Reexamination of the study results yields some novel insights about relationships among student readiness to learn, teacher effectiveness, and mathematics achievement, and identifies some connections that are somewhat unsurprising. Each of the findings are expanded upon in the sections that follow.
Student Readiness to Learn (RQ1)
Regarding RQ1, we found that when faculty perceive students are ready to learn, the studentsâ mathematics achievement scores are higher. Conversely, students who do not appear to their teachers to be ready to learn have lower mathematics achievement scores. Focusing on the studentsâ own attitudes toward learning is counter to the current narrative of school accountability, which holds teachers and principals accountable for student results regardless of student motivation (Rooney, 2015).
But should we be surprised at the important role the individualâs attitude plays in his/her own learning? Perhaps not. School psychologists have, for years, pointed to the importance of motivation as a key contributing factor to learning (see, e.g., Keller, 2010). In fact, Tambunan et al. (2021) conducted a study of 277 middle grades students in Indonesia and found that student motivation was a key factor in their achievement. Similarly, Oyedeji (2017) conducted a study of 360 students in 12 secondary schools in Nigeria and found that studentsâ own intrinsic motivation was the single greatest factor influencing studentsâ attitudes toward mathematics.
A learnerâs motivation may also be heavily influenced by parents. Herges et al. (2017) conducted a study of 65 middle grades mathematics students in the midwestern United States and found a significant link among student motivation, parental involvement, and mathematics achievement. In sum, the research is fairly clear that a childâs intrinsic motivation makes a dramatic impact on their ability to achieve success.
An important starting point for school leaders to consider in helping improve student motivation to learn is the philosophy of education a school chooses to employ. There are several philosophical approaches to education, each with its own core beliefs and implications for classroom practice. Four of the most influential modern educational philosophers are Immanuel Kant, Maria Montessori, John Dewey, and Friedrich Froebel. A core belief in the Kantian philosophy of education is that learners need order, systems, and discipline to learn effectively, and learning should therefore be standardized with clear structure and rules (Churton, 2009). Montessori education is predicated on the core belief that students should be given as much autonomy as possible in the learning process. As a result, Montessori classrooms are set up with many opportunities for productive play (Morrison, 2014). Dewey believed students learn best when they receive a democratic education in which they have a voice in their own learning. In the classroom, students should experience hands-on education so they can learn by doing (Schmidt, 2010). Froebelâs philosophy, which gave rise to the kindergarten movement, is based on the belief that self-development in children should be fostered through the use of age-appropriate learning tools. In the classroom, Froebel advocated the use of songs and learning games so children would enjoy learning (Morrison, 2014). If students are not ready to learn, it may be that the philosophy being employed by a school is not working for that student population. For example, Wilson (2015) conducted research to investigate how parents choose schools and found that parents often choose schools that use an approach matching their childâs needs. Thus, a vital question that schools need to consider is what is the environment they are creating, and is it promoting a desire within students to achieve and be ready to learn mathematics?
A further consideration for establishing whether students are ready to learn is to consider whether the basic needs of safety, shelter, food, clothing, and well-being are being met (Maslow, 1998). Reardon and Portilla (2016) found an income achievement gap for a group of three cohorts of kindergarteners. They determined there were significant gaps in the achievement of groups from the 90th percentile of income to those from the 10th percentile (referred to as the 90/10 gap). In the middle grades, bullying presents a particularly pernicious threat to studentsâ feeling of safety and their ability to be in a learning mindset (Smith & Kearney, 2017). One way to address this is through restorative practice circles. In restorative practice circles, students can resolve conflicts by speaking/listening to one another with the aim of developing strong classroom communities (Gregory et al., 2021). The example of restorative practice circles is just one way that teachers can help students to be ready to learn.
School climate refers to stakeholdersâ perceptions of the school environment, including formal and informal structures, leadership influence, and relationships between constituents (Hoy & Miskel, 2012). Researchers have developed a wide variety of school climate surveys to measure specific aspects of the school environment such as: collegial leadership, principal influence, academic emphasis, and trust. Utilizing school climate surveys is an important first step in school improvement efforts. The next step is to work with a wide variety of stakeholders (including administrators, teachers, students, and parents) to examine root causes that have led to areas of concern and to come together to address these areas either at the individual (remediation) or organizational levels. For example, Kearney et al. (2013) conducted research into the links between school climate variables and student achievement within 149 Texas schools, in which they found that mindful leadership made a statistically significant contribution to the variance in student achievement in both math and reading. Part of mindful leadership is being attuned to feedback from students and staff. Thus, asking teachers their perceptions of student readiness to learn may provide useful information in identifying attitudes and improving learning in middle grades mathematics.
Math Teacher Effectiveness
The results of RQ2 demonstrate that when students perceive teachers as being effective at mathematics instruction, they tend to have higher mathematics achievement scores. Conversely, students who perceive of their teachers as being less effective demonstrate lower levels of mathematics ability. This result is somewhat novel because it is rare to ask middle grades students to reflect on the effectiveness of their teachers. Vazire and Carlson (2011) asserted that people are often more likely to have an accurate perception of others as compared with perceptions of self. To demonstrate this idea, Back et al. (2009) conducted a study of 130 subjects in Germany and found that people have blind spots regarding their own flaws, particularly in regard to extraversion and neuroticism. While there are certainly exceptions, it is apparent that, in general, individuals can be less aware of their own limitations than they are of those around them.
Measuring effectiveness in teachers is not a new idea. Many teachers receive regular evaluation, whether formal or informal, from their administrators, their peers, their students, and themselves. At the college level, it has become standard to ask students for feedback about their professors. Miller and Seldin (2014) reported that in 2014, 94% of universities reported using course evaluations to solicit feedback from students on a variety of success indicators including content knowledge. It is not uncommon to see studentsâ opinions about schooling being solicited at the secondary level. Giraldo-Garcia et al. (2021) noted an increasing movement toward student advisory committees that give students a voice, particularly regarding school and classroom climate initiatives. When considering the effectiveness of mathematics teachers in particular, a straightforward method of evaluation is to gauge whether the instructions they provide (if followed) will lead students to the correct mathematical answers (Sonnert et al., 2018). However, caution must be taken when determining effectiveness on this characteristic alone. Newton et al. (2010) established that student ch...