Effectiveness of Private Tutoring in Mathematics with Regard to Subjective and Objective Indicators of Academic Achievement: Evidence from a German Secondary School sample/Effektivit?t Von Nachhilfeunterricht in Mathematik Im Hinblick Auf Subjektive Und Objektive Indikatoren der Schulleistung: Befun

l. IntroductionPrivate tutoring is a wide-spread phenomenon all over the world. In addition to mainstream education many students attend private lessons in academic subjects which are already covered at school. For example in Germany, where the presented empirical analyses were executed, according to a recent representative study nearly 24% of 12 to 21 year old secondary school students currently attend private tutoring (Leven, Quenzel, & Hurrelmann, 2010). This number resembles the proportion of tutored students in neighboring countries like England and France. In many Eastern European, African and East Asian countries up to 50% to 80% of the students, especially in higher grades, are privately tutored (Bray, 2009). This tutoring may be provided on a one-to-one basis as well as in small or even large groups, though this last form is not common in Germany. Students may attend private tutoring for different reasons: as a kind of additional day-care after school, to meet up with their peers, or to avoid tensions at home caused by academic problems. But the main reason for private tutoring is to improve academic achievement at school or in high stakes exams at the end of secondary school (Bray, 2009). Therefore, on the school system level in the middle of secondary schooling private tutoring has mostly remedial purposes: With the exception of few countries like, e.g., South Korea, on average privately tutored students perform below the non-tutored students (Baker, Akiba, LeTendre, & Wiseman, 2001). A specific feature of the school system in Germany, is tracking according to the students' academic achievement. Consequently, private tutoring is not simply most prevalent between low performing students of an age or grade cohort but between low performing students within each academic track and relative to its specific achievement level (Guill, 2012). Despite the large number of students who take part in private tutoring, there is little research whether private tutoring reaches its main goal of improving academic achievement. Therefore, the advantages privately tutored students have compared to their counterparts can hardly be quantified. Even if it is well-known that private tutoring is more easily accessible for students from wealthy families (Bray, 2009), it remains unclear whether or to what extent private tutoring or specific types of private tutoring increase social disparities in academic achievement.In this paper we would like to contribute to closing this research gap by analyzing the effects of private tutoring in a large sample of German students in secondary school. The following outline is given: Section 2 sketches a theoretical model of private tutoring on academic achievement at school. Further, it gives a literature review about current research on the effectiveness of private tutoring. Section 3 outlines the leading research questions for the empirical analyses. Section 4 gives the description of the methodological approach. Section 5 describes the results of the empirical analyses. Finally, Section 6 discusses these results.2. Theoretical background and literature reviewUp to now, there is no well-established comprehensive theoretical model how private tutoring effects the tutees' academic achievement. Consequently, studies focusing on the global question of whether private tutoring is worthwhile or not usually propose only an eclectic array of reasons why private tutoring might support the students' learning process (e.g., Ryu & Kang, 2010; Smyth, 2009; Unal, Ozkan, Milton, Price, & Curva, 2010). Looking for a theoretical framework of the effects of private tutoring for our own analyses and given the close relationship of private tutoring and classroom teaching, we discuss the adoption of a model of classroom teaching. Here, we opted for Helmke's (2009) offer-usage model of instructional effects for the simplicity of its basic idea: On the one side, school offers learning opportunities to the students depending on the instructional quality of the lessons. …