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Mathematics standards specify the mathematics students should know and be able to do. Mathematics standards are typically organized into five mathematical content areas including: numbers and operations, measurement, geometry, algebra, data and probability. Standards may also develop desired mathematical abilities such as conceptual understanding, computation and reasoning skills.

Contents 1 APEC Member Math Standards 2 Analysis of Standards 3 Parallel and Sequential Course Structure 4 See also

APEC members differ in the degree of centralization of mathematics and other standards. Most APEC members have a central set of standards approved by the Ministry responsible for education. However, several APEC members, including Canada and the United States, do not have nationally-set standards, but each province/state determines their own.

APEC Member Math Standards

A summary table comparing 2007 math standards from 9 APEC members is shown below.

Summary Table Comparing Math Standards from APEC Member
Economy	National/Regional Standards	Organization	Years Included	Middle and Secondary Structure: Parallel and Sequential
Australia Statements of Learning	Regional. National documents are guidelines for states and territories	Statements of Learning: Every other year beginning with Year 3	Years 3, 5, 7, & 9	Sequential
China Grades 1-9  Grades 10-12	National	Primary & Lower Secondary: three year spans Upper Secondary: single years	Primary: Years 1-3 Years 4-6 Lower Secondary: Years 7-9 Secondary: Years 10 & 11	Parallel
Japan	National	All Levels: Single Years	Years 1-11	Parallel
Korea Grades 1-10 Grades 11-12	National	All Levels: Single Years	Years 1-12	Sequential
Malaysia	National	All Levels: Single Years	Years 1-6	Sequential
New Zealand	National with significant flexibility at the regional level.	Primary & Lower Secondary: Year spans with concentration at alternating years	Pre-kindergarten-Year 4 (Year 1 Focus) Kindergarten-Year 6 (Year 3 Focus) Year 2- 8 (Year 5 Focus) Year 3- 10 (Year 7 Focus) Year 6-12(Year 9 Focus) Year 7-12(Year 10 Focus) Year 8- Post-Secondary (Year 11 Focus) Year 9- Post-Secondary(Year 12 Focus)	Sequential
Singapore	National	Primary & Lower Secondary: Single Years Upper Secondary: Two year span	Primary & Lower Secondary: Years 1-9 Upper Secondary: Years 9-10	Sequential
Chinese Taipei Grades 1-9 High School (math I) High School (math II)	National	All Levels: Single Years	Years 1-12	Sequential
United States (MA)	Regional by state.	All Levels: Two year spans	Pre-kindergarten & Kindergarten Years 1-2 Years 3-4 Years 5-6 Years 7-8 Years 9-10 Years 11-12	Sequential
United States (NAEP)	Cumulative national assessment framework.	All Levels: Four year spans	Years 1-4 Years 5-8 Years 9-12	Sequential

Analysis of Standards

 A comparative analysis of the above mathematics (and science) standards is being undertaken by Achieve, an organization devoted to improving standard setting in the United States. The Achieve initial findings, presented at the 2008 APEC Education Ministerial, included an in-depth analysis to identify the common core mathematics (and science) topics covered across standards from different APEC Economies. The common core topics were defined as topics present in two-thirds of the standards at each grade range (see table below):   

• In mathematics, topic agreement across standards is greatest in the lower and middle grades, with the least topic agreement among upper secondary grades (10-12).
• In science the situation is reversed from mathematics.  The lowest rate of topic agreement is found in the primary grades 1-6 and the greatest topic agreement occurs in biology in the upper secondary grades. 

These results suggest that APEC Economies may want to compare their standards against the common core in primary and middle math and secondary science and focus joint work on developing a common core for upper mathematics and primary and secondary science. 

                                                       Percent of Topics Common to At Least Two-Thirds of APEC Economies Mathematics or 
                                                       Science Standards                                                             

Math	Grade 1-6 Average		Grade 7-9 Average	Grade 10-12 Average
	76% Range: 71%-89%		68% Range: 59%-85%	34% Range: 28%-55%
Science	Grade 1-4 Average	Grade 5-6  Average	Grade 7-10 Average	Biology Average
	35% Range: 22%-53%	43% Range: 31%-53%	67% Range: 56%-82%	81% Range: 72%-91%

                                                           Source: Achieve (2008)

Although the mathematics standards identify the content to be taught for particular grades and courses, but in the upper grades students have discretion over course taking   depending upon their system's course requirements. The results in the table below show that U.S. students have more discretion and a much lower percentage of students who take the more difficult mathematics courses -- less than 15 percent of U.S. high school graduates ever enroll in trigonometry, statistics or calculus. In most other systems, the percentages who are exposed to the rigorous mathematics courses is in excess of eighty percent.  

Percent of Upper Secondary Graduates Who Take the Following Mathematics Courses

	Lin Eq	Quad Eq	Log Eq	Trig Eq	Geo Pln	Geo Analy	Stat	Calc
China	100	100	100	100	100	100	100	100
Chinese Taipei (GR=100%)	100	100	100	100	100	100	100	0
Indonesia (GR=90%)	100	100	100	100	100	100	100	100
Japan (GR=100%)	100	100	87	87	79	87		87
N.Z. (GR=75%)	100	100	100	100	100	100	100	100
U.S. (GR=75%) 1	95	68	68	10	75		8	13
Source: APEC government member submissions of official statistics. 1Submission based on National Assessment of Educational Progress (NAEP) 2005 transcript study of high school graduates.   Notes: GR = Graduation Rate

In an effort to strengthen high school enrollment in mathematics, U.S. states are increasing course requirements in mathematics for high school graduation.

Parallel and Sequential Course Structure

The majority of APEC members sequence mathematics courses so that students are exposed to only one major math content area within a semester or year. Thus, a typical sequential course pattern is first year algebra, geometry, second year algebra, trigonometry, calculus and statistics. If students do not make it past geometry they are never exposed to the later mathematics work, although they may have all the necessary prerequisites.

The parallel math-course sequence followed by China and Japan teach several mathematical topics during the same semester or year, although they may be taught at different times. To illustrate, 

• The first year Japanese mathematics course in upper secondary (grade 9) includes algebra concepts consisting of linear equations, inequalities, and quadratic functions; and also, geometric measurement and basic trigonometric functions.
• The second year course delves deeper into functions and trigonometry and adds a section on the key calculus ideas of derivatives and integration.   

See also

• Mathematics Education
• Mathematics Assessments
• Mathematics Instruction (lesson study)