Mathematics and mathematics education: Content and people, relation and difference

A broad view of mathematics education takes it as the study of how people learn and do mathematics. Starting with this view, the actual and potential relationships of mathematics education as are search discipline to mathematics as a field of knowledge and activity and to the mathematicians carrying out that activity are analyzed. This leads to the picture of a gulf between the two scientific communities which are based in different cultures of thinking and research. A (meta-)study of mathematics and all its facets termed here mathematicology is proposed. It could serve as common ground for cooperative studies by mathematicians and mathematics educators. Thereby the gulf will not necessarily become narrower but abridge over the differences and mutual misunderstandings could be built.     

Some Problems of 2D Morphological and Median Filters

lintroductionMOrpnologicalandnlediantiltersasaclassofnonlineardiscretetilters11avegotWideapplicationsinsignalandimageprocessing.Incontrastwithlinearfilters,medianfiltersandtheirgenerationsareattractivebecausetheyareeasytoimplenlentandcansuppressimpulsenoi…     

The rewarding effects of number and surface area of food in rats

Visual cues have an important role in food preference for both rats and humans. Here, we aim to isolate the effects of numerosity, density, and surface area on food preference and running speed in rats, by using a forced-choice maze paradigm. In Experiment 1, rats preferred and ran faster for a group of multiple smaller pellets rather than a single large pellet, corroborating previous research (Capaldi, Miller, & Alptekin Journal of Experimental Psychology: Animal Behavior Processes, 15(1), 75–80, 1989). Further experiments tested the prevailing hypothesis that multiple food pieces are more reinforcing because they occupy a larger surface area. Experiment 2 controlled for numerosity by utilizing a continuous food: mashed potatoes flattened to cover a larger surface area or rounded into a ball. The rats preferred and ran faster for the flattened potatoes, suggesting surface area plays a role in quantity estimations. Finally, in Experiment 3, rats displayed no preference or difference in running speed between a group of scattered and clustered pellets when number of pellets were kept constant. Taken together, these results suggest that density has an important role in food perception—that is, the rewarding effect of higher numerosity or larger surface area is removed when the food does not fill out the entire space. Alternative explanations and implications for human diet are discussed.