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This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in fraction multiplication settings. UTGs account for the constraint of working memory in sequencing mental actions to solve mathematical tasks. They also explain the power of units coordinating structures in offloading demands on working memory. At the end of the article, we consider some of the research implications for these findings--specifically, ways that UTGs can lend explanatory and illustrative power to analyses of students' mathematics.

The emerging field of mathematics educational neuroscience provides researchers with new approaches to understanding mathematical development, as well mathematics itself. This paper focuses on the role of the hand in constructing mathematics through activity. We rely on Piaget's distinction of three kinds of activity: sensorimotor activity, internalized actions, and interiorized operations--to review results from neuroscience studies. These distinctions and related neuroscience findings contribute to a new sense of mathematical embodiment. They also provide implications for mathematics instruction.

The number and algebra strand of the "Australian Curriculum: Mathematics" (2015) advocates for holding together the study of number and algebra across years K-8--a position that mathematics educators have endorsed in many countries. This recommendation along with the report "Shape of the Australian Curriculum: Mathematics" (2009), which states that during years 7-10 students' understandings of mathematics, "include(s) a greater focus on the development of more abstract ideas," led the authors to ask the following questions about their instruction for year 7 students on integers (ACMNA, 280): (1) What models do we commonly use with students to teach them about integers and integer addition?; (2) Do these models support students for success in algebra?; and (3) How can instruction about integers and integer operations help students prepare for more abstract understandings of integers that are useful for algebra? The key issue in extending from addition with whole numbers (the positive integers) to addition with integers, generally, is the establishment of negative integers. This article outlines a card game that helps teachers develop a more abstract model for integers and integer addition with students in a fun and engaging context.

Background: Students' ability to construct and coordinate units has been found to have far-reaching implications for their ability to develop sophisticated understandings of key middle-grade mathematical topics such as fractions, ratios, proportions, and algebra, topics that form the base of understanding for most STEM-related fields. Most of the related research on unit coordination relies on time-intensive clinical interviews and teaching experiments. In this study, we investigate the work of 93 sixth-grade students on a written assessment containing whole number and fraction contexts using both continuous and discrete quantities, and how this work can be used to assess stages in students' construction and coordination of units. Our investigation is guided by the following general research questions: (1) What forms of written work evidence the construction of and operation on composite units (units made up of other units)? (2) How does the categorization of students based on responses from a written assessment compare to written performance on a set of tasks conveying a continuous whole number multiplicative context? Results: We documented the different ways students represented composite units in their written work. In particular, student written work on tasks that included figurative unit items provided the greatest variety of evidence regarding students' construction of and operation on composite units. However, written evidence from partitioning tasks did not seem as promising for distinguishing student stages. Students' performance on decontextualized bar tasks involving continuous quantities was found to be consistent with students' level of unit coordination based on written work providing evidence for the validity of stage categorizations. Conclusions: Our findings shed light on the affordances and constraints associated with particular stages in unit construction and coordination that a student brings to bear on tasks provided in a formal, written assessment. These findings provide promising evidence for scaling up the assessment of students construction and coordination of units through the use of written assessments instead of time-intensive clinical interviews.

This is the second of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. In Part I, I discussed the formation of arithmetical units and composite units. Here I continue on to the construction of iterable units and disembedding. Finally, I look at the role of the stages of unit construction in making additive and multiplicative coordinations. Throughout I link terms used by various learning researchers. [For Part 1, see EJ1084354.]

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage the construction of the first numerical schemes, and continues on through the construction of a three-level structure of coordinated units, which is necessary for upper-level mathematics. Along the way I disambiguate terminology in order to increase the accessibility of this useful theory to a wider group of learning researchers.

This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in fraction multiplication settings. UTGs account for the constraint of working memory in sequencing mental actions to solve mathematical tasks. They also explain the power of units coordinating structures in offloading demands on working memory. At the end of the article, we consider some of the research implications for these findings--specifically, ways that UTGs can lend explanatory and illustrative power to analyses of students' mathematics. [ABSTRACT FROM AUTHOR]

Introduction: Many small hospitals in British Columbia are altering their role in maternity care or abandoning it altogether. This paper explores the role of maternity care in the sustainability of rural communities in northern BC. Methods: We carried out a qualitative case study by conducting an ethnographic examination of 4 communities with varying levels of maternity care services. Results: Although maternity care is not the only factor to influence community sustainability, it does intersect with other economic and social conditions. Maternity care affects a variety of forms of community capital, including economic development, social ties and relations, and the cultural meanings of childbirth. Conclusion: Decision-makers should take into account the community-wide consequences of changes to the role and function of maternity care facilities. Introduction : Beaucoup de petits hopitaux de la Colombie-Britannique modifient leur role dans les soins en maternite ou l'abandonnent entierement. Dans cette communication, nous analysons le role des soins en maternite dans la viabilite des communautes rurales du nord de la Colombie-Britannique. Methodes : Nous avons procede a une etude de cas qualitative en analysant l'ethnographie de quatre communautes offrant divers niveaux de services de soins en maternite. Resultats : Meme si les soins en maternite ne sont pas le seul facteur qui joue sur la viabilite des communautes, ils se conjuguent a d'autres conditions economiques et sociales. Les soins en maternite ont une incidence sur divers aspects du capital communautaire, y compris le developpement economique, les relations et les liens sociaux, ainsi que la signification culturelle de l'accouchement. Conclusion : Les decideurs devraient tenir compte des repercussions a l'echelle communautaire de la modification du role et du fonctionnement des etablissements de soins en maternite., INTRODUCTION The purpose of this paper is to explore the relation between maternity care services and community sustainability. It has been hypothesized that maternity care plays an important, yet often [...]

Background: Emerging evidence that meaningful relationships with knowledge users are a key predictor of research use has led to promotion of partnership approaches to health research. However, little is known about health system experiences of collaborations with university-based researchers, particularly with research partnerships in the area of health system design and health service organization. The purpose of the study was to explore the experience and perspectives of senior health managers in health service organizations, with health organization-university research partnerships. Methods: In-depth, semi-structured interviews (n = 25) were conducted with senior health personnel across Canada to explore their perspectives on health system research; experiences with health organization-university research partnerships; challenges to partnership research; and suggested actions for improving engagement with knowledge users and promoting research utilization. Participants, recruited from organizations with regional responsibilities, were responsible for system-wide planning and support functions. Results: Research is often experienced as unhelpful or irrelevant to decision-making by many within the system. Research, quality improvement (QI) and evaluation are often viewed as separate activities and coordinated by different responsibility areas. Perspectives of senior managers on barriers to partnership differed from those identified in the literature: organizational stress and restructuring, and limitations in readiness of researchers to work in the fast-paced healthcare environment, were identified as major barriers. Although the need for strong executive leadership was emphasized, “multi-system action” is needed for effective partnerships. Conclusion: Common approaches to research and knowledge translation are often not appropriate for addressing issues of health service design and health services organization. Nor is the research community providing expertise to many important activities that the healthcare system is taking to improve health services. A radical rethinking of how we prepare health service researchers; position research within the health system; and fund research activities and infrastructure is needed if the potential benefits of research are to be achieved. Lack of response to health system needs may contribute to research and ‘evidence-informed’ practice being further marginalized from healthcare operations. Interventions to address barriers must respond to the perspectives and experience of health leadership. [ABSTRACT FROM AUTHOR]

Context • This paper outlines how radical constructivist theory has led to a particular methodological technique, developing second-order models of student thinking, that has helped mathematics educators to be more effective teachers of their students. Problem • The paper addresses the problem of how radical constructivist theory has been used to explain and engender more viable adaptations to the complexities of teaching and learning. Method • The paper presents empirical data from teaching experiments that illustrate the process of second-order model building. Results • The result of the paper is an illustration of how second-order models are developed and how this process, as it progresses, supports teachers to be more effective. Implications • This paper has the implication that radical constructivism has the potential to impact practice. [ABSTRACT FROM AUTHOR]

The article presents the views of Catherine Ulrich commenting the article "Examining the Role of Re-Presentation in Mathematical Problem Solving," on the use of generic phrase for mathematics education community. It is the author's view which outlines the involvement of radical constructivist research in mathematics for day-to-day mathematics instructions. The author also suggests the mental actions in construction for coordinate quantitative relationship.

An introduction is presented in which the editor discusses various reports published within the issue which include the place of mathematics in the school curriculum, the varying roles of teachers in mathematical learning, and the qualitative and quantitative approaches in mathematics education.

An introduction to the journal is presented in which guest editors discuss elementary and secondary mathematics education.