Cognitive load in algebra: element interactivity in solving equations

Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side only. In an experiment, middle school students (N?=?71) were randomly assigned to the balance and inverse methods to complete a pre-test, an acquisition phase and a post-test. Pre-test and post-test comparisons found that the inverse group outperformed the balance group for those equations that involved high element interactivity. Instructional efficiency measures further confirmed that the balance method imposed higher cognitive load. The inverse method was capable of reducing cognitive load due to the interacting elements.     

First-graders’ knowledge of multiplicative reasoning before formal instruction in this domain

Our study investigated children’s knowledge of multiplicative reasoning (multiplication and division) at the end of Grade 1, just before the start of formal instruction on multiplicative reasoning in Grade 2. A large sample of children (N = 1176) was assessed in a relatively formal test setting, using an online test with 28 multiplicative problems of different types. On average, the children correctly answered more than half (58%) of the problems, including several bare number problems. This indicates that before formal instruction on multiplicative reasoning, children already have a considerable amount of knowledge in this domain, which teachers can build on when teaching them formal multiplication and division. Using analysis of variance and cross-classified multilevel regression analysis, we identified several predictors of children’s pre-instructional multiplicative knowledge. With respect to the characteristics of the multiplicative problems, we found that the problems were easiest to solve when they included a picture involving countable objects, and when the multiplicative situation was of the equal groups semantic structure (e.g., 3 boxes of 4 cookies). Regarding student characteristics, pre-instructional multiplicative knowledge was higher for children with higher-educated parents. Finally, the mathematics textbook used in school appeared to have influenced children’s pre-instructional multiplicative knowledge.     

Example-Based Learning in Heuristic Domains: A Cognitive Load Theory Account

One classical instructional effect of cognitive load theory (CLT) is the worked-example effect. Although the vast majority of studies have focused on well-structured and algorithmic sub-domains of mathematics or physics, more recent studies have also analyzed learning with examples from complex domains in which only heuristic solution strategies can be taught (e.g., troubleshooting, mathematical proving). Is learning by such examples also effective, and do the same instructional design principles apply? We discuss the main findings of an own research program and of related studies that addressed such questions. We found that CLT’s basic design principles also hold true for heuristic domains: Reduce extraneous load by employing examples, maximize germane load by fostering self-explanations, prevent cognitive overload by pretraining in the case of difficult learning materials, and by focusing attention on the most relevant aspects. Other typical CLT assumptions (e.g., better provide information for novice learners) were not confirmed in its generality. The present findings extend the applicability of CLT but also identify some potentially too simplistic assumptions.     

Concurrent and Subsequent Associations Between Daily Digital Technology Use and High‐Risk Adolescents’ Mental Health Symptoms

Adolescents are spending an unprecedented amount of time using digital technologies (especially mobile technologies), and there are concerns that adolescents’ constant connectivity is associated with poor mental health, particularly among at‐risk adolescents. Participants included 151 adolescents at risk for mental health problems (M_age = 13.1) who completed a baseline assessment, 30‐day ecological momentary assessment, and 18 month follow‐up assessment. Results from multilevel regression models showed that daily reports of both time spent using digital technologies and the number of text messages sent were associated with increased same‐day attention deficit hyperactivity disorder (ADHD) and conduct disorder (CD) symptoms. Adolescents’ reported digital technology usage and text messaging across the ecological momentary assessment (EMA) period was also associated with poorer self‐regulation and increases in conduct problem symptoms between the baseline and follow‐up assessments.