The objective of Experiment I was to determine whether establishing conditioned reinforcement for engaging in math for pre-kindergarten students was possible using the three conditioning procedures outlined in previous research for conditioning book stimuli. The purpose of Experiment II was to determine whether this change in preference for engaging in math had an effect on 6 pre-kindergarten participants’ rate of learning math. In Experiment I a counterbalanced pre- and post-intervention ABAB/BABA functional analysis and a delayed multiple probe across dyads design, was used to measure the indirect and direct reinforcement value of math for each participant. Indirect measures referred to a functional analysis where the participants’ rate of responding to a performance task during a 1-min session when Play-Doh® was delivered as a reinforcer was compared to their rate of responding when math was delivered as a reinforcement operation. Direct measures referred to the number of 5-s intervals (out of 60) each participant engaged in math when given math worksheets and Play-Doh®. The individualized reinforcement intervention consisted of a sequence of conditioning procedures until a defined successful outcome resulted. First learn units were delivered, then stimulus-stimulus pairing, and then observational conditioning-by-denial. Learn unit instruction resulted in the establishment of conditioned reinforcement for the first dyad, while the stimulus-stimulus pairing procedure was necessary for the remaining dyad. The purpose of Experiment II was to test if establishing conditioned reinforcement for math would change rate of learning. The dependent variable was each participant’s rate of learning as measured by the number of learn units required to meet mastery criterion for 4 units of the Multiple Exemplar Functional Math (MEF-Math) curriculum. The dependent variable, rate of learning, was tested using a multiple probe design. The independent variable was the establishment of conditioned reinforcement for math using individualized reinforcement procedures as detailed in Experiment I. The intervention also consisted of a multiple probe design on testing the effect of the individualized reinforcement procedures on establishing conditioned reinforcement. Three participants required learn units, 2 participants required the stimulus-stimulus pairing procedure, and 1 participant required observational conditioning-by-denial to establish conditioned reinforcement for math. Results showed an educationally significant acceleration of learning following the establishment of conditioned reinforcement for math across all 6 participants. Results are discussed in terms of the significance of early math instruction.

Rerandomization (Morgan & Rubin, 2012) is designed for the elimination of covariate imbalance at the design stage of causal inference studies. By improving the covariate balance, rerandomization helps provide more precise and trustworthy estimates (i.e., lower variance) of the average treatment effect (ATE). However, there are only a limited number of studies considering rerandomization strategies or discussing the covariate balance criteria that are observed before conducting the rerandomization procedure. In addition, researchers may find more difficulty in ensuring covariate balance across groups with small-sized samples. Furthermore, researchers conducting experimental design studies in psychology and education fields may not be able to gather data from all subjects simultaneously. Subjects may not arrive at the same time and experiments can hardly wait until the recruitment of all subjects. As a result, we have presented the following research questions: 1) How does the rerandomization procedure perform when the sample size is small? 2) Are there any other balancing criteria that may work better than the Mahalanobis distance in the context of small samples? 3) How well does the balancing criterion work in a sequential rerandomization design? Based on the Early Childhood Longitudinal Study, Kindergarten Class, a Monte-Carlo simulation study is presented for finding a better covariate balance criterion with respect to small samples. In this study, the neural network predicting model is used to calculate missing counterfactuals. Then, to ensure covariate balance in the context of small samples, the rerandomization procedure uses various criteria measuring covariate balance to find the specific criterion for the most precise estimate of sample average treatment effect. Lastly, a relatively good covariate balance criterion is adapted to Zhou et al.’s (2018) sequential rerandomization procedure and we examined its performance. In this dissertation, we aim to identify the best covariate balance criterion using the rerandomization procedure to determine the most appropriate randomized assignment with respect to small samples. On the use of Bayesian logistic regression with Cauchy prior as the covariate balance criterion, there is a 19% decrease in the root mean square error (RMSE) of the estimated sample average treatment effect compared to pure randomization procedures. Additionally, it is proved to work effectively in sequential rerandomization, thus making a meaningful contribution to the studies of psychology and education. It further enhances the power of hypothesis testing in randomized experimental designs.

In two experiments, I tested the effects of a curriculum-based intervention on preschool students’ degree of stimulus control for bidirectional naming (BiN) across familiar and unfamiliar word-picture relation levels of complexity. In Experiment I, I used a multiple probe design to test the effects of the curriculum-based intervention on the degree of BiN for familiar word-picture relations. All four participants in the first experiment demonstrated an increase in the degree of BiN for familiar picture-word relation, with three participants meeting the incidental BiN criterion level of 80% across three response topographies. In Experiment II, I compared the curriculum-based intervention and repeated novel naming experience (RNNE) on preschool students’ degree of BiN and learning. The dependent variables were 1) degree of stimulus control for BiN across familiar and unfamiliar word-picture relations 2) learn units to criterion across math and reading 3) percentage of correct responses to unconsequated post-math and reading instruction probes. I investigated whether the method of acquisition of BiN, a curriculum based or RNNE, has differential effects on the dependent variables. Three out of four participants who received the curriculum-based intervention acquired BiN for picture-word relations following a novel experience, while one out of four participants under the RNNE condition acquired BiN. The results of the study suggest that a curriculum-based instruction can simultaneously induce BiN while teaching academic objectives to preschool students. Experiment II also implicates the effects of a technology-mediated intervention on developing academic and verbal behavior development cusps even in young children.