This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining how two Japanese expert teachers successfully apply open-ended problems in their mathematics class. The Open-Ended Approach (OPA) framework consists of two main sections: Understanding Mathematical Knowledge and Applying Mathematical Knowledge. The sections were cross-analyzed with students’ responses to provide a comprehensive analysis of how teachers use various techniques to support students. It is proposed that teachers can use this framework to create an environment that promotes learning with open-ended as well as other open problems in their mathematics classroom. The OPA framework can contribute to teacher education, the design of mathematics curricula and to educational research.

Children from southern and northern Brazil have a basic knowledge of plants, which they observe during their everyday life. Children ages between 3 to 10 years old (kindergarten & primary school), but the majority of them in the age group of 4-5 (total 145) were asked to draw what they think is a plant (total sample=332). Afterwards, a equal number of boys and girls randomly chosen were interviewed individually (mix ability) to list plants they said they knew and where they had seen them. Then they were asked to give exemplars of the local plants which they had seen. These data from the exploratory study show that pupils are in touch with their environment and recognize plants that are part of it. The everyday experiences of these children in school and out of school, at home and in leisure activities with family and friends, contribute to their knowledge about plants and such knowledge is complemented in the preschool and primary school classes by appropriate teaching. Educational implications of these findings are discussed.

The objective of this study is to examine the teacher and parent views on the instruction of 5th grade students by branch teachers. This study is designed according to the phenomenology design and uses qualitative data. In order to collect data, open- ended questions were asked to 18 teachers and 16 parents of 5th grade students on the subject, and the responses were analyzed. According to the results of the study, for parents, the disadvantageous aspects of instruction of 5th grade students by branch teachers are that the students could not express themselves in the new class, there is no one knowing and monitoring them closely in the new class and students have difficulty in doing the performance homework. On the other hand, advantageous aspects for students according to parents are that branch teachers give instruction as they have command on the subject and students take multiple teachers as models. The study found the disadvantageous aspects for teachers as having difficulty in completing the curriculum, following homework and maintaining classroom discipline.

Facilitating effective mathematics learning and higher mathematics achievement have long been recognized as a key to the scientific and technological advancement of the African continent. While the central role that language proficiency plays in mathematics teaching and learning has received an overwhelming research attention in the literature over the past two decades, this is not the case among African policy-makers and political leaders. Drawing mainly from our professional experiences as mathematics educators and from the international research literature, our primary intent in this paper is to answer this question: How does the learning of mathematics in English at the basic school level help or hinder students’ mathematical proficiency? To answer this question, the paper is organized as follows. The first part, the introduction, gives a brief overview of the language of learning and teaching in Africa. The second part describes the method and conceptual framework undergirding the research. In the third section, we have analyzed the effects of mathematics learning and teaching through English for basic students whose mother tongue is a Ghanaian language. The conclusion offers four recommendations for developing and improving the mathematics proficiency of students in basic schools.