The purpose of this article is to introduce collective musical cognition as a mode for developing diagnostic critical thinking in music at all levels of the educational continuum--kindergarten through graduate school. It defines and illustrates how collective musical cognition is influenced by relevance, dialogue, and reflection as social and…

This study investigates the relationship between study methods and exam performance in introductory physics courses. Data were collected over 3 years through surveys to examine students' study habits, perceived effectiveness of techniques, and the correlation between time allocation and exam grades. Results indicate that high-achieving students…

Approximately 75.0% of the students in a district in the Bronx, New York, failed to meet grade level state standards in mathematics The district leadership team had implemented numerous improvement efforts but saw little progress. Grounded in Lave and Wenger's Social Learning Theory, adapting Wenger and Snyder's Community of Practice research, and…

Commonly used methods to simulate the oxidation-reduction (redox) titration curves include the three-step method and the rigorous method. The simple three-step method simulates the redox titration curve with the assumption that the reaction is complete, which is widely used in undergraduate quantitative analysis courses. For the rigorous…

Prior work has established that cognitive and perceptual processes influence students' attention to notational structures in mathematical expressions, which in turn affects their problem-solving approaches and performance. Advances in educational technology provide opportunities to further investigate these processes, improve student learning, and…

This study investigates how learners collaboratively construct embodied geometry knowledge in shared VR environments. Three groups of in-service teachers collaboratively explored six geometric conjectures with various virtual objects (geometric shapes) under the guidance of a facilitator. Although all the teachers were in different physical…

This study investigates how learners collaboratively construct embodied geometry knowledge in shared VR environments. Three groups of in-service teachers collaboratively explored six geometric conjectures with various virtual objects (geometric shapes) under the guidance of a facilitator. Although all the teachers were in different physical…

Engineering design has been central to technology education. Currently, online collaborative platforms for designers are widely used as digital forms of an engineer's notebook. However, traditional forms are still valued as the medium of engineering design during the conceptual phase of design since a paper notebook and pen or pencil allow…

Since the first descriptions of design research (DR), there have been calls to better define it to increase its rigour. Yet five uncertainties remain: (1) the processes for conducting DR, (2) how DR differs from other forms of research, (3) how DR differs from design, (4) the products of DR, and (5) why DR can answer certain research questions…

This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show "Car Talk," hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1…

An increasing number of introductory physics courses are seeking to incorporate "authentic practices," and a large area of focus in this trend is the incorporation of computational problems into the curriculum. These problems offer students an opportunity to engage with the programming practices and numerical problem-solving methods used…

Open-ended problem-solving skills have been identified as employable skills, which undergraduate students will need to have in order to cope with real-life problems in their workplaces after graduation. However, the development and assessment of these skills have been inconsistent across courses offered in universities. This research examined…

Schema-based instruction (SBI) was used to teach nine middle school students with high-incidence disabilities (HID) to solve proportional reasoning word problems. A multiple-baseline-across-groups design was used to determine student understanding of the SBI process. The design consisted of three phases including baseline, SBI process, and…

The research on deductive reasoning in mathematics education has been predominantly associated with the study of proof; consequently, there is a lack of studies on logical reasoning per se, especially with young children. Analytical reasoning problems are adequate tasks to engage the solver in deductive reasoning, as they require rule checking and…

Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence…