We discuss the importance of bringing teaching to the forefront of instructional design. We do so by describing the process of developing an instructional sequence for early number, using design research. The instructional sequence was developed with the specific aim of supporting teaching, conceived as a complex and demanding job, not reducible…

Background: Learning trajectories (LTs) in early mathematics curriculum and teaching have received increasing attention (Baroody et al., 2019; Clements, 2007; Clements & Sarama, 2021; Maloney et al., 2014; Sarama & Clements, 2009). For example, LTs were a core construct in the National Research Council (2009) report on early mathematics…

The 3Ds Career Planning Program is a sequential learning activity consisting of three stages: Diagnosing (8 activities), Designing (9 activities), and Doing (2 activities). These stages help students determine their future careers by exploring themselves and the world of careers, creating paths to desired jobs, and putting their plans into action.…

The Precipitating Change Project was a 5-year development, implementation, and research study of an innovative 4-week middle school curricular unit in computational weather forecasting that integrates students' learning and use of meteorology and computational thinking (CT) concepts and practices. The project produced a list of CT skills and…

Research suggests some sequences of examples and problems (i.e., EE, EP) are more effective (higher test performance) and efficient (attained with equal/less mental effort) than others (PP, sometimes also PE). Recent findings suggest this is due to motivational variables (i.e., self-efficacy), but did not test this during the training phase.…

How do children develop associations among number symbols? For Grade 1 children (n = 66, M = 78 months), sequence knowledge (i.e., identify missing numbers) and number comparison (i.e., choose larger number) predicted addition, both concurrently and indirectly at the end of Grade 1. Number ordering (i.e., touch numbers in order) did not predict…

Learning in natural environments is often characterized by a degree of inconsistency from an input. These inconsistencies occur, for example, when learning from more than one source, or when the presence of environmental noise distorts incoming information; as a result, the task faced by the learner becomes ambiguous. In this study, we investigate…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

In the current conceptualisations of Problem Based Learning and how we practice it, the students are expected to possess the necessary academic competencies in order to study through PBL. However, a desk research reveals that students in many cases don't have the necessary understanding or conceptual comprehension of disciplines such as problem…

Because of their brief nature, vignettes are a strategic way to highlight or explore complex instructional practices. Using a qualitative approach, we examined how the use of vignettes in a Vignette Activity Sequence contributed to secondary mathematics preservice teachers' understanding of the Mathematical Practices and the Mathematics Teaching…

This study investigates the capacity of elementary-level Chinese second language learners to memorize serial verb sentences based on the results of a questionnaire. Our findings show that adult second language learners employ the concept of temporal sequence in language learning, consciously or unconsciously, whether or not the chronological…

We explored the possibility of publication bias in the sleep and explicit motor sequence learning literature by applying precision effect test (PET) and precision effect test with standard errors (PEESE) weighted regression analyses to the 88 effect sizes from a recent comprehensive literature review (Pan & Rickard, 2015). Basic PET analysis…

In a single large-scale study, we demonstrate that verbal sequence learning as studied using the classic Hebb repetition effect (Hebb, 1961)--the improvement in the serial recall of a repeating sequence compared to nonrepeated sequences--is resilient to both wide and irregular spacing between sequence repetitions. Learning of a repeated sequence…

In addition to developing teaching, clinical supervision, and research skills, new entrants into the counselor education workplace will also face the challenging responsibility of gatekeeping. Gatekeeping can be both anxiety-provoking and time-intensive for new faculty members. To enhance the confidence and competence of new entrants into…

In the current research, we tested the idea that the proximity of contrasting categories in a learning sequence would determine the features to which participants attend in a categorization task. For the first experiment, we designed a 4-category structure in which pairs of categories could be perfectly distinguished using 1 feature. Two of the…