The purpose of the present study was to explore the effects of the effects of  teachers’ encouragements on mathematics self-efficacy of students who participated in the remedial- instruction programs.  Although students in Taiwan have ranked at the top in mathematics in various international evaluation programs, such The Trends in International Mathematics and Science Study (TIMSS) and The Program for International Student Assessment (PISA), the differences between the high achievers and low achievers are the largest in the participating areas (Lin, Wu, & Hung, 2013; Taiwan PISA National Center, 2014).  As a result, the Minister of Education in Taiwan promote the Project Implementation of Remedial Instructions (PRIORI) for the low achievers. 

Variances in mathematics self-efficacy could explain for the variances in mathematics achievements effectively (Lu & Lin, 2013; Taiwan PISA National Center, 2014).  Zuffianò, Alessandri, Gerbino, Kanacri, Di Giunta, Milioni and Caprara （2013） found that self-efficacy measured in the beginning of a semester could explain for the academic achievements in the end of the semester. Therefore, if one can elevate the students self-efficacy in mathematics could have effects on the mathematics achievements.  According to Bandura (1994), students self-efficacies could be influenced by their previous achievement in certain fields and persuasion of significant others. Bandura, Barbaranelli, Caprara, and Pestorelli (1996) found that parental aspiration for academic achievements could explain for children's aspiration for academic success.  Pajares, Johnson and Usher (2007) also found that encouragements from significant others could have effects on ones' self-efficacy.  Students who participated in the PRIORI have very few successful experiences in mathematics, that could lower their mathematics self-efficacies.  As a results, the incentives and encouragements of teachers or significant others could be the major sources of enhancing their self-efficacy in mathematics.

The incentives and encouragement teachers provide during their instruction could have different effects on students learning (Blackwell, Trzesniewski, & Dweck, 2007; Deci, Koestner, Ryan, 1999; Dweck, 2007; Lepper, Greene, Nisbett, 1973; Muller & Dweck, 1998).  In this study, the researcher tried to explore what kind of incentives and encouragements teacher used most often in the remedial instructions and how  these incentives and encouragement could have effects on students self-efficacy in mathematics.

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