Early algebraic thinking is the reasoning engaged in by 5- to 12-year-olds as they build meaning for the objects and ways of thinking to be encountered within the later study of secondary school algebra. Ever since the 1990s when interest in developing algebraic thinking in the earlier grades began to emerge, there has been a steady growth in the…

Learning analytics (LA) provides tools to analyze historical data with the goal of better understanding how curricular structures and features have impacted student learning. Forward-looking curriculum design, however, frequently involves a degree of uncertainty. Historical data may be unavailable, a contemplated modification to curriculum may be…

Purpose: Our purpose was to investigate the effect of generalization of participation in parkour from physical education classes to organized parkour recess. Methods: A total of 143 (64 girls and 79 boys) third-grade elementary school children received a 12-lesson parkour sport education season in physical education. Voluntary participation in…

It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

Research has shown that training diagonal targets in a matrix may result in correct responses to the nondiagonal targets within the same matrix and novel targets from a separate matrix. This study replicated prior research using matrix training to teach tact noun-verb combinations to 3 male participants with autism who use a speech generating…

Psychology research often focuses on interactions, and this has deep implications for inference from non-representative samples. For the goal of estimating average treatment effects, we propose to fit a model allowing treatment to interact with background variables and then average over the distribution of these variables in the population. This…

We conducted a descriptive exploratory study in which we analyzed 313 sixth to eighth grade students' answers to a word problem, accompanied by diagrams, involving generalization in an algebraic functional context. In this research, we jointly addressed two objectives: (a) to determine the strategies deployed by students to generalize and (b) to…

Mathematical reasoning, a fundamental aspect of human cognition, poses significant challenges for artificial intelligence (AI) systems. Despite recent advancements in natural language processing (NLP) and large language models (LLMs), AI's ability to replicate human-like reasoning, generalization, and efficiency remains an ongoing research…

It is known that teacher noticing skills improve through different interventions such as video clubs, lesson study, and short-term professional development programs. However, it is not known whether this improvement is permanent and whether teachers can transfer their noticing skills into the classroom. It is extremely important to provide an…

Educational research enquiries differ based on philosophical beliefs and assumptions regarding researchers' explicitly stated views. This paper critically explores the most dominant philosophical stances in social research sciences, namely positivism, interpretivism and pragmatism. It begins with an overview of the role of the aforementioned…

By design, randomized experiments (XPs) rule out bias from confounded selection of participants into conditions. Quasi-experiments (QEs) are often considered second-best because they do not share this benefit. However, when results from XPs are used to generalize causal impacts, the benefit from unconfounded selection into conditions may be offset…

While interest in active avoidance has recently been resurgent, many concerns relating to the nature of this form of learning remain unresolved. By separating stimulus and response acquisition, aversive Pavlovian-instrumental transfer can be used to measure the effect of avoidance learning on threat processing with more control than typical…

Generalization of learning can arise from 2 distinct sources: failure to discriminate a novel test stimulus from the trained stimulus and active extrapolation from the trained stimulus to the test stimulus despite them being discriminable. We investigated these 2 processes in a predictive learning task by testing stimulus discriminability…

Over the last decade, iterated learning studies have provided compelling evidence for the claim that linguistic structure can emerge from non-structured input, through the process of transmission. However, it is unclear whether individuals differ in their tendency to add structure, an issue with implications for understanding who are the agents of…

In five experiments, we established and explored the contrast diversity effect--the effect of diversity of negative evidence on inductive inferences drawn from a single observation of a target exemplar. In Experiments 1 through 3, we show that increasing the diversity of negative evidence in a contrasting category led people to infer that a target…