The results ofthe present study and the findings of other research studies agreed as far asthe importance of the extended preschool education attendance is concerned,Martin, Mullis, Foy and Stanco and OECD recommended that more years ofpre-school education attendance were linked to higher achievement inmathematics (as cited by Karakolidis et al., 2016).  According to the data available online,Shanghai student-teacher ratio (junior high school) fell gradually from 13.91 personsin 2005 to 11.

49 persons in 2014. However, the result of this inquiry depictsthat mathematics teacher-student ratio was statistically significant. Thisresult does not mean that the positive benefits of larger class size accordingto Bolton’s (2008) experience, “larger is sometimes better” be ignored. The empirical evidence on teacher-student ratio (T-Sratio) is mixed.

In fact, several studies conclude that there are no effects ofT-S ratio on student achievements. However, there are also compelling findingsdemonstrating a positive effect of increased T-S ratio on student learning,especially for low achievers and students from lower socioeconomic backgrounds,Blatchford, Bassett, Goldstein, & Martin; Finn & Achilles; Falch,Sandsør, & Strøm; Hoxby; Leuven & Løkken, Fredriksson, Öckert, , Buckingham, Wheldall, & Beaman; Fien et al.; Vaag Iversen (as cited by O.J. Solheim et al.

, 2017). The use ofPISA data was another asset to this study which has grounded its findings on alarge and representative sample of 15-year-old students in Shanghai-China. Interms of the statistical analysis, this study applied the most suitablestatistical technique for the clustered nature of the data so as to provide thehighest possible quality of evidence (Field, 2013). Students’ mathematicsachievement depends on various factors that add to large proportion of unexplainedvariance. For example, students’ and school socio-economic status,instructional practices, affective characteristics and school environment, justto mention few. Future study can be administered via different existinglarge-scale international assessment data like Trends in Mathematics andScience Study (TIMSS), Progress in International Reading Literacy Study (PIRLS)and Southern and Eastern African Consortium for Monitoring Educational Quality(SACMEQ).

There is the dire need for further empirical analysis, becausedifferent data bases foster different contextual and background variables.In addition tothis, the inquiry of PISA data are cross-sectional, therefore it does notacknowledge establishment of causal relationships (Cohen et al., 2011). It onlymeasures fifteen year old students’ mathematics achievement. Therefore, futureresearch should carry out longitudinal studies that follow students over a longperiod of time, so as to survey whether specific mediations can lead to bettermathematics performance. In a nutshell, this study only analyzedShanghai-China, therefore should certainly be taken into consideration whilegeneralizing the findings.

Finally, we recommend that preschool educationattendance should be extended to three years or more while teacher-studentratio should be reduced to 6 persons to 1 teacher in junior and senior highschool among the least/developing countries and 9 persons to 1 teacher in thedeveloped countries, to foster mathematics high performance and thereby lead tolifelong influence on science and technology.

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