Background: The ability to translate concrete manipulatives into abstract mathematical formulas can aid in the solving of mathematical word problems among students, and metacognitive prompts play a significant role in enhancing this process. Aims: Based on the concept of semantic congruence, we explored the effects of metacognitive prompts and…

To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving…

This study aimed to investigate children's potential for reasoning by analogy utilizing a newly-developed computerized dynamic test, and the potential differential influence of executive functions (cognitive flexibility, attention, and planning) on static and dynamic measures of analogical reasoning. Participants included 64 children (mean age =…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

Purpose: This paper aims to compare two types of prompts, encouraging participants to think about real-world examples or engineering principles to show how these two approaches can result in vastly different design practices. Design/methodology/approach: Two studies (N = 20, N = 40) examine the impact of two different prompts. Non-expert students,…

Engineering design was integrated into K-12 science education in the "Next Generation Science Standards" (NGSS Lead States, 2013), but teaching design remains a challenge for educators. Design problems are ill-defined, ill-structured, and complex problem-solving tasks. Their solutions require creativity and recursive, metacognitive…

Background: Engaging students in computer-assisted guided inquiry learning has great potential to scaffold their scientific understanding: Students are expected to improve their scientific problem-solving skills, and at the same time gain a deep conceptual understanding of the subject-matter. Additional generative activities such as creating video…

Self-assessment is essential to scientific literacy as stated by the National Research Council Committee on Conceptual Framework for the New K-12 Science Education Standards and has since been incorporated into the Next Generation Science Standards. However, little empirical evidence documents which instructional tools are beneficial in improving…

Studies on whether fixation cues provided in the first episode of divergent thinking tasks influence creative outcomes after incubation, as they do for convergent problem-solving tasks, remain limited. This research examined the beneficial effects of incubation using the delayed- and immediate-incubation paradigms. Participants in Experiment 1…

Much of our real-life decision making is bounded by uncertain information, limitations in cognitive resources, and a lack of time to allocate to the decision process. It is thought that humans overcome these limitations through "satisficing," fast but "good-enough" heuristic decision making that prioritizes some sources of…

This study investigates representational code-switching (RCS) by considering three high school students' communications in the process of comparing and contrasting pairs of representations (e.g., equation and graph) in the context of rational functions. Supporting this study is research in the realms of students interacting with mathematical…

Structured problem-solving lessons are used to explore mathematical concepts such as pattern and relationships in early algebra, and regularly used in Japanese Lesson Study research lessons. However, enactment of structured problem-solving lessons which involves detailed planning, anticipation of student solutions and orchestration of whole-class…

The purpose of this research is to investigate the relative effectiveness of using three different question-prompt strategies on promoting metacognitive skills and performance in ill-structured problem solving by examining the interplay between peer interaction and cognitive scaffolding. An ill-structured problem-solving task was given to three…

Research suggests that learners will likely spend a substantial amount of time looking at the model's face when it is visible in a video-based modeling example. Consequently, in this study we hypothesized that learners might not attend timely to the task areas the model is referring to, unless their attention is guided to such areas by the model's…

An alternating treatments design with a control condition was used to evaluate and compare the effects of two taped-problem interventions on addition fact fluency. Both taped-problem interventions were identical with the exception of the time delay between the auditory cue of the problem and the answer. One condition used a 2-s delay and the other…