This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…

Eddie Woo discusses the importance of problem solving in mathematics education. He points to the need for teachers to carefully consider the approaches they use to best support the growth of problem-solving abilities in students.

While never a loved organisation, Ofsted's reputation has perhaps never been so low. Amid a myriad of calls for reform or abolition, former HMI Adrian Lyons reflects on his 20 years of inspection with over 16 years employed by Ofsted as an HMI. He concludes that one of the biggest problems with Ofsted is its frequent change in policy, activity and…

Creativity is increasingly seen as a key human capability that can be deliberately developed. Correspondently, a proliferation of tools, techniques, and methods are available in the academic and popular literatures. Creative problem-solving (CPS) is one framework among these, and has a 70-year history of research and development. This essay…

My concern in this article is how the university might become more distributed, less concentrated in particular places and times, and more permeable to different sorts of interests. In order to do this, I have written a partly autobiographical reflection on an attempt to practice the work of the university differently. It is the early story of a…

Purpose: This paper engages Olaf Zawacki-Richter and Insung Jung in a frank and penetrating conversation that seeks to ground, frame, and problematise research in the field conceptualised as "open, distance and digital education" (ODDE). Taking as starting point the recent publication of the landmark "Handbook of Open, Distance, and…

Early interventionists may frequently encounter ethical dilemmas due to the complex nature of early intervention (EI) service delivery (e.g., EI system infrastructure and building and sustaining collaborative relationships within the system). Therefore, the purpose of this research study was to explore the experiences of EI professionals related…

Students of art-based higher educational programs use artistic practices and academic methods to explore complex societal topics and produce artistic outcomes that embody new knowledge and insights. Universities have an essential role in helping to shape sustainable futures, and art-based research frequently explores complex and abstract topics,…

Introduction: The What Works Clearinghouse (WWC) reviews rigorous research on educational interventions with a goal of identifying "what works" and making that information accessible to educators and policymakers. In rating the quality of causal research, the WWC has historically prioritized internal validity over external validity. One…

Increased use of computer-based assessments has facilitated data collection processes that capture both response product data (i.e., correct and incorrect) and response process data (e.g., time-stamped action sequences). Evidence suggests a strong relationship between respondents' correct/incorrect responses and their problem-solving proficiency…

The purpose of the study was to compare the deficit profiles of two important types of mathematics difficulties. Three cognitive measures (working memory, processing speed, and reasoning), two mathematics measures (numerical facts retrieval and mathematics vocabulary), and reading comprehension were assessed among 237 Chinese fourth-grade…

We take up this qualitative inquiry as a means of practicing and advocating for a deeper understanding of South Korean teachers' pedagogy and perspectives in multicultural education, moving beyond surface-level critiques. Through the lens of postcolonial theory, this study highlights how government-led multicultural education places teachers in a…

The purpose of this study is to investigate the metacognitive strategies that middle school students used in the process of solving problems individually. The study group consisted of 37 middle school students in the eighth grade. The students were asked one non-routine word problem, and their written answers were collected. After solving the…

Solving mathematical (math) word problems (MWP) automatically is a challenging research problem in natural language processing, machine learning, and education (learning) technology domains, which has gained momentum in the recent years. Applications of solving varieties of MWPs can increase the efficacy of teaching-learning systems, such as…

Policy makers increasingly call on higher education to prepare learners for challenges such as global health emergencies or ecological crises. These can be understood as 'wicked problems', which are unbounded, complex and resist simplistic definition. Wicked problems involve stakeholders with incompatible value positions and attempted solutions…