Investigation of Prospective Preschool Teachers’ Beliefs about Mathematics Teaching and Learning

Preschool teachers' beliefs about mathematics are crucial for qualified mathematical learning environments because children need to develop mathematical concepts based on their level of mathematical knowledge. Therefore, the purpose of this research is to determine prospective preschool teachers' beliefs about mathematics teaching and learning and to examine the effect of different variables on these beliefs. This research involved 884 prospective preschool teachers as the research sample at three state universities in Turkey. A belief Scale on mathematics teaching and learning was used as a data collection tool. The results showed that prospective teachers had positive beliefs about mathematics teaching. Moreover, there was a significant difference on prospective teachers’ beliefs in accordance with grade levels. On the other hand, according to the type of prospective teachers’ high school graduation, there was a significant difference in favor of prospective teachers who graduated from vocational high schools in the “mathematical learning” and “nature of mathematics” sub-scales of the scale.

How Elementary Teaching Candidates’ Learning Opportunities Are Associated with Their Knowledge, Self-Efficacy, and Beliefs

Background/Context Many elementary teacher education programs seek to prepare candidates to enact ambitious mathematics instruction that supports students in engaging in rigorous, conceptually rich mathematics tasks. Extant literature suggests that preparedness to engage in ambitious elementary mathematics instruction is multifaceted and includes teaching candidates’ mathematical knowledge for teaching (MKT), self-efficacy with regard to teaching mathematics, and pedagogical beliefs about mathematics. Prior research has produced findings that provide discrete, and at times conflicting, information about teacher preparation. Purpose/Objective/Research Question/Focus of Study This study examined how elementary candidates’ learning opportunities in mathematics content courses, mathematics methods courses, and student teaching were moderated by their reports about the quality of their experiences in courses and field placements to seem to affect their MKT, self-efficacy, and beliefs. Population/Participants/Subjects The study participants were 220 elementary teaching candidates who were in their final year of teacher preparation at four universities in three states. Research Design We employed multivariate path analysis, an approach that is purposefully designed to probe heterogeneity in teaching candidates’ experiences in courses and clinical placements. Data Collection and Analysis We administered two surveys to each study participant: an elementary teaching candidate survey, which included measures of mathematics teaching self-efficacy and pedagogical beliefs about mathematics, and an MKT survey. Findings/Results The number of mathematics content courses that elementary candidates took was positively associated with their MKT and mathematics teaching self-efficacy only when they also reported having positive experiences learning mathematics. When candidates reported increased opportunities to engage with representations, decompositions, and approximations of mathematics teaching practices in mathematics methods courses, this was associated with higher MKT scores and pedagogical beliefs about mathematics. When candidates reported that their cooperating teacher was a high-quality mentor, increased opportunities to observe, attempt, and receive feedback on mathematics teaching practices during their field experience were associated with mathematics teaching self-efficacy and pedagogical beliefs about mathematics. Conclusions/Recommendations The findings from this multivariate path analysis, which account for both the reported quantity and the perceived quality of elementary teaching candidate experiences, may shed light on conflicting findings in prior literature. There is little agreement in extant literature about associations between facets of teacher preparation and candidate knowledge, self-efficacy, or beliefs. Explaining the positive associations in some samples and lack of associations in others may have more to do with the quality of teaching candidate experiences than with whether a candidate was exposed to a particular opportunity to learn.

Teacher Support for Argumentation: An Examination of Beliefs and Practice

Supporting students in making mathematical arguments is an important part of discourse practices in mathematics classrooms. Differences in teachers’ support for collective argumentation have been observed and documented, and the importance of the teacher’s role in supporting collective argumentation is well established. This article seeks to explain differences in teachers’ support for argumentation by examining two student teachers’ beliefs about mathematics, teaching, and proof to see which beliefs are visible in their support for argumentation. Assisted by a framework for argumentation and a commitment to teachers’ beliefs and actions as sensible systems, we found that teachers’ beliefs about the role of the teacher, particularly with respect to giving explanations, were more visible in their support for collective argumentation than other beliefs about mathematics or proof.