Many gifted students fail to be diagnosed, preventing them from receiving an education that is adapted to their characteristics, with activities that challenge their minds. Mathematics is one of the subjects in which they can demonstrate talent, where they often exhibit high skills in solving problems, handling numbers and performing spatial…

Creative thinking transforms existing information, either from long-term memory or external sources, into new representations and innovative ideas. Creative thinking is an activity that processes received information to produce new representations and innovative ideas. Developing this skill is essential for students; however, recent research has…

In this dissertation, I utilize the post-structural philosophy of Gilles Deleuze and Fe´lix Guattari as a lens for investigating the proof process. Deleuze and Guattari were both post- structural philosophers who, like many in this tradition, troubled traditional notions related to stable identities, meaning, language, and mathematics. For…

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…

This study explored 54 preservice elementary teachers' identification and modification of mathematical tasks in raising cognitive demand and examined the features of their modified tasks. The study collected data using a three-phase activity: (a) identifying the level of cognitive demand of the given task, (b) modifying the low cognitive demand…

Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

The challenge posed by algebra story problems creates a significant hurdle for many students, transcending both the mathematical content of the problem and the specific instructional background received. This study offers a distinctive contribution to the existing literature by focusing on the cognitive conditions essential for comprehension in…

In this theoretical essay, I build on complexity theory and commognition to theorize the ways in which failure to teach/learn mathematics (FTLM) emerges through the dynamic interactions among teacher, learner, and curriculum demands. I focus on two main concepts of complexity theory: emergence in dynamic systems and attractor states (stable,…

The retention of fundamental mathematical skills is imperative to provide a foundation on which new skills are developed. Educators often lament about student retention. Cognitive scientists and educators have explored teaching methods that produce learning which endures over time. We wanted to know if using spaced recall quizzes would prevent our…

Interleaved practice combined with comparison prompts can better foster students' adaptive use of subtraction strategies compared to blocked practice. It has not been previously investigated whether all students benefit equally from these teaching approaches. While interleaving subtraction tasks prompts students' attention to the different task…

After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…

This study aims to investigate the effect of the online flipped learning model (OFLM) when integrated into a mathematics course in an emergency remote teaching process on seventh grade students' academic achievement, their attitudes towards their mathematics course, and their cognitive load. The study was designed as a crossover experimental…

Mathematical word problem-solving skills are crucial for students across their lives, yet solving such tasks poses challenges for many. Therefore, understanding the characteristics of mathematical word problems that are associated with students' performance is important. The objective of this systematic review and meta-analysis was to evaluate the…

Successful adoption of proven effective practice strategies such as distributed practice may contribute to much-needed improvement in mathematics performance. However, it is not yet fully understood if distributed practice is beneficial for long-term retention of complex procedural knowledge and, if so, for which initial practice performance level…