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,…

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…

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…

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)

A sample of 328 freshman economics students is disaggregated by the students' gender, previous knowledge of economics, attitudes toward economics, and innate abilities. Results show that students learn more economics if they take microeconomics before macroeconomics. Appended are 14 references. (MLF)

A neuromathematical model of information processing applied to science learning is expanded to include two coefficients representing the motivational state of the learner. The inclusion of these coefficients (which are described) permits modeling of the effects of variations in motivation on the rate and amount of information in learning tasks.…

This document reviews the use of mathematical models of learning for research in the learning of science concepts. Three mathematical models for the representation of concept learning are presented. (SL)

Combines the concept of self-worth in sociology and educational psychology with economic modeling to analyze the influence of competition on student learning. Finds, for example, that students prone to negative self-worth are motivated not to study hard in courses involving strong competition, thereby adopting a strategy of winning by not losing.…

A sample of 24 subjects was presented with 800 addition problems to test a general model of simple and complex addition. According to this model, an addition problem is encoded and verified by column, with specific addition strategies determined by the size of the problem. Two hundred problems each of the following four types were presented: (1)…

This paper is a theoretical discussion of several functions of knowledge systems based on the idea of partial matching, that is, comparison of two or more descriptions by identification of their similarities. Several knowledge system functions are described in terms of partial or best matchings including analogical reasoning, inductive inference,…

This final report of a National Institute of Education project explores Bayesian statistical analysis as a paradigm for educational impact studies, particularly studies on the education of the disadvantaged. The position of the report is that much of what is wrong with educational research can be attributed to the use of an inappropriate model for…

This research has as its basic premise the belief that physical and mental skills are highly similar, enough so in fact that computation paradigms such as the ones used in Artificial Intelligence research about predominantly mental skills can be usefully extended to include physical skills. This thesis is pursued experimentally by the…

Studied the teaching and learning of fractions in two matched groups of 10 9-10-year-olds in the Netherlands. In the experimental group, fractions were introduced using the bar and number line as mental models, while the control group used fair sharing and the circle model. The experimental group showed more proficiency in fractions after 1 year.…