The purpose of this study was to examine the effects of fifth-grade mathematics teachers' efficacy (MTE) on their students' mathematics self-efficacy (SMSE) and mathematical achievement (SMA) in classrooms. Two mathematics efficacy instruments were administered to 58 classes (i.e. 58 teachers and 1244 fifth-graders respectively) to gather data associated with SMA scores in school. Statistical analyses were applied to the obtained data. The findings revealed that MTE beliefs significantly influenced both SMSE and SMA. Additionally, SMSE had a mediative impact on the effect of MTE on SMA. Subsequent to a discussion of the findings, suggestions were proposed for further improvement of mathematics teachers' efficacy and, in turn, for enhancing fifth-graders' mathematics self-efficacy and mathematical achievement in the future.
The main purpose of this research was to explore the developmental process of and possible changes in beginning elementary mathematics teachers' efficacy. Beginning teachers with and without mathematics and science backgrounds were also compared to explore differences in their efficacy development. A multiple-case study method with a process and recursive design was employed in this study. The participants were six beginning elementary mathematics teachers purposefully selected from Taichung, Taiwan. Data were collected through interviews, recordings, observations, and reflection notes and then analyzed by immersion and editing analytic techniques. Based on the data analysis, a five-gradation developmental model and its characteristics of elementary beginning mathematics teacher efficacy was developed and proposed. The findings demonstrated the developmental process of this five-gradation model and its continuity and cyclical nature. Moreover, beginning mathematics teachers, who were at the same efficacy levels, tended to exhibit substantial similarities but slight differences in their developmental processes. This study also verified that the construct of internal and external factors played a significant role in cyclically contributing to continuous efficacy development. The implications of beginning mathematics teachers' efficacy and their professional development that derived from the findings and discussions were proposed, as well as a recommendation for further exploration on their efficacy development.KEY WORDS: efficacy development, elementary beginning mathematics teacher, professional development, teacher efficacy
The intention of this study was to improve the learning deficiency in algebraic learning and to enhance Taiwanese middle students' learning achievement and interest in algebra. By using a grade skipping experimental design, the research team intended to find out an effective way to benefit these students' leaning in abstract algebraic concepts. Therefore, this study aimed to explore how the "realistic context" instructional design influenced 8th graders' performance on algebraic grade skipping learning of "linear programming". A quasi-experimental design with a post-test was employed in this study. Samples were selected purposely from thirty-six 8th graders of a junior high school as the Experimental Group, while seventy-nine 12th graders of a senior high school were chosen as the Control Group. Data were mainly gathered by the linear programming achievement test after executing the instruction. Statistical analyses were performed to answer the research question. Findings indicated that there was no significant difference between 8th graders (Experiment) and 12th graders (Control) on the performance of the linear programming achievement test. This result indicated that the instructional material with a realistic context design used in this study did help students to learn the abstract algebra effectively.
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