Sustainable changes in teacher practices: a longitudinal analysis of the classroom practices of high school mathematics teachers

This study examines the effects of professional development on various aspects of teachers’ mathematics instruction. Using data collected between 2005 and 2009, we examined the extent to which the instructional practices of 49 US high school teachers who participated in content-based, sustained professional development changed over time. We found that changes in several aspects of their instructional practices followed somewhat different patterns. Teachers made statistically significant and steady changes in mathematical discourse, instructional clarity, and the development of students’ mathematical habit of mind, but not in student interactions or in the use of multiple representations.     

Hardness measurement of natural and hybrid turf soccer fields

Understanding the surface hardness of soccer fields is essential to evaluate the risk of injury and also its influence on the playing behavior of soccer players. In this context, newly developed hybrid turf systems have to be tested for their surface hardness with regard to the increased risk of injury on hard sports surfaces. The hardness of a soccer field can be quantitatively measured using an apparatus with a cylindrical weight that is dropped from a defined height. Since this procedure was first used for road construction, there are few studies investigating its use on sports grounds. This has led to inconsistencies in methodology and the absence of evaluation guidelines for classifying the hardness of soccer fields. This paper considers how turf systems (natural turf and hybrid turf) differ in their hardness and how this method can be used for different soccer turf systems. Natural turf systems, stitched turf systems, hybrid turf-bearing layer systems and woven mat systems were investigated. The assessment results from a comparative representation of hardness values of different soccer fields. By comparison, natural turf systems were found to be the softest, while woven mat systems were the hardest. Furthermore, the parameters that might affect the hardness were investigated. The influence of the measured soil parameters decreases with an increasing number of measurements per measuring point. Turf system-specific correlations make it possible to reduce the amount of measurement effort.