Accessing prospective early years’ teachers’ knowledge on fractions in order to design tasks for developing teachers’ MKT

Fractions is perhaps one of the most complex and difficult topics pupils explore in the early years of schooling. Difficulties in learning this topic may have its genesis in the fact that fractions comprise a multifaceted construct (Kieren, 1995) or can be conceived as being grounded in the instructional approaches employed to teach fractions (Behr, Harel, Post & Lesh, 1993). Thus, students’ limited understanding might be related to how their teachers understand and interpret fractions — it’s thus related with teachers’ knowledge and practice. Although there is a generalized agreement on teachers’ role on/for students learning, most research on fractions focus on students, leaving aside teachers’ role (and their knowledge on the topic). Thus, teachers’ training has in certain respects been left behind. We still know little about how teachers’ knowledge on fractions influences students’ broader view of mathematics, and its connection and evolution within and along schooling. Aimed at conceptualize ways of improving teachers’ knowledge, training and practices, it’s of fundamental importance to access the areas of knowledge (here conceived as mathematical knowledge for teaching (MKT) (Ball, Thames & Phelps, 2008) in which (prospective) teachers are more deficitaries.

Electro-olfactograms in response to chromatographic fractions of food-related odorants in the Senegalese sole, Solea senegalensis

The Bohr effect, which can be most generally defined as the influence of pH on the oxygen binding affinity of proteins, is a common feature of respiratory pigments, ranging from the haemocyanins of molluscs and crustaceans to the haemoglobins of vertebrates. Its physiological role is generally seen in the facilitation of oxygen release from respiratory pigments during tissue acidosis. The magnitude of the effect can be influenced by a multitude of factors such as temperature, carbon dioxide, chloride ions, organic phosphates and the investigated pH range. Here we present data on the maximal alkaline Bohr effect in haemoglobins from a large number of species covering all vertebrate classes, obtained at physiological temperatures in the presence of 100 mM chloride ions and the absence of carbon dioxide and organic phosphates.