An assessment model for proof comprehension in undergraduate mathematics

Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in undergraduate mathematics. Building on Yang and Lin’s (Educational Studies in Mathematics 67:59–76, 2008) model of reading comprehension of proofs in high school geometry, we contend that in undergraduate mathematics a proof is not only understood in terms of the meaning, logical status, and logical chaining of its statements but also in terms of the proof’s high-level ideas, its main components or modules, the methods it employs, and how it relates to specific examples. We illustrate how each of these types of understanding can be assessed in the context of a proof in number theory.     

Upending the Grammar of the Conventional Religious School

This article provides an overview and analysis of a relatively new phenomenon: congregational schools that have altered the conventional grammar of schooling, either through their structural arrangements or through their curricular approaches. Five pre-bar/bat mitzvah models are discussed: family schools, schools as communities, informal / experiential programs, afterschool/day care programs, and those that deconstruct and reconstruct the conventional model. In addition, three curricular innovations are examined: project based learning, learning organized around the interests and abilities of the students, and Hebrew Through Movement. Also considered are the factors that are necessary to the survival and proliferation of these new structures and curricular arrangements.     

The relationship between lower body stiffness and injury incidence in female netballers

The aim of this study was to provide contemporary information on injury rates in an elite and sub-elite netball population and to explore the relationship between lower body stiffness and lower body injuries. One elite and two sub-elite teams of female netballers (n = 29) performed the vertical hop test to assess active lower body stiffness (K_vert) and myometry to assess quasi-static stiffness. Lower body injuries were monitored via self-reporting and liaison with physiotherapists. Twelve lower body non-contact injuries were sustained by 10 players, equating to 11.29 lower body injuries per 1,000 exposure hours. The most commonly injured sites were the calf (33%) and ankle (25%). No significant differences between K_vert of injured and non-injured players were reported, however, injured elite players recorded significantly higher season mean quasi-static stiffness in the soleus (p = 0.037) and Achilles (p = 0.004) than non-injured elite players. Elite and sub-elite netball players recorded a higher injury incidence than previous reports of injuries in recreational netballers. Within the constraints of the study, relatively high stiffness of the soleus and Achilles appears to be related to lower body non-contact injury incidence in female netballers, particularly at the elite level. These results provide a basis for development of injury prevention strategies.