Motivation and Learning in Mathematics Pre-service Teachers

Based on a review of literature of conceptual and procedural knowledge in relation to intrinsic and extrinsic motivation, the purpose of this study was to test the relationship between conceptual and procedural knowledge and intrinsic and extrinsic motivation. Thirty-eight education students with a mathematics focus (elementary or secondary) in their junior, senior, or fifth year completed a survey with a Likert scale measuring their preference to learning (conceptual or procedural) and their motivation type (intrinsic or extrinsic). Findings showed that secondary mathematics focused students were more likely to prefer learning mathematics conceptually than elementary mathematics focused students. However, secondary and elementary mathematics focused students showed an equal preference for learning mathematics procedurally and sequentially. Elementary and secondary students reported similar intrinsic and extrinsic motivation. Extrinsically motivated students preferred procedural learning more than conceptual learning. While there was no statistically significant preference with intrinsically motivated students, there was a trend favoring preference of conceptual learning over procedural learning. These results tend to support the hypothesis that mathematics focused students who prefer conceptual learning are more intrinsically motivated, and mathematics focused students who prefer procedural learning are more extrinsically motivated.

Intrinsic characteristics of the proton pump in the luminal membrane of a tight urinary epithelium. The relation between transport rate and delta mu H.

A number of tight urinary epithelia, as exemplified by the turtle bladder, acidify the luminal solution by active transport of H+ across the luminal cell membrane. The rate of active H+ transport (JH) decreases as the electrochemical potential difference for H+ [delta mu H = mu H(lumen) - mu H(serosa)] across the epithelium is increased. The luminal cell membrane has a low permeability for H+ equivalents and a high electrical resistance compared with the basolateral cell membrane. Changes in JH thus reflect changes in active H+ transport across the luminal membrane. To examine the control of JH by delta mu H in the turtle bladder, transepithelial electrical potential differences (delta psi) were imposed at constant acid-base conditions or the luminal pH was varied at delta psi = 0 and constant serosal PCO2 and pH. When the luminal compartment was acidified from pH 7 to 4 or was made electrically positive, JH decreased as a linear function of delta mu H as previously described. When the luminal compartment was made alkaline from pH 7 to 9 or was made electrically negative, JH reached a maximal value, which was the same whether the delta mu H was imposed as a delta pH or a delta psi. The nonlinear JH vs. delta mu H relation does not result from changes in the number of pumps in the luminal membrane or from changes in the intracellular pH, but is a characteristic of the H+ pumps themselves. We propose a general scheme, which, because of its structural features, can account for the nonlinearity of the JH vs. delta mu H relations and, more specifically, for the kinetic equivalence of the effects of the chemical and electrical components of delta mu H. According to this model, the pump complex consists of two components: a catalytic unit at the cytoplasmic side of the luminal membrane, which mediates the ATP-driven H+ translocation, and a transmembrane channel, which mediates the transfer of H+ from the catalytic unit to the luminal solution. These two components may be linked through a buffer compartment for H+ (an antechamber).