Joanne Mulligan

• PhD(Macq) MEd (UNSW) BEd(Syd)
• Macquarie University

Knowledge mobilization is becoming increasingly important for research collaborations, but few methodologies support increased knowledge sharing. This study provides insights, using a reflective narrative, into a transdisciplinary knowledge-sharing investigation of the connectivity of educational research to that of other disciplines. As an exempla...

As part of the Connecting Mathematics Learning through Spatial Reasoning project, a Spatial Reasoning Mathematics Program (SRMP) intervention was implemented with one cohort of 30 students in grades 3 through 4. The SRMP embedded transformation skills in learning sequences comprising repeating and growing patterns, 2D and 3D relationships, structur...

The connection between spatial reasoning and mathematics learning and pedagogy in primary school children has been the subject of an increasing number of studies in recent years. There has been no comprehensive analysis, however, of how studies based on spatial reasoning interventions may lead to improvements in students’ mathematics learning in sc...

An awareness of pattern and structure (AMPS) is critical in young children's mathematical development (Mulligan & Mitchelmore, 2009). AMPS is formally assessed in the early years of school (K-3), in structured conditions using predetermined materials, requiring verbal and written responses. However, children also express mathematical thinking non-v...

This position paper proposes that a relationship between young children's embodied mathematical concepts and their awareness of mathematical pattern and structure (AMPS) (Mulligan & Mitchelmore, 2009) develops through play. Theoretical perspectives on the development of schematic patterns, the embodiment of mathematical understandings, and the deve...

This chapter focuses on the neuro-cognitive, cognitive and developmental analyses of whole number arithmetic (WNA) learning. It comprises five sections. The first section provides an overview of the working group discussion. Section 7.2 reviews neuro-cognitive perspectives of learning WNA but looks beyond these to explain the transcoding of numeral...

This chapter provides an overview of the ICME 23 Study panel on special needs in research and instruction in whole number arithmetic. It starts with a general introduction by Verschaffel about the state of affairs in and the major issues and challenges for research and educational practice in the field of mathematical learning difficulties (MLD). A...

Early development of mathematical patterns and structures has been the focus of a suite of studies with four- to eight-year olds comprising the Australian Pattern and Structure Project over the past decade. Awareness of Mathematical Pattern and Structure (AMPS) has been identified and measured, and found to be indicative of general mathematical ach...

Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new pathw...

The mathematical proficiencies in the Australian Curriculum: Mathematics of understanding, problem solving, reasoning and fluency are intended to be entwined actions that work together to build generalised understandings of mathematical concepts. A content analysis identifying the incidence of key proficiency terms (KPTs) embedded in the content de...

Research affirms that pattern and structure underlie the development of a broad range of mathematical concepts. However, the concept of pattern also occurs in other fields. This theoretical paper explores pattern recognition, a neurological construct based on the work of Goldberg (2005), and pattern as defined in the field of mathematics to highlig...

This paper reports an intervention phase of a design study aimed to assist second-grade Filipino children in solving addition word problems in English, a language they primarily encounter only in school. With Filipino as the medium of instruction, an out-of-school pedagogical intervention providing linguistic and representational scaffolds was impl...

At what age do young children begin thinking mathematically? Can young children work on mathematical problems? How do early childhood educators ensure young children feel good about mathematics? Where do early childhood educators learn about suitable mathematics activities? A good early childhood start in mathematics is critical for later mathemat...

Contemporary research from a psychology of mathematics education perspective has turned increasing attention to the structural development of mathematics as an explanation for the wide differences in mathematical competence shown upon school entry and in the early school years. Patterning, multiplicative reasoning and spatial structuring are three...

The development of patterning strategies during the year prior to formal schooling was studied in 53 children from 2 similar preschools. One preschool implemented a 6-month intervention focusing on repeating and spatial patterns. Children from the intervention group demonstrated greater understanding of unit of repeat and spatial structuring, and m...

This paper provides an overview of The Numeracy Research in NSW Primary Schools Project. An interview-based Numeracy Assessment Instrument K-6 and a Numeracy Achievement Scale monitored students' numeracy growth using Rasch modelling. Students from Trialling schools demonstrated greater than expected numeracy growth compared with their counterparts...

Young Filipino children are expected to solve mathematical word problems in English, which is not their mother tongue. Because of this, it is often assumed that Filipino children have difficulties in solving problems because they cannot read or comprehend what they have read. This study tested this assumption by determining whether presenting word...

The development of patterning strategies during the year prior to formal schooling was studied in 53 children from two similar preschools. One preschool implemented a 6-month intervention focussing on Repeating and Spatial patterns. An interview-based Early Mathematical Patterning Assessment (EMPA) was developed and administered pre- and post-inter...

This issue comes at a time when mathematics education research is becoming more intently focused on the development of "structure" as salient to generalised mathematics learning. Not surprisingly the attention on structure creates particular synergies with the increasingly rich field of research on algebraic thinking and arithmetic processes, parti...

Recent educational research has turned increasing attention to the structural development of young students’ mathematical thinking. Early algebra, multiplicative reasoning, and spatial structuring are three areas central to this research. There is increasing evidence that an awareness of mathematical structure is crucial to mathematical competence...

A large-scale numeracy research project was commissioned by the Australian Government, involving 4732 Australian students from 91 NSW primary schools. Rasch analysis was applied in the construction of a Numeracy Achievement Scale (NAS) in order to measure numeracy growth. Following trialling, a pool of 244 items was developed to assess number, spac...

Virtually all mathematics is based on pattern and structure. A mathematical "pattern" is any predictable regularity, usually involving numbers or space. In every pattern, the various elements are organised in some regular fashion. The way a pattern is organised is called its "structure," which may be numerical or spatial. In this article, the autho...

A case study monitored the development of 53 preschoolers' mathematical patterning skills in two similar preschools, one of which implemented a 6-month Intervention promoting patterning concepts. Pre- and post-Intervention assessment data and follow-up data evaluated the impact of the Intervention on the growth of Repeating and Spatial Patterns. In...

To sum up, the case studies have demonstrated a gap between the intended and the implemented mathematics assessment — both in the Australian School A and the Chinese School C. The data suggest that limitations in time, resources, professional training, and parental support were the main reasons for this gap in School A. For School C, large class si...

A broad descriptive study of 103 first graders and 16 longitudinal case studies found that children's perception and representation of structure1 generalised across a wide range of mathematical domains. Children's strategies showing use of pattern and structure were determined from task-based interviews. A high positive correlation (0.944) was foun...

Two-year longitudinal case studies of 16 Sydney children extended a study of 103 first graders' use of structure across a range of mathematical tasks. We describe how individual's representations change through five stages of structural development. Children at the pre-structural stage showed inconsistent development presenting disorganised represe...

In a descriptive study of 103 Grade 1 children, including 16 longitudinal case studies, we investigated the use of mathematical structure across a range of mathematical tasks. Children's structural development was inferred from their imagistic representations, supported by analysis of problem-solving behavior during videotaped task-based clinical i...

This paper promotes the idea that mathematics learning can be reorganised to be almost completely 'data driven'. In particular, the paper focuses on ways in which technology can be used as a tool to promote the effective development of data handling skills

Describes a classroom-based model for professional development that allows teachers to gain further insight into matching learning experiences with a child's potential. (ASK)

An exploratory study of77 high ability Grade 5 and 6 children investigated links between their understanding of the numeration system and their representations of the counting sequence 1–100. Analysis of children’s explanations, and pictorial and notational recordings of the numbers 1–100 revealed three dimensions of external representation—pictori...

Children’s solutions to a variety of multiplication and division word problems were analysed in a cross-sectional pilot study of 34 children from Grades K to 2. Responses indicated a wide range of strategies used and these were further classified into developmental levels of strategy use. Because these data reflected the SOLO Taxonomy developmental...

A school-based numeracy initiative, conducted in one NSW metropolitan primary school, trialled an innovative approach to improving mathematics for low achievers. The project involved 683 low-achieving students aged from 5 to 12 years, 27 teachers, and three researchers over a 9-month period. A Pattern and Structure Assessment (PASA) interview and a...

2010) Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in kindergarten. This paper provides an interim report of a large empirical evaluation study in progress. An intervention was implemented to evaluate the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on Kindergarten students' mathe...

A Numeracy Assessment Instrument K-6 (NAI) and a Numeracy Achievement Scale (NAS) using Rasch measurement were developed to monitor students' numeracy growth in the Numeracy Research in NSW Primary Schools Project. A sample of 1900 students from 20 Case Study schools, 10 Trialling schools and 10 Reference schools was assessed using the NAI. Student...

Pattern and structure are central features of mathematics, occurring in different contexts such as tables, diagrams, graphs and computer images. ~esearch has shown that children whose early mathematical representations show pattern and structure have a better chance of achieving well in mathematics later on. It is not known how young children devel...

This paper presents case study data from an exploratory study investigating six preschoolers' patterning skills using three learning modes: concrete materials, screen-based technological tools, and combined modes. Children using dynamic interactive software and virtual manipulatives to solve pattern-eliciting tasks engaged in more "experimental" re...

This paper describes some key findings from the analysis of video data comprising part of the SIMERR project "Mathematical thinking of pre-school children in rural and regional Australia: Research and practice". This analysis focused on the identification of young children's mathematical thinking as it occurred naturalistically in two different pre...

This paper reports changes in children’s mental computation solution strategies for multiplication and division applied word problems (involving 1, 2 and 3-digit numbers combinations). The study followed 95 Queensland children from Year 4 through to the end of Year 6. The children’s responses showed a development from simple counting to use of deri...