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.

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…

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…

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 use of written or graphic representations is essential in mathematics. Graphic representations are mainly used and researched as instruments for problem solving. There is a gap in research for interventions that use learner-generated graphic representations as documents for reflection processes for promoting the development of children's…

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…

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…

This empirical paper reports on the development of a professional development initiative, namely the word sum-wheel, which teachers developed collaboratively. The study's objective was to determine how teachers' mathematics word problem-solving instruction could be enhanced through the development of the word-sum wheel using participatory action…

This article uses the concurrent mixed methods design to explore the errors made by 171 Grade Seven learners in algebraic problem-solving within the Assin Central Municipality in Ghana. The participants were categorized into low-achieving and high-achieving groups based on their performance in a pretest, to help provide a detailed examination of…

This cohort-sequential study explored the working memory (WM) structures that underlie growth in mathematical word problem solving (WPS) performance in elementary school emergent bilingual children whose first language (L1) is Spanish. To this end, children (N = 429) in Grades 1, 2, and 3 in southwest U.S. school districts at Wave 1 were…

Children with mathematical difficulties need to spend more time than typically achieving children on solving even simple equations. Since these tasks already require a larger share of their cognitive resources, additional demands imposed by the need to switch between tasks may lead to a greater decline of performance in children with mathematical…

Changes in U.S. textbooks indicate that U.S. first-grade students in the Common Core era were exposed to a wider variety of word problem types than students in previous generations were. We compared the performance of U.S. first graders in the Common Core era with that of previous generations in solving 11 types of additive word problems to…

Learning mathematics is difficult for many students, especially students with mathematics learning disabilities MLD. To improve the academic achievement for students with MLD, educational legislations (IDEA 2004; ESSA 2015) mandate that schools must use evidence-base core curricula. Textbooks conveys the intended values and principles for…