## Introduction

Mathematics as the subject performs a number of significant functions in the life of any student. The way of how a curriculum is introduced and implemented by teachers influences considerably the work of a teacher him/herself and the possibilities of the learners to comprehend new information. This is why much attention is usually paid to the curriculums and the methods of their development and improvement under different conditions.

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In this paper, there are two curriculums under consideration: Singapore mathematics curriculum that differs from other frequently implemented curriculums by the necessity to make students solve problems independently, and Everyday Math curriculum that is developed in the city of Chicago and now implemented in some schools of Indiana. The point is the chosen curriculums contribute a lot the sphere of education, and the more attention is paid to their weaknesses, strengths, and effectiveness, the better results in education may be achieved.

The application of Singapore Math curriculum in the United States should promote better understanding of the subject between various students as well as identification of the disadvantages of the exited curriculums. Some Indiana schools are chosen among the rest to evaluate how Singapore Math curriculum may influence the process of education in case it is implemented by several teachers. The success of the above-mentioned implementation should be also useful for some other educational workplaces as well as for teachers and learners to perform their roles accordingly.

## Learning environment of the Singapore Math Curriculum

The main task of the paper is to revise the existed curriculums and check how they match the standards set by NCTM. In spite of the fact that the main subject of the paper is Singapore Math curriculum, some attention is also paid to Everyday math curriculum that is develop by the Chicago teachers. The identification of the second curriculum is obligatory for a thorough analysis of the first curriculum, its positive and negative aspects.

Singapore Math curriculum is one of the widely spread methods to teach math for children. Though it has a number of characteristics which differentiate it from the rest of the standard practices, this curriculum is in demand among a variety of schools. Such popularity may be based on the learning environment provided: spiral approaches (the material that has been taught once should not be repeated again in the same year) and unusual introduction of new concepts (the scheme is the following – concrete – pictorial – abstract).

In fact, Singapore Math curriculum has been identified as a perfect worldwide educative approach due to its excellence (Frank Schaffer Publications & School Specialty Publishing, 2009). To provide students with the possibilities to succeed in education and make use of various techniques and skills, Singapore Math curriculum should be improved and implemented accordingly. This curriculum promotes the use of thinking skills like appropriate communication and strong reasoning, development of metal solution of problems instead of memorizing various facts and figures.

This is why learning environment for the chosen Singapore Math curriculum should be full of illustrative examples and explanations which are clear for the learners of different age. Students should realize that they are a significant part of a serious activity that is practiced in the chosen community, and their achievements impact further development of the events as well as their personal understanding of the matter.

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## Plan of Action

The plan of actions has to be identified to make sure that the curriculum is evaluated properly. It has to address clearly special needs required for the curriculum as well as the expectations of teachers and learners. To succeed in the developing plan, it is necessary to weight personal skills and possibilities in regard to the current conditions. A plan of action presupposes a number of steps which have to be taken in a certain order; the most important steps are identified below:

- Brief evaluation of the curriculums under consideration: Singapore Math curriculum as the most successful approach in the world and Everyday Math as the curriculum that is based on solving real-life problems;
- Identification of strengths and weaknesses of the curriculums and their conformity with the NCTM Math Standards;
- Analysis of the conditions under which the curriculums are implemented in Indiana schools and the outcomes which are observed among students with different level of knowledge and abilities;
- Definition of the skills which may be developed under the two different approaches;
- Comparison of the textbooks, assessments, and methods which are used in Singapore Math curriculum and in Everyday Math curriculum;
- Contrast between the areas of strengths identified in Singapore Math curriculum and Everyday Math curriculum that is originated from Chicago;
- Evaluation of different texts which help to understand the essence of Singapore Math curriculum, Everyday Math curriculum, and the NCTM standards which are spread all over the whole world;
- Understanding of the ways of how curriculums may be developed and implemented to the existed educational systems and how teachers and learners have to use the offered ideas by the curriculum standards;
- Analysis of functions of the curriculum as well as roles which have to be performed by a teacher and a learners at the end of the project should help to realize how effective the chosen strategies could be.

This plan of action defined is considered to be a crucial step in the process of the existing curriculum revision. The peculiar feature of the revision is that Singapore Math curriculum is not only revised and evaluated but also compared with another widely spread curriculum (Everyday Math) so that the identification of weaknesses and strengths is possible.

## Rationale

The development of the rationale for the curriculum revision is an important step to be taken in this paper. It is obligatory to create a clear and effective idea using the specified learning environment and prove the correctness of the chosen curriculum so that there are no doubts about the importance of the chosen curriculum as well as its urgency and effectiveness for the current learning environment.

The point is that the vast majority of learners suffer because of inabilities to grasp and use the material learnt the way it is required by the teachers. A number of inconveniences appear because of inabilities to weight the cons of what is got and the pros of what may be got from the curriculum. This is why it is necessary to analyze each detail and each circumstance under which a learner has to study new material and find practical application to his/her theoretical knowledge.

In general, Singapore Math curriculum is an approach that may considerably influence student understanding of the material; Indiana schools may be also improved with the help of the chosen curriculum even considering the fact that some American curriculums, like Everyday Math, have been already implemented into the system; the effectiveness of the existed curriculum is great indeed, and its revision is a unique chance to evaluate its strong and weak points and compare what is so special about Singapore Math curriculum and what is omitted in the American curriculums offered.

## Literature Review

Statistics shows that the achievements demonstrated by the students from Singapore are really high; they took the first place in the 2003 TIMSS that is Trends in International Mathematics and Science Study (SingaporeMath, 2002). This is probably one of the first reasons of why the vast majority of educators want to apply the curriculum that is spread among the Singapore educational system.

The point is that learning environment supported in Singapore is more gender biased (Khine & Fisher, 2003), but still, it is not the reasons to refuse an idea of the curriculum implementation. So, what is so special about Singapore Math curriculum? And why do so many people find it obligatory to introduce the curriculum to various American schools?

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One of the first purposes that had to be achieved during the development of Singapore mathematics curriculum is to develop students’ abilities and make them able to solve problems at the highest levels (Leung, 2006). The essence of the curriculum under consideration is that all chosen textbooks and assessments are used in order to promote learners to solve problems by means of model drawing the way it is recommended by in the NCTM Curriculum that introduces a kind of public voice of education in Math (National Council of Teachers of Mathematics, 2010).

The explanation of some new concepts and ideas has to be as clear and simple as possible, and even the students who have English as their second language are able to grasp the essence and make use of their gained knowledge in future. The spread of mathematical problem solving processes depend on a variety of aspects, and the most important are student and teachers’ skills, different concepts to be considered, processes which are required to be considered, and metacognition as a means to grasp comprehension of the matter.

There are several aspects which are defined by the NCTM Standards: the attribute of connectedness, strong identity abilities, a kind of capacity to cope with uncertainty, and capacities to build a certain community (Germain-McCarthy, 2001; Spitzer & Roddick, 2007). The chosen curriculum offered for Singapore students meets the vast majority of the standards mentioned above. However, it is not enough to understand how appropriate the chosen curriculum can be from the NCTM perspective but from the perspective of learning environment provided.

To understand this issue better, it is possible to consider Everyday Math curriculum and evaluate the environment inherent to this approach. As well as Singapore mathematics curriculum, EM curriculum focuses on solving various real-life problems in Math in order to balance whole-class learning and self-directed learning (The University of Chicago School Mathematics Project: Everyday Mathematics, n.d.).

However, it is not the only similarities that may be traced between the two curriculums under consideration. One of the most powerful strength of the curriculums is the possibility to provide students with various opportunities to learn new concepts and improve their practice skills (Goldring & Berends, 2009). The researches show that the chosen program, Everyday Math, cause only good reviews from different teachers in the United States of America (Orange, 2002). Finally, the results of the PSSA tests which have been discussed with one of the teachers from Indiana University of Pennsylvania. Though the results are not the highest in the region, they are still above the average, so that students prove how progressive in Math they can be.

For example, the number score math among the students of PA is about 60, students from Jefferson demonstrated higher results (about 73), and students from Huntington were not as successful as other students, their results are about 30 points (Personal communication). This is why, taking into consideration the fact this curriculum is already known to the public and approved by a variety of teachers and supported by many learners, Singapore Math curriculum should be also successfully applied to the chosen educational system.

## Specified philosophy in the curriculum

Each curriculum has to correspond to a particular philosophy that helps to define the material, requirements, and tendencies to be used. It is known that students cannot understand what kind of material they have to learn and relation to education should be better chosen. To organize the process of education and to define the necessities of various curriculums, five schools introduced their own philosophies, still, only three of them are in use around the whole world. They are progressivism, perennialism, and essentialism.

The chosen Singapore mathematic curriculum is characterized by the basics of perennialism and progressivism. On the one hand, this curriculum is developed to help learners identify and solve problems without constant repetitions. These are the characteristics which are inherent to Perennialists. Students have to be assured of their proper understanding of the matter and appropriate development of students’ capacities to give reasons.

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On the other hand, some traits of progressivism may be also observed in the chosen curriculum. Math learning is based on posing questions so that the whole child but not only the content is taken into consideration. Students have to study the materials in accordance with a particular system in order to be able to make independent decisions, plan their own actions, and select the issues which are interesting for them.

In other words, the idea that students have to learn more and educators have to teach less is perfectly observed in Singapore Math curriculum as well as in Everyday Mathematics program. With the help of philosophy identification, it is easier to define the purposes students and tutors set during the process of education. The peculiar feature of the curriculum under consideration is that students should be always encouraged to take some actions, to learn new material, and to make use of their own creativity to achieve the desirable success in the chosen sphere. Mathematics is the subject that helps to understand how to solve problems the best way it may be, this is why the ideas of perennialism and progressivism will be always in demand between those who are involved into Singapore Math curriculum.

## Learning theory helps to define the roles of a teachers and a learner

There are two basic learning theories that may be applied to the curriculum under consideration, cognitive learning theory and behavioral theory. To comprehend what learning theory may be applied in the chosen curriculum, it is necessary to comprehend the essence of both theories.

Behavioral theory is based on the idea that the educational process is connected with student personal experiences, and cognitive theory is all about mental processes which predetermine human activities. In the curriculum, these two learning theories are evident because students have to rely on their personal activities and experience gained as well as on their mental activities. In fact, the chosen learning theories are related to teacher and student’s roles during the education process.

For example, a teacher has to provide learners with clear directions and standards which have to be followed. The main task of teachers’ activities is to evaluate information and choose the best methods to explain new material and the criteria according to which student knowledge could be evaluated. Learners, in their turn, have to remember about the necessity to perform their own roles and functions.

First, students are free to make some choices and define the necessity to study this or that material. In Singapore Math curriculum, much attention is paid to problem solving, this is why student choice is crucial in here. The teachers from the Indiana schools admit that they have been implementing the curriculums for several years, and the progress of students is recognizable. Students become involved into education processes as they have a variety of purposes as well as methods to cope with assignments.

In some Indiana schools, Singapore mathematics curriculum may be implemented on the basis of special textbook series which are usually published by private companies. These companies may include teachers, research, or even some other educators from the same community. It is also possible to make use of some standardized tests like SAT. However, the success of the implemented curriculum is based on teacher’s characteristics and the way of how he/she performs the role. These skills may be of general teaching nature or content knowledge, etc.

Similar to the NCTM Standards, Singapore Math curriculum aims at improving the process of mathematics education among the students of the same Indiana community. Considering the ideas and peculiarities of the curriculum, the role of the learner is to make a choice in time and be as attentive to the details as possible to meet the standards set.

## The function of the curriculum

The peculiar feature of Singapore Math curriculum is the possibility to utilize a kind of spiral approach with the help of which students should not pay much attention to the material that has been studied before. In other words, the main function of the curriculum is to increase the level of teaching and to avoid the process of “reteaching”. In fact, this function helps to differentiate the chosen curriculum among the rest techniques which are implemented in the United States and in Indiana schools in particular.

The vast majority of teachers find it obligatory to repeat new material for several times and to revise topics in order to make sure that students comprehend information. Still, the function of this curriculum is more learner- and knowledge – centered as it helps to avoid repetitions and engage students in developing illustrative examples to give reasons and solutions.

## Conclusion

Singapore Math curriculum is one of the most popular techniques used by the teachers from East. However, due to considerable cultural integration and searches for some effective educative techniques, it seems rather effective to implement Singapore Math in some Indiana schools and improve the existed school system. The attention to such teaching method as the use of visual images and various illustrations makes the vast majority of teachers focus on new details and new roles which have to be performed by learners.

After a deep analysis of Singapore Math and its comparison to the existed Everyday Math curriculum, it has been identified that the evident strength of the curriculum is the possibility to avoid repetitions and focus on teaching new material and improving students’ problem solving skills.

## Reference List

About Everyday Mathematics. (n.d.). *The University of Chicago School Mathematics Project: Everyday Mathematics*. Web.

About NCTM. (2010). *National Council of Teachers of Mathematics*. Web.

Frank Schaffer Publications & School Specialty Publishing. (2009). *Singapore Math 70 Must-Know World Problems, Level 2*. Columbus, Ohio: Carson-Dellosa Publishing.

Germain-McCarthy, Y. (2001). *Brining the NCTM Standards to Life: Exemplary Practices for Middle Schools*. Larchmont, NY: Eye on Educaiton.

Goldring, E.B. & Berends, M. (2009). *Leading with Data: Pathways to Improve Your School*. Thousand Oaks, CA: Corwin Press.

Khine, M.S. & Fisher, D.L. (2003). *Technology-Rich Learning Environments: A Future Perspective*. Singapore: World Scientific Publishing.

Leung, F.K. & International Commission on Mathematical Instruction. (2006). *Mathematics Education in Different Cultural Traditions: A Comparative Study of East Asia and the West New ICMI Studies Series*. New York: Springer.

Orange, C. (2002). *The Quick Reference Guide to Educational Innovations: Practices, Programs, Policies, and Philosophies*. Thousand Oaks, CA: Corwin Press.

SingaporeMath. (2002). Why Singapore Math Books? *SingaporeMath.com*. Web.

Spitzer, J.S. & Roddick, C.D. (2007). *Succeeding at Teaching Mathematics, K-6*. Thousand Oaks, CA: Corwin Press.