From Concrete to Abstract: Teaching for Transfer of Learning when Using Manipulatives

One of the most important uses of manipulatives in a classroom is to aid a learner to make connection from tangible concrete object to its abstraction. In this paper we discuss how teacher educators can foster deeper understanding of how manipulatives facilitate student learning of math concepts by emphasizing the connection between concrete objects and math symbolization with, preservice elementary teachers, the future implementers of knowledge. We provide an example and a model, with specific steps of how teacher educators can effectively demonstrate connections between concrete objects and abstract math concepts.

The Cell Agglutination Agent, Phytohemagglutinin-L, Improves the Efficiency of Somatic Nuclear Transfer Cloning in Cattle (Bos taurus)

One of the several factors that contribute to the low efficiency of mammalian somatic cloning is poor fusion between the small somatic donor cell and the large recipient oocyte. This study was designed to test phytohemagglutinin (PHA) agglutination activity on fusion rate, and subsequent developmental potential of cloned bovine embryos. The toxicity of PHA was established by examining its effects on the development of parthenogenetic bovine oocytes treated with different doses (Experiment 1), and for different durations (Experiment 2). The effective dose and duration of PHA treatment (150 microg/mL, 20 min incubation) was selected and used to compare membrane fusion efficiency and embryo development following somatic cell nuclear transfer (Experiment 3). Cloning with somatic donor fibroblasts versus cumulus cells was also compared, both with and without PHA treatment (150 microg/mL, 20 min). Fusion rate of nuclear donor fibroblasts, after phytohemagglutinin treatment, was increased from 33 to 61% (P < 0.05), and from 59 to 88% (P < 0.05) with cumulus cell nuclear donors. The nuclear transfer (NT) efficiency per oocyte used was improved following PHA treatment, for both fibroblast (13% versus 22%) as well as cumulus cells (17% versus 34%; P < 0.05). The cloned embryos, both with and without PHA treatment, were subjected to vitrification and embryo transfer testing, and resulted in similar survival (approximately 90% hatching) and pregnancy rates (17-25%). Three calves were born following vitrification and embryo transfer of these embryos; two from the PHA-treated group, and one from non-PHA control group. We concluded that PHA treatment significantly improved the fusion efficiency of somatic NT in cattle, and therefore, increased the development of cloned blastocysts. Furthermore, within a determined range of dose and duration, PHA had no detrimental effect on embryo survival post-vitrification, nor on pregnancy or calving rates following embryo transfer.