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...     

Professional noticing of coordinated mathematical thinking

Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms.     

Teaching Science as a Process,Not a Set of Facts

Science & Education - The widespread misperception of science as a deliverer of irrefutable facts, rather than a deliberative process, is undermining public trust in science. Science education...     

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.     

Small Circles: Mobile Telephony and the Cultivation of the Private Sphere

This article examines how we use mobile telephony to maintain our physically and socially closest social circle. The analysis is based on traffic data gathered from Norway using approximately 24 million calls and texts made by private individuals. Previous research has shown that our temporal and spatial movement is highly predictable and that the majority of calls and text messages are sent to only four to six different persons. This article extends this research by examining both tie strength and the distance between the interlocutors in urban and rural settings. The findings show that even as information and communication technologies (ICTs) potentially put the world at our fingertips, the mobile phone is an instrument of a more limited geographical and social sphere. Approximately two-thirds of our calls/texts go to strong ties that are within a 25-km radius.     

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.