Concreteness Fading in Mathematics and Science Instruction: a Systematic Review

A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the advantages and disadvantages of concrete and abstract materials considered independently, we argue for an approach that moves beyond this dichotomy and combines their advantages. Specifically, we recommend beginning with concrete materials and then explicitly and gradually fading to the more abstract. Theoretical benefits of this “concreteness fading” technique for mathematics and science instruction include (1) helping learners interpret ambiguous or opaque abstract symbols in terms of well-understood concrete objects, (2) providing embodied perceptual and physical experiences that can ground abstract thinking, (3) enabling learners to build up a store of memorable images that can be used when abstract symbols lose meaning, and (4) guiding learners to strip away extraneous concrete properties and distill the generic, generalizable properties. In these ways, concreteness fading provides advantages that go beyond the sum of the benefits of concrete and abstract materials.     

“I am” versus “we are”: Effects of distinctive variants of self-talk on efficacy beliefs and motor performance

Abstract

Before completing a team-based dart-throwing activity, 80 undergraduates were randomly assigned to one of three pre-performance self-talk conditions: (a) self-talk statements that focused upon one's personal capabilities, (b) self-talk statements emphasizing the group's capabilities, or (c) a control condition where neutral statements were implemented. Participants in all conditions subsequently rated their confidence in their own (i.e. self-efficacy) as well as their team's (i.e. collective efficacy) capabilities, before carrying out the task. Overall, self-efficacy, collective efficacy, and performance indicators were all greatest for individuals who practised self-talk focusing on the group's capabilities, as opposed to individual-focused and neutral conditions. Findings are considered with respect to their novel theoretical contribution to the social cognition literature and their implications for fostering efficacy perceptions and team performance.     

Asymmetric translation between multiple representations in chemistry

Experts are more proficient in manipulating and translating between multiple representations (MRs) of a given concept than novices. Studies have shown that instruction using MR can increase student understanding of MR, and one model for MR instruction in chemistry is the chemistry triplet proposed by Johnstone. Concreteness fading theory suggests that presenting concrete representations before abstract representations can increase the effectiveness of MR instruction; however, little work has been conducted on varying the order of different representations during instruction and the role of concreteness in assessment. In this study, we investigated the application of concreteness fading to MR instruction and assessment in teaching chemistry. In two experiments, undergraduate students in either introductory psychology courses or general chemistry courses were given MR instruction on phase changes using different orders of presentation and MR assessment questions based on the representations in the chemistry triplet. Our findings indicate that the order of presentation based on levels of concreteness in MR chemistry instruction is less important than implementation of comprehensive MR assessments. Even after MR instruction, students display an asymmetric understanding of the chemical phenomenon on the MR assessments. Greater emphasis on MR assessments may be an important component in MR instruction that effectively moves novices toward more expert MR understanding.     

Approaching 18% efficiency of ternary organic photovoltaics with wide bandgap polymer donor and well compatible Y6 : Y6-1O as acceptor

A series of ternary organic photovoltaics (OPVs) are fabricated with one wide bandgap polymer D18-Cl as donor, and well compatible Y6 and Y6-1O as acceptor. The open-circuit-voltage (V_OC) of ternary OPVs is monotonously increased along with the incorporation of Y6-1O, indicating that the alloy state should be formed between Y6 and Y6-1O due to their excellent compatibility. The energy loss can be minimized by incorporating Y6-1O, leading to the V_OC improvement of ternary OPVs. By finely adjusting the Y6-1O content, a power conversion efficiency of 17.91% is achieved in the optimal ternary OPVs with 30 wt% Y6-1O in acceptors, resulting from synchronously improved short-circuit-current density (J_SC) of 25.87 mA cm⁻², fill factor (FF) of 76.92% and V_OC of 0.900 V in comparison with those of D18-Cl : Y6 binary OPVs. The J_SC and FF improvement of ternary OPVs should be ascribed to comprehensively optimal photon harvesting, exciton dissociation and charge transport in ternary active layers. The more efficient charge separation and transport process in ternary active layers can be confirmed by the magneto-photocurrent and impedance spectroscopy experimental results, respectively. This work provides new insight into constructing highly efficient ternary OPVs with well compatible Y6 and its derivative as acceptor.