Previous research demonstrated that some children inappropriately solve multiplicative missing-value word problems additively, while others inappropriately solve additive missing-value word problems multiplicatively. Besides lacking skills, children's preference for additive or multiplicative relations has been shown to contribute to those errors.…

Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study…

Relational reasoning, the ability to detect meaningful patterns, matures through adolescence. The unique contributions of verbal analogical and nonverbal matrix relational reasoning to science and maths are not well understood. Functional magnetic resonance imaging data were collected during science and maths problem-solving, and participants…

Reasoning, our ability to solve novel problems, has been shown to improve as a result of learning experiences. However, the underlying mechanisms of change in this high-level cognitive ability are unclear. We hypothesized that possible mechanisms include improvements in the encoding, maintenance, and/or integration of relations among mental…

Individual differences in executive function (EF) are well established to be related to mathematics achievement, yet the mechanisms by which this occurs are not well understood. Comparing representations (problems, solutions, concepts) is central to mathematical thinking, and relational reasoning is known to rely upon EF resources. The current…

Recent evidence suggests that people are highly efficient at detecting conflicting outputs produced by competing intuitive and analytic reasoning processes. Specifically, De Neys and Glumicic (2008) demonstrated that participants reason longer about problems that are characterized by conflict (as opposed to agreement) between stereotypical…

Introduction. In this study, we focus on the relationship between the students' mathematical thinking and their non-mechanically identified eye-movements with the purpose to gain deeper understanding about the students' reasoning processes and to investigate the feasibility of incorporating eye-movement information in everyday pedagogy. Method.…

Multivariate pattern analysis can be combined with Hidden Markov Model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application…

Many students encounter difficulties in science and mathematics. Earlier research suggested that although intuitions are often needed to gain new ideas and concepts and to solve problems in science and mathematics, some of students' difficulties could stem from the interference of intuitive reasoning. The literature suggests that overcoming…

This study investigated how people reason about simple mechanical devices and physical systems, and how reasoning methods and understanding of a device evolve over a period of exposure. Twelve students attending the Teachers College at Columbia University (New York) participated in the first of two experiments; and 10 students attending the same…

Eighty-nine children between four and nine years of age solved mazes varying in the presumed appropriateness of advance or improvisational planning. Results of the study show that children's planning strategies are adapted to circumstances and suggest that older children may be more proficient in this adaptation than are younger children. (RH)

The 12th iteration of the International Conference on Educational Data Mining (EDM 2019) is organized under the auspices of the International Educational Data Mining Society in Montreal, Canada. The theme of this year's conference is EDM in Open-Ended Domains. As EDM has matured it has increasingly been applied to open-ended and ill-defined tasks…