B R I E F L Y No. 11 • NOVEMBER 2011 Emma Näslund-Hadley Armando Loera
N O T E D
INSIDE THE MATH CLASSROOM: WHAT MAKES A TEACHER EFFECTIVE?
S um m a r y: What actually goes on inside Latin American math classrooms? Do teachers in higher-performing countries teach math differently from those in lower-performing ones? To explore these questions, the IDB went inside math classrooms in three countries. For quantitative indicators on teaching practices, we used a methodology that had explained test score differences across Japan, the United States, and Germany, complemented by graphic maps of pedagogical flows. This note, based on initial and partial results from our analysis, highlights the math teaching practices that appear to be most effective.
Latin American Math Classes Are Black Boxes The generally poor performance of Latin American students on international math exams is well documented (OECD 2009, IEA 2007). It is also well known that within the region, students in some countries perform better than their peers in others (UNESCO-LLECE 2008). Some of these learning differences are likely related to the characteristics of teachers, students, and schools: teachers’ years of experience and training levels, students’ socioeconomic backgrounds, and the conditions of school infrastructure (Levin and Lockheed 1993; UNESCO-LLECE 2008). Beyond such associated factors, not much is known about how variations in learning relate to differences in the pedagogical approach used in Latin American classrooms.
Large-Scale Video Recordings Produce Quantitative Indicators Since very little is known about how math lessons are conducted in Latin American schools, the IDB decided to go inside the classroom. We set out to identify cross-country differences in teaching practices by filming sixth-grade samples in three countries. Of the three countries selected for the study, two— Paraguay and the Dominican Republic—perform at the bottom of the regional comparative test, SERCE, and one is a top performer, the Mexican state of Nuevo Leon. In 2010 we filmed math classes in 291 schools, covering over 84 percent of the SERCE sixth-grade sample for the three countries. We wish to thank the Knowledge Economy Fund of the Inter-American Development Bank for financing this study. Edited by Steven B. Kennedy • Design and layout by Laura C. Johnson
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The views and interpretations in this document are those of the authors and should not be attributed to the Inter-American Development Bank, or to any individual acting on its behalf. This note may be freely reproduced provided credit is given to the Education Division–SCL, Inter-American Development Bank.
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IDB Briefly Noted
Table 1. Pedagogical Flows in Classrooms (%) Drill, practice, and memorization of concepts
Drill, practice, and memorization of procedures
Drill, practice, and memorization of both concepts and procedures
Student-centered discovery
Paraguay
6
36
58
0
Dominican Republic
19
38
33
10
Nuevo Leon (Mexico)
9
14
32
45
Total sample
11
30
43
16
Source: IDB video study.
Consistent with the well-known 1995 TIMSS1 videotape study of eighth-grade classrooms in Japan, Germany, and the United States, each teacher was filmed once (Stigler and others 1999). The results cannot be used to draw reliable conclusions about individual teachers given the limited observation of each educator and because the fact of being filmed is likely to encourage teachers to perform at their very best, while also possibly causing anxiety that may affect instruction. But, as was successfully demonstrated through the TIMSS video study, this type of data allows researchers to identify classroom discourse and teaching practices that are characteristic of teachers from a specific country. The analysis of the classes is done using a coding instrument called Videograph, which allows researchers to quantify the occurrence of different classroom activities and create a spectrum of precise indicators. The quantitative indicators emerging from the Videograph analysis were complemented by graphic maps of the pedagogical flows in the classrooms (Loera 2006 and 2009). The graphic maps helped classify the teaching styles into four categories that range from styles that focus on mathematics procedures to those that seek to engage students in the critical, conceptual exploration of math problems (Skemp 1987). The downside of this type of qualitative video research is that it is very time consuming. So far, just half of the urban math classrooms have been analyzed across the three countries. Although it is premature to reach definite conclusions from the study, the results obtained from initial data from urban areas reveal some interesting patterns.
A Typical Math Class A teacher in Paraguay begins her sixth-grade math class by having the students read, in unison, the definition of the term percentage. Without any conversation about the meaning of what they have just read, the teacher asks a student to read a math problem on the blackboard that involves proportions. The teacher solves the problem by demonstrating the procedure for calculating a percentage value, and asks the students to copy it in their notebooks. The students are then asked to solve the same problem with different number values. The class wraps up without any teacher or group reflection on the topic they have just covered. Our study indicates that this teaching style, sometimes referred to as “traditional,� prevails in all three countries. In this note, we present two graphic map indicators and one Videograph indicator (presented in the three tables) that illustrate the prevalence of this teaching style. We also discuss a Videograph indicator on the prevalence of interruptions, showing interesting cross-country differences in the management of math classrooms.
Certain Classroom Practices Appear to Be Associated with Higher Levels of Learning Teachers in the sample countries rely heavily on the presentation and repetition of math procedures, sometimes combined with drill, practice, and memorization of concepts (table 1). Students spend their time copying from the blackboard and plugging numbers into formulas. Only in Nuevo Leon have we identified a sizable proportion of teachers who seek to move beyond a mere procedural understanding to actively engage students in activities that may endow them with analytical and critical-thinking skills. Even there, however, the drill, practice, and memorization approaches predominate. 1. Trends in International Mathematics and Science Study
Inside t he Math Classroom: What Makes a Teacher Ef fective?
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Table 2. Proportion of Class-Time that Teachers Spend on Different Activities (%) Teacher-led presentations
Dictation
Questions and answers
Other
Paraguay
54
18
14
14
Dominican Republic
54
16
7
23
Nuevo Leon (Mexico)
43
10
26
21
Total sample
50
15
16
19
Source: IDB video study.
Teacher-led presentations take up the most class time in all three countries (table 2). But on this indicator, too, teachers in Nuevo Leon are the outlier, displaying a slightly less teacher-centered approach and using more classroom time to ask questions and listen and react to student responses. Although the teaching practices in Nuevo Leon were found to be more student-centered, even there there is ample room for increasing student involvement. Student participation in the identification of alternative problem-solving methods is widely believed to be central to the development of a conceptual mathematics understanding (NCTM 2000; Hiebert and others 1997). But in none of the Latin American classes analyzed so far did students present alternative solutions. It is clear from the TIMSS video study (though the TIMSS students were in eighth grade), that teachers in Japan do the most to challenge their students to identify alternative solution methods to math problems (table 3). Interruptions are more prevalent in lower-performing countries. In the Dominican Republic more than half the classes suffered from at least one interruption unrelated to the math class. In Nuevo Leon and Paraguay the proportion of classes that suffered from at least one interruption was the same (40 percent), although the average interruption was much longer in Paraguay: 11 minutes compared to 5.5 minutes in Nuevo Leon. The TIMSS videotape study reveals that interruptions were much less frequent in Germany, Japan, and the United States. Notably, zero math class interruptions were documented in Japanese eighth-grade classes.
Initial Findings and Next Steps In this study we shift the attention from teacher characteristics and attributes to how teachers work in the classroom. Since the analyzed sample consists of schools in urban areas—where learning levels tend to be higher than elsewhere—the teaching practices observed so far should be of a higher standard than the average of the entire sample. Yet the results from the proportion of our sample already analyzed reveal teachers who rely heavily on rote memorization of routine computational operations and the regurgitation of facts. These teachers provide students with little evaluative feedback. As we move forward we hope to explore potential links between specific classroom practices and tools and various levels of student achievement.
Table 3. Lessons in Which Students Present Alternative Solutions to Math Problems (%) Paraguay
0
Dominican Republic
0
Nuevo Leon (Mexico)
0
IDB video study
0
Germany
14
Japan
42
United States
8
TIMSS video study
21
Source: IDB video study.
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IDB Briefly Noted
References Hiebert, James, Thomas P. Carpenter, Elizabeth Fennema, Karen C. Fuson, Diana Wearne, and Hanlie Murray. 1997. Making Sense: Teaching and Learning Mathematics with Understanding. Portsmouth, NH: Heinemann. IEA (International Association for Evaluation of Educational Achievement). 2007. Trends in International Mathematics and Science Study (TIMSS). http://timss.bc.edu/TIMSS2007/idb_ug.html. Levin, Henry M., and Marlaine Lockheed. 1993. Effective Schools in Developing Countries. London: The Falmer Press. Loera Varela, Armando. 2006. La práctica pedagógica videograbada. Mexico: Universidad Pedagógica Nacional. ———. 2009. Práctica Pedagógica en la Enseñanza de las Matemáticas y la Ciencia: Una Propuesta de Diagnóstico: SERCE Videos. Unpublished IDB report. Mexico. NCTM (National Council of Teachers of Mathematics). 2000. Principles and Standards for School Mathematics. Reston, VA: NCTM. OECD (Organisation for Economic Co-operation and Development). 2009. Program for International Student Assessment (PISA) 2009. www.oecd.org/edu/pisa/2009 Skemp, Richard. 1987. The Psychology of Learning Mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates Publishers. Stigler, James W., Patrick Gonzales, Takako Kawanaka, Steffen Knoll, and Ana Serrano. 1999. The TIMSS Videotape Classroom Study: Methods and findings from an Exploratory Research Project on Eighth-Grade Mathematics Instruction in Germany, Japan, and the United States. National Center for Education Statistics. Washington, DC. UNESCO-LLECE (United Nations Educational, Scientific and Cultural Organization-The Latin American Laboratory for Assessment of the Quality of Education). 2008. Primer Reporte SERCE Segundo Estudio Regional Comparativo y Explicativo. Los Aprendizajes de los Estudiantes de América Latina y el Caribe. Chile: OREALC-UNESCO.
About the Authors Emma Näslund-Hadley is a senior education specialist in the Education Division of the IDB. Armando Loera is an independent education consultant and author of several books about video research.
Inside t he Math Classroom: What Makes a Teacher Ef fective?