Working Together: Integrating Computational Modeling Approaches to Investigate Complex Phenomena

Journal of Science Education and Technology - Complex systems are made up of many entities, whose interactions emerge into distinct collective patterns. Computational modeling platforms can provide...     

Incorporating Uncertainty Into Parallel Analysis for Choosing the Number of Factors via Bayesian Methods

A number of psychometricians have suggested that parallel analysis (PA) tends to yield more accurate results in determining the number of factors in comparison with other statistical methods. Nevertheless, all too often PA can suggest an incorrect number of factors, particularly in statistically unfavorable conditions (e.g., small sample sizes and low factor loadings). Because of this, researchers have recommended using multiple methods to make judgments about the number of factors to extract. Implicit in this recommendation is that, when the number of factors is chosen based on PA, uncertainty nevertheless exists. We propose a Bayesian parallel analysis (B-PA) method to incorporate the uncertainty with decisions about the number of factors. B-PA yields a probability distribution for the various possible numbers of factors. We implement and compare B-PA with a frequentist approach, revised parallel analysis (R-PA), in the contexts of real and simulated data. Results show that B-PA provides relevant information regarding the uncertainty in determining the number of factors, particularly under conditions with small sample sizes, low factor loadings, and less distinguishable factors. Even if the indicated number of factors with the highest probability is incorrect, B-PA can show a sizable probability of retaining the correct number of factors. Interestingly, when the mode of the distribution of the probabilities associated with different numbers of factors was treated as the number of factors to retain, B-PA was somewhat more accurate than R-PA in a majority of the conditions.     

App-Based Manipulatives and Explicit Instruction to Support Division with Remainders

ABSTRACT

In theory, both virtual manipulatives and explicit instruction are viable options to support students with disabilities as they learn mathematics. This study explored the effect of a treatment package—an app-based virtual manipulative (Cuisenaire® Rods) in conjunction with explicit instruction—on students’ acquisition and generalization of solving problems involving division of whole numbers with remainders. Three middle school students with disabilities participated in this multiple baseline, multiple probe across participants single case design study. Each of the students acquired the mathematical behavior of being able to solve division with remainders problems. In other words, a functional relation existed between the intervention package of explicit instruction and the Cuisenaire® Rods app-based manipulative and students’ accuracy in solving division with remainders problems. Yet, two students failed to generalize the skill without the explicit instruction and use of the app-based manipulative.     

A Case Study Exploring the Identity of an In-Service Elementary Science Teacher: a Language Teacher First

Teachers are central to providing high-quality science learning experiences called for in recent reform efforts, as their understanding of science impacts both what they teach and how they teach it. Yet, most elementary teachers do not enter the profession with a particular interest in science or expertise in science teaching. Research also indicates elementary schools present unique barriers that may inhibit science teaching. This case study utilizes the framework of identity to explore how one elementary classroom teacher’s understandings of herself as a science specialist were shaped by the bilingual elementary school context as she planned for and provided reform-based science instruction. Utilizing Gee’s (2000) sociocultural framework, identity was defined as consisting of four interrelated dimensions that served as analytic frames for examining how this teacher understood her new role through social positioning within her school. Findings describe the ways in which this teacher’s identity as a science teacher was influenced by the school context. The case study reveals two important implications for teacher identity. First, collaboration for science teaching is essential for elementary teachers to change their practice. It can be challenging for teachers to form an identity as a science teacher in isolation. In addition, elementary teachers new to science teaching negotiate their emerging science practice with their prior experiences and the school context. For example, in the context of a bilingual school, this teacher adapted the reform-based science curriculum to better meet the unique linguistic needs of her students.

     

Situated Simulation-Based Learning Environment to Improve Proportional Reasoning in Nursing Students

Proportional reasoning is the basis for most medication calculation processes and is fundamental for high-quality care and patient safety. We designed a simulated Medication Mathematics (siMMath) environment to support proportional reasoning in transitioning via concreteness fading between two mediators. The first mediator is simulated nursing tools of medication preparation. The second is a ratio-table setup which is used as a goal representation, which enables one to spatially hold in place different quantities in their relative proportion. We conducted a two-part study with nursing students. Part 1 was a quasi-experimental pretest–intervention–posttest design assessing the effectiveness of learning, by evaluating four categories of medical calculation questionnaire items (solid medications, unit conversion, concentrations, infusion rates). We used the Noelting proportional reasoning test to evaluate the generalizability and abstraction of proportional reasoning. Part 1 included an experimental group (n = 96) learning with siMMath, and a comparison group (n = 73) learning with an equation-based lecture approach. Part 2 employed a case study design to characterize the learning process. The experimental group’s learning gains were significantly higher than the comparison group’s for the two most challenging categories of the medication calculation problems questionnaire, namely concentrations and infusion rates. Furthermore, the experimental group’s learning gains were significantly higher than the comparison group’s for formal operational reasoning on the Noelting test. Students who used a ratio-table setup scored significantly higher on the Noelting posttest questionnaire. Nursing students who learned with the siMMath environment overcame difficulties in proportional reasoning to the highest levels and extended this understanding to other contexts.     

Planning of distance-learning projects

Author of Aspectos operativos en universidades a distancia.     

The learning of response patterns in choice situations

This study presents a theory by which to understand how pigeons learn response patterns in simple choice situations. The theory assumes that, in a choice situation, patterns of responses compete for the final common path; that the competition is governed by two variables, the overall reinforcement probability obtained by emitting the patterns,T, and the differences in reinforcement probabilities among the patterns,D; and that the ratioD/T determines the final strength of specific response patterns. To test these predictions, three experiments were run in which pigeons were more likely to receive food when they pecked the momentarily least-preferred of three response keys. On the basis of previous research, it was predicted that the birds would be indifferent among the keys (molar aspect) and would also acquire a response pattern that consisted of pecking each key once during three consecutive trials (molecular aspect). The present theory went further and predicted that the strength of that pattern would increase with the ratioD/T. In the first two experiments,D was manipulated whileT remained constant, and in the third,T was manipulated whileD remained constant. The results agreed with the theory, for the strength of the response pattern increased withD and decreased withT, whereas overall choice proportions were always close to the matching equilibrium.