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.

Differential Cytoplast Requirement for Embryonic and Somatic Cell Nuclear Transfer in Cattle

Effective activation of a recipient oocyte and its compatibility with the nuclear donor are critical to the successful nuclear reprogramming during nuclear transfer. We designed a series of experiments using various activation methods to determine the optimum activation efficiency of bovine oocytes. We then performed nuclear transfer (NT) of embryonic and somatic cells into cytoplasts presumably at G1/S phase (with prior activation) or at metaphase II (MII, without prior activation). Oocytes at 24 hr of maturation in vitro were activated with various combinations of calcium ionophore A23187 (A187) (5 microM, 5 min), electric pulse (EP), ethanol (7%, 7 min), cycloheximide (CHX) (10 micro g/ml, 6 hr), and then cultured in cytochalasin D (CD) for a total of 18 hr. Through a series of experiments (Exp. 1-4), an improved activation protocol (A187/EP/CHX/CD) was identified and used for comparison of NT efficiency of embryonic versus somatic donor cells (Exp. 5). When embryonic cells from morula and blastocysts (BL) were used as nuclear donors, a significantly higher rate of blastocyst development from cloned embryos was obtained with G1/S phase cytoplasts than with MII-phase cytoplasts (36 vs. 11%, P < 0.05). In contrast, when skin fibroblasts were used as donor cells, the use of an MII cytoplast (vs. G1/S phase) was imperative for blastocyst development (30 vs. 6%, P < 0.05). Differential staining showed that parthenogenetic, embryonic, and somatic cloned BL contained 26, 29, and 33% presumptive inner cell mass (ICM) cells, respectively, which is similar to that of frozen-thawed in vivo embryos at a comparable developmental stage (23%). These data indicate that embryonic and somatic nuclei require different recipient cytoplast environment for remodeling/ reprogramming, and this is likely due to the different cell cycle stage and profiles of molecular differentiation of the transferred donor nuclei.

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.