Class Size and Student Achievement: Observations of Public Schooling in São Paulo and California

Daniel Clark Orey, Ph.D.,
Professor of Mathematics and Multicultural Education,
California State University, Sacramento
 Sociedade Internacional de Educação de Crianças
SIEC - Rio de Janiero, RJ, Brasil
Novembro de 1999

Introdução

Seis meses como professor visitante na Pontifícia Universidade Católica de Campinas (PUCC), em 1998, com bolsa de estudos pela Fulbright, permitiu ao Professor Orey interagir com educadores matemáticos de mais 30 escolas da região. Durante este tempo, Professor Orey participou de aproximadamente 150 horas de observação, em salas de aula da Escola Técnica Estadual "João Belarmino", em Amparo, São Paulo. Amparo possui uma população de 65.000 habitantes e está distante, de carro, aproximadamente, 2.5 horas da cidade de São Paulo e 45 minutos da cidade de Campinas. Professor Orey encontrou aspectos triviais notáveis entre a instrução escolar de ambos os países: Brasil e Estados Unidos. As observações que neste documento estão sendo efetuadas, foram coletadas de dados retirados de literatura professional, de escolas nos estados de São Paulo e California, bem como do "Third International Mathematics and Science Survey (TIMSS). Isto também faz parte de um estudo piloto, que utiliza professores visitantes de matemática, internacionais, para trabalhar com alunos de ensino fundamental e médio, e, que estão destinados ao fracasso pessoal e escolar. Planos Educacionais em ambos os países são diversos, o que inclui aspectos importantes como: política, cultura e economia. O Brasil é um legítimo representante do que podemos encontrar na grande maioria dos países do mundo, pois utiliza uma estrutura formalizada de currículos estadual e nacional. Nos Estados Unidos, a situação é atípica, pois não existe um currículo nacional "formalizado". Assim, todas as escolas americanas são controladas localmente ou pela comunidade, onde cada estado é responsável pela gestão do currículo. Qualquer educador ou leigo, que superestime as condições educacionais em qualquer um dos dois países, pode cometer facilmente seríssimos erros. E isto, pode tornar-se um problema, pois as realidades: políticas, educacionais culturais e econômicas, diferem de um país para outro. Então, para que possamos discutir as próprias percepções, esperamos que os leitores entendam que continuamos a reconhecer que quaisquer comparações efetuadas, neste documento, entre culturas, são moldadas, definitivamente, pelas contínuas experiências do observador, por seus preconceitos e por suas limitações pessoais.

Introduction

Six months as a Fulbright visiting scholar at the Pontifícia Universidade Católica de Campinas (PUCC) in 1998 allowed Professor Orey to interact with mathematics educators in 30 or more schools in the region. During his time there, Orey conducted approximately 150 hours of classroom observation at the Escola Técnica Estadual "João Belarmino" in Amparo, São Paulo. Amparo (population 65,000) is about 2.5 hours from the city of São Paulo and about 45 minutes from Campinas. Orey found remarkable commonalties between schooling in both Brazil and the United States. The observations made here are gleaned from data taken the professional literature, from schools in the states of California and São Paulo, as well as from the Third International Mathematics and Science Survey (TIMSS). It is also part of a pilot study using visiting international mathematics teachers to work with at-risk inner city middle and high school students. Educational plans in both our countries are diverse - including important aspects of politics, culture and economics. Brazil is fairly representative of what can be found in the majority of the world - using some form of formal national and state curriculum. The United States is atypical in that no "formalized" national curriculum exists. All school control is at the local or community level, with each state taking responsibility for the curriculum. Anyone over-generalizing conditions in each country can easily make very serious mistakes. This becomes a problem when the educational realities of politics, culture and economics differ from country to country. So as we discuss our own perceptions, we hope here that readers will understand that we continue to recognize that any cross-cultural comparisons made here are definitively framed by the observer's ongoing experiences, biases, and personal limitations.
 
 

California Dreaming

The observations initially made by Professor Orey unearthed some what of a paradox for him and led him to invite Professor Rosa to work with secondary math students in California. There is a paradox related to the question that bothers many North American educators: "Why is it that so many American school children display such dismal performance in schooling in general, and specifically in reading and mathematics?" Indeed some scholars studying the American educational systems generally describe them in three words - fun, easy and dumb. With such things as shopping malls and theme parks fast becoming the major cultural icon, most people agree it is fun place to live, work and visit. Life for the vast majority of people in California is easy. As well, our life, though not quite as glamorous as depicted in film and television, is dynamic, often exciting - from simple acts of paying bills, shopping, gaining of access to information, to more difficult task of educational opportunities. Simply put, daily life in California is far easier than just about anywhere on the planet.

On the other hand, in California we have approximately 300 languages spoken, every race and religion can be found here as well. It is very common to enter just about any suburban or inner city school and see children in classrooms with 5 to 6 languages. It is equally diverse in regards to religion and race. This diversity, has been with Californians from the very start - the ecology is one of the most diverse ecological habitats on the planet - the original inhabitants (once numbering almost a million at the time of the conquest) had over 35 linguistic groups. California it seems has and will always be diverse. It is what has fueled the techno-economic renaissance that has reached virtually every square meter on the planet. But to enter our public schools, you would never guess that this miracle ever occurred — forms of instruction, curriculum, technology and materials are often 25 to 50 years old. Our schools rarely relate to the outside reality and work environment.

With all this ease and enjoyment, there seems to be a terrible price being paid - the population is becoming seemingly less intelligent. Poll after poll indicates that people in the USA do not know basic things - the location and names of states and capitals, multiplication tables and the like. People cannot resolve basic problems. Situations such as basic geographic knowledge, measuring space to install flooring, compute percentages for tips at a restaurant are extremely difficult for many people. The authors have heard that there is a television program in Scandinavia that travels to the USA and asks people basic things about our country that most people outside of the USA know the humor lies in the ignorance of the population. Yet our children find it difficult to focus on any activity or job that requires any struggle what so ever - something that requires interaction or work - is quickly rejected as being "too hard".

A case in point. The Brazilian visiting teacher Mr. Rosa has observed the following at his school. The environment is best described as "difficult", as 3/4 of the kids are eligible for some form of public assistance (free lunches and breakfast, welfare assistance, etc), there are 35 languages spoken there, and many live in difficult situations at home. The reason that Mr. Rosa was invited to work at Encina is that the school is remarkable for its social and community outreach programs. Encina High (approximately 750 students) is renown for its community counseling services, work-school programs, its art gallery, and a school for young parents and their newborn children.

What is observed at Encina so far is a form of disassociation with the curriculum by the students. The 15 ninth graders (14-year-olds) in each of Mr. Rosa's classes were having trouble with computing area and circumference of a circle during one recent observation. This was despite the fact that they have worked with this subject repeatedly since the fourth grade. After two weeks of intensive work with the kids, we gave them a quiz - this quiz had at the top of the page the formulas, which Mr. Rosa and I also posted on the board and brought to their attention. Yet the students still needed us to help them, and over 3/4 could not do the problems on the quiz without some form of prompting. This is quite interesting to us and as we are using ethnomathematical concepts by working to try and make this sort of activity real to the kids. The curriculum and activities use real life situations and questions. The students are highly distractible, and reject the concept of mathematics in its entirety. They find it nearly impossible to expend even a minute amount of energy in the engagement in their daily math activities. We are encouraged when they connect to us even for a moment. The enormous peer pressure is to NOT succeed in school, yet they all have dreams and desires, and hopes like any other child their age.

American Academic Performance

The performance of American children is dismal in mathematics and science as documented in numerous international studies, most notably the Third International Mathematics and Science Survey (TIMSS). As yet, and despite the data to the contrary, no real consensus exists as to why this occurs in the United States. The leading role in technology, finance, and military expertise as exerted by American influence (often in the name of globalization) does not seem to coincide with the data from this report. What allows the USA to lead is best explained by the simple law of averages: a minority of highly intelligent and creative people who maintain all technological systems sustains a large population. Despite almost universal access to a vast variety of tools and techniques within a relatively supportive learning environment, the majority of the children do not achieve to the international standard. The paradox, it seems, is that the richest most powerful nation in the history of the planet cannot resolve the problem of access and equity for the majority of its students.

In both our countries, educators, administrators, politicians, policy makers, students and the general populace at large find the implementation of what "works" for children increasingly difficult. As well, it seems that both the professional and popular literature maintain a certain focus on the altogether easy to see, or the negative aspects related to the modern reality of public education. Brazilian teachers, students, and families cope with extremely complex and difficult questions. This experience and energy has given birth to numerous projects and an outstanding level of research. Educators in other countries need to see and hear about these successes.

If one listens only to the mass or popular media, one is easily led to believe that all is lost in relation to public education. Of course there is much room for improvement, and it is an important goal of this project to address many of these improvements. Yet the myriad forms of educational privatization possess a definite and to be honest, self-serving power to sustain or create privatized and market-driven educational options. This has extremely serious consequences for democracy, and just as seriously contributes to the continual dismemberment of public education worldwide.

The Observations

The following discussion will focus upon observations related to student performance and class size made in Amparo and Sacramento. Future aspects of this work plan to examine aspects related to homework, school environment and student attitudes as related to achievement. As this work at the pilot stage, it is not the purpose of this article to outline in detail our data. However, we would like to share with the reader brief examples of how we came to some basic conclusions using methods aligned with ethnographic observations.

As stated early, Orey initially has spent over 150 hours observing teaching in a technical high school in the interior of São Paulo State. Amparo is a city of over 65,000 people of varied ethnic and socio-economic backgrounds similar in many ways to his own urban area in California. The majority of his observations in Amparo were made during Monday mornings from 9 to 12, and Friday evenings from 7 to 11pm. In Amparo, the class sizes ranged from 25 to 45 students in class. Instruction was varied using mostly teacher explanation, student interaction and notebooks and the chalkboard. As well, Professor Orey now spends all day Friday in Mr. Rosa's classes as an ethnographic observer. The project has so far linked six university students who serve as service learning participants as 1:1 tutors.

Class Size

The literature on class size in the United States is mixed. In California recent movements have reduced class size from an average of 25 pupils to 15. As well, an increased emphasis on student achievement scores has redefined what teachers can and cannot do in class. A number of school districts have engaged in projects where reading is taught for 3 hours, using scripted lessons, the same for mathematics. Much of the research from around the world shows us that students in reduced class size may score only slightly better in math than students in larger classes on standardized achievement test measures. In Australia, Flemish Belgium, and France, students in larger classes did significantly better in math than those in smaller classes. Class size reduction made little difference in math performance in Canada, Germany, Iceland, South Korea, and Singapore (Pong, 1999). For students in 10 nations around the world, class size reduction had the opposite or no effect on math scores.

The following section describes terms found in the literature related to class size reduction. According to Agron (1999), class size reduction means the displacement of students who will need to be housed somewhere. According to Zahorik (1999), class size reduction in a variety of formats increased attention to individual students. Teachers of smaller classes individualized instruction, but not necessarily the content. Smaller classes promote student learning and offered a more pleasant environment for the pupils and teacher (Mueller, Chase and Walden, 1988).

The perception in the United States (Lord, 1999; Zahorik, 1999): is that small classes are better because they promote:

• Higher student achievement;
• More access to college for the students;
• Students can take more challenging courses;
• Students drop-out less frequently than students who attend larger classes;
• Teachers come to know students personally; and
• A slight increase in the use of hands-on activities, such as the use of manipulative activities and cooperative grouping

However, some unfavorable arguments exist in relation to reduced class size as being implemented in California. Some researchers claim that any benefit of reduced class size is minimal when other ways to increase achievement that are more effective and less costly than class size reduction might be implemented first. Pong (1999) in research released in California found that in reduced scores rose slightly on standardized tests, but that teacher quality suffered (emergency credentials were granted, and many unqualified teachers were needed to teach subjects they were not trained or qualified to teach); and schools were forced to take needed resources from other equally vital programs to achieve the reduction in class size.

For class size reduction to succeed there are problems that need be solved (Zahorik, 1999; Agron, 1999). If reduced class size is to be effective answers need to be resolved for the severe shortages of credentialed teachers and classrooms. Most school districts are not able to keep up with the growing demand for space and facilities. Many school districts are finding that they also must raise funds for increased construction projects.

However, most seriously, evidence suggests that because of these shortages (either perceived or real), many districts are turning towards models of direct or programmed instruction to reach testing goals that were often implemented by state legislatures who wish to raise dismal test scores. As districts are forced to hire unqualified, part-time or uncredentialed teachers to fill shortages, the direct or programmed instructional model seems to be an unintended consequence. Because of this, class size reduction has done little if nothing to change students from largely passive learners, to more active engaged and interactive learners. Teachers in reduced classes did little to engage students who not engaged in problem solving, and decision making.

There exists some evidence in the United States that small classes are beneficial for some grades (kindergarten through third grade and eight-grade math classes). Large classes were defined as having between 19 and 29 students, while small classes had 6 to 18. In Brazil and some other countries in South America, as well as in Israel, classes often have between 40 or 50 students. The data suggests that the performance of students from larger classes is the similar as students from smaller classes.

Conclusions

Future work in this project seeks to increase the link between University and public schools, by using peer mentor / tutors. We also hope to continue to examine the effects of overall school environment: homework, facilities, access to resources, furniture and technology on student attitudes and achievement. Strange as it may seem, I continuously observe a strange phenomenon. Those students attending school in truly difficult or complicated environments, but staffed by capable and dedicated faculty - learn. I have also begun to see a turn around in the United States, as the data from the TIMSS study suggests.
 
 

Bibliography

Acknowledgements

Professor Orey wishes to thank his other graduate students without whose tireless efforts in uncovering the resources and ideas as expressed here, would have made this article impossible: Milton Rosa, Ramandeep Bains, Rose Litsa, Jackie George, Amandeep Bains, Melia Sims, Sedah That, Mandeep Bains, John Kirk, Zacharie Button, Margaret Cambron, Craig Waechtler.