This study investigated the different effects of teacherstudent rapport on urban and rural students' math learning via mathematics self-efficacy and mathematics anxiety in China. The participants were 8145 urban and rural fourth graders (mean age = 10 years old) in a central city of China.

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Preparing future mathematics teacher educators (MTEs) with knowledge that are needed to effectively support pre-service teachers (PSTs) is very important. However, little attention was paid to MTEs’ knowledge development, which is multifaceted and complex. This study investigates successes, challenges, and tensions that four international graduate MTEs and one mathematics teacher educator (TE) experienced in developing their identity as math teacher educators. In total, 20 h of interactive interviews were analyzed by using qualitative methods. Emerging themes include how MTEs establish a sense of credibility and how they feel they are navigating multiple identities. Among the graduate MTEs, credibility was described as having the following: (a) knowledge of and experience teaching in the US education system; (b) experience in teaching using a problem-solving approach; (c) the ability to enact theory in practice. While navigating multiple identities, graduate MTEs recognize their ethnic identities are central and influence their perceptions of self as MTEs, and how they think they are perceived by others. The results highlight the importance of understanding MTEs tensions and challenges and provide “in-the-moment” support along the journey of becoming teacher educators.

The present study aims to compare the geometry standards in U.S. Common Core State Standards of Mathematics (CCSSM) and Chinese Compulsory Education Mathematics Curriculum Standards (CMCS) through the lens of van Hiele levels. The study considered a standard unit as one or multiple learning expectation(s) and placed each learning expectation into van Hiele levels. By examining the van Hiele level distributions of the learning expectations and major topics, this study investigated how CCSSM and CMCS propose the students' development of geometric thoughts. The findings reveal different emphases in geometry learning expectations of CCSSM and CMCS. Specifically, (a) Geometry standards in CCSSM are more general, whereas geometry standards in CMCS are more specific; (b) CMCS shows a more consistent progression through grade bands than CCSSM; (c) CCSSM makes more connections between various aspects within a topic and across multiple topics than CMCS; (d) CCSSM highlights Dynamic Geometry Environments (DGEs), whereas CMCS underscores abstract and rigor at the upper level. Implications of this study and suggestions for future revisions for both standards are discussed.