Connecting expectations of Te Whāriki and The New Zealand Curriculum: Examples of mathematical practices

The first year of primary school aims to be closely connected with early childhood education, yet this is often invisible in the curriculum of specific subjects. This paper sets out an approach that uses mathematical practices as a curriculum tool that reconceptualises school mathematics. Using the early childhood mathematics framework of Te Kākano, the strands of mathematical practices are important descriptors of mathematical activity for children. We describe examples of mathematical learning from both early childhood and the first year of school, and make a case for using mathematical practices as a conceptual tool for designing a mathematics curriculum in the first years of school.

Opening tasks, opening minds – a rediscovery of the open-ended approach

Open-ended tasks are designed such that they may have more than one correct solution or may be solved in more than one way. Although such tasks constitute an irreplaceable tool for prompting young learners to be actively and creatively involved in mathematical discourse, their implementation poses a challenge. Primary school students in Poland are usually offered algorithmic and rote teaching methods and are thus very often deprived of important elements of successful mathematics learning. The ubiquitous teacher-centred approach dedicates little time to any contribution from learners. The aim of this design research was to implement a change in early childhood mathematics education. The change comprised students creating and/or solving open-ended tasks in groups, thus promoting dialogic teaching. The results confirmed that students who are challenged with openended tasks through dialogic teaching not only genuinely engage in their activities, develop a better number sense and flexibility of thinking, but also help each other gain a deeper understanding of new concepts. Captured in this research were the synergistic images of the beauty of children’s reasoning and the beauty of mathematics as an open subject – an incentive for others to begin their journey with freedom of speech for young mathematicians.

Playing Mathematics in Early Childhood Based on Semiotics

Playing mathematics in early childhood based on semiotics gives children the opportunity to identify objects, look for signs and interpret signs so that they can solve problems in games. This study aims to describe semiotic based early childhood mathematics play activities. The research was conducted at the PAUD Lab School, Muhammadiyah University of Jember. The research subjects were 5 children from group B. The results showed that the activities of playing mathematics in early childhood based on semiotics were (1) collecting information related to semiotic-based math games, (2) looking for objects that matched the game and counting the number of objects found, (3) looking for relevant signs and signs. that are relevant to the number of objects found, (4) associated with signs of knowledge that have been previously possessed and look for all signs according to the objects found, (5) the child retells the play that has been done