2 2 2 3 3 | ||
December 2007 | Unit4: Adding And Subtracting Up To 9.
| 1 2 3 | Using The Addition Sign (+) Adding Two Numbers Families Of Numbers From2 To9 Exercises And Activities. | 2 4 3 | |
January 2008 | Unit4: (Continued).
| 4 5 6
| Using The Subtraction Sign(-) Subtracting Two Numbers The Relation Between Addition And Subtraction Exercises And Activities General Exercises. | 2 4 4 | |
February 2008 | Unit1: Numbers Up To 99.
| 1 2 3 4 5 6 7 | Zero The Number Ten Family Of Number 10 Perfect Tens Ones And Tens The Place Value Ordering And Comparison Exercises And Activities | 3 2 3 4 3 2 6 | Second Term |
March 2008 | Unit2: Adding And Subtracting Up To 99. | 1 2 | Adding Up To 99 Subtracting Up To 99 Exercises And Activities | 5 8 | |
April 2008 | Unit3: Geometry And Measurement.
| 1 2 3 4 5 6 7 8 | Solids Solids And Shapes Symmetry Money Capacity Days Of The Week Length Measuring Lengths Exercises And Activities | 3 2 3 2 1 2 3 6 | |
May 2008 | Unit4: Statistics. | 1 | Statistics Exercises And Activities | 8 |
Objectives of P1
OBJECTIVES
- Recognize the set.
- Describe the set.
- Classify the objects to sets according to a specific property.
- Compare between two sets using the equivalence between the elements.
- Recognize the empty set without mention its name.
- Recognize the property of adding zero
- Recognize numerical examples of the properties of adding up to 9 without mention the name of the property.
- Solve simple open numerical sentences including the equality and the inequality.
- Solve simple daily problems on addition and subtraction.
- Recognize a simple numerical extension patterns and complete its elements.
- Recognize mathematical models included numerical sentences for a simple daily situation.
- Compare between the different things and describe quantitative changes or nature on it.
- Count freely and with understanding the numbers of elements in small sets up to 9
- Relate the meaning of the number to its symbol and its name and use that in dealing with simple life situations.
- Recognize the concept of arrangement of numbers.
- Arrange the numbers from zero to ten.
- Determine the facts of the numbers.
- Recognize the meaning of addition and subtraction up to 9.
- Recognize the place value of the digits of the numbers up to 99.
- Add 2-digit numbers with renaming.
- Subtract 2-digit numbers with renaming .
- Perform adding and subtracting operations quickly.
- Do mental calculations.
- Use the signs <, > or = to compare two numbers.
- Recognize the meaning of half an quarter.
- Read and write Half and Quarter in letters and in digits.
- Recognize the topological positions (up/down – in front of/behind-into/out-left/between/right)
- Recognize the shapes(square-triangle-circle-rectangle)
- Determine the shapes properties.
- Analyzing some shapes to its elements.
- Structure the simple shapes.
- Recognize the symmetric meaning using some activities.
- Complete some shapes to be symmetrical shapes.
- Recognize the units of money.
- Recognize the capacity using non standard units.
- Recognize the days of the week and arrange them.
- Recognize the length.
- Recognize some non-standards units to measure length.
- Use standard units to measure units.
- Collect data from the environment.
- Represent data using photos.
- Represent data using number line.
- Investigate some information from the data.
syllabus of P4
Mathematics syllabus of primary four 2007/2008
Month | Subject | Terms |
September & October 2007 | Unit1: Large numbers and operations. Hundred thousands-Millions-Milliard -Adding and subtracting large numbers -Multiplying two numbers | First term |
November 2007 | Unit1: (continued) Division-tests and activities.
Divisibility-divisibility by 2 - divisibility by 5 - divisibility. By 3. | |
December 2007 | Unit2: (continued). Factors and the prime numbers- Factorize a number -Common factors. -Highest common factors -Lowest common multiple. | |
January 2008 | Unit2: (continued). Application of the highest common factors and lowest common multiple -solving tests and activities | |
February 2008 | Unit1: Fractions Equal fractions –the simplest form of the fractions –L.C.M. of the denominators –the whole number in the form of fraction-Mixed numbers-tests and activities. | Second term |
March 2008 | Unit1: (continued) Comparing fractions –Adding and subtracting fractions-Multiplying and dividing fractions-tests and activities. | |
April 2008 | Unit2: Geometry Measuring angles- drawing angles –sum of measures of the angles of the triangle- types of triangles- activities | |
May 2008 | Unit3: Representation of data. Data representation using broken line –tests of the unit –general tests |
Teacher
Inspector Director
Objectives of P4
OBJECTIVES
(1) Learn large numbers such as millions and milliards, and how to read a large number and understand the place value of the digits of the number.
(2) Learn how to compare and order large numbers by quantity
(3) Learn and master the fundamentals of the addition and subtraction of large numbers in column form
(4) Learn and master the fundamentals of the multiplication with a two-digit multiplier in column form
(5) Learn and master the fundamentals of division with a single/two-digit divisor in column form
(6) Recognize the meaning of divisibility (divisible numbers) and understand the numbers from such viewpoint.
(7) Understand the meaning and relationship between factors and multiples, and deepen their feel for numbers.
(8) Understand the meanings of common factors and common multiples, and understand how to find them.
(9) Understand the meanings of the highest common factor and lowest common multiple, and how to calculate them.
(10) Understand the meaning of prime numbers. Students should be able to express a given number as a product of prime numbers.
(11) Understand the characteristics of numbers in multiples of 2, 5, and 3.
(12) Identify equal fractions, understanding how to reduce fractions (to a common denominator)
(13) Compare and order the values of fractions with different denominators
(14) Understand mixed fractions, with a good grasp of the correlation between fractions and whole numbers
(15) Understand and deal with the addition/subtraction of fractions
(16) Understand and deal with the multiplication/division of fractions
(17) Consider a fraction as a number, to have a wider concept of number
(18) Measure given angles using of a protractor.
(19) Draw figures of angles of a given size.
(20) Measure interior angles of a triangle using a protractor.
(21) Determine the type of triangle based on the length of its sides.
(22) Determine the type of triangle based on the size of its angles.
(23) Collect and organize materials according to type and purpose.
(24) Represent materials and two-dimensional tables as a line graph.