Reconceptualizing Symbolic Magnitude Estimation Training Using Non-declarative Learning Techniques.

It is well-documented that mathematics achievement is an important predictor of many positive life outcomes like college graduation, career opportunities, salary, and even citizenship. As such, it is important for researchers and educators to help students succeed in mathematics. Although there are undoubtedly many factors that contribute to students' success in mathematics, much of the research and intervention development has focused on variations in instructional techniques. Indeed, even a cursory glance at many educational journals and granting agencies reveals that there is a large amount of time, energy, and resources being spent on determining the best way to convey information through direct, declarative instruction. The proposed project is motivated by recent calls to expand the focus of research in mathematics education beyond direct, declarative instruction. The overarching goal of the presented experiment is to evaluate the efficacy of a novel mathematics intervention designed using principles taken from the literature on non-declarative learning. The intervention combines errorless learning and structured cue fading to help second grade students improve their understanding of symbolic magnitude. Results indicate that students who learned about symbolic magnitude using the novel intervention did better than students who were provided with extensive declarative support. These findings offer preliminary evidence in favor of using learning combination of errorless learning and cue fading techniques in the mathematics classroom.

Unique Mechanisms for the Availability of Declarative Memory Elements and the Strengthening of Cognitive Operations.

The purpose of this study was to investigate the role of memory for prior cognitive operations and availability of declarative memory elements in long-term semantic priming. The impetus for this investigation was the role of working memory (WM) in complex cognitive processing. Empirical estimates of WM are too limited to explain complex cognitive processes. Therefore, contemporary models of WM propose access to long-term memory (LTM) to expand these limits. The priming literature provides one theoretical mechanism for access to LTM: long-term semantic priming. However, explanations for long-term semantic priming include both increased availability of LTM elements and the facilitation of prior cognitive operations. Our goal was to examine if the facilitation of prior cognitive operations is dependent on the availability of previously encountered LTM elements. A task used in previous research proposed to capture the facilitation of cognitive operations coupled with a directed forgetting manipulation was used to examine this relationship. Three experiments were conducted to that end. All experiments resulted in facilitation of the procedure of categorization. Experiments 1 and 2 additionally found relatively poor recognition for items that participants were told to forget despite the fact that categorization was facilitated for related items. Experiment 3 resulted in similarly poor recognition for category names that participants were told to forget. Taken together, the experiments in this investigation demonstrate a clear separation between the cognitive operations and declarative elements of the categorization task. Namely, the continued availability of declarative elements is not necessary for the subsequent facilitation of categorization operations.