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The current study aimed to reveal the changes to the identities of two tenth graders in mathematics learning at a Japanese high school during the COVID-19 pandemic from the perspective of learning from home versus learning in the classroom. The following research questions are raised: How has the pandemic situation affected and changed Japanese students' triadic relationship between knowledge, practice, and identity? What overlooked equity issue in this triadic relationship is caused by the pandemic? Two male students participated in and completed semi-structured interviews that asked how they managed to study at home during the school shutdown. First, we extracted from the transcript the part concerning the interviewees' difficulties in studying mathematics at home, as well as the role of mathematics lessons and their classmates. Secondly, we classified their utterances into three categories (identity, practice, and knowledge sentences), based on their grammatical patterns. The study results delineated the dynamic and complicated relationships among the three elements. Students lost opportunities to (1) obtain positive social feedback on their mathematical behaviors and (2) learn the social aspects of mathematical problem-solving, such as what strategy was socially acceptable and authorized. We also pointed out an overlooked soft equity issue; rich learning resources are substantially unavailable to students owing to the lack of appropriation of necessary knowledge and positive self-identification, despite the assurance of accessibility to such resources. We should continue to tackle helping learners construct their identities during future unexpected events.

Background: Early childhood education (ECE) has recently been introduced in Zambian government schools, leading to a need to examine the quality of mathematics lessons. Aim: This study focussed on guided play lessons on shapes in pre-mathematics classes and examined how they could be implemented and what children could learn in the class. Setting: The lessons were conducted in two early childhood mathematics classes in two different schools in Zambia. Methods: A qualitative design-based research method was applied. For data collection, teachers implemented a trial lesson in one school and a main lesson in another school in Lusaka, the capital of Zambia. Results: In the first lesson, the activity differed from what was planned and discussed. In the second lesson, the content and objective of the guided play were changed from those of the trial lesson. In the main lesson, children engaged in a more basic activity involving shapes and created many kinds of shapes that they were familiar with in and out of school. This was particularly effective for children in terms of explicitly learning the basic features of the shapes and important mathematical ideas such as congruency, similarity and symmetry. Conclusion: The main lesson was successful because the level of mathematical content was more appropriate for the children and allowed them to enjoy the activity. Two points regarding developing more effective lessons for ECE, to identify pupils' readiness and sociocultural status, were also assessed and discussed.

One of the biggest challenges for primary school children is moving beyond the use of counting in calculation. The purpose of this study was to investigate how Zambian Grade 1 to Grade 4 children at primary school see a group of 10 as an effective pattern and structure with the given concrete material. The study consisted of three phases consisting of two pilot studies and the main study, during which a total of 146 children from Grades 1-4 were asked during interviews to perform certain tasks. These tasks focused on number competencies related to counting objects, recognising number patterns and structures of concrete objects, expressing numbers of concrete objects, and composing and decomposing numbers. The response categories of the PASA (Pattern and Structure Assessment) framework in number competencies were modified to analyse the data. The aim of the analysis was to identify the degree of the acquired pattern and structural thinking. The results of the two pilot studies showed that, in formal addition with two-digit numbers, all children counted without identifying 'groups of 10' while some used concrete materials, some recognised numbers in a pattern and identified a 'group of 10', which has not been previously observed in Zambia. The main survey showed that children were able manipulate concrete objects and to recognise a 'group of 10' in the given 10-frames. The results confirm that children have the potential to develop the skill of transitioning from manipulating concrete objects for calculations but this is missing in the current Zambian syllabus. The findings offer new insights about positive learning processes in Zambian primary school students. The results can help to provide appropriate support in class and at curriculum level.