Integer Play and Playing with Integers (Chapter Two of Exploring the Integer Addition and Subtraction Landscape: Perspectives on Integer Thinking)

This chapter describes instances of play within a teaching episode on integer addition and subtraction. Specifically, this chapter makes the theoretical distinction between integer play and playing with integers. Describing instances of integer play and playing with integers is important for facilitating this type of intellectual play in the future. The playful curiosities arising out of integer addition and subtraction tended to be concepts that we think of prerequisite knowledge (e.g., magnitude or order, sign of zero) or knowledge that is more nuanced for integer addition and subtraction (e.g., how negative and positive integers can “balance” each other). Instances of integer play and playing with integers are connected to the work of mathematicians, highlighting the importance of play in school mathematics

Blood product transfusion in emergency department patients: A case-control study of practice patterns and impact on outcome

Definitions of comorbid conditions. (DOCX 13 kb

Preservice Teachers\u27 Temperature Stories for Integer Addition and Subtraction

Ninety-eight elementary and middle school preservice teachers posed eight stories for integer addition and subtraction number sentences. Stories that were posed about temperature were analysed using a modified Marthe‘s (1979) framework for integer problem types. This framework was modified based on the stories provided by the preservice teachers. This paper reports on the problem types utilized by the preservice teachers. Results highlight that preservice teachers do not frequently use some problem types. Also, results may indicate that some number sentence types (e.g., -23 – -5=☐) support different problem types (e.g., State-State-Translation)

Conceptual Models for Integer Addition and Subtraction

In this article, we report the findings of a study conducted with 6 Grade 8 students in the United States. The students posed stories for open number sentences involving addition and subtraction of integers. We analysed the stories posed by the students to build models that describe the conceptual structures behind these posed stories – the conceptual models for integer addition and subtraction. These four conceptual models for thinking about and using integer addition and subtraction include Bookkeeping, Counterbalance, Relativity, and Translation, and are generated from the students’ posed stories. We also provide profiles of conceptual model use for two of the 6 students that describe how the students posed stories to accommodate conceptual model use, such as posing unconventional or unrealistic stories or changing the structure of the number sentences. The conceptual models and descriptions of how the students used them provide perspective into student thinking about integers and contexts, highlighting the mathematics of the students, and calling for a re-examination of contexts used in school mathematics

Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem

Previous research has documented that preservice teachers (PSTs) struggle with under- standing fraction concepts and operations, and misconceptions often stem from their understanding of the referent whole. This study expands research on PSTs’ understanding of wholes by investigating pictorial strategies that 85 PSTs constructed for a multistep fraction task in a multiplicative context. The results show that many PSTs were able to construct valid pictorial strategies, and the strategies were widely diverse with respect to how they made sense of an unknown referent whole of a fraction in multiple steps, how they represented the wholes in their drawings, in which order they did multiple steps, and which type of model they used (area or set). Based on their wide range of pictorial strategies, we discuss potential benefits of PSTs’ construction of their own representations for a word problem in developing problem solving skills

Emergency department hyperoxia is associated with increased mortality in mechanically ventilated patients: A cohort study

Definitions of comorbid conditions. (DOCX 13 kb

What Does It Take to Be a Fox? New Horizons for Communities of Practice

In this theoretical research report we reflect on the challenges of becoming more fox-like in mathematics education work. Using a communities of practice motivating theoretical lens, we compare and discuss the differences in defining, creating, and accessing knowledge between virtual and scholarly communities of practice in mathematics education. We present four claims that virtual communities of practice in mathematics education are inherently foxy work. As part of our claims, we discuss how scholarly communities of practices are inherently hedgehog work. We conclude with a list of recommendations of those within the scholarly communities of practice in mathematics education. These recommendations include looking toward the successful fox-like attributes of the virtual communities in mathematics education

Growth factors for clinical-scale expansion of human articular chondrocytes : Relevance for automated bioreactor systems

The expansion of chondrocytes in automated bioreactors for clinical use requires that a relevant number of cells be generated, starting from variable initial seeding densities in one passage and using autologous serum. We investigated whether the growth factor combination transforming growth factor beta 1/fibroblast growth factor 2/platelet-derived growth factor BB (TFP), recently shown to enhance the proliferation capacity of human articular chondrocytes (HACs), allows the efficiency of chondrocyte use to be increased at different seeding densities and percentages of human serum (HS). HACs were seeded at 1,000, 5,000, and 10,000 celIS/cm(2) in medium containing 10 bovine serum or 10,000 cells/cm(2) with 1 chondrogenic capacity of post-expanded HACs was then assessed in pellet cultures. Expansion with TFP allowed a sufficient number of HACs to be obtained in one passage even at the lowest seeding density and HS percentage and variability in cartilage-forming capacity of HACs expanded under the different conditions to be reduced. Instead, larger variations and insufficient yields were found in the absence of TFP. By allowing large numbers of cells to be obtained, starting from a wide range of initial seeding densities and HS percentages, the use of TFP may represent a viable solution for the efficient expansion of HACs and addresses constraints of automated clinical bioreactor systems