Can teachers and mathematicians communicate productively? The case of division with remainder

Is it possible that a meeting of mathematicians and primary school teachers will be productive? This question became intriguing when one professor of mathematics initiated a professional development course for practicing primary school teachers, which he taught alongside a group of mathematics Ph.D. students. This report scrutinizes the uncommon meeting of these two communities, who have very different perspectives on mathematics and its teaching. The instructors had no experience in primary school teaching, and their professed goal was to deepen the teachers’ understanding of the mathematics they teach, while teachers were expecting the course to be pedagogically relevant for their teaching. Surprisingly, despite this mismatch in expectations, the course was considered a success by teachers and instructors alike. In our study, we analyzed a lesson on division with remainder for teachers of grades 3–6, taught by the professor. The framework used for the data analysis was mathematical discourse for teaching, a discursive adaptation of the well-known mathematical knowledge for teaching framework. Our analysis focuses on the nature of the interactions between the parties and the learning opportunities they afforded. We show how different concerns, which might have hindered communication, in fact fueled discussions, leading to understandings of the topic and its teaching that were new to all the parties involved. The findings point to a feasible model for professional development where mathematicians may contribute to the education of practicing teachers, while they are gaining new insights themselves.     

The North Wind and the Sun

The north wind and the sun are good friends.But one day they quarrelabout something. “I am stronger than you.”the cold north wind says.“Indeed you arenot.I’m stronger than you,”answers the soft,warm sun. Just then they see a man walking along the road. “I can get that man’s hat off his head,”the wind says.     

Building preschool teachers’ capacity for teaching Chinese to ethnic minority children in Hong Kong: A qualitative study

ABSTRACT

Teaching Chinese to second language learners is a challenge for preschool teachers in Hong Kong so effective teacher professional development programmes are urgently needed to enhance their knowledge and skills. An Integrative Model Teacher Professional Development Programme which incorporates three theoretical underpinnings (i.e., culturally responsive teaching, meaningful and pleasurable learning, and effective teaching of Chinese as a second language) is designed to equip preschool teachers with knowledge, skills, and awareness in teaching Chinese to ethnic minority students. Through qualitative interviews with 15 in-service preschool teachers who joined the Programme, teachers’ perceptions and changes in three theoretical areas of teaching Chinese to ethnic minority students were explored. Particularly, teachers increased their awareness of ethnic minority cultures, developed empathy with ethnic minority children and their families, gained knowledge of implementing culturally responsive teaching and meaningful and pleasurable learning of Chinese. The role of teacher sharing in effective professional development was highlighted.     

Bottling fog? The quest for instructional management

Elsewhere, the authors have unpacked instructional leadership and have documented that such leadership is associated with more effective schools. Indeed, there has been for a considerable time nearly universal acceptance that learning-centered leadership should provide the central platform on which leadership is enacted. In this paper, a less sanguine narrative is provided on instructional management. Specifically, it documents that for all the evidence and recognition of importance, learning-focused leadership remains a small domain of action for leaders at the school and district levels. It then focuses on both the culture of the profession of school administration and the nature of schooling to explain why in the face of considerable energy and effort only marginal improvements have been realized in deepening instructional leadership. It closes with an analysis of possible paths going forward.     

Coteaching in Counselor Education: Preparing Doctoral Students for Future Teaching

This phenomenological study explored 10 counselor education doctoral students' coteaching experiences with faculty members. Three coteaching structures identified from the data were relational, operational, and developmental. A definition of coteaching supported by the findings is presented. Implications for counselor education programs, limitations, and directions for future research are discussed.     

The role of stroke knowledge in reading and spelling in Chinese

The present study examined the types of orthographic knowledge that are important in learning to read and spell Chinese words in a 2‐year longitudinal study following 289 Hong Kong Chinese children from Grade 1 to Grade 2. Multiple regression results showed that radical knowledge significantly predicted children's word reading and spelling performance across the years. Stroke knowledge contributed both concurrently (Grade 1) and longitudinally (Grade 2) to children's spelling performance after controlling for rapid naming, phonological awareness, morphological awareness and radical knowledge. These findings support the significance of radical knowledge in Chinese reading and spelling and the specific role of stroke order knowledge in Chinese spelling. The findings have implications for the design of an effective curriculum for teaching children to spell Chinese characters.     

Genotype-environment correlations for language-related abilities: implications for typical and atypical learners

Recent behavioral genetic research has shown that genetic propensities are associated with individual differences in experiences, and thus, what may appear to be environmental effects can reflect genetic influence. This study examines passive genotype-environment correlations (GECs) for language-related abilities by comparing environment-child language associations in adoptive and nonadoptive families. The results provide evidence for the genetic mediation of the association between home environmental variables, such as the provision of toys and games, maternal involvement, and degree of intellectual/cultural orientation with children's language-related abilities. Developmental changes in passive GECs are considered, and the implications for typical and atypical learners are discussed.     

The conceptual change approach to improving teaching and learning: An evaluation of a Hong Kong staff development programme

This paper reports a study ofthe effectiveness of an innovative approach tostaff development, the conceptual changeapproach, which attempts to change teachers'frameworks for conceptualising teaching andlearning. The evaluation investigated theprogramme at three levels: the impact on theconceptions of teaching of the participants,the resultant impact on teaching practices, andthe consequential effect on student learning.Encouraging results were obtained. Theprogramme brought about detectable conceptualchange or conceptual development in two-thirdsof the sample group. Subsequently, all the`changed' teachers received better ratings ontheir teaching practices from their students inthe following academic year while none of thosewho did not change their conceptions showedsimilar gains in student rating scores. Aresultant positive impact on their students'studying approaches was observed for half ofthe teachers who changed their conceptions.