This article proposes an interconnected framework, "Ways of thinking in STEM-based Problem Solving," which addresses cognitive processes that facilitate learning, problem solving, and interdisciplinary concept development. The framework comprises critical thinking, incorporating critical mathematical modelling and philosophical inquiry,…

Statistical learning refers to the ability to identify structure in the input based on its statistical properties. For many linguistic structures, the relevant statistical features are distributional: They are related to the frequency and variability of exemplars in the input. These distributional regularities have been suggested to play a role in…

Information changes as it is passed from person to person, with this process of cultural transmission allowing the minds of individuals to shape the information that they transmit. We present mathematical models of cultural transmission which predict that the amount of information passed from person to person should affect the rate at which that…

Cross-situational learning has recently gained attention as a plausible candidate for the mechanism that underlies the learning of word-meaning mappings. In a recent study, Blythe and colleagues have studied how many trials are theoretically required to learn a human-sized lexicon using cross-situational learning. They show that the level of…

There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…

Schwartz and Martin ("Cogn Instr" 22:129-184, 2004) as well as Kapur ("Instr Sci", this issue, 2012) have found that students can be better prepared to learn about mathematical formulas when they try to invent them in small groups before receiving the canonical formula from a lesson. The purpose of the present research was to investigate how the…

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

It is suggested that both similarity and analogy involve a process of structural alignment and mapping. The structure mapping process is described as it has been worked out for analogy, and this view is then extended to similarity and used to generate new predictions. (SLD)

The method of scoring is used to obtain maximum likelihood estimates of the parameters in White and Clark's (EJ 075 122) learning hierarchy validation model. From the proportion of the population possessing only the superordinate skill in a pair of hierarchical skills, and its variance, the hypothesis of inclusion is tested. (Author/CTM)

The problem of designing computer programs that will approach human capabilities in pattern recognition is discussed. Human beings are much better at recognizing patterns that are highly structured than at recognizing patterns that are not. In contrast, a computer system's performance in pattern recognition is almost independent of the amount of…

The study is concerned with the problem of determining stimulus discrimination thresholds in non-human vertebrates. In constrast to conventional methods of teaching differentiation of various stimuli by fixed reinforcement schedules, stimulus discrimination threshold determination is related to a teaching system that adjusts to continuously…

In this paper the mathematical structures of Bourbaki, the Piagetian developmental structures, and Polya's heuristic structures are compared. (SD)

Three different strategies of choosing items for presentation in a simple list learning situation are compared. The instructional task was to teach the correct response to a number of stimulus items, using a paired-associate teaching procedure. Only one item could be presented on a given trial and the total number of trials was limited. The…

A FORTRAN 77 program is described that computes both the different response success-error patterns and their summary statistics for learning and forgetting in fixed trial experiments using a two-stage Markov model. (Author/GDC)