Primary Mathematics Pedagogy at the Intersection of Education Reform, Policy, and Culture

Comparative Insights from Ghana, Singapore, and the US

Sarah Murray, Princess Allotey

• Editore: Routledge
• Anno: 2021
• ISBN:
  9781000480207
• Edizione: 1
• Argomento: Education
• Categoria: Comparative Education

This volume provides an in-depth, comparative examination of how primary mathematics education is influenced by national education reform, policy, local resources, and culture in three different countries.

By drawing on first-hand observations and interviews, as well as analysis of policy documents and learning resources, the book considers the viability of transferring best practices in primary mathematics education across global contexts. Three diverse countries – Ghana, the US, and Singapore – are explored. Similarities and differences are highlighted, and the influence of national and regional initiatives related to pedagogical strategies, teacher education, and cultural expectations are considered, to offer an insightful examination of how best practices might be shared across borders.

This book will benefit researchers, academics, and postgraduate scholars with an interest in international and comparative education, mathematics, and educational policy. Those with a specialization in primary mathematics education, including pedagogy and teacher preparation, will also benefit from this book.

Chapter 1 The Contemporary Relevance of Comparative Education in Primary Mathematics

DOI: 10.4324/9781003172468-1

Introduction

Imagine that a high-progressing Grade 4 student, in a classroom in Singapore, is sitting at a round table with four other students. They are using a heuristic to solve questions on fractions. Their teacher approaches them and guides the students through questions with which they are struggling. More than 7,000 miles away from Singapore, a Grade 4 student in a Ghanaian classroom is investigating number operations. The student uses different stones of varying sizes, obtained outside the classroom, to represent a number’s place value. The teacher goes to each student to assess their understanding of the concepts under study. About 6,000 miles from Ghana, an advanced Grade 4 student in the US reviews the process for solving a multi-part question on fraction equivalence. The student goes through previous worksheets from his binder to familiarize himself with the foundational concepts of fraction equivalence. His teacher checks over his attempt at the multi-part question and identifies any missing steps. Can the teachers in these three classrooms learn from each other on how mathematics is taught in their cultural contexts? Can we identify similar pedagogical practices in these three classrooms?

These scenarios depict the authors’ experiences observing, teaching classes, or both in Ghana, Singapore, and the US. Even though each scenario does not necessarily represent all the intricacies in pedagogy that are affected by factors such as culture, language competencies, and resource availability, they provide local perspectives that assist with comparing the education systems of the three countries. To commence further examination of mathematics pedagogy in these three settings, an exploration of the concept of comparative education in the global context is needed in conjunction with working definitions for specific terms arising in the study. An analysis of existing comparative education frameworks including strong evidence for the selection of Ghana, the US, and Singapore for our case studies is provided. Consequently, this chapter is divided into the following sections:

1. The Importance of Comparative Education in the 21^st Century
2. Defining Key Terms: Globalization, National Identity, Global Village, and Global Competency
3. An Analysis of Existing Comparative Education Frameworks and Methodologies
4. A Justification for Ghana, Singapore, and the US

The Importance of Comparative Education in the 21st Century

With the introduction of diverse education policies, it has become essential for nations to learn from the educational systems of different countries including pedagogical practices that have proven to be both beneficial and sustainable. Taking this role, comparatist David Phillips (2000) states that, “It provides opportunities to learn from the experiences of others” (p. 297). Despite the complexities that arise from comparing somewhat different cultures, the increase in interconnectedness across different regions of the world has made it more possible for researchers to conduct comparative education studies. To lay the foundation for discussions on comparative education, a working definition is established and the importance of comparative education in the contemporary world is highlighted. We will also give an overview of some classic comparative studies including the Third International Mathematics and Science Study (TIMSS) Video Study report, the Kassel Project, and the Learners’ Perspective Studies.

Postlethwaite provides the following explanation for comparative education: “[examining] two or more entities by putting them side by side and looking for similarities and differences between or among them. In the field of comparative education, this can apply both to comparisons between and comparisons within systems of education” (as cited in Kaiser & Yang, 2017, para. 3). This will be the working definition for our comparison between the mathematics educational systems of Ghana, Singapore, and the US in their local contexts. Even though there are multiple definitions for comparative education, this is representative of our goal to examine and compare common pedagogical practices within primary mathematics education and teacher preparation in the three countries and to obtain rich insights into best practices that can be implemented in another country’s local context.

The value of comparative education research cannot be emphasized enough. We identify three reasons why this research field has been sustained over to the 21st century. The three main themes highlighting the importance of comparative education research in connection to this study include the:

1. advancement of different educational systems.
2. appreciation of complexities in educational systems.
3. analysis of the influences of one educational system on another.

Given that each nation or region of the world experiences its own unique educational challenges, it is imperative for countries to consider the achievements of others and to determine best practices that can be implemented in their own contexts. This relates to the first theme above since a country can advance progress in its educational system by learning from others (Arnove, 2013, p. 6; Kaiser & Yang, 2017, para. 2). A classic example is the 2005 US American Institutes of Research (AIR) study, which examined Singapore mathematics educational systems and recommended that “varied pictorial representations of mathematical concepts found in Singaporean texts” should be incorporated into the US mathematics curriculum (Ginsburg et al., 2005, p. xvi).

The second theme involves the development of an understanding of why there are differences and similarities across education systems including cultural, economic, and national contexts (Arnove, 2013, p. 4; Kaiser & Yang, 2017, para. 3). This is crucial given that countries can effectively borrow and implement best practices from other countries if they can identify and appreciate the complex cultural contexts that affect educational achievements in countries of interest. For example, developed countries, which tend to have higher economic and sociological status, can more feasibly implement initiatives from other developed countries (Arnove, 2013, p. 5). However, less developed countries might find it more challenging to borrow policies or initiatives, which require relatively higher economic investments.

Even though countries might consider their own educational systems as distinct, Arnove (2013) contends that one country’s educational system can affect another country’s (p. 9) just like the phenomenon of the butterfly effect. In this context, a “butterfly effect” happens when a policy or initiative in one country influences the educational system of another country. For example, research shows that the Concrete-Pictorial-Abstract (CPA) approach in Singapore stemmed from Bruner’s Enactive-Iconic-Symbolic as far back as the 1970s (Leong et al., 2015, p. 4). It is important to note here that Jerome Bruner was an American psychologist (Smith, 2002) whose work influenced the US educational curriculum reform in the mid-1900s (Bruner, 1971, p. 18). This example solidifies Arnove’s (2013) argument that we acknowledge and understand how transnational interactions influence other countries’ educational systems (p. 9). The third theme is essential to consider given that, as the world becomes more connected in the 21st century, it is assured that one country’s policies and initiatives can affect that of other countries. We will further discuss this theme in Chapter 4 of this monograph, considering insights from classrooms in Ghana, Singapore, and the US.

It is also important to note here that these themes are not distinct but interact in complex ways. For example, as comparative education researchers analyze the impact of educational systems on each other, they also identify potential action steps toward the future advancement of education systems for teaching and learning in other countries. This connects the first and third themes, i.e., advancement of different educational systems and analysis of the influences of one educational system on another. In addition, an appreciation of the complexities in different educational systems also sparks a discussion on how school systems can be advanced through effective borrowing and lending – connecting the first and second themes. This further highlights the complexities that arise in comparative education research (Leung et al., 2006, p. 5) despite the simple explanation given in the working definition provided by Postlethwaite in an earlier paragraph of this section. This sets the pace for exploration of classic comparative education studies that have influenced educational systems of countries across the globe.

Classic Comparative Education Studies

This subsection explores four comparative education studies including the Kassel Project, the Learners’ Perspective Study (LPS), Zhao and Singh’s (2011) study, and Stigler and Hiebert’s (1999/2009) assessment of the TIMSS (p. 15). We will provide an overview of the motivation, goals, methods, and findings of each study while emphasizing how these studies advanced the discourse and action steps in the field of comparative education. For each comparative education study, we will also identify specific findings and recommendations made from the selected country under study.

The first comparative study we consider is from Stigler and Hiebert’s (1999/2009) Teaching Gap book. The goal of the study was to highlight the contributions that teachers make to advance educational systems around the world (Stigler & Hiebert, 1999/2009, p. xvii). The phrase, Teaching Gap, was inspired by the differences in current pedagogies practiced in the US and the pedagogical practices “needed to achieve the educational dreams of the American people” (Stigler & Hiebert, 1999/2009, p. xviii). The researchers analyzed videos that captured activities in Grade 8 mathematics classrooms in Germany, Japan, and the US video study, which began in 1993 (Stigler & Hiebert, 1999/2009, p. xvii; Stigler & Hiebert, 1999/2009, p. 15). Despite the cross-cultural differences, Stigler and Hiebert (1999/2009) were able to identify similarities in pedagogical practices. An analysis of the videotapes indicated that US lessons generally involved an evaluation of students’ understanding of past concepts, an illustration of problem-solving methods for the current topic, “seatwork” activities for students, and finally an evaluation of these “seatwork” activities by the teachers (Stigler & Hiebert, 1999/2009, pp. 80–81). However, in the German classrooms, teachers evaluated students’ understanding of past concepts but also adopted class activities that involved all students (Stigler & Hiebert, 1999/2009, p. 81). One interesting recommendation from Stigler and Hiebert’s (1999/2009) study was that the US should focus more on improving teaching methods rather than teacher competency (p. 10) (see TIMSSVIDEO, n.d. for details of the TIMSS 1999 Video Study). This recommendation emphasizes the critical role that teachers play in the student learning process and justifies our goal to observe and examine teacher pedagogy in our three countries of interest. The next study also connects with this same research goal.

The Kassel Project was a longitudinal comparative mathematics study led by the University of Exeter’s Centre for Innovation in Mathematics Teaching (Kaur, 2017, p. 47) from 1993 to 1996 (Kaur & Yap, 1996, p. 15). The countries involved in the study were England, Scotland, Germany, Australia, Czech Republic, Finland, Greece, Holland, Hungary, Hong Kong, Japan, Norway, Poland, Singapore, and Florida (US) (Kaur & Yap, 1996, p. 15). The goal of the project was to understand mathematics pedagogy in the selected countries and to propose best practices for classroom instruction (Kaur & Yap, 1996, p. 15). It is important to note here that these goals also further connect with our comparative study. In Singapore, about 2,400 students from seven schools were assigned to take mathematics tests in 1995 and a subset of the students were selected for an interview (Kaur & Yap, 1996, p. 15). In addition, 43 Grade 8 and 9 students were observed during mathematics instruction and pertinent information was recorded using codes and “descriptive statistics” (Kaur, 2017, p. 47). The researchers found that teachers were focused on completing specific tasks during classroom instruction including guiding students through “step-by-step” approaches to solving mathematics questions (Kaur, 2017, p. 47). Teachers used classroom resources, including the board and school texts, to achieve class objectives (Kaur, 2017, p. 47) and mostly adopted whole-group instruction (Kaur & Yap, 1996, p. 16). The students observed were alert, “quiet”, and “task-oriented” (Kaur, 2017, p. 47). An additional mathematics test conducted in 1996 indicated a relation between students’ mathematics skills and their application of concepts (Kaur & Yap, 1998, p. 450). Teachers were encouraged to incorporate more application-based experiences in mathematics instruction (Kaur & Yap, 1998, p. 451). This study highlights the significance of classroom observations since it presents the researcher with the opportunity to see real-life interactions between teachers and their students. This motivates our decision to observe Singaporean classrooms for our case study. However, video data also provides researchers with another perspective of mathematics classrooms discussed in the next paragraph.

The LPS was a video-based comparative mathematics study started by Professor David Clarke (University of Melbourne, Australia) in 1999 (Kaur, 2017, p. 50). The countries involved in the study were Australia, Germany, Japan, and the US (Kaur, 2017, p. 50). The goal of the project was to analyze Grade 8 mathematics teaching and learning through observations of multiple lessons in a particular orde...