Children’s multiplicative thinking as the recognition of equal group structures and the enumeration of the composite units was the subject of this research. In this paper, we provide an overview of ...the Multiplication and Division Investigations project. The results were obtained from a small sample of Australian children (
n
= 21) in their first year of school (mean age 5 years 6 months) who participated in a teaching experiment of five lessons taught by their classroom teacher. The tasks introduced children to the “equal groups” aspect of multiplication. A theoretical framework of constructivist learning, together with research literature underpinning early multiplicative thinking, tasks, and children’s thinking, was used to design the research. Our findings indicate that young children could imagine equal group structures and, in doing so, recognise and enumerate composite units. As the children came to these tasks without any prior formal instruction, it seemed that they had intuitive understandings of equal group structures based on their life experiences. We argue that the implications for teaching include creating learning provocations that elicit children’s early ideas of multiplication, visualisation, and abstraction. The research has also shown the importance of observing children, listening to their explanations of their thinking, and using insights provided by their drawings.
This paper reports from a case study which explores kindergarten children’s mathematical abstraction in a teaching–learning activity about reflection symmetry. From a dialectical perspective, ...abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes “a point of view from which the concrete can be seen as meaningfully related” (van Oers & Poland
Mathematics Education Research Journal
, 19(2), 10–22,
2007
, p. 13–14). A cultural-historical semiotic perspective to embodiment is used to explore the characteristics of kindergarten children’s mathematical abstraction. In the selected segment, two 5-year-old boys explore the concept of reflection symmetry using a doll pram. In the activity, the two boys first point to concrete features of the sensory manifold, then one of the boys’ awareness gradually moves to the imagined and finally to grasping a general and establishing a new point of view. The findings illustrate the essential role of gestures, bodily actions, and rhythm, in conjunction with spoken words, in the two boys’ gradual process of grasping a general. The study advances our knowledge about the nature of mathematical abstraction and challenges the traditional view on abstraction as a sort of decontextualised higher order thinking. This study argues that abstraction is not a matter of going from the concrete to the abstract, rather it is an emergent and context-bound process, as a genuine part of children’s concrete embodied activities.
Increased efforts are needed to meet the demand for high quality mathematics in early years classrooms. Despite the foundational role of geometry and spatial reasoning for later mathematics success, ...the strand receives inadequate instructional time and is limited to concepts of static geometry. Moreover, early years teachers typically lack both content knowledge and confidence in teaching geometry and spatial reasoning. We describe our attempt to deal with these issues through a research initiative known as the Math for Young Children project. The project integrates effective features of both design research and Japanese Lesson Study and is designed to support teachers in developing content knowledge and new approaches for teaching geometry and spatial reasoning. Central to our Professional Development model is the integration of four adaptations to the Japanese Lesson Study model: (1) teachers engaging in the mathematics, (2) teachers designing and conducting task-based clinical interviews, (3) teachers and researchers co-designing and carrying out exploratory lessons and activities, and (4) the creation of resources for other educators. We present our methods and the results of our adaptations through a case study of one Professional Learning Team. Our results suggest that the adaptations were effective in: (1) supporting teachers’ content knowledge of and comfort level with geometry and spatial reasoning, (2) increasing teachers’ perceptions of young children’s mathematical competencies, (3) increasing teachers’ awareness and commitment for the inclusion of high quality geometry and spatial reasoning as a critical component of early years mathematics, and (4) the creation of innovative resources for other educators. We conclude with theoretical considerations and implications of our results.
While there is much written on students' emotions in learning mathematics, as yet, few studies have investigated students' experiences in the early grades (age: 4-9). Our research examining young ...students' mathematics autobiographies - first-hand accounts of the experience of learning mathematics - provides insight into how students' images of mathematics and their feelings about learning mathematics at this age are shaped by contextual influences. In this article, we particularly focus on the multiple contextual influences evident in such autobiographies, including parents' voices and the cultural norms associated with classroom practices. Our analysis reveals how students' prior and current experiences of early years' classroom practices and also their relationships with parents are drawn on in voicing images of, and emotional relationships with, mathematics. Through the use of mathematics autobiographies, including student drawings, this article adds to the existing body of literature on emotion and mathematics learning, by revealing young children's complex emotional relationships with mathematics.
This paper explores the outcomes of the first year of the implementation of a mathematics program (Representations, oral language and engagement in Mathematics: RoleM) which is framed upon research ...relating to effectively supporting young Indigenous students' learning. The sample comprised 230 Indigenous students (average age 5.76 years) from 15 schools located across Queensland. The pre-test and post-test results from purposely developed language and mathematics tests indicate that young Indigenous Australian students are very capable learners of mathematics. The results of a multiple regression analysis denoted that their ability to ascertain the structure of patterns and to understand mathematical language were both strong predictors of their success in mathematics, with the latter making the larger contribution.
Students living in disadvantaged contexts and whose second language is English (ESL) are at risk of not succeeding in school mathematics. It has been internationally recognised that students' ...socioeconomic background and their achievements in mathematics is more pronounced for Australian students. This gap is even more prominent for students who also have English as their second language (ESL). This paper explores the impact of the representations, oral language and engagement in mathematics (RoleM) learning experiences on ESL students' performance in mathematics in the early years (foundation-year 2). All students participating in the study are from disadvantaged contexts (n=461). The sample comprised 328 students who identified themselves as having English as a second language (ESL) and 133 mainstream students. Pre- and post- tests were conducted at the commencement and completion of each school year. All students demonstrated a significant improvement on their post-test scores, with ESL students displaying greater gains than the mainstream students. Additionally, students' results were meeting norm- referenced expectations for students of the same age. A hypothesised taxonomy was developed to further investigate which types of test items foundation ESL students displayed greatest gains. ESL students again outperformed the mainstream cohort on all levels of test categorisation, including questions that were linguistically and conceptually challenging for foundation students. Author abstract, ed
By introducing the concept of the “interactional niche in the development of mathematical thinking” (NMT), a new approach, in which the cultural historic and the interactionistic strands of ...socio-constructivist theories merge, will be presented. This concept is to be understood as an attempt to develop a theory about the generation of mathematical thinking of children in the ages between three and ten. Two specific niches will be described that arise under the condition of children’s non-canonical solutions and corresponding improvisation by (nursery) teacher and children.
Australian students from disadvantaged contexts who speak English as a second language (ESL) are at risk of being developmentally vulnerable when compared to their peers (Gonski et al., 2011). This ...article presents selected findings from a large-scale longitudinal study designed specifically for young students in disadvantaged contexts. It reports the positive students' gains, and the challenges teachers faced while engaging and supporting students in developing their understanding of mathematics. Data were collected from Early Years students (Foundation to Year 2) across three schools with large identified ESL cohorts (N = 379). Additionally, data were also collected from the participating students' teachers (N = 35). The students were tested twice yearly, while the teachers were interviewed three times during the year(s) they participated in the project. The improvements in the students' pre- and post-test scores were statistically and educationally significant. The teachers identified two main challenges as they implemented a program called Representations, Oral Language and Engagement in Mathematics (RoleM). First, relates to language and communication difficulties when teaching students whose first language was not Standard Australian English, and second, the teachers had to rethink their pedagogical practices after participating in RoleM professional learning. The results of this study add to the literature with regard to the pedagogical approaches used to teach mathematics to ESL students. In particular by providing evidence that the concepts of representing and communicating mathematics are intertwined, and thus teaching mathematics as a linguistic experience should be avoided.
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