This study aims to examine changes in teaching and learning conceptions and sense of efficacy as well as relationships between them. Data were collected from 121 Korean preservice teachers before and after a 4-week teaching practicum. The results indicated that constructivist conceptions of teaching and learning increased over the practicum period and teacher efficacy shifted as well. In addition, correlations among the constructs were strengthened over the practicum period. Interestingly, constructivist conceptions related to differentiated education were not significant, while traditional conceptions related to teacher-guided lessons were significant after the practicum. These results imply that Korean preservice teachers still place value on the traditional perspective, even though constructivism dominates the current educational policies of Korea.

While the field of mathematics education strives to promote equitable mathematics learning and identifies it as a core instructional practice, less is known about its effective enactment. As teachers' teaching practices are dependent on their views and beliefs, this study investigated 133 elementary pre-service teachers' (PSTs') interpretations of diverse learners' learning experiences and proposed accommodations for them as reflected in their lesson planning process. Findings showed that PSTs came up with some strategies that are often suggested in teacher education literature, such as using multiple modes of representation and various grouping strategies. However, their responses were generic in nature rather than specific to diverse learners. Also, it was noted that many PSTs' interchangeably referred to the English Language Learners (ELLs), struggling learners, and culturally diverse learners, inferring that they thought that culturally diverse students must have been ELLs and that ELLs or culturally diverse students must have been weaker students in math. We found that the PSTs used their own frames while filtering and discarding information about diverse student populations to develop instructional plans, rather than based on the results of assessments of learning. We suggest that it is the critical first step to unwrap PSTs' unproven assumptions to better equip them for working with all of their future students.

This study examines how open-ended tasks can be implemented with the support of redefined learning goals and teaching practices from a student-centered perspective. In order to apply open-ended tasks, learning goals should be adopted by individual student's cognitive levels in the classroom context rather than by designated goals from curriculum. Equitable opportunities to share children's mathematical ideas are also attainable through flexible management of lesson-time. Eventually, students can foster their meta-cognition in the process of abstraction of what they've learned through discussions facilitated by teachers. A pedagogical implication for professional development is that teachers need to improve additional teaching practices such as how to tailor tasks relevant to their classroom context and how to set norms for students to appreciate peer's mathematical ideas in the discussions.

Pennsylvania is one of the states that adopted the Common Core State Standards for Mathematics (CCSSM) and crafted its own standards (The PA Core State Standards). Pennsylvania teachers are required to have a clear understanding of the PA Core Standards. It is timely and appropriate to study Pennsylvania teachers' beliefs, as the standards have been adopted and implemented for several years since the revision of the PA Core Standards (2014). This study examined how eight western Pennsylvania elementary school teachers' beliefs about teaching and learning mathematics related to the SMP. To this end, I conducted an in-depth interview with each participating teacher. The in-depth interviews featured the teachers' overarching mathematical instructional goals and their productive beliefs. Furthermore, I linked these beliefs with the CCSSM Standards for Mathematical Practice (SMP).