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As conveners of the ICMI Study 22: Task Design in Mathematics Education, we are in the privileged position of developing an overview of the issues and influences described in this volume and other areas of activity relevant for task design. In this chapter we summarise the state of this field of research and provide glimpses of the contents of each chapter, finally suggesting areas for progress in research. We also make an argument, from our own experience, for accessibility of such research for designers and practitioners.

Part 1 Chapter 1: Frameworks and principles for task design.- Chapter 2: Features of task design informing teachers' decisions about goals and pedagogies.- Chapter 3: Accounting for student perspectives in task design.- Chapter 4: Design and use of textbased tasks. Chapter 5: The Role of Tools and Representations in Designing Mathematics.- Chapter 5: The Role of Tools and Representations in Designing Mathematics.- Part 2 Chapter 6: E-Textbooks for Mathematical Guided Inquiry: Design of Tasks and Task Sequences.- Chapter 7: Didactic engineering as a research methodology: from fundamental situations to study and research paths.- Chapter 8: The Critical Role of Task Design in Lesson Study.- Chapter 9: Possible presentation by Jan de Lange, Freudenthal Institute.- Part 3 Commentaries : Chapter 10: Commentary on chapters 1, 2 and 3.- Chapter 11: Commentary on chapters 1, 4, and 5.

This chapter focuses on the design of text-based tasks in textbooks, downloadable materials, and other forms of text-based communication. Tasks may be freestanding or may form part of a task collection with a prepared order, such as in a textbook series or as a resource from which teachers or students may choose. The chapter looks at content decisions, the implications of author intentions for design and learning, and visual aspects of prepared text-based tasks. An international range of text-based tasks is used to illustrate differences in how conceptual coherence and mathematical challenge are intended to be achieved and the different views of the nature of mathematics that might be developed.

The mucosal immune status of Australian Antarctic personnel was monitored during six wintering expeditions at two Australian Antarctic Research Stations, Casey in 1992, 1993, 1994, and Mawson in 1992, 1995, 1996. Salivary immunoglobulin and albumin levels were examined for differences between stations and expeditions, and for monthly changes over the expedition year. Salivary IgA and IgM concentrations were on average higher for the 1993 Casey expeditioners, and all salivary protein levels were lower for 1996 Mawson expeditioners compared to levels of the other expeditions. The change in salivary IgA and IgM concentrations over the 1-year period revealed a consistent pattern between expeditions. Salivary IgA levels were lower in March, April and May compared to other months of the year (P = 0.0002). Salivary IgM levels were lowest in the first 4 months of the year, with peak levels in June and July (P < 0.0001). There were no changes in salivary IgG and albumin concentrations over the expedition year. Though the cause of the changes in salivary IgA and IgM levels over the year is unknown, the changes could reflect alterations in mucosal immunity in response to stressors associated with isolation.

In this paper I look at the roles of unison response in the teaching and learning of mathematics. The early part of the paper is based on a collection of field-data from mathematics lessons in Cape Town. A variety of purposes are identified as being used for unison responses. I examine these in relation to their mathematical meanings, to assumptions about oral traditions and to further uses of chorused response described by Tahta and others.

Examples, illustrations, occurrences, and instances play a central role in the learning of mathematics. Deliberately getting students to generate examples is a particularly powerful tool in teaching, but, while some of the possibilities they offer are used by many teachers, their full potential is rarely exploited. The authors came to this notion through reflection on their experience of observing teachers in classrooms, of getting students to take initiatives, and of creating examples while working on their own mathematics. They examine the roles played by examples constructed and generated by students, give illustrations and analyses of the use of this tool, and develop a theory for the act of exemplification as an act of cognition. A framework is developed for researchers and practitioners to further this work.

Read alongside the next article by Geoff Tennant, Anne Watson's observation of low attainers ‘caught in the act’ of thinking in mathematically sophisticated ways is illuminating and has a number of important implications, not least for the training of support staff. ‘Is it possible’ she asks, ‘to structure work so that higher-order thinking is encouraged and noticed even in simple mathematical situations?’

The purpose of this paper is initially to present findings which identify components of the practices of teachers acting as assessors of students' mathematics in the normal course of classroom work. At an informal level such practice is found to be complex and intimately related to every aspect of teaching and learning. It is found that even teachers who have undergone some assessment training may underestimate the role of interpretation of evidence, and questions about equity in the uses of teachers' judgements are raised in relation to awareness and practice. It is suggested that more care needs to be taken over the formation and use of ‘professional judgements’ within systems of assessment.

Research conducted over the last few decades has consistently highlighted the importance of the quality of infant attachment to primary caregivers in the fostering of positive child developmental outcomes both during the infancy period and beyond. However, the evidence is less conclusive regarding specification of the antecedent infant and caregiver behaviors, contextual factors, and interactive processes likely to produce optimal attachment relations. Although for many years the search for antecedents has focused primarily on caregiver sensitivity, researchers have recently recognized that attachment emerges based on a complex array of individual and environmental factors interacting in complex and often nonlinear ways. Scientific attempts to more precisely specify the origins of attachment behavior seem to have been thwarted by the limitations inherent in traditional models of development. Therefore, the purpose of this paper is to explore application of dynamic systems theory to the study of attachment relations. Attachment theory and research are reviewed initially, followed by an overview of the basic tenets of dynamic systems theory. Based on specification of the dynamic components of attachment relations and an analysis of the central tenets of the dynamic systems perspective, an effort is made to illuminate the appropriateness of a dynamic systems framework as a guide for future conceptual and empirical work in the area of attachment. Specific ideas for applying a dynamic systems methodology to the study of attachment in early childhood are provided.

Mathematics teaching in the UK has undergone several major externally imposed changes during the last decade. Current practices display a range of epistemological and pedagogical assumptions and behaviours, depending on teachers' interpretation of, adoption of and belief in current statutory requirements for teaching and assessment. This paper examines in detail differences within the informal assessment practices of 30 UK mathematics teachers. It is found that these illustrate several of the paradigmatic differences that permeate studies of human behaviour on a grander scale. Since informal assessment decisions can lead directly or indirectly to differentiated access to the curriculum and high-stakes grading, the use of teacher assessment as a focus for examining differences illuminates the possible inequities which might arise for pupils. Examination of differences within one system and one society gives information about effects of different educational practices which, were they to show up between soc...

Symbolic play constitutes a prominent index of early cognitive competence. How is symbolic play in young children affected by contexts of person and place? Is symbolic play in young children stable? This methodological study shows that young children play at about the same level with different people (mother and a stranger who behaves much like mother) and at about the same level in different settings (the familiar home versus the unfamiliar laboratory). Mothers did not differ in their symbolic play between home and laboratory either. Child and mother symbolic play also showed significant (medium to large effect size) short-term stability. In the case of symbolic play, cross-contextual generalizations appear generally warranted.

Language development is thought to be associated with other domains of mental activity that require representational capacity, like symbolic gesture. Study 1 explores associations between multiple measures of language and gesture across the third and fourth years of life. Results indicate stability in language, partial stability in gesture, and concurrent and longitudinal associations between language and gesture. Study 2 further explores language-symbolic gesture relations by measuring more finely which aspects of language relate to the symbolic representation of actions with objects and by exploring associations between symbolic gesture and a performance (nonverbal) measure of general intellectual ability.

NICU nurses have an important role to play in many aspects of parent education. This article stresses the need for an increased focus on teaching parents about the central role that self-regulation will play in their infant's neurobehavioral development not only during the early infancy period but throughout all of childhood and adolescence. Suggestions are made about how to conceptualize the relation between cognition and emotions in humans and how to help parents understand that continued vigilance concerning potential problems in attention and self-regulation will be necessary.

Adhesion inhibitors that block the attachment of pathogens to host tissues may be used synergistically with or as an alternative to antibiotics. The wide-spread bacterial adhesin Multivalent Adhesion Molecule (MAM) 7 has recently emerged as a candidate molecule for a broad-spectrum adhesion inhibitor which may be used to prevent bacterial colonization of wounds. Here we have tested if the antibacterial properties of a MAM-based inhibitor could be used to competitively inhibit adhesion of methicillin-resistant Staphylococcus aureus (MRSA) to host cells. Additionally, we analyzed its effect on host cellular functions linked to the host receptor fibronectin, such as migration, adhesion and matrix formation in vitro, to evaluate potential side effects prior to advancing our studies to in vivo infection models. As controls, we used inhibitors based on well-characterized bacterial adhesin-derived peptides from F1 and FnBPA, which are known to affect host cellular functions. Inhibitors based on F1 or FnBPA blocked MRSA attachment but at the same time abrogated important cellular functions. A MAM7-based inhibitor did not interfere with host cell function while showing good efficacy against MRSA adhesion in a tissue culture model. These observations provide a possible candidate for a bacterial adhesion inhibitor that does not cause adverse effects on host cells while preventing bacterial infection.

Previous research suggests that young children have difficulty producing actions with imagined objects (pantomimes): They frequently substitute a body part to represent the object involved in the action. This response has also been observed in neurologically impaired adults. Study 1 examined the comprehension and production of pantomimes in 3- and 5-year-old children and normal adults to explore further this aspect of representational ability. Results indicate that young children not only have difficulty producing imaginary object representations in contrast to normal adults, they also have difficulty comprehending imaginary object representations and are better at comprehending pantomimes with a body part representation. The results from the pantomime comprehension task were replicated in Study 2 with 3- and 4-year-olds. These findings are discussed in the context of the development of representational ability as children demonstrate increasing independence from concrete environmental support in their knowledge about actions.

We report a study which investigated how mathematics graduates and engineering undergraduates studied sequential tables of values with the aim of deriving a function. By recording the eye-movements of participants as they tackled this task, we found that there were substantial individual differences in the strategies adopted by participants. However, these strategy choices appeared to be unrelated to both the mathematical background of participants, and their success rates.

Preface Introduction Is there a substitute for experience in learning? Low attaining students can think mathematically Numeracy recovery: a pilot scheme for early intervention with young children with numeracy difficulties What do children see? A study of children's representations of numbers and operations Difficulties in extending counting John's access to Pythagoras' theorem: inclusion and entitlement in action Count me out: task refusal in primary mathematics Working through complexity: an experience of developing mathematical thinking through the use of Logo with low attaining pupils A study of progression in written calculation strategies for division Using graphics calculators with low attaining pupils Generalising arithmetic: an alternative to algebra (or things to do with a plastic bag) Watching, listening and acting: a case study of learning support assistants in primary mathematics lessons Responsive questioning in a mixed-ability group Inclusion and entitlement: equality of opportunity and quality of curriculum provision.

For a practice field to be of greatest value in developing global leadership capability, it needs to be constructed so as to combine meaningful cultural and national issues with realistic interpersonal dynamics. Examines how two practice fields designed to facilitate systems thinking and organizational learning – Foodcorp International and Globalcorp – accomplish this task. Both are behavioural simulations (not computer simulations) and each creates a realistic context, a microworld, for people to interact on business and global issues. Both can be used to: (1) bring to the surface cultural assumptions in a social‐business context where they can be observed, tracked and discussed relative to various effectiveness criteria; (2) create a team capable of performing with a shared vision and common mental models; and (3) develop leaders who can create as well as accommodate microcultural norms. Preliminary results using this practice field approach are supportive of these objectives. A growing number of organizations (e.g. Apple Computer, Citicorp, American Express, AT&T, Northern Telecom, Glaxo) and educational institutions (e.g. University of Michigan, Dartmouth College, Indiana University, New York University, the University of Tampa) use such tools in their educational efforts. This permits a rigorous examination of the utility of these tools in management development. Describes the approach, provides two examples of how microworld practice fields are used, and shares the results of the research under way.

This paper elaborates the notion of a personal example space as the set of mathematical objects and construction techniques that a learner has access to as examples of a concept while working on a given task. This is different from the conventional space of examples that is represented by the worked examples and exercises in textbooks. We refer to three studies spanning the age range of learners, from school-age learners to pre-service teachers learning maths and professional mathematicians. Their constructions of examples are used as evidence of their personal example spaces. From these, we identify characteristics of such spaces that provide insight into learning mathematics. This perspective informs teaching by giving access to how personal knowledge is structured and what might enhance that structure. © 2011 Elsevier Inc.

Medication-related safety incidents are a source of concern to patients, policy makers and clinicians. The role of education in improving safety-critical practices in health care is poorly appreciated. This pilot study aimed to initiate collective discussion among professional groups of clinical staff about a range of medicine-related patient safety issues which were identified from a local incident reporting system. In engaging staff to collectively reflect on reported medication incidents we attempted to uncover a deeper understanding of local contextual issues and potential educational needs.A mixed method study was conducted involving categorical analysis of 1058 medication incident reports (Phase 1) and the use of three mixed focus groups of clinical staff (Phase 2) in three acute hospitals in one locality in NHS Scotland.Focus group transcript analysis produced four main themes (e.g. the medical role) and 12 related sub-themes (e.g. pharmacological education and skill mix for administration of medicines) concerning medication-related practices and possible educational interventions.While it is necessary to review reported incident data and disseminate the educational messages for the improvement of quality, this traditional risk management process is inadequate on its own. Reporting systems can be enhanced by collective examination of reported information about medicines by local clinical teams. We identified a strong message from the focus groups for learning about each other and from each other, and that the method piloted may be an important inter-professional mechanism for improvement.

Several research studies have looked at the relationship between static personality traits and patient satisfaction but few studies have looked at the dynamic building blocks of emotional intelligence as they relate to patient satisfaction. Only a few previous research studies have preliminarily evaluated this relationship and determined that certain subsections of emotional intelligence were both negatively and positively correlated to patient satisfaction scores. This article evaluates the methodology under which these studies were conducted. The framework was found to be flawed due to limited sample size, the invalidity of satisfaction surveys, and the evolving contextual relationship between physicians and patients.

We illustrate our approach to using mathematical tasks with prospective teachers to promote complex thought about what it means to do and learn mathematics. Prospective teachers are enculturated into ways of thinking about teaching mathematics which persist, by and large, when they are in school. We offer tasks organised to challenge their instant responses, and support the development of habits of probing mathematical meaning as the starting point for thinking about teaching.

Caregiver activities during play with infants and toddlers are explored, considering both social and didactic types of parent-child interactions and the ways in which child play is enhanced during interactions with a sophisticated and responsive partner.