Instructions and recipes in mathematical proofs

Educational Studies in Mathematics - In mathematics education research, proofs are often conceptualized as sequences of mathematical assertions. We argue that this ignores proofs that contain...     

Conceptualising Intergenerational Lived Experience: Integrating Art–Moving–Well-Being across Disciplines,Communities and Cultures

Art and movement are motivating forces in, through, and beyond education. As populations age, there is an increasing need to support physical and social well-being. Yet, since the onset of the COVID-19 pandemic, there has been a reported exponential increase in feelings of loneliness across generations. Complex challenges require trans-disciplinary solutions, and this paper represents a joint effort within and across disciplines, communities and cultures to find ways to ameliorate this silent epidemic. In this paper, we propose a cross-disciplinary conceptual framework where Aboriginal Artists and Knowledge Holders, Teacher Educators, and Physical and Occupational Therapists come together to explore theoretical and pedagogical insights that encompass intergenerational art–moving–well-being practices, reducing feelings of loneliness and improving social connections across generations. There are two main aims of this paper; first, to better understand current studies that report on integrating art–moving–well-being practices, and the effect this has on health and well-being of intergenerational participants (under 10-year-olds, 20+ year olds and 50+ year olds). Second, based on community needs, the long-term aim is to propose a flexible art–moving–well-being conceptual model that is scalable, sustainable and based on social and relational support systems. We propose a model that is flexible and adaptable within and across our local community and beyond. We argue that feelings of loneliness are unique to each individual, and there is a need to connect specific intergenerational programmes with art–moving–well-being practices that readily engage and integrate varied communities and cultures in sustainable ways and thus, contribute to thriving communities.     

Caregiver speech predicts the emergence of children's emotion vocabulary

Learning about emotions is an important part of children's social and communicative development. How does children's emotion-related vocabulary emerge over development? How may emotion-related information in caregiver input support learning of emotion labels and other emotion-related words? This investigation examined language production and input among English-speaking toddlers (16–30 months) using two datasets: Wordbank (N = 5520; 36% female, 38% male, and 26% unknown gender; 1% Asian, 4% Black, 2% Hispanic, 40% White, 2% others, and 50% unknown ethnicity; collected in North America; dates of data collection unknown) and Child Language Data Exchange System (N = 587; 46% female, 44% male, 9% unknown gender, all unknown ethnicity; collected in North America and the UK; data collection dates, were available between 1962 and 2009). First, we show that toddlers develop the vocabulary to express increasingly wide ranges of emotional information during the first 2 years of life. Computational measures of word valence showed that emotion labels are embedded in a rich network of words with related valence. Second, we show that caregivers leverage these semantic connections in ways that may scaffold children's learning of emotion and mental state labels. This research suggests that young children use the dynamics of language input to construct emotion word meanings, and provides new techniques for defining the quality of infant-directed speech.     

A combined microfluidic-microstencil method for patterning biomolecules and cells

Despite the myriad of soft lithography based micropatterning methods available to researchers, it is still challenging to define small features (10–100 μm) that are spaced far apart (1–10 mm). In this report, we describe a combined microfluidic-microstencil patterning method that can produce multifunctional substrates of small features, O(10 μm), with a large pitch, O(1 mm). In that, we fabricate microstencils using an UV curable polyurethane (Norland Optical Adhesive 81) with dense arrays of 10–100 μm holes. Overlaying arrays of microfluidic channels over these microstencils allow for the control of the spacing between features and the ability to pattern multiple substrates. We show that this method is capable of patterning soluble proteins, fibrillar insoluble collagen, liposomes, cells, and nanoparticles. We demonstrate the utility of the method by measuring platelet adhesion under flow to three adhesive proteins (insoluble fibrillar collagen, laminin, and reconstituted acid solubilized collagen fibers) in a single assay.     

The construction of an interfacial valve-based microfluidic chip for thermotaxis evaluation of human sperm

Thermotaxis has been demonstrated to be an important criterion for sperm evaluation, yet clinical assessment of thermotaxis capacity is currently lacking. In this article, the on-chip thermotaxis evaluation of human sperm is presented for the first time using an interfacial valve-facilitated microfluidic device. The temperature gradient was established and accurately controlled by an external temperature gradient control system. The temperature gradient responsive sperm population was enriched into one of the branch channels with higher temperature setting and the non-responsive ones were evenly distributed into the two branch channels. We employed air-liquid interfacial valves to ensure stable isolation of the two branches, facilitating convenient manipulation of the entrapped sperm. With this device, thermotactic responses were observed in 5.7%-10.6% of the motile sperm moving through four temperature ranges (34.0-35.3 °C, 35.0-36.3 °C, 36.0-37.3 °C, and 37.0-38.3 °C, respectively). In conclusion, we have developed a new method for high throughput clinical evaluation of sperm thermotaxis and this method may allow other researchers to derive better IVF procedure.     

Excluding Primary School Children – The Outcomes Six Years On

This article reports and discusses a study which followed up, through case records, 726 children excluded permanently, indefinitely or for fixed–term periods in 1993/4 in 10 LEAs. The outcomes at secondary level in 1998/9 were found to be moderately poor with the problems intensifying for half the sample. Forty six per cent had further primary school exclusions and 36 per cent received exclusions in their secondary education. Looked–after children and those with special educational needs fared worse and achieved less. Case studies showed the kinds of commitment and support that can work even with very difficult cases.