Singapore Maths Compared of Purposeful Design

INTRODUCTION:

SOUTH AFRICA:

The World Economic Forum’s annual report on financial development, released in October 2012, placed South Africa last in a ranking of 62 countries in the quality of mathematics and science education. The forum’s report pointed to a high correlation between human capital and the degree of financial development in countries.

The 2011 census results, released in 2012, showed that a decade ago 2.7% of men and 2% of women who had tertiary qualifications in South Africa had qualifications in the fields of natural, physical and mathematical sciences.

By 2011, this had declined to 2% of men and 1.8% of women On 17 April 2013, the Mail and Guardian reports: South Africa has ranked its maths and science education has second last in the world, ahead of Yemen, according to a World Economic Forum report. Forty-three percent of South African grade five learners failed to reach the lowest international benchmark, in contrast to 5% of grade four learners internationally.

This means that they have not yet mastered the basic reading skills required to access and retrieve information for reading comprehension purposes," the Pirls (Progress in International Reading Literacy Study) report stated.

It further revealed that about 90% of the grade four learners tested in English or Afrikaans attained the lowest international benchmark, while between 24% and 57% of children writing in all nine official languages did not achieve it.

Learners tested in Sepedi and Tshivenda achieved the lowest results, according to the study.
In December 2012 the Department of Education has released the Annual National Assessment (ANA) results, which provides a bleak picture of educational performance. The performance in mathematics is however extremely worrying. The results show that the largest number of South African students have been assessed to score below 30% in Grades 3, 6 and 9. When a student scores between 0-29%, this is described as “not achieved”. The scoring used by the Department of Basic Education is as follows:

Rating Percentage Description
Level 1 0-29 Not achieved
Level 2 30-39 Elementary achievement
Level 3 40-49 Moderate achievement
Level 4 50-59 Adequate achievement
Level 5 60-69 Substantial achievement
Level 6 70-79 Meritorious achievement
Level 7 80-100 Outstanding achievement

The graphic below summarises the data, showing that 9 out 10 South African students in Grade 9 do not even score above 30% in mathematics.
                                         
The data paints a worrying state on mathematics education in South Africa. The performance across Grades 3, 6 and 9 indicate that performance levels drop as students move to higher grades.

SINGAPORE:

Singaporean students ranked first in the world in mathematics on the Trends in International
Mathematics and Science Study-2003 (TIMS); U.S. students ranked 16th out of 46 participating nations at grade 8 (Mullis, et al., 2004). Scores for U.S. students were among the lowest of all industrialized countries. Because it is unreasonable to assume that Singaporean students have mathematical abilities inherently superior to those of U.S. students, there must be something about the system that Singapore has developed to teach mathematics that is better than the system we use in the United States.

Singapore’s superior performance on the Trends in International Mathematics and Science Studies (TIMSS) in 1995, 1999, and 2003 affirms the high quality of Mathematics education in Singapore (Ministry of Education Singapore, December 16, 2004).

Analysis of these evidentiary streams finds Singaporean students more successful in mathematics than their U.S. counterparts because Singapore has a world-class mathematics system with quality components aligned to produce students who learn mathematics to mastery. These components include Singapore’s highly logical national mathematics framework, mathematically rich problem-based textbooks, challenging mathematics assessments, and highly qualified mathematics teachers whose pedagogy centers on teaching to mastery. Singapore also provides its mathematically slower students with an alternative framework and special assistance from an expert teacher.

Singapore’s mathematics framework defines expectations about what students should know and be able to do in mathematics. Singapore’s well-defined syllabus describes mathematical topics and outcomes grade by grade within broad mathematical strands. Singapore gives its teachers much of the credit for its education success. Singapore’s teachers “lie at the heart of all we do in education” (Ministry of Education, Singapore, 2001c).

UNITED STATES OF AMERICA:

The U.S. mathematics system does not have similar features. It lacks a centrally identified core of mathematical content that provides a focus for the rest of the system. Its traditional textbooks emphasize definitions and formulas, not mathematical understanding; its assessments are not especially challenging; and too many U.S. teachers lack sound mathematics preparation. As a result, the United States produces students who have learned only to mechanically apply mathematical procedures to solve routine problems and who are, therefore, not mathematically competitive with students in most other industrialized countries.

However the U.S. mathematics system has some features that are an improvement on Singapore’s system, notably an emphasis on 21st century thinking skills, such as reasoning and communications, and a focus on applied mathematics. However, if U.S. students are to become successful in these areas, they must begin with a strong foundation in core mathematics concepts and skills, which, by international standards, they presently lack.

COMPARISON BETWEEN PURPOSEFUL DESIGN MATHEMATICS and SINGAPORE MATHS

ACSI wanted to ensure that the curriculum we offer our schools via Purposeful Design is indeed the best in comparison with world standards. It was important for us to ensure that we remain true to our calling in offering an alternative that is Bibically sound and distinctively Christian as wel as a rigiourously intellectual and  academic.

We have drawn the following conclusions:
• Purposeful Design’s Mathematics Curriculum  meets or exceeds all of the national standards and has documented its close alignment to the Common Core Standards in the USA.

Both series are strong in problem solving.
• Singapore Math uses a specific square model for problem solving
• Purposeful Design also provides a specific problem solving guide. As a new concept is taught students use that concept in solving problems.

• Feedback from schools moving away from Singapore Math is that parents sometimes find it difficult to help their children with homework because of the teaching methods employed.
• Feedback from upper level math teachers after Purposeful Design  has been implemented at lower grade levels is that they notice a change in the foundational learning of students using Purposeful Design  mathematics, especially in the area of fractions and abstract concepts

• Singapore math assumes that once major concepts are taught, they do not need to be retaught.
• Purposeful Design provides a regular review of all concepts.

Advantages of Purposeful Design Mathematics
• Purposeful Design provides solid understanding of concepts through the use of manipulatives and modeling.
• Differentiated instruction is integrated into the “Directed Instruction” component of the lesson, addressing the various learning styles of students in the classroom.
• Basic facts and operations are taught while developing concepts through the use of manipulatives, investigation, and hands-on activities.
• Algebra and geometry strands are woven through the entire series, beginning in kindergarten.
• Tools for enrichment, recovery and practice are provided.
• Emphasis on math vocabulary through the use of math journals at each grade level.
• Designed to be teacher, not textbook-driven, Purposeful Design  provides the necessary tools for teachers to be successful.
• Since the series is concept-based, the majority of the lesson is often taught through manipulatives and modeling before students open their texts. Proper use of manipulatives and modeling are provided for in the Teacher Edition.

Contributions made by:
• Marikita Evangelista: Retired Professor: De La Salle University, Manila Phillipines
• Sheilamarie Uy Eiaw: Human Resource Department Head, MGC New Life Christian Academy, Metro Manila, Philippines.
• Cindi Banse: Math and Science Support Specialist, ACSI Colorado Springs

Compiled by:
• Anna-Marie Russell: ACSI Director South Africa