Expectancy Value Theory

   Strong teacher-student relationships are integral to academic achievement, as they nurture a safe environment for students and foster rapport (Lewist et al., 2012). Wubbels et al. (2006) characterize positive teacher-student relationships as “a rather high degree of teacher influence and proximity towards students” (p. 25). Students who feel motivated and supported by their teachers tend to achieve higher academically, as teachers encourage them to take risks and grapple with even the most challenging mathematical concepts (Lewis et al., 2012). Specifically, learner-centered relationship approaches to teaching, which encourage autonomy in learning, lead to higher levels of critical and creative thinking (Cornelius-White, 2007), a fundamental aspect of belief systems that promote self-efficacy (Hughes, 2011; Ryan & Patrick, 2001). Self-efficacy is especially important because it is typically linked to feelings of belonging and self-esteem, which, in turn, influence a child’s perception of their academic abilities (Hughes, 2011). These qualities foster classrooms in which adolescent students develop a positive relationship with school and are therefore more willing to engage and commit to their learning (Hafen et al., 2015; Hughes, 2011; Pianta et al., 2012; Ryan & Patrick, 2001). Developmental theory supports the notion that engaged and sensitive teachers, particularly those who teach adolescent students, recognize that relationships are crucial to the connection between learning and academic growth (Hafen et al., 2015). A foundational aspect of educational development is strong, positive teacher-to-student feedback (Kluger & DeNisi, 1996). Hattie and Timperley (2007) define feedback as “information provided to an agent (e.g., teacher, peer, book, parent, experience) regarding aspects of one’s performance or understanding” (p. 102). Positive feedback increases a child's willingness to engage in cognitively demanding activities, leading to higher self-esteem and self-efficacy (Hattie & Timperley, 2007). Conversely, feedback that contradicts students' beliefs can harm academic outcomes and may undermine their self-perception (Hattie & Timperley, 2007). Although proper teacher preparation helps increase student academic achievement, cognitive barriers still play a significant role in a student’s mathematical capabilities.