Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K-Grade 12 to develop flexibility in students' mathematical understanding and to provide them…

In this study, it was investigated whether it would be possible to observe abstraction processes of secondary school 7th graders using the Revised Bloom's Taxonomy. For this purpose, eight students participated in the study. The study was conducted at a state secondary school in Turkey. Purposeful sampling method was used in the selection of…

In typical school mathematics, students experience problem solving in different ways. Sometimes students learn about problem solving by being introduced to different strategies, such as making a table or drawing a picture. Other times, problem solving is presented as a context for applying previously learned mathematics skills and concepts.…

Using question 28 from the May Problems to Ponder in volume 114, the author and her seventh- and eighth-grade students launched into a discussion of creativity, linearity, piecewise, and recursive definitions of functions. This pattern to ponder provided rich mathematical opportunities for all students in her middle school classroom.

There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of…

Because of their traditional programming structures that have user-hostile interfaces and complicated syntax, programming languages education doesn't catch students' attention and most of them find programming difficult and consider it as a job that only professionals can do. In order to minimalize the difficulty and drawback and help students…

In this article, we leverage ideas from the theory of coevolutionary computation to analyze interactions of students with problems. We introduce the idea of "informatively" easy or hard concepts. Our approach is different from more traditional analyses of problem difficulty such as item analysis in the sense that we consider Pareto…

Society needs creative problem solvers to work towards solutions of complex global issues such as climate change. Design thinking is a way to solve problems creatively. Unfortunately, in-service teachers are largely unfamiliar with design thinking and their students rarely engage in design thinking during class. To familiarize teachers with design…

The motion equations of a body under gravity and resistance linearly dependent on speed are usually analysed by solving differential equations. In this paper we report a derivation not explicitly involving differential equations but instead based on some elementary mathematical operations. The derivation uses only knowledge covered in a typical…

Even after many decades of productive research, problem solving instruction is still considered ineffective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the…

Aim: In the current study we aimed to investigate the relation between creativity and mathematical problem solving in the upper grades of elementary school. Methods: To examine how student's levels of general creativity were related to their performance on different types of geometrical problems, a geometry test with diverse problems was…

One of the well-known approaches to creativity differentiates between creative person, process, product, and press. In the study presented in this paper we focus on creative process and product associated with Problem Posing through Investigation (PPI) by experts in mathematical problem solving. We link the creative process to creativity of PPI…

This study explores narratives about critical moments in mathematics learning written by K-8 pre-service teachers' (PSTs) in the United States over a 20-year period. These critical moments, such as a single memorable task, course, test, or comment from a teacher, had a powerful and sustained impact on PSTs' mathematics identities, which they…

Connections between creativity and leadership often focus on how fostering creativity can help an organization. Despite the value that creativity can bring to organizations, Mueller et al. (2011) found that creative people themselves are not seen as leadership material. Yet many people with creative backgrounds do take on leadership roles,…

Technology, Engineering, and Mathematics (STEM) fields are in high demand. These fields all require sufficient math ability. However, many university students suffer from math anxiety. This study conducted an experiment to explore the influence of math anxiety on university students' challenging math problem-solving behavior and whether autonomy…