## Point Reduction Class

List of Figures Abstract 1 Introduction 1.1 Problem 1.1.1 Definition of children 1.1.2 Definition of educational success 1.1.3 Model 1.2 Methodology 2 Quantitative studies 2.1 Significant positive effects of small class size 2.1.1 Project Prime Time in Indiana 2.1.2 Tennessee STAR 2.1. 3 Long-term studies 2.2 No significant positive effects of small class size 2.2.1 The statewide mandate in Florida 2.2.2 Hoxby’s method 2.3 Third International Mathematics and Science study (TIMSS) 2.4 Summary of research 2.4.1 General overview: Hanushek’s vote counting summaries 2.4.2 Potential effects of small class size 3 Interview analysis 3.1 Class size from teacher’s perspective 3.2 Class size from student’s perspective 4 Summary of findings 5 Discussion 5.1 Cost analysis 5.1.1 Cost-benefit analysis 5.1.2 Cost-effectiveness 5.2 Other teaching methods in small classes? 5. 3 Policy Implications 6 Conclusion and Outlook Appendix Teacher Interviews Student Interviews Opportunities in Small Classes Bibliography List of Figures Figure 1: Causality Class Size – Educational Eďolg Figure 2: Learning Outcomes of White and Minority Children Figure 3: Summary of Hanushek’s Vote Count Figure 4: Effect sizes of a meta-analysis of learning influences Figure 5: Extension of the model to include teacher quality Figure 6: Extension of the model to include teacher quality Figure 7: Differences in time spent on different tasks in large and small classes Figure 8: Educational attainment of civil servant children and working-class children

## Abstract

The problem of this paper is the question whether class size has an influence on the educational success of children and with which other factors this interacts. By means of an economic analysis, different quantitative studies that can prove a significant positive influence on educational success were compared with studies that cannot find a significant positive success. These findings were extended by including structured interviews with teachers and students. Although the influences of class size have been studied for decades, further research is still empirically relevant due to a lack of evidence. Findings show divergence both among studies and between studies and interviews. While studies such as the Prime Time Project and the Tennessee STAR Experiment clearly favor small class size, the majority of studies found little significant positive influence of class size on educational achievement. The teachers and students interviewed showed a strong tendency toward smaller classes because individual support is better there. Based on these results, the model of causality between class size and educational success was extended to include teacher quality, other influences, and external factors. This relational model implies an indirect effect of class size on various influences such as feedback, motivation, or community, which then in turn have a positive effect on educational success. However, this effect can only unfold if the teacher recognizes the potential and adapts teaching methods to a small class. Consequently, in order to have a lasting impact on children’s educational success, we should move away from looking at class size in isolation. However, further research is essential to prove this. Keywords: class size, class size reduction, educational success, teacher quality

## 1 Introduction

Overcrowded classes, noise, overworked teachers, poor grades – teachers and parents like to demonize large class sizes and believe that children achieve higher learning success in small classes than in large ones. At first glance, the arguments in favor of small class sizes seem plausible: the noise level would be lower, the students could concentrate better on a task and participate more interactively in class. Furthermore, they could interact more with other children in the class and the relationship with the teacher would also be more personal. In addition, teachers would have more time to devote to each student’s individual questions and homework. All in all, children in small classes would receive more intensive and individualized support than those in large classes and would therefore have better grades. Educational researchers such as Jürgen Baumert and Wilfried Bros argue that this is not the case. The educational success in small classes would be just as great as that in large classes (cf. Ebel, 2011). Numerous studies found no differences in learning success by reducing class size. Does a small class size contribute to a high-quality school education or are the effects rather to be classified as small? The aim of this paper is to use an economic analysis to find out whether class size has a significant impact on children’s educational success. For this purpose, the controversial opinions are contrasted and discussed further.

### 1.1 Problem

In the following, the research question ‘Does class size have an influence on the educational success of children’ will be explained in more detail. For this purpose, the question will be broken down into individual parts and finally explained in their relation.

#### 1.1.1 Definition of children

The question explicitly refers to the impact on children. Legally, the term child is not regulated, but in legal usage, people who have not yet reached the age of fourteen and are therefore not of criminal age are referred to as children. In the statistical sense, children are often defined as those people who do not yet have any descendants of their own and still live with at least one parent (cf. JuraforumWiki editorial team, 2013). The Convention on the Rights of the Child has coined another definition. According to Article 1, a child within the meaning of the Convention is ״any human being who has not attained the age of eighteen years, unless under the law applicable to the child majority is attained earlier’ (Federal Ministry for Family Affairs, Senior Citizens, Women and Youth, 2015). When considering whether class size affects children’s educational success, children are considered according to this convention, as a precise age differentiation is often not listed. However, it is reasonable to assume that students attending elementary or secondary school are under eighteen years of age or only slightly different from the definition. Consequently, studies that focus, for example, on the relationship between class sizes and educational success at universities or vocational high schools are excluded from the analysis because the participants in these studies are usually older than eighteen.

#### 1.1.2 Definition of Educational Success

The aim of this paper is to find out whether class size has an impact on the educational success of children. In order to discuss this in more detail, a definition of the question component educational success is necessary. Traditionally, education has been understood as an elaborative and appropriative engagement with the world and as the self-realization of human beings, which enables self-development and emancipation (cf. Büchner, 2003). Above all, however, it is state-recognized educational qualifications that represent long-term educational success and are thus distinguished from selective school performance measured at a particular point in time in specific subjects (cf. Diefenbach, 2008). Consequently, education today largely refers to institutional education at schools, universities et cetera, which is also referred to as formal education (cf. Rohlfs, 2011). Educational success and educational failure thus ultimately determine career opportunities and social advancement and relegation. However, there is also education that runs parallel to the content taught in schools and is not included in this definition (cf. Grundmann, 2003). This is also referred to as nonformal education and takes place outside the formal institutions of the education system, for example in sports clubs or tutoring. The focus here is on voluntary participation. Another form of education that develops incidentally more as a process is informal education. Learning starts spontaneously from the individual and takes place in an unplanned and uncritical way. In the informal context, education is therefore not subject to any control or formal requirements and is not goal-oriented, so that no certification of education is possible (cf. Rohlfs, 2011). In the problem definition of the paper, non-formal and informal education are neglected, since the research question explicitly focuses on formal education in schools. Educational success is mainly measured by test scores in the studies presented. For this reason, it is necessary to check the results for other influences in order to exclude possible biases. For example, it may occur that a student is heavily involved in non-formal education and thus academic performance improves regardless of class size.

#### 1.1.3 Model

The theory of the thesis implies that children in small class sizes achieve better results than children within large class sizes. Consequently, in reference back to the general research question, the flypothesis pair is: Ho: Class size does not have a positive impact on children’s educational achievement. H1: Class size has a positive influence on children’s educational success. Class size represents the independent variable, which is exogenously given and affects the dependent, endogenous variable – educational success (cf. Figure 1). Thus, the test is whether there is causality between class size and educational achievement. Note that the dependent and independent variables could be modified by other exogenous variables, causing a bias in the results. Educational attainment could be influenced by non-formal or informal education, as mentioned in 1.1.2. Thus, it is possible that the higher success is not due to a smaller class size, but to, for example, active participation in sports clubs, where discipline and ambition are encouraged. Consequently, this may also affect the child’s learning behavior. Class size can also be influenced externally, for example by government intervention or decisions made by the school. For example, weaker students might be assigned to a smaller class and stronger ones to larger classes. Thus, the effects would no longer be comparable or meaningful. In the following literature review, it is important to examine other exogenous influencing factors as well, if they are identifiable in the study. Based on a literature analysis and collection of own data, it is examined whether the null hypothesis can be rejected (cf. Bryman & Bell, 2015). Abbildung in dieser Leseprobe nicht enthalten Figure 2: Causality class size – educational eďolg. Educational Success

### 1.2 Methodology

In order to get to the bottom of the research question, studies on the influence of class size on children’s educational success were searched for using the search portals PRIMO and Google Scholar. Only quantitative studies were relevant. Qualitative studies were excluded due to their lack of empirical relevance. These were then subdivided with regard to their results. In order to gather additional information, additional interviews were conducted with both teachers and students. Three teachers from a middle school, one teacher from a high school, and three students from a 12th grade high school were interviewed in more detail about the topic of different class sizes. The reason for the selection of exactly these students is the assumption that they can sufficiently reflect their experiences regarding the influence of class size due to their almost completed school education and their accompanying maturity. Since the interviews are only supporting qualitative material, the number of interviewees was kept relatively small. Existing literature and interview findings are first analyzed and then critically discussed in terms of answering the research question. Based on this, possible policy implications are given.

## 2 Quantitative Studies

The following chapter considers studies that rely on quantitative analysis based on test scores. Studies that produced significantly positive results and those that did not are differentiated. The Prime Time project in Indiana, the Tennessee STAR experiment and studies based on it, a study from Florida, and Hoxby’s method are examined in more detail. At the end of the chapter, results from different countries are compared and a general conclusion on the current state of research is drawn.

### 2.1 Significant Positive Effects of Small Class Size

#### 2.1.1 Prime Time Project in Indiana

The U.S. state of Indiana implemented a two-year program in 1981 to investigate the effects of reduced class sizes. This initially set the student-teacher ratio at 14:1 in 24 different second grades. After two semesters of implementation, which showed positive effects on student reading and math skills, the program was eventually expanded statewide as Project Prime Time by the Indiana state Department of Education. The first phase of the project began in 1984 and lasted until 1985 and included only first grades with an average class size of 18 children. In the second phase, from 1985 to 1986 it was expanded to include second grades and finally third grades in 1986 to 1987 (see Bain & Achilles, 1986). The purpose of the study was to examine effects of the Prime Time Project on reading and mathematics skills of second graders taught in a small class for two years (cf. McGiverin et al., 1989). For the meta-analysis, data are collected from six randomly selected schools. These results are compared to three other randomly selected schools that did not experience class size reduction (cf. McGiverin et al., 1989). The random selection of schools minimizes the potential bias in the independent variable that can occur due to externalities (cf. Bryman & Bell, 2015). The selected studies rely on the mean scores achieved on the ,Cognitive Abilities Tesť, the ,Iowa Tests of Basic Skills’, and the ,Stanford Achievement Tesť, which represent three different achievement tests. The results of this analysis indicate that the academic achievement of children in prime time classes who were taught in small classes for two years improved by a standard deviation (SD) of 0.34, which is an educationally significant value. In contrast, the comparison group achieved a non-significant value of -0.15 SD1. Based on these results, the authors conclude that smaller classes achieve significantly higher test scores than their cohorts in larger classes (see McGiverin et al., 1989). Because it is unclear whether small classes were kept small throughout the school day, it is questionable whether the improved performance was truly due to the reduction in class size. Furthermore, Normally, a value greater than 0.25 is considered significant at the 95% confidence interval. However, a value greater than 0.33 is also pedagogically significant (Wolf, 1986). the actual fixed class size of 18 students per class was not always adhered to, so that the size of a small class varied between 18 and 31 (cf. Hattie, 2005). The non-formal background of the children was also insufficiently investigated, which is why it is unclear whether the occurring effect is not also due to other influences. Consequently, a need exists for further research on the effects of class size reduction.

#### 2.1.2 Tennessee STAR

The Tennessee STAR project is the most influential study in class size research. It was inspired by the Prime Time project, described in more detail in Section 2.1.1, and began in Tennessee in 1985 (see Hattie, 2005). Part of the study involved 79 elementary schools in 42 districts. Here, kindergartners were randomly assigned to classes with a regular size of 22 to 26 students, small classes with 13 to 17 students, or classes with full-time assistant teachers/teachers. The classes with assistant teachers did not differ from regular classes, but the intention was to show that school success is independent of teachers and is determined only by class size. Female teachers were also randomly assigned to different classes. The division into the individual classes was maintained until the third grade (cf. Nye et al., 2000). Randomization here again minimizes bias due to external effects (cf. Bryman & Bell, 2015). The purpose of the study is to compare learning outcomes in reading and mathematics skills across class types and to draw possible conclusions about the influence of class size on children’s achievement. A hierarchical linear model is used to analyze the results (see Nye et al., 2000). In the following, the most important findings are explained in more detail. On average, children in small classes achieved higher test scores in reading and math than children in other classes, with statistically significant differences across all class types (cf. Finn & Achilles, 1999). Results show advantages in small classes of 0.15-0.18 SD for Year 1, 0.22-0.27 SD for Year 2, and 0.19-0.26 SD for Years 3 and 4. (cf. Hattie, 2005). Effects on test scores increased monotonically the longer children were in small classes (cf. Nye et al., 2000). Differences between regular classes and regular classes with aide cannot be found (cf. Finn & Achilles, 1999). Of interest is the difference between minority children and what were termed white children in the study (cf. Figure 2). Minority children’s learning outcomes were significantly higher than white children’s learning outcomes from Year 1 to Year 3 (cf. Hattie, 2005). Consequently, it can be concluded that minority children benefit more from small classes than white children. The reason for this could be that white children come from more educated social backgrounds and thus were already able to gain literacy and numeracy skills in early childhood as part of non-formal and informal education, allowing for less of an increase than minority children. Figure 2: Learning gains of white and minority children (Hattie, 2005, p. 391). Figure not included in this sample Children who were in small classes in the first three years show higher engagement in fourth grade-they more often take the initiative or put more effort into learning activities than children who were previously in larger classes. Further analysis suggests that these positive behavioral changes persist and that less discipline is needed in the future (Finn & Achilles, 1999). These results imply all-encompassing positive effects of small class size large enough to be educationally significant. However, Project STAR does not answer all of the important questions-for example, the study does not include a cost-benefit analysis, and it is also unclear exactly how small classes lead to greater learning outcomes (cf. Nye et al., 2000). These aspects are discussed in more detail in point 5 of the paper.

#### 2.1.3 Long-term studies

Past studies such as the Prime Time and STAR projects have shown that reduced class size leads to significant positive learning gains. However, to determine whether these gains were just inventory, it is necessary to conduct long-term studies. To this end, Finn et al. (2005) examined whether attending a small class in elementary school increased the likelihood of high school graduation. To do this, they continued to monitor participants in the STAR project even though the project actually ended at the completion of the third grades. The results show that children taught in a small class also had better outcomes, both in all subsequent years and in all subjects, than children who attended a large class. Further, the likelihood of taking a college admissions test increases for these children, and these effects are particularly large for minority children (see Whitmore, 2001). This suggests a strong relevance of formal education for these children, as it can be assumed that they do not enjoy sufficient additional support in the non-formal sphere, such as family and sports clubs. This confirms the short-term positive effects of minority children in the Tennessee STAR project. High school graduation rates increase monotonically with length of time in a small class size. However, these results are significant only for students who were in a small class for four full years. For shorter durations, the results are not different from children who attended regular class sizes from the beginning. Thus, to achieve a positive academic effect, children must learn in a small class for four full years of elementary school (see Finn et al., 2005). Wilde et al. (2011) observed participants in the project through 2010, looking at the impact of small class size on college attendance, college completion, and chosen field of study. The result of the study showed that participants who attended a small class in elementary school were 2.7 percentage points more likely to attend college. In this case, the probability of completing college increases by 1.6 percentage points. Further, participants are 1.3 percentage points more likely to earn a degree in a well-paying field. These positive effects are again strongly found among participants who were from minority backgrounds. This confirms the relevance of formal education for these children is confirmed. Fredriksson et al. (2013) went one step further and examined the impact of small primary school classes in Sweden on later earnings. Results show that income increases by 1.2 percentage points relative to the average when class size is reduced. Wages increase by 0.6 percentage points. Further results show that attending a small class, however, does not increase the probability of finding a job. Consequently, the increased income does not depend on an increased probability of finding a job. All results here are significant. One reason for this could be that the higher potential cannot be sufficiently signaled in job applications and thus only becomes apparent in everyday working life, which can be responded to with more frequent wage increases. The cost-benefit ratio of this study is discussed further in section 5.1.1.

### 2.2 No Significant Positive Effects of Small Class Size

In November 2002, Florida residents voted by an absolute majority to amend their state constitution to require a universal cap on class sizes in elementary and secondary schools. Beginning in 2010/2011, there should be no more than 18 children in early kindergarten classes and in the first three grades of elementary school, and no more than 22 children from fourth through eighth grade. From ninth to twelfth grade, a class is to consist of no more than 25 students. The changes resulting from the mandate were considered controversial by the federal government because it added about $4 billion a year in costs. In 2009, there were an average of 18.6 children in a class after the implementation of Florida’s class size reduction policy, a reduction of about 23.2 percentage points since 2003 (see Chingos, 2012). Data for this study is provided by the K-20 Education Data Warehouse (EDW). These data include results from various tests. The analysis shows that before a class size reduction, the number of children in the experimental and control groups remained constant over the years. After the mandate change, the average number of children in a class in the experimental group decreased as expected. Florida’s Comprehensive Assessment Test (FCAT) scores are used for further analysis. Results of district and school analyses show a small positive effect at best, but test score improvements approach zero. Three years after the new class-size policy was implemented, math skills of children in middle school did not change relative to comparison groups, while reading skills actually did not decline significantly. Similar results were seen for children in elementary school – math and reading skills remained the same or were slightly lower than those of the comparison group. However, it is problematic to compare these results with other studies because they do not compare the effect of class reduction with the effect of providing additional equivalent resources. For example, in Project STAR, discussed in Section 3.1.2, children in smaller classes were allocated more additional resources than children in larger classes. It is thus impossible to distinguish the effect of class size reduction and the effect of additional resources (see Chingos, 2012). Consequently, class size reduction does not improve test scores, but positive changes in non-cognitive skills, such as delinquency and violence rates, have been found on a school-by-school basis (cf. Chingos, 2013). #### 2.2.2 Hoxby’s Method. In a quasi-experimental study, Hoxby (2000) examined classes in Connecticut whose size variation was due to natural population changes. The study implicated two different methods, both of which yielded similar results. The first method looked at changes in class size attributable to idiosyncratic population differences. The second method exploits large jumps in class sizes triggered by maximum regulations. For example, here there would be only one class if there were 25 students, but there would be two if there were 26 children. Using these two methods, no relationship between success and class size can be found. Both small effects and effects where minority children benefited cannot be demonstrated, unlike studies already explained. One advantage of this study is that teachers and children did not know they were part of a study, so bias due to changing behavior can be ruled out (cf. Hoxby, 2000). However, the study also shows limitations. The tests were administered in the fall, so the students/students differed from those in the following fall. As a result, Hoxby’s results are biased toward zero (cf. Jepsen & Rivkin, 2009). This should be countered by the fact that school changes are relatively rare in Connecticut, so that 93% of the children remained in the same class over the course of the study the next year (cf. Hoxby, 2000). […] Equipment classes, in terms of sling design, refer to different fall protection measures that can be installed specifically on roofs. The definition of the equipment classes is derived from DGUV Information 201-056. When planning protective measures on roofs, the question arises as to which type of protection must be used. In answering this question, it should be said that collective protection always takes precedence over individual protection (cf. ArbSchG). Equally important is the imperative of prevention (cf. DGUV Regulation 1). ## What equipment classes are distinguished? The German Social Accident Insurance (DGUV) distinguishes between four equipment classes. ### Equipment class 4 Workplaces and traffic routes are designed in accordance with applicable building regulations for public spaces. Where applicable, further regulations apply, for example for escape routes. Equipment class 4 allows private persons to access the roof areas/areas. ### Equipment class 3 Fall edges at workplaces and traffic routes are secured by collective protective measures. Protective railings or side guards can be used here. Equipment class 3 allows untrained personnel to enter the roof surface / area. No instruction is required. Access to the roof area must be considered separately. ### Equipment class 2 Fall edges at workplaces and traffic routes are secured by horizontal anchor devices. Rope safety systems that can be driven over or rail safety systems can be used here. Equipment class 2 allows only instructed skilled personnel to access the roof area. Rope and rail safety systems make it possible to work with a preventive restraint system. Equipment class 2 can be supplemented at exposed points by individual anchor points. supplemented points. ### Equipment class 1 Fall edges at workplaces and traffic routes are secured by individual anchor points. Here, the individual anchor points must be placed at specific distances from each other and from the fall edge in order to secure the entire roof area. Equipment class 1 allows only instructed skilled personnel to access the roof area. Single anchor points only offer the possibility of a point restraint system. When working along the edge of the fall, the preventive system is not effective. A fall accident is possible here. Correctly used PPE limits the impact of the fall on the body and the anchor point absorbs the energy. Even when PPE is used correctly, injuries cannot be ruled out. The casualty must be rescued from the harness as quickly as possible. Temporary rope safety systems are assigned to equipment class 1. When used correctly, they increase safety for the user, but are not part of the structural system. ### Selection of the appropriate equipment class The selection of the appropriate equipment class depends on the people who will be accessing the roof surface/area and how frequently they will need to do so. • 1: Single anchor points • 2: Permanently installed rope or rail safety systems with intermediate holders that can be driven over • 3: All-round side protection (e.g. railings) • 4: Planning in accordance with public space regulations ## Table of contents • Material characteristics of the seam • Quality of the design • Notch effect of the seam We will now examine the three influencing factors in more detail. ## Material properties of the seam In the area of the weld seam, a change in the material properties of the base material occurs as a result of welding (indice G). In the favorable case, there is a joint (Indize V) that satisfies the inequality: ### Method Click to expand$\sigma_{G weld} > \sigma_{V weld} $. This means that the allowable stress is greater than the stress that occurs. However, it is often the case that martensitic embrittlement occurs in the heat-affected zone as a result of welding. Then the inequality changes to: ### Method Click to expand$\sigma_{G weld} \le \sigma_{V weld} $At the same time, incipient cracks also occur where there is different deformation behavior between the weld and the base metal. Because the latter depends on the welded joint, the structural design and the direction of loading, Wöhler lines and Smith diagrams specifically tailored to welded joints exist for particularly important applications. ## Quality of the design How load-bearing a welded joint really is in practice depends not least on the design class of the weld. The classification is based on the following criteria Execution and testing of the welding process, both of which have an influence on the limit value. Usually, three quality classes of welding operations are distinguished: • Grade 1: The welding operation is performed by a certified welder who has not passed his examination at the factory. After welding, a complete weld inspection is then carried out using radiographic methods such as ultrasonics. If necessary, the welds are then machined.$\rightarrow $Welding professional • Grade 2: Here, too, the welding process is carried out by a certified welder who has not taken his examination at the factory. After welding, an inspection is performed, but it is not fully completed. Also, the welds are not reworked. Welds that follow this grade are the norm in the field.$\rightarrow $skilled welder with sufficient welding knowledge. • Grade 3: Here, neither the welder nor the weld is subjected to testing. The results are comparatively modest.$\rightarrow $student trainee after brief instruction from foreman. To better visualize the differences between the grades in terms of strength, a brief numerical example: ### Example Click here to expandCompared to grade 2 has Grade 1 has a 20% higher strength. Compared to grade 1 has Grade 3 has a 50% lower strength. These differences indicate that certain components can only be assigned to a specific grade. • Clearly to Grade 1 are to be assigned: Piston rods, crane hooks, turbine rotors or pressure vessels. • The grade 2 can be assigned to: Gearbox housings, wheel rims or containers • In grade 3 you will find the simplest components such as: Racks, stands or boxes. ## Notch effect of the weld As a result of the welding process residual stresses and notch effectsas you may be familiar with from production engineering. ### Note Click here to fold out Residual stresses and welding distortion are primarily dependent on the component geometry and the welding process. Nevertheless, they can be favorably influenced by applying weld sequence technologies, i.e., the execution sequence. One possibility is to spot weld first (tack welding) and then weld through. From the given influences, application-specific calculation methods have been developed, some of which are standardized and contain different regulations. These regulations concern: • the determination of$ \sigma_{zul} $and$ \tau_{zul} \$
• the rules for the selection of the hypothesis to be applied
• the amount of collateral to be taken into account

Point Reduction Class.