Teacher knowledge for modelling and problem solving

This article reports on a study that has researched teacher professional learning in lesson study communities that enquired into how we might better support students develop skills in problem solving and mathematical modelling. A rationale for professional development of this type, both in in terms of its structure and focus, is presented followed by an illustrative description from the study of a typical research lesson and issues raised in the post-lesson discussion. This is used to provide insight into some of the key issues to consider in developing teacher knowledge for modelling and problem solving

Professional learning through the collaborative design of problem-solving lessons

This paper analyses lesson study as a mode of professional learning, focused on the development of mathematical problem solving processes, using the lens of Cultural-Historical Activity Theory. In particular we draw attention to two activity systems, the classroom system and the lesson-study system, and the importance of making artefacts instrumental in both. We conceptualise the lesson plan as a boundary object and use this to illustrate how professional learning takes place through the introduction of carefully designed artefacts that draw on teachers’ professional knowledge of potential student approaches, and to the nature of progression in problem-solving processes. We identify the roles of instrumentalisation and instrumentation in supporting professional learning as these artefacts are prepared for use before a lesson and as they are again used as catalysts for reflection in post-lesson discussions. These artefacts are seen to effectively facilitate the socially-situated learning of all participants. We conclude that the design of artefacts as boundary objects that support teaching and professional learning in their respective activity systems may be fundamental to the success of lesson study as a collaborative venture

Understanding issues in mathematical problem solving and modeling: lessons from lesson study

At the heart of our concern, and research, has been to understand how, in classroom learning, students might develop capabilities towards mathematical literacy (Steen, 2001). We have sought to gain insight into how to teach students to be able to apply mathematics effectively to solve problems that arise in a range of different contexts. We have, therefore, researched professional learning communities in which teachers work together and learn from each other, informed by ‘knowledgeable others’ who have research-informed expertise

Professional learning through the collaborative design of problem-solving lessons

This paper analyses lesson study as a mode of professional learning, focused on the development of mathematical problem solving processes, using the lens of Cultural-Historical Activity Theory. In particular we draw attention to two activity systems, the classroom system and the lesson-study system, and the importance of making artefacts instrumental in both. We conceptualise the lesson plan as a boundary object and use this to illustrate how professional learning takes place through the introduction of carefully designed artefacts that draw on teachers’ professional knowledge of potential student approaches, and to the nature of progression in problem-solving processes. We identify the roles of instrumentalisation and instrumentation in supporting professional learning as these artefacts are prepared for use before a lesson and as they are again used as catalysts for reflection in post-lesson discussions. These artefacts are seen to effectively facilitate the socially-situated learning of all participants. We conclude that the design of artefacts as boundary objects that support teaching and professional learning in their respective activity systems may be fundamental to the success of lesson study as a collaborative venture

The NOURISH randomised control trial: Positive feeding practices and food preferences in early childhood - a primary prevention program for childhood obesity

Background Primary prevention of childhood overweight is an international priority. In Australia 20-25% of 2-8 year olds are already overweight. These children are at substantially increased the risk of becoming overweight adults, with attendant increased risk of morbidity and mortality. Early feeding practices determine infant exposure to food (type, amount, frequency) and include responses (eg coercion) to infant feeding behaviour (eg. food refusal). There is correlational evidence linking parenting style and early feeding practices to child eating behaviour and weight status. A focus on early feeding is consistent with the national focus on early childhood as the foundation for life-long health and well being. The NOURISH trial aims to implement and evaluate a community-based intervention to promote early feeding practices that will foster healthy food preferences and intake and preserve the innate capacity to self-regulate food intake in young children. Methods/Design This randomised controlled trial (RCT) aims to recruit 820 first-time mothers and their healthy term infants. A consecutive sample of eligible mothers will be approached postnatally at major maternity hospitals in Brisbane and Adelaide. Initial consent will be for re-contact for full enrolment when the infants are 4-7 months old. Individual mother- infant dyads will be randomised to usual care or the intervention. The intervention will provide anticipatory guidance via two modules of six fortnightly parent education and peer support group sessions, each followed by six months of regular maintenance contact. The modules will commence when the infants are aged 4-7 and 13-16 months to coincide with establishment of solid feeding, and autonomy and independence, respectively. Outcome measures will be assessed at baseline, with follow up at nine and 18 months. These will include infant intake (type and amount of foods), food preferences, feeding behaviour and growth and self-reported maternal feeding practices and parenting practices and efficacy. Covariates will include sociodemographics, infant feeding mode and temperament, maternal weight status and weight concern and child care exposure. Discussion Despite the strong rationale to focus on parents’ early feeding practices as a key determinant of child food preferences, intake and self-regulatory capacity, prospective longitudinal and intervention studies are rare. This trial will be amongst to provide Level II evidence regarding the impact of an intervention (commencing prior to age 12 months) on children’s eating patterns and behaviours. Trial Registration: ACTRN1260800005639

A Glycemia Risk Index (GRI) of Hypoglycemia and Hyperglycemia for Continuous Glucose Monitoring Validated by Clinician Ratings

BackgroundA composite metric for the quality of glycemia from continuous glucose monitor (CGM) tracings could be useful for assisting with basic clinical interpretation of CGM data.MethodsWe assembled a data set of 14-day CGM tracings from 225 insulin-treated adults with diabetes. Using a balanced incomplete block design, 330 clinicians who were highly experienced with CGM analysis and interpretation ranked the CGM tracings from best to worst quality of glycemia. We used principal component analysis and multiple regressions to develop a model to predict the clinician ranking based on seven standard metrics in an Ambulatory Glucose Profile: very low-glucose and low-glucose hypoglycemia; very high-glucose and high-glucose hyperglycemia; time in range; mean glucose; and coefficient of variation.ResultsThe analysis showed that clinician rankings depend on two components, one related to hypoglycemia that gives more weight to very low-glucose than to low-glucose and the other related to hyperglycemia that likewise gives greater weight to very high-glucose than to high-glucose. These two components should be calculated and displayed separately, but they can also be combined into a single Glycemia Risk Index (GRI) that corresponds closely to the clinician rankings of the overall quality of glycemia (r = 0.95). The GRI can be displayed graphically on a GRI Grid with the hypoglycemia component on the horizontal axis and the hyperglycemia component on the vertical axis. Diagonal lines divide the graph into five zones (quintiles) corresponding to the best (0th to 20th percentile) to worst (81st to 100th percentile) overall quality of glycemia. The GRI Grid enables users to track sequential changes within an individual over time and compare groups of individuals.ConclusionThe GRI is a single-number summary of the quality of glycemia. Its hypoglycemia and hyperglycemia components provide actionable scores and a graphical display (the GRI Grid) that can be used by clinicians and researchers to determine the glycemic effects of prescribed and investigational treatments

The GEOTRACES Intermediate Data Product 2014

The GEOTRACES Intermediate Data Product 2014 (IDP2014) is the first publicly available data product of the international GEOTRACES programme, and contains data measured and quality controlled before the end of 2013. It consists of two parts: (1) a compilation of digital data for more than 200 trace elements and isotopes (TEIs) as well as classical hydrographic parameters, and (2) the eGEOTRACES Electronic Atlas providing a strongly inter-linked on-line atlas including more than 300 section plots and 90 animated 3D scenes. The IDP2014 covers the Atlantic, Arctic, and Indian oceans, exhibiting highest data density in the Atlantic. The TEI data in the IDP2014 are quality controlled by careful assessment of intercalibration results and multi-laboratory data comparisons at cross-over stations. The digital data are provided in several formats, including ASCII spreadsheet, Excel spreadsheet, netCDF, and Ocean Data View collection. In addition to the actual data values the IDP2014 also contains data quality flags and 1-? data error values where available. Quality flags and error values are useful for data filtering. Metadata about data originators, analytical methods and original publications related to the data are linked to the data in an easily accessible way. The eGEOTRACES Electronic Atlas is the visual representation of the IDP2014 data providing section plots and a new kind of animated 3D scenes. The basin-wide 3D scenes allow for viewing of data from many cruises at the same time, thereby providing quick overviews of large-scale tracer distributions. In addition, the 3D scenes provide geographical and bathymetric context that is crucial for the interpretation and assessment of observed tracer plumes, as well as for making inferences about controlling processes

Preparing for workplace numeracy: a modelling perspective

The starting point of this article is the question, “how might we inform an epistemology of numeracy from the point of view of better preparing young people for workplace competence?” To inform thinking illustrative data from two projects that researched into mathematics in workplace activity and the teaching and learning of modelling in the classroom is used albeit, by necessity, briefly. Analysis draws attention to the crucial role that understanding the structure of the contextual situation plays in developing a mathematical model of this. It is at this coupling of reality and mathematics that insight into, and understanding of, both mathematics and reality can be developed—or not. This important issue is illustrated with reference to two specific workplace situations that draw on understanding of fraction as gradient and explore how we might use a model of this to scaffold understanding of both reality and mathematics and how each might support the other. With a focus on model formulation during classroom activity attention is then drawn to how students tend to work towards reaching a solution to a particular problem with the consequence that their mathematical representation of the reality does not easily allow for consideration of variation of key factors. In conclusion a research agenda is proposed that seeks to inform an epistemology of numeracy by focussing on numerate activity at the nexus of reality and mathematics by (1) structuring mathematical knowledge using mathematical models that might be used to provide insight into a range of models of workplace realities, and (2) requiring student engagement with repeated use of models in ways that emphasise exploration of variability in key factors of the realities that the models represent