Understanding Linear Function: a Comparison of Selected Textbooks from England and Shanghai

This study describes a comparison of how worked examples in selected textbooks from England and Shanghai presented possible learning trajectories towards understanding linear function. Six selected English textbooks and one Shanghai compulsory textbook were analysed with regards to the understanding required for pure mathematics knowledge in linear function. Understanding was defined as being at five levels: Dependent Relationship, Connecting Representations, Local Properties Noticing, Object Analysis and Inventising. These levels were developed by examining the most prominent theories from the existing literature on understanding function. Findings suggested that the English textbooks constrained the structural aspect of understanding linear function due to a point-to-point view of function, while the Shanghai textbook which focussed on a variable view of function overemphasised the algebraic approach. The discussion explored the drawbacks to each approach and what teachers or textbook writers could do to balance these two approaches in order to facilitate students’ understanding towards a structural view of linear function.     

A Didactic Sequence of Elementary Geometric Optics Informed by History and Philosophy of Science

The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic process without a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the teaching and learning process in mathematics but has been used in other disciplinary fields. It will be used in this work in order to clear up the main obstacles in the teaching-learning process of geometric optics. We proceed to argue that since Newton’s approach to optics, in his Book I of Opticks, is independent of the corpuscular or undulatory nature of light, it is the most suitable for a constructivist learning environment. However, Newton’s theory must be subject to a proper didactic transposition to help overcome the referred alternative concepts. Then is described our didactic transposition in order to create knowledge to be taught using a dialogical process between students’ previous knowledge, history of optics and the desired outcomes on geometrical optics in an elementary pre-service teacher training course. Finally, we use the scheme-facet structure of knowledge both to analyse and discuss our results as well as to illuminate shortcomings that must be addressed in our next stage of the inquiry.     

Curriculum Interventions for Area Measurement Instruction to Enhance Children’s Conceptual Understanding

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children’s ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional geometry. Participants were 131 fourth graders, recruited from a city in northern Taiwan, and 1 instructor. The results confirmed the effectiveness of an enriched curriculum integrating knowledge of 2-dimensional geometry in enhancing children’s conceptual understanding of area measurement. The group that received the enriched curriculum outperformed the other groups that received the curricula stressing only 2-dimensional geometry or numerical calculations for area measurement in solving the area problems requiring mathematical judgments and explanations. The curriculum also facilitated children’s reasoning in distinguishing between the perimeter and area of a rectangle, which required higher-order mathematical thinking. Interview data revealed that approximately all children from the 3 intervention groups could identify the mathematical subject-matter components highlighted in the curricula. Interviewees tended to consider the use of formulae to solve area measurement problems to be important, despite some differences in learning gains among the 3 groups. In interviews, the participating instructor revealed a change of perspective regarding the importance of offering students opportunities for manipulation and geometric operations when teaching area measurement, prompted by curriculum enactment.     

Implications of a Cognitive Science Model Integrating Literacy in Science on Achievement in Science and Reading: Direct Effects in Grades 3–5 with Transfer to Grades 6–7

Reported are the results of a multiyear study in which reading comprehension and writing were integrated within an in-depth science instructional model (Science IDEAS) in daily 1.5 to 2 h daily lessons on a schoolwide basis in grades 3–4–5. Multilevel (HLM7) achievement findings showed the experimental intervention resulted in significant and consistent direct effects in grades 3–4–5 and complementary transfer effects in grades 6–7 on both ITBS Science (+1.08 Grade Equivalent Units [GE]) and ITBS Reading (+.57 GE). Discussed are implications of the findings and related research for changing grade K-5 curriculum policy to allocate increased instructional time for integrated science instruction.     

Physical Sciences Preservice Teachers’ Religious and Scientific Views Regarding the Origin of the Universe and Life

This paper explores final-year physical sciences preservice teachers’ religious and scientific views regarding the origin of the universe and life. Data was obtained from 10 preservice teachers from individual in-depth interviews conducted at the end of the Science Method module. Their viewpoints were analyzed using coding, sorting, and categorizing. They attributed the origin of the universe and life to a blend of theistic, intelligent design or scientific beliefs. Moreover, their academic backgrounds, exposure to topics in Cosmology in the Science Method module, and classroom dialogues did not significantly influence or change their original religious beliefs. However, the dialogues did create an awareness of their own reflected positions regarding the tenacity of beliefs in religion and their inadequate cosmological understandings. The paper has implications for Science Education in addressing preservice teachers’ religious beliefs in contrast to scientific evidence.     

Interculturalism,Intercultural Education,and Chinese Society

Globalization is bringing about a new paradigm of super-diversity which is resulting in all societies becoming more culturally diverse. Interculturalism, as a new model which responds to this increasing diversity, rejects all forms of discrimination based on differences, instead embracing reciprocity and accommodation. Interculturalism theory is characterized by integration, cohesion, and intercultural dialogue. Compared to multiculturalism theory, interculturalism theory discusses how to make a society more cohesive and accommodate people from different cultures. Interculturalism features a stronger sense of whole. Therefore, in intercultural education, intercultural competence is highlighted in order to catalyze dialogue between people from different groups. Interculturalism has a role in increasing the current level of diversity within contemporary Chinese society. Furthermore, Confucius’ ideal of Great Harmony, which values integration while respecting differences, echoes the tenets of interculturalism. In conclusion, interculturalism can serve as an effective theory for cultivating a shared society.     

Reciprocal learning: One teacher’s narrative

This paper is a personal narrative from the perspective of one teacher in Toronto who participated in the Canada–China Reciprocal Learning in Teacher Education and School Education Partnership Grant Project. I took part in a Sister School partnership between 2013 and 2017. Over the four years, I came to understand relationships in an international professional learning community. Participating in the project gave me the benefit of seeing my practice through an international lens. For my students, it offered a global citizenship experience. Although there are numerous professional development opportunities in Toronto, this partnership extends beyond a lunch and learn, or a full day professional learning. The commitment to my partners has fueled my desire to incorporate new teaching ideas and has required ongoing reflection on my own teaching practice. In this article, I will explain some of the challenges, stages of development, reciprocal learning, and implications for future international professional learning communities.