1,721,115 research outputs found
From Routine Textbook Problems to Non-Routine Teaching and Learning in Classrooms.
No full textThe paper consists of two parts. In part 1, the author reports a study of textbooks with a focus on the representation of problem types. A total of 19,711 problems from the senior secondary textbook series from two popular publishers were analyzed with a framework of seven categories of problem representation. Results indicate that over 90% of the problems are routine problems. Seeing textbooks as an important agent for interpreting the curriculum, the results indeed do not present an optimistic picture for developing students’ mathematical thinking. In Part 2, the author draws upon the results from accumulated research efforts to illustrate: (1) what were the students’ possible expectation in an examination-oriented culture influenced by routine tasks; and (2) the strategies for transforming routine problems to non-routine mathematics learning experiences based on the data of some special lessons
In search of an exemplary mathematics lesson in Hong Kong: An algebra lesson on factorization of polynomials.
No full textThe author here describes an exemplary grade-8 algebra lesson in Hong Kong, taken from the data of the learners’ perspective study. The analysis presents a juxtaposition of the researcher’s analysis of the lesson with the teacher and students’ perspectives of the lesson. The researcher’s perspective applies the theory of variation for which the main concern of learning is the discernment of the key aspects of the object of learning and that the description of variations delineates the potential of the learning space. Some persistent features were illustrated, namely, the teacher talk was a major input in teaching; the technique of variation was used in the design of the mathematical problems and the dimensions of variation created in the class interaction provided a potential learning environment; the teacher taking seriously the student factor into account in his philosophy and practice. From the standpoint of enculturation, the teacher’s influence as an enculturator is intentional, significant and influential
From The Confucian Tradition To The Digital Era: The Case Of Mathematics Teaching In Hong Kong
No full textRecent years have witnessed an increase in research focused on studying on perspectives of Chinese mathematics instructions. The sustained interest is partly due to the outstanding performances of Chinese students in international studies such as the Trends in International Mathematics and Science Study (TIMSS, Mullis, et al., 2012) and the Programme for International Student Assessment (PISA, OECD, 2014); and partly due to the shared interest in comparative studies of instructional practice across different cultural systems. What have we learned about in mathematics classrooms from international studies? Findings of international studies suggest that how the teacher used the tasks so that the cognitive demand of the learning tasks could be sustained is very important. Despite the good performances of Hong Kong students in international studies, there is a gap between traditional classroom practice and the long established goals for promoting generic capacity in mathematics learning; most of the traditional learning tasks in Hong Kong classrooms are apparently routine and serving a demonstrative purpose as a result of the highly competitive systems. Based on triangulation of the findings of the analysis of the mathematics lessons at different levels, the study shown some robust features in the traditional mathematics teaching practice in Hong Kong classrooms in contrast to some innovative scenarios in a special mathematics lesson. Finally, the author re-examines the robust features in the context of curriculum reforms and the cultural context of Confucian tradition.link_to_subscribed_fulltex
Developing students’ positive attitude and mathematics competence in a digital environment: Lessons from university-school partnership
No full textWhat is positive attitude? Attitude is a way of seeing something. If we analyse the quote of Sterling Welling Sill closely, we may roughly get an idea of positive attitude in contrast to negative attitude. Positive attitude is linked to words and phrases, such as, ambitious (with a vision), enthusiastic, loyal / commitment / sense of responsibility, good grades, industrious, follow instruction; whereas negative attitude may linked to words and phrases, such as, lazy, dull undependable, poor grades, discouragement, lack of industry, failure to follow instruction, etc. Interplay with Chinese Confucianism, we may also link attitude with culture. As a Chinese, we may like to ask: What is the attitude to learning proposed under Confucianism? Positive learning attitude linked with thinking is worthy, in other words, learning should be “deep learning” (Biggs, 1991 ) and Lee, 2006). Learning is thus about making inquiry and finding answers. According to the Confucian scholar of Southern Song Dynasty, Zhu Xi, Without the effort of inquiry and seeking for answers, there will be no achievement. Hence, one may say that generic positive values in learning as such can in fact share between cultures, between different geographical regions and between different time zones. In the research ground of psychology, attitude is about goals and motivations, and is a well-investigated area. In the presentation, positive attitude for learning will be discussed in the light of the goal theories in psychology, extending to the recent mindset theories with a link to new findings in neuroscience. With respect to the question: What is mathematics competence in a digital environment? I use the case of the development of Hong Kong curriculum as an example. Via three University-partnership projects, lessons for various aspect essential to learning taken place in classroom are discussed. Finally, the author argues that in the 21st century it is essential for a technology-supportive learning environment designed for nurturing the young generation to have: a positive attitude and a growth mindset, learning with intrinsic motivation, a collaborative spirit and self-discipline, as well as a wise and selective use of technology
A story of his own lesson: an example from Hong Kong
Get PDFThe paper describes the practical realisation of competence in the classroom of an 8th grade Hong Kong mathematics teacher. The teacher was selected as competent on the recommendation of local researchers. Video of 18 consecutive lessons, three post-lesson teacher interviews, and thirty-six post-lesson student interviews provided a platform for understanding the teacher’s teaching philosophy in practice. Mr. X was a teacher with more than twenty years of experience in both primary and secondary mathematics teaching. He was active in teaching, curriculum development and research acti…postprin
Algebra problem types in Hong Kong senior secondary mathematics textbooks: Changes in the new senior secondary curriculum
No full text
Teaching the Graphical Method of Solving Equations: An Example in the Shanghai Lessons
No full textThe introduction of graphs represents a milestone in the understanding of algebra. The invention of the coordinate system in the 17th century opened a new gateway for the development of new topics and invention in the history of mathematics (Bell, 1953). In the personal learning path prescribed for school students in the curriculum, the experience of this new topic makes it possible to see at a glance the relationship of numbers represented as equations as alternatives for lines and curves in a plane
Teaching Algebra Through Variations: Contrast, Generalization, Fusion, and Separation
No full textTeaching with variation is recently identified to be an important feature of Chinese mathematics lessons, contributing to a factor conducive for learning. The theoretical stance promoted within the Variation Theory of Learning is that learning involves experiencing by which the learners develop a way of seeing or experiencing. Hence, it is very important for learners to discern the critical features of the object of learning, which can be referred to as the topic of the lesson. Further application of the ideas to learning experiences in lessons, discernment is made possible when variation concerning the critical aspects of the object of learning is embedded in the design of the instructional tasks or in the interaction between teacher and students and between peers. Within this paper we provide empirical examples from algebra lessons in Hong Kong and Shanghai, to illustrate key skills in creating useful patterns of variation in the teaching and learning namely contrast, generalization, fusion and separatio
- …
