From APEC HRDWG Wiki

On behalf of the Asia-Pacific Economic Cooperation (APEC) and the United States Department of Education, Achieve, Inc. conducted an analysis of the mathematics standards and science standards. This Analysis aims to qualify how the standards are organized, and to identify common content and performance expectations of APEC member economies’ standards.

Achieve, Inc. is an independent, bipartisan, non-profit education reform organization based in Washington, DC that helps states raise academic standards and graduation requirements, improve assessments, and strengthen school and student accountability. In this study, Achieve did work on behalf of APEC to compare and contrast education standards in mathematics in twelve APEC economies.

To download the full report by Achieve, click here.

Contents 1 Overview of Study 1.1 International Benchmarking 2 Goals 3 Methodology 4 Findings 4.1 Qualitative Aspects of Standards 4.2 Core Content Expectations 4.3 Performance Expectations 5 Conclusion

Overview of Study

Standards are the primary policy tool for defining expectations for what students must learn and teachers must teach.  Standards provide a framework for the development and use of textbooks and other instructional materials, assessments and teacher preparation. Achieve analyzed the mathematics standards for students in 12 of APEC's 21 member economies. 

In June 2008 in Lima, Peru, the Education Ministers at the 4th AEMM approved the new Education Ministers' 21st Century Agenda in support of math and science. This subject matter can no longer be viewed as relevant only to scientists and engineers. Mastering mathematical principles is essential to navigating the data-driven and technological world of the 21st century, no matter one's industry. Because APEC could not agree more, it is utilizing international benchmarking as a tool to compare and contrast mathematics standards across twelve APEC economies, beginning with this analysis. APEC's Mathematics Standards are available in translation on the Mathematics Standards page.

International Benchmarking

International benchmarking (such is this analysis) is increasingly seen as an important way to gauge America’s expectations and competiveness in relation to other nations. International benchmarking is an important measuring tool for improving education standards among APEC's member economies as it provides for a comparison of successful education methods. International benchmarking is a means for economies to learn about successful school improvement measures from others across the globe.

International benchmarking:

• Allows for one economy to benefit from the experience of another economy.
• Creates an opportunity for schools and educators across the globe to share best practices and learn from the successes of others.
• Greatly expands opportunities for cross-cultural communication and allows collaboration of ideas through the internet.
• Provides models of high performing, as well as rapidly improving, economies to others who may not possess access to such models in a local school system or economy.
• Creates a world laboratory for new ideas and collaboration.

In this case, we used international benchmarking as a tool to study math standards. Math standards allow us to identify what students should know and be able to do at different ages and grade levels.

Goals

This analysis aims to determine similarities and differences among the 12 participating APEC member economies' expectations and priorities in three key areas:

Qualitative aspects of standards: Determining whether the standards are organized into single grade levels or multiple grade bands, how the standards are organized in regard to key strands, broad topics, and what level of detail they contain.
Core content expectations: Presenting topics economies address in their standards, the extent to which those topics are common across most or all of the economies, and the proportion of economies standards that is made up of the common topics.
Performance expectations: Describing the emphasis given to various levels of performance skills evident in the member economies' standards.

Methodology

The APEC economies in this study volunteered for participation and maintained involvement throughout the process, providing English-language copies of their standards, data about their students, and explaining their educational systems and the approach under girding their standards. Analysts assigned multiple content and performance codes to each block of text defined as a standard. The coding framework utilized includes two components: a.) content categories, which address the topics covered; and b.) performance expectations, which address what students are expected to do with the content.

Click here for more on the Achieve Study Methodology.

Findings

The purpose of this analysis was to determine the similarities and differences among the 12 participating APEC member economies' expectations and priorities in three main areas:

1. Qualitative aspects of standards (determining whether the standards are organized into single grade levels or multiple grade bands, how the standards are organized in regard to key strands and broad topics, and what level of detail they contain);
2. Core content expectations (describing what topics economies address in their standards, the extent to which those topics are common across most or all of the economies, and the proportion of economies standards that is made up of the common topics); and
3. Performance expectations (describing the emphasis given to various levels of performance skills-- procedural skills, conceptual understanding skills, strategic problem solving and reasoning skills-- evident in the member economies' standards).

Qualitative Aspects of Standards

• Five economies used single grade approach (e.g. 3rd grade, 4th grade), three used grade spans (e.g. grades 3-5), and four used blended approach (grade-by-grade at some levels, span at others).
• In grades 1-6, the three strands Geometry: Position, Visualization & Shape; Number; and Measurement compose 70% of economies’ standards.
• In grades 10-12, those three strands diminish to 20%, whereas the strand Functions, Relations & Equations increases to 48% and Data Representation, Probability and Statistics increases to 20%.
• The percentages for grades 7-9 are between those points (50% for Geometry: Position, Visualization & Shape; Number; and Measurement; 22% for Functions, Relations and Equations; and 14% for Data Representation, Probability & Statistics).

• Grade Level v. Grade Span Approach: Analysts examined whether APEC economies organized their standards by grade level or grade span.  The majority of APEC economies studied organize their mathematics standards by grade level.

 

• Years of Required Mathematics Instruction: It was found that, while all economies begin mathematics instruction at grade 1, if not earlier in the kindergarten year, there is some variation in the total number of years of mathematics required across economies, ranging from nine to eleven years.

 

¹ In the United States, all but four states have set statewide graduation requirements.  Of the remaining states, 18 require four years of high school mathematics, 22 require three years and the remaining six require two years.  For more information about state graduation requirements, click here.

• Strand Organization & Emphasis by Grade Span: Analysts noted that the emphasis on certain domains of mathematics shifts clearly across all grade spans, as demonstrated by this graph.  Note that emphasis on Number, Measurement and Geometry (position, visualization and shape) diminishes over time, while in contrast, emphsais on Functions, Relations and Equations increases over time.

• Level of Detail: This table shows variation in the level of detail provided by the APEC economies that were studied.  Some of this variation may be due to language barriers. As the table below indicates, some exonomies use descriptive language and/or provide elaborations or examples in their mathematics standards.  Others use sparer, shorter statements to convey what students need to know.

Core Content Expectations

• Lower secondary has the largest number of common topics, followed by primary.
• Across the countries Number Sense, Number Operations and Measurement are emphasized at the primary level.
• Upper secondary has the least commonality, which is likely the result of a greater number of curricular choices at that level.

APEC set out to examine the core content included in the standards across the different economies to determine the extent to which there is commonality. To do this, we analyzed the topics treated by each economy at each grade level or span. Although there is variation across economies, it was found that there are a number of topics that are common across economies. The data was divided into three grade level spans: primary (grades 1-6); lower secondary (grades 7-9); and upper secondary (grades 10-12). Although the standards may be written in varying degrees of detail and may be introduced and emphasized at different grade levels, there is an identifiable set of common topics across most or all of the economies participating in this study at each grade span.

Performance Expectations

• Most economies place greatest emphasis on lower-level performance expectations in their standards.
• This is due partly to the fact that economies often address both lower-level recall skills and more advanced skills in a single standard.
• At primary, 82% of performances consist of Level 1 and 2 skills, with only 5% addressing Levels 4 and 5.
• At lower secondary, 79% consist of Level 1 and 2 skills, with 12% addressing Levels 4 and 5.
• In upper secondary, 73% consist of Level 1 and 2 expectations, while 17% of the emphasis is at Levels 4 and 5.

For Math, grade spans used were Primary (1-6), Lower Secondary (7-9) and Upper Secondary (10-12)

The cognitive skill expectations of the standards from the 12 economies in this study were analyzed.  Of great interest is the balance of basic skills, such as recall, and advanced skills, such as applying advanced mathematical reasoning.

• Mathematics Performance Categories & Levels: Performance expectations have been grouped into a hierarchy of levels approximating increasing levels of cognitive demand.  The levels, in increasing order of cognitive demand, are: (1) Recall, (2) Using routine procedures and tools to solve problems, (3) Using more complex procedures and conceptual understanding to solve problems, (4) Formulating problems and strategizing/critiquing solution methods, (5) Applying advanced reasoning skills.  Each level has its own specific set of skills which must be acquired to successfully complete the level.

• Emphasis of Performance or Cognitive Skills across Grade Spans: Analysts found that most of the economies place the greatest emphasis on the Level 1 and 2 performance expectations, and less emphasis on Level 5.
• Variation among Economies: One interesting finding of the study is that there was certain variation among the economies.  For example, New Zealand dedicates 45 percent of its performance expectations for grades 10-12 to the top three levels, as compared to 27 percent average of all the economies.  China places the heaviest emphasis among the economies on the highest performance skill, and Korea's standards use language focused on memorization, basic representation and the performance of routine procedures, with almost no attention given to the other skills.

Conclusion

Achieve's report points to a set of common content expectations for students-- although the size and nature of the common set varies across grade levels and disciplines.  Though the study found common aspects regarding the content and performance skill demands, qualitatively, there was, nevertheless, a great deal of variation across economies in terms of the structure, volume and level of detail in their standards.  This result is not surprising, given the different educational, economic and cultural contexts in each economy.

Standards define expectations for what students must know and be able to do.  They provide a framework for the development of textbooks and other instructional materials, and help to shape teacher preparation and ongoing training.  However, it is important to note that there are other mechanisms for communicating what students are expected to know, such as assessments, curriculum and instruction, that must be considered as well whenever student learning is discussed. 

The analysis serves an important purpose in providing a lens through which the APEC economies can examine the similarities and differences among their standards in their efforts to determine the extent to which they have consistent expectations of students within their own systems and across economies.